All Submission Categories

Plumbing the Pudding Model of the Atom

Authors: Eric Stanley Reiter
Comments: 11 Pages.

We will explore in this sequence: 1) the experimental evidence initiating the nuclear model, 2) ER’s (author) experimental repeat, 3) threshold model vs quantization, 4) ER’s past experiments with gamma ℽ and alpha α rays, 5) ER’s recent tests splitting the α upon a crystal surface, and 6) conclusion. In addition to a serious challenge to quantization, this report reveals how so-called nucleons can diffract. We know of experiments that show what appears to be nucleon interference (1, 2). If you do not think this is a problem, please read up on the measurement problem. The short answer to this problem is: if it diffracts, it is a wave. We explain particle-like effects as thresholds.
Category: Quantum Physics

Charge Quantization, the Topology of the Universe, and the Hopeful Abolition of Monopoles

Authors: Warren D. Smith
Comments: 18 Pages. Paper on internet since 2000, now uplaoded to VIXRA for archival purposes.

This is the first of a 3-part series of papers on "the shape of the universe." Inspired by P.A.M.Dirac's discovery that the existence of even one "magnetic monopole" would logically force electric charge to be quantized (explaining why all electrons have the same charge, protons the exactly-opposite charge, etc), I show that a tiny magnetic field "trapped in the topology of the universe" also would logically force that. Which universes does this idea work in? We show it works for every compact 3-manifold topology for the universe except two. We then re-examine monopoles, showing their existence would cause a lot of nasty problems, and none have ever been detected.
Category: Relativity and Cosmology

On the Shape of the Universe

Authors: Warren D. Smith
Comments: 10 Pages. Paper on internet since 2003, now uplaoded to VIXRA for archival purposes.

This is the second of a 3-part series of papers on "the shape of the universe." Bright objects such as quasars are observed to be uniformly distributed on the sky-sphere. We prove a theorem that if this is true for almost every observer-location (i.e. the location of the Earth is not special in this respect) then the universe must be a "harmonic manifold." We also argue that the universe must be an orientable 3-manifold not containing any closed geodesic whose traversal causes "twist." We also discuss incompletely-convincing evidence that the universe contains a nonzero finite number of short closed geodesics passing through the Earth. If that is genuine, we prove our assumptions winnow down the possible topologies for the universe to only 3 possibilities: "flat 3-torus" and its degenerate versions with some paralelipiped sidelengths infinite.
Category: Relativity and Cosmology

Discrete Random Variables

Authors: Teo Banica
Comments: 400 Pages.

This is an introduction to probability and discrete random variables. We first discuss games, counting and basic probability, with the mathematics of the binomials and factorials recalled, and with everything explained with numerous illustrations. Then we get into the theory of discrete random variables, with the basic theory explained, with illustrations, notably with results about the binomial and Poisson laws. Then we discuss more advanced distributions, such as the Bessel, hypergeometric and beta binomial ones, with methods from both algebra and analysis. We end with an introduction to continuous phenomena, advanced combinatorics, random matrices and freeness.
Category: Statistics

On the Finiteness and Shape of the Universe

Authors: Warren D. Smith
Comments: 31 Pages. Paper on internet since 2004, now uploaded to VIXRA for archival purposes.

This is the last of a 3-part series of papers on "the shape of the universe" and includes summary of the prior two. At the end is a chart allowing you to choose your favorite set of assumptions (from among those we consider) whereupon it tells you the conclusions deducible from those assumptions about the topology of the universe. This and the prior papers also includeddiscussion of "reasons the universe is 3-dimensional." As far as I know my analyses of these matters go considerably beyond all others; but quite possibly if "real topologists" got involved then considerably more could be said.
Category: Relativity and Cosmology

The Einstein and Landau-Lifshitz Pseudotensors — a Mathematical Note on Existence

Authors: Stephen J. Crothers
Comments: 4 Pages.

For a closed system, the conservation of energy and momentum has been affirmed through a vast array of experiments. In an attempt to reconcile the General Theory of Relativity with these findings, Einstein constructed, ad hoc, his so-called pseudotensor [A. Einstein, Ann. Phys. 49, 769 (1916)]. Yet this solution fell outside the tensorial mathematical structure of his theory. Landau and Lifshitz also constructed, ad hoc, an even more complex pseudotensor, as a proposed improvement upon the work of Einstein [The Classical Theory of Fields (Addison-Wesley Press, Inc., Cambridge, MA, 1951)]. Their pseudotensor is symmetric, unlike that proposed by Einstein. They advance that their pseudotensor yields a conservation law which also included angular momentum. However, once again, this approach leads to a mathematical construct which is not a tensor and thereby falls outside the very mathematical structure of Einstein’s theory. Both pseudotensors, whether that advanced by Einstein or by Landau and Lifshitz, violate the rules of pure mathematics and therefore can hold no place in physics.
Category: Relativity and Cosmology

Vaccum Unified Solitonic Condensate Theory

Authors: Ibrahim Khalid, M. Golebiowski
Comments: 98 Pages. License: CC BY NC ND (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The Vacuum Unified Solitonic Condensate Theory is a way to understand the world around us. It says the space or the Vacuum Unified Solitonic Condensate Theory is like a liquid. You can squeeze it. Move it around. The Vacuum Unified Solitonic Condensate Theory has some rules that physicists know. These rules help us understand how things like electrons and protons and neutrons work.These tiny things are like knots in the Vacuum Unified Solitonic Condensate Theory. They have properties like mass and charge and spin. The Vacuum Unified Solitonic Condensate Theory helps us understand where these properties come from. We can use the Vacuum Unified Solitonic Condensate Theory to figure out the mass of electrons and protons and neutrons. We just need to use some ideas about the Vacuum Unified Solitonic Condensate Theory.The Vacuum Unified Solitonic Condensate Theory also helps us understand charge. Electric charge is like a twist in the Vacuum Unified Solitonic Condensate Theory. This twist is always the same. The Vacuum Unified Solitonic Condensate Theory can help us understand the weak forces too. It can help us understand how they are related to the Vacuum Unified Solitonic Condensate Theory.The Vacuum Unified Solitonic Condensate Theory even helps us understand gravity. Gravity happens when the Vacuum Unified Solitonic Condensate Theory gets dense in some places and not in others. The Vacuum Unified Solitonic Condensate Theory can help us understand how atoms work. It can help us understand why some things decay. The Vacuum Unified Solitonic Condensate Theory makes some predictions. We can test these predictions to see if the Vacuum Unified Solitonic Condensate Theory is correct.
Category: High Energy Particle Physics

A Problem in the Theory of Surfaces

Authors: Abdelmajid Ben Hadj Salem
Comments: 2 Pages. In French. Comments welcome.

In this note, we present a problem in the theory of surfaces. The equations for the surface $(Sigma)$ were inspired by the monograph cited in the references, published by the eminent Japanese mathematicians Katsumi Nomizu and Takeshi Sasaki.
Category: Geometry

Post-Carroll Algebra, Conformal Extensions, and Field Theories

Authors: Mojtaba Najafizadeh
Comments: 32 Pages.

By incorporating leading c -dependent corrections to the Carroll transformations, we introduce the post-Carroll transformations". We demonstrate that these transformations are consistent with post-Carrollian mechanics [1]; furthermore, they give rise to the so-called post-Carroll algebra". We show that, unlike the Carroll algebra, this new structure allows for a central charge in higher dimensions; we refer to it as the Carroll{Bargmann algebra". To construct conformal extensions, we first build the conformal extension of the post-Carroll algebra and study field theories invariantunder this symmetry. We then construct the conformal extension of the Carroll{Bargmann algebra, referred to as the Carroll{Schrodinger algebra", and demonstrate that it precisely matches the symmetry algebra of the higher-dimensional Carroll{Schrodinger theory [2]. Finally, we derive the general form of two-point functions in a post-Carrollian CFT, which in 1 + 1 dimensions exhibits both electric and magnetic sectors, while in higher dimensions only the magnetic sector survives.
Category: High Energy Particle Physics

The Missing Electric Aharonov-Bohm Test and the Search for the Electromagnetic Scalar Mode

Authors: Renato Vieira dos Santos
Comments: 8 Pages.

The electromagnetic four-potential $A^mu = (Phi/c, mathbf{A})$ comprises a scalar potential $Phi$ and a vector potential $mathbf{A}$. In gauge-invariant electrodynamics, gauge symmetry together with the Lorenz condition $partial_mu A^mu = 0$ ensure that only the two transverse photon polarizations are physical, while the scalar degree of freedom decouples. Whether this elimination holds in all physical regimes is an empirical question that has never been tested in configurations where the electric field vanishes but the potentials vary in time. We ask whether the scalar mode, described by the quantity $lorenzScalar = partial_mu A^mu$, can leave a physical imprint on matter that is detectable in the electric Aharonov-Bohm effect. The original configuration proposed in 1959---time-dependent potentials applied to shielded conducting cylinders---has never been experimentally realized. We show that a phenomenological coupling $propto lorenzScalar,bar{psi}psi$ yields a phase shift proportional to $1-cos(omega T)$, orthogonal to the standard $sin(omega T)$ prediction. A frequency sweep can cleanly separate the two contributions. We outline a realistic electron interferometry experiment, analyze the dominant systematic (fringe fields), and argue that such a test is within reach of existing technology. The question is testable: a null result would provide the first empirical bound on a physical scalar mode in a field-free regime; a positive signal would indicate that the gauge-fixing procedure discards a genuine degree of freedom. Either outcome illuminates the foundations of gauge theory.
Category: Quantum Physics

Toward Charge-Dependent Tests of the Equivalence Principle: a Phenomenological Parameter and an Unexplored Frontier

Authors: Renato Vieira dos Santos
Comments: 15 Pages. Published in PRD: https://doi.org/10.1103/frfk-vp26

We introduce and define the phenomenological parameter $kappa$, defined by $Delta a/g = kappa , Delta(q/m)$, to quantify potential linear coupling between electric charge and gravitational acceleration. A synthesis of existing precision equivalence principle experiments yields the first quantitative estimate of the effective sensitivity to this coupling: $|kappa| < 2.1 times 10^{-4}~si{kilogrampercoulomb}$ at 95% confidence level. This constraint is approximately 11 orders of magnitude less stringent than corresponding bounds on composition-dependent violations, revealing that the electromagnetic axis remains a largely underexplored frontier in empirical gravity. We connect $kappa$ to established frameworks---the Standard-Model Extension and the $THepsilonmu$ formalism---showing that it occupies a region of parameter space untouched by existing high-precision tests. An effective field theory analysis shows that dimension-six operators that couple curvature directly to the electromagnetic field strength are suppressed by the minuscule terrestrial spacetime curvature ($G_N ho_oplus sim 10^{-55}~text{GeV}^2$) and are therefore phenomenologically irrelevant. Consequently, a future measurement of $kappa$ at an accessible level would not probe minimal geometric couplings but would signal physics beyond minimal gravitational EFT, such as mediation by light scalar fields as in Einstein-Maxwell-Dilaton theory. We examine the Schiff-Barnhill effect, the primary systematic background for any such measurement, and show how it can be separated from a genuine signal. We outline the necessary experimental strategy, focused on maximizing charge-to-mass ratio differences, to transform this overlooked axis into a targeted probe for new physics.
Category: Relativity and Cosmology

A Preprint Republic at a Crossroads: Governance, Transparency, and the Future of arXiv as a Public Good

Authors: Renato Vieira dos Santos
Comments: 8 Pages.

The arXiv preprint repository, founded in 1991, has become the de facto dissemination platform for physics, mathematics, computer science, and increasingly other quantitative disciplines, hosting over 2.4 million articles and serving millions of users worldwide. In mid-2026, its governance will transition from Cornell University Library to an independent nonprofit entity governed by a board of directors and supported by private philanthropy. This article provides a data-driven examination of that transition, placing it within the history of the repository and the broader political economy of scholarly communication. Drawing on public submission statistics, moderation records, documented controversies, and historical precedents from academic publishing, we identify six structural risks: opaque governance, centralized editorial control, financial unsustainability, systemic bias, erosion of scientific pluralism, and potential mission drift toward privatized gatekeeping. We argue that the moment before institutional inertia sets in is precisely when the research community must insist on binding transparency and accountability mechanisms. We propose a set of concrete safeguards---a community-elected advisory council, mandatory transparency reporting, an independent moderation ombuds, a free-access charter, and periodic external audits---that can preserve arXiv's identity as a public good without compromising operational agility. The manuscript itself has been submitted to arXiv as a real-time test of the moderation system's openness to self-examination.
Category: General Science and Philosophy

A Pedagogical Reconstruction of Maxwell's Equations: How Charge Conservation, Helmholtz's Theorem, and the Speed of Light Make Them Natural

Authors: Renato Vieira dos Santos
Comments: 8 Pages.

Maxwell's equations are traditionally introduced as four independent postulates, each grounded in a distinct experimental law. Although empirically sound, this approach can obscure the logical structure that unifies them. This paper offers a pedagogical reconstruction based on local charge conservation, Helmholtz's theorem, and the experimental fact that electromagnetic disturbances propagate in vacuum with speed (c). A few natural auxiliary assumptions -- linearity, locality, and the simplest possible coupling to sources -- are stated explicitly. From the continuity equation and the physical necessity of a mediating field we argue that the electric and magnetic fields must be introduced. Helmholtz's theorem then demands that both divergences and curls of these fields be specified; coupling them to the available scalar and vector sources yields the inhomogeneous equations. Consistency with charge conservation forces the displacement current, making it a logical requirement rather than an empirical addition. The homogeneous equations follow from the same framework: (abla cdot mathbf{B} = 0) is the most parsimonious choice consistent with experiment, and requiring wave propagation at speed (c) fixes Faraday's law uniquely as (abla times mathbf{E} = -partial_t mathbf{B}). Once Maxwell's equations are established, the Lorentz force density (homathbf{E} + mathbf{J}timesmathbf{B}) emerges as the only dimensionally consistent expression compatible with the local conservation of momentum derived directly from the field equations. The argument employs only elementary vector calculus and is accessible to advanced undergraduates. We suggest that this unified narrative, which reveals the internal coherence of electromagnetism, can serve as a valuable complement to the traditional empirical presentation.
Category: Education and Didactics

Charge-Dependent Equivalence Principle Violation from Kinetic Mixing of the Photon with a New Long-Range Vector Field

Authors: Renato Vieira dos Santos
Comments: 11 Pages.

The weak equivalence principle (WEP) has been tested with extraordinary precision over the past decades, but invariably with electrically neutral bodies. This leaves a fundamental blind spot: does gravity feel electric charge? A recent phenomenological analysis introduced a parameter $kappaphen$ to quantify this unexplored sector, but lacked a consistent field-theoretic origin. In this work we show that the simplest mechanism is kinetic mixing between the standard photon and a new massless vector field $X_mu$ that mediates a long-range fifth force coupled to the ordinary mass current. The single gauge-invariant dimension-four operator $frac{xi}{2}F_{muu}X^{muu}$ preserves causality and unitarity. By adopting the action in which both fields couple to their respective currents with the same sign convention, the two-body potential is fully symmetric and exactly satisfies Newton's third law, rendering the model free of any mathematical pathology.The fifth force between equal masses is repulsive, a known property of vector-mediated interactions, but its contribution to the neutral gravitational acceleration is absorbed into the measured Newtonian constant.For a static, spherically symmetric source, the mixing induces an electric field proportional to the Newtonian gravitational field, leading to a charge-dependent acceleration from which we identify $kappaphen = -ximu_0,G_X/G_N$, where $G_X$ is the fifth-force coupling strength.The symmetric cross term $propto q_1m_2+q_2m_1$ in the two-body potential gives rise to dipole radiation from compact binaries, providing a direct link to pulsar-timing constraints.We derive explicit constraints from the Cassini bound on the PPN parameter $gamma$, from lunar laser ranging on $alpha_1$, and from the Hulse--Taylor pulsar, showing that the model is compatible with all existing data while providing a clear roadmap for future experimental tests.
Category: Relativity and Cosmology

Cosmology from a Rastall-Inspired Variational Theory of Gravitation

Authors: Renato Vieira dos Santos
Comments: 9 Pages.

We propose a novel gravitational theory inspired by Rastall's idea of non-conserved energy-momentum, but formulated through a consistent variational principle. After developing a Lagrangian density that naturally incorporates matter-geometry coupling, we study cosmological consequences and fit parameters using recent Hubble function $H(z)$ data. According to model selection criteria (AICc and BIC), we obtain competitive models relative to $Lambda CDM.$ In our framework, the cosmological constant emerges from energy exchange between spacetime geometry and matter content, providing an alternative to vacuum energy interpretations. Our formulation provides a self-consistent variational foundation for non-conservative gravity, offering a potential resolution to the cosmological constant problem through dynamical energy exchange rather than vacuum energy.
Category: Relativity and Cosmology

A Least-Squares Optimization Model for Quad Mesh Offset

Authors: Zitao Xu
Comments: 10 Pages.

This article presents a least-squares optimization model for quadrilateral mesh offsets. Starting from an initial offset mesh generated from a base quad mesh, the method improves offset quality by introducing tangential corrections at offset vertices and solving for them globally. Each correction is represented by two scalar variables associated with two independent directions taken from the corresponding base quad, so that the optimization preserves the intended offset distance while allowing the offset mesh to adjust tangentially.For each quad, the objective function is constructed from local shape-preservation terms together with a center-consistency term, so that the optimized offset quad remains as consistent as possible with the shape and size of the corresponding base quad while reducing local crimping and shearing. The resulting formulation is a global least-squares problem over the mesh and leads to a sparse linear system. Examples in both convex and concave regions show that the method can significantly improve the quality of quad-mesh offsets and can be applied iteratively for further improvement.
Category: Geometry

TauPhi Numbers

Authors: Walter A. Kehowski
Comments: 8 Pages.

Let tau(n) be the number of divisors of n and let phi(n) denote the number of relatively prime numbers less than n. A number is called refactorable if and only if tau(n) divides n. It is known that phi(n) divides n if and only if n is 3-smooth. Furthermore, n/phi(n)=2 when n is a power of two and n/phi(n)=3 otherwise. Define lambda(n)=lcm(tau(n),phi(n)). Then n/lambda(n) is in {1,2,3} and n is called a tauphi-number. It is the purpose of this note to show when lambda(n)=n, called the unital tauphi-numbers.
Category: Number Theory

Quantifying Relational Structure in Quantum Measurement: An Axiomatic Account of Recursive Observation Depth

Authors: Agus Mulia Bakti
Comments: 20 Pages.

We formalize the relational pair (O, M), observer and observed system, as a primitive mathematical object governed by three operational axioms. From this structure we define Recursive Observation Depth (n^k), the length of the longest informative measurement chain an observer O can perform on a system M through a Positive Operator-Valued Measure (POVM). Five propositions about n^k are proved: monotonicity, relational dependence, a characterization of superposition, an exact value for a compatible (classical) observer, and, for a generic informationally complete observer, the impossibility of a terminal state, from which the divergence of n^k follows. Rank appears only as a special case, attained when the observer's measurements are mutually compatible; once they become informationally complete and incompatible, n^k diverges. We test the framework against four no-go theorems. It is consistent with Bell, Kochen—Specker, and No-Cloning on independent structural grounds, and consistent with PBR conditionally, provided the quantum state is taken to be a property of the relation (O, M) and not of the system alone. Wigner's Friend is resolved within this framework without further postulates. The Born rule is not derived, and no new experimental predictions are offered.
Category: Quantum Physics

Reasons the Photon Mass Should be Exactly Zero

Authors: Warren D. Smith
Comments: 5 Pages.

We argue from general relativity that if photons had mass, then charged black holes could not exist. But there is evidence they do exist. Also, big violations of Maxwell's laws would occur, even in regions far from black holes. This is the first evidence that photons really have zero, as opposed to just very small, mass. We also point out that the presence of extragalactic magnetic fields suggests |m_γ|⪅10^-64kg. Two independent lines of argument, one based on extragalactic magnetic fields and very conservative bounds on current densities, the other based on Voyager spaceprobe magnetometer measurements,both find |m_γ|⪅1.7×10^-56kg. These numbers are respectively 10¹⁰ and 60 times stronger than the best previous experimental bound. Finally, we consider the fact that massless quantum fields have additional symmetries. While it is tempting to try to use that as further justification for masslessness, it ultimately seems wrong.
Category: Classical Physics

Invisibility is Uncomfortable

Authors: Warren D. Smith
Comments: 3 Pages. Paper on www since 1993 now uploaded to VIXRA for archival purposes.

As a consequence of information-theoretic limitations arising from thermodynamics form a previous paper, we conclude that the sustained wearing of a "cloak of invisibiliity" is impossible.
Category: Thermodynamics and Energy

Perturbative String Theory and Its Non-Perturbative Probes

Authors: Sutirtha Mukherjee
Comments: 292 Pages.

Perturbative string theory treats a moving string as a two-dimensional surface and studies the quantum field theory of the fields living on it. Removing the two gauge freedoms of that surface, the freedom to relabel its points and the freedom to rescale its metric, by the Faddeev--Popov method produces a nilpotent BRST charge $Q_B$, and its cohomology $H(Q_B)$ is the physical spectrum of the string. The condition $Q_B^2=0$ fixes the number of spacetime dimensions at twenty-six for the bosonic string and ten for the superstring. At one loop the surface is a torus, and its modular invariance chooses the allowed spectrum, the GSO projection of the superstring, and the charge lattices the theory can carry. The same degeneration limit gives unitarity, since the amplitude factorizes on physical intermediate states. When that intermediate state is a massless one emitted into the vacuum, its coefficient is a tadpole, and requiring the tadpole to vanish is what picks out an allowed background. For the unoriented open string, this condition, equivalently the cancellation of gauge anomalies, forces the gauge group $SO(32)$. These results, and the tree and loop amplitudes built from them, make up the perturbative theory. Perturbation theory is limited to weak coupling, and reaching strong coupling relies on a set of non-perturbative probes that supersymmetry protects. A single cylinder stretched between two D-branes can be understood in two ways, as a loop of open string and as a closed string exchanged across the gap, and equating the two fixes the tension of a D-brane and shows that its Ramond-Ramond charge is quantized in the smallest unit Dirac allows. The masses of the bound states the branes form, the $(p,q)$ strings, and the D0-brane threshold bound states are set exactly by the supersymmetry algebra. Because these tensions, charges, and masses do not move with the coupling, they can be compared across two descriptions of the physics. The $(p,q)$ strings fill out the $SL(2,mathbb Z)$ multiplet behind the S-duality of type~IIB, and the D0-branes become the momentum modes of an eleventh dimension that opens up in strongly coupled type~IIA. The same protected states count the microstates of a black hole and reproduce its Bekenstein-Hawking entropy, and D-branes sourcing a warped throat give a four-dimensional gauge theory that confines while keeping one massless particle.
Category: Quantum Gravity and String Theory

Viscous Time Theory & Birch—Swinnerton-Dyer

Authors: Raoul Bianchetti, Payam Danesh
Comments: 10 Pages.

We develop a precise arithmetic version of Viscous Time Theory by replacing the original Sobolev field space with a finite Hilbert model of the Selmer complex. The VTT passive Hessian creates an anchored space for arithmetic. When we use a Schur complement it gets rid of the memory coupling. This results in an operator. The Bloch-Kato Selmer group is a sector, for this operator. The VTT passive Hessian and the Bloch-Kato Selmer group are connected in this way. The free part of the Bloch-Kato Selmer group gives us the Mordell-Weil rank. The finite arithmetic memory is what captures the Tate-Shafarevich and the Tamagawa contributions. The height-energy layer is also important. It connects with the Néron-Tate regulator. This connection happens through Arakelov and nonarchimedean potential theory. The VTT passive Hessian and the Néron-Tate regulator are related in this way. The main result is a rigorous VTT—BSD reduction theorem: after the active determinant germ is compared with L(E,s) at s=1, the BSD rank formula and refined leading coefficient follow. In this paper, we establish the variational, cohomological, height-theoretic and determinant-line structure needed for that comparison and it identifies the remaining analytic theorem.
Category: Algebra

Complexity of Minimization

Authors: Warren D. Smith
Comments: 15 Pages. On internet since 2000; uploading to VIXRA for archival purposes.

An important problem in numerical analysis is trying to minimize (or maximize) a real function F(x₁,x₂,...,x_d) of d real variables. We investigate (and survey) its computational complexity borderlines.

Results include (precise theorem statements are in the text): Minimizing, e.g., functions specified by polynomial formulas involving both trigonometric and ordinary arguments, is undecidable. Hence consider plain rational functions; we'll show minimizing these (more precisely, deciding whether the minimum lies below some threshold) is in NP. If the sum of the numerator and denominator degrees of a (multivariate) rational function is ≤4, then finding all its local minima is in P, except for the 4+0 case of a quartic polynomial (or its reciprocal) in which case it is NP-complete. (There is a slight caveat for the case 3+1; the "polynomial" runtime unfortunately depends also on an additional parameter, but for practical purposes this does not matter.) Indeed, even deciding whether a specified point is a localmin is NP-complete for a quartic. Minimizing a linear function in a cube is polynomial, but minimizing a quadratic in a cube is NP-complete. Minimizing a quadratic in a ball is in P, but it is NP-complete for a quartic (cubics: unknown). In all theseNP-completeness results, even approximating the value of the min is NP-complete, and the problems remain NP-complete even if all integers are input in unary. The P minimization algorithms for low degree rational functions involve new techniques of "multi-stage minimization" and "dimension reduction."

Minimizing functions "unimodal on lines," is in P. Solving systems of nonlinear equations F&8407;(x⃗)=0 is in P, if all the nonlinear functions $F_k are monotonic on lines. We present evidence that minimizing strictly unimodal functions (with exactly one minimum, and no saddlepoints) is exponentially hard; but if additionally the function obeys certain derivative bounds, then hardness seems to occur precisely when there are extremely long "winding valleys."
Category: Data Structures and Algorithms

Some Short Remarks on the Riemannian Hypothesis, Concerning the Zero-Finding Theorem

Authors: Holger Döring
Comments: 3 Pages. In German

At first, this description is no proof but a compact synopsis of the Riemanian prime-number-problem and its zero-states, seen and interpreted with the eyes of a theoretical physicist. Ergo there are mostly themes described, how the theorem can be handled by quantum mechanical descriptions and historical found partial solutions. Nevertheless there are some own ideas in it and in this way it may be that it can be useful as an assist for the goal. Here is the systematic summary of the entire thought experiment. It links every physical concept of hyperbola string of beads model with its exact mathematical equivalent in number theory. A more detailed paper will follow.
Category: Mathematical Physics

Computational Complexity of Synthetic Chemistry Basic Facts

Authors: Warren D. Smith
Comments: 8 Pages. On internet since 1997; uploading to VIXRA for archival purposes. Related paper: Molecular tinkertoys.

Three negative results:

1. Given a set of allowed starting materials and allowed chemical reactions, the problem of determining whether a chemical of specified structure is synthesizable is Turing undecidable.
2. The question of whether it is synthesizable in N steps is NP-complete. These 2 results apply in a general abstract setting and do not prove anything about how hard the problem is with any specific set of starting materials and allowed reactions. In particular we prove nothing about the case when the starting materials are all commercially available chemicals and the reactions are all known reactions!
3. The IUPAC naming scheme for assigning names to organic compounds will assign ambiguous names to most N-atom compounds and requires great chemical expertise. We show that both these problems are avoidable with alternative naming schemes, There are unquestionably {it far} simpler and better methods to name chemical compounds than the IUPAC scheme.

All 3 of these facts are almost trivial from the viewpoint of modern computer science, but I don't think they've been mentioned in the chemical literature.

Positive results: We discuss algorithms for finding out how to solve the synthesis problem (of determining whether something is synthesizable, and what the best synthetic process is). An interesting generalization of the famous "shortest path problem" in directed graphs arises in which the paths become synthetic trees, the graphs become hypergraphs, and the distances become synthetic costs. This problem is soluble either by generalizing Dijkstra's algorithm or the dynamic programming algorithm. Despite the fact that these algorithms are highly efficient as a function of the size of the hypergraph, in practice because the hypergraph arising from chemistry is enormous, that is inadequate. We discuss methods for ameliorating this.
Category: Chemistry

The Payment Verification Model for Digital Cash Point of Sale Systems

Authors: Lukas Saul, Robert Gludo, Jonathan Gludo
Comments: 6 Pages.

With public ledger digital cash payments comes a new type of point of sale (POS) system which has been implemented by several devices and apps. The "payment verification model" for POS minimizes security risk and associated fees while enabling merchants to adopt their point of sale system to different numéraires and different payment currencies. In this paper we outline this system and its advantages and operation. We provide the first systematic security taxonomy, privacy mitigation strategies, and accounting integration guidance specifically for payment verification POS systems.
Category: Economics and Finance

Relativistic Geometrical Horizons(rgh) in Both the Original Versions of Alcubierre and Natario Warp Drives

Authors: Fernando Loup
Comments: 26 Pages.

In 1994 Alcubierre developed the first warp drive work using the original 3+1 ADM-MTW formalism.Seven years later in 2001 the same original 3+1 ADM-MTW formalism appeared in the first part of the second warp drive work developed by Natario. But in 1997 the concept of the Relativistic Geometrical Horizon RGH was introduced by Hiscock in his work about the Alcubierre warp drive. According to Hiscock if the time component of a given spacetimemetric tensor becomes null g_(00)=0 a Horizon similar to the Event Horizon of the Schwarzschild black hole appears. The Alcubierre warp drive suffers from this pathology because in a given point of the Alcubierre warped regionthe g_(00)=0 appears generating the Alcubierre Horizon equivalent to the Event Horizon of the Schwarzschild black hole.The Natario warp drive was formulated in polar coordinates in a2+1 spacetime.A dimensional reduction of the Natario warp drive from a 2+1 to a 1+1 spacetimes in a given point of the Natariowarped region the g_(00)=0 appears generating the Natario Horizon in a 1+1 spacetime.But in the original Natario warp drive in polar coordinates in a 2+1 spacetime the g_(00)=0 never appears.Due to the presence of a second spatial dimension the g_(00)=0 can be avoided.
Category: Relativity and Cosmology

Eddington’s Mass-Luminosity Relation and the Laws of Thermodynamics

Authors: Stephen J. Crothers, Pierre-Marie Robitaille
Comments: 8 Pages.

Ever since its formulation by A. S. Eddington, the mass-luminosity relation has been viewed as a triumph for theoretical astronomy and astrophysics. The idea that the luminosity of the stars could be controlled solely by their mass was indeed a revolutionary concept. The proof involved two central aspects: (1) the belief that stars could be treated as ideal gases in hydrostatic equilibrium, and (2) that the opacity of Capella could be used as a reference mark applicable to other stars. Yet, when the mass-luminosity relation was advanced, no thought was given to the need for thermodynamic balance. Within thermodynamic expressions, not only must the dimensions (hence units) be consistent on each side of the equals sign, but the extensive nature of the properties must also balance. Namely, thermodynamic expressions must be balanced by properties which are extensive to the same degree. In this regard, mass is an extensive thermodynamic property and can be represented by a homogenous function of degree 1. Conversely, the luminosity of a star is neither extensive nor intensive, but rather can be represented by a homogenous function of degree 2/3. Consequently, the mass-luminosity expression is thermodynamically unbalanced and stands in violation of the laws of thermodynamics.
Category: Astrophysics

The Electrodynamic Origin of Black Holes (Part 1)

Authors: Raul Fattore
Comments: 17 Pages.

The electrodynamic origin of black holes as well as the electrodynamic origin of the gravitational force developed in the present study will contribute to a better understanding of how our universe works and obeys the real-world physics demonstrated by the more than proven laws of electrodynamics.This study presents a new perspective that will clarify and demystify many aspects about the origin of the gravitational force through a newly derived equation with terms that are absent in basic Newton’s gravitational law. It will also be demonstrated the decay of the gravitational force, the origin of black holes, what they really are, how they are formed, how they evolve, the real radiation spectrum, what particles are the constituents of black holes, what particles are to be found outside a black hole, the wavelength shift (or redshift) of black holes, and other properties.- Do "receding" galaxies really mean that the universe is expanding?- Is it scientifically serious to accept that gravity is not a force, but a "geometrical effect" caused by mass?- Is it scientifically serious to accept that "geometrical gravity" lacks a unique unit of calculation, because it depends on what is being calculated?- Can it be scientifically acceptable that a lump of Newtonian mass bends EM radiation?- Can monochromatic radiation emission from black holes be scientifically acceptable?- Can it be scientifically acceptable that some types of black holes do not rotate?
Category: Astrophysics

The Electrodynamic Origin of Black Holes (Part 2)

Authors: Raul Fattore
Comments: 37 Pages.

The electrodynamic origin of black holes as well as the electrodynamic origin of the gravitational force developed in the present study will contribute to a better understanding of how our universe works and obeys the real-world physics demonstrated by the more than proven laws of electrodynamics.This study presents a new perspective that will clarify and demystify many aspects about the origin of the gravitational force through a newly derived equation with terms that are absent in basic Newton’s gravitational law. It will also be demonstrated the decay of the gravitational force, the origin of black holes, what they really are, how they are formed, how they evolve, the real radiation spectrum, what particles are the constituents of black holes, what particles are to be found outside a black hole, the wavelength shift (or redshift) of black holes, and other properties.- Do "receding" galaxies really mean that the universe is expanding?- Is it scientifically serious to accept that gravity is not a force, but a "geometrical effect" caused by mass?- Is it scientifically serious to accept that "geometrical gravity" lacks a unique unit of calculation, because it depends on what is being calculated?- Can it be scientifically acceptable that a lump of Newtonian mass bends EM radiation?- Can monochromatic radiation emission from black holes be scientifically acceptable?- Can it be scientifically acceptable that some types of black holes do not rotate?
Category: Astrophysics

Best Play for Imperfect Players and Game Tree Search: Part I (Theory)

Authors: Eric B. Baum, Warren D. Smith
Comments: 41 Pages.

This is part I (theory) of a 2-part paper about a new, non-minimaxing, approach to search in game-trees such as Chess and Go. Its first point is that minimaxing is NOT the best decision-making (i.e. chess-move-selection) process based on inexact merely-statistical estimates about the "goodness" of the chess positions at the leaves of a search tree. Its second point is that going down the game tree to some fixed depth, then stopping, is NOT the best choice of chess-positions for your search to explore. "BPIP search" is a way to make better decisions based on any particular search tree, and a way to explore better trees. As of year 2026, BPIP still has not yet been used by chess and go programs, but if were might enable them to get substantially stronger. Would it? I would like to know, but never found out because I abandoned my attempts to write strong chess and go programs as just too difficult a programming task for me.

I originally wrote this paper and put it on the internet in 1993, and at that time "Monte Carlo game tree search" and today's highly advanced selective alphabeta variants did not yet exist, computer chess was weaker than the best humans, and computer go far weaker than decent human amateurs. Later, go programmers invented "Monte Carlo game tree search" which can be regarded as a "poor man's BPIP" (although they did not realize that). MCGTS has been used in go programs with great success.
Category: Artificial Intelligence

Fermi-Born-Infeld Electrodynamics: a Nonlinear Theory with Physical Gauge

Authors: Renato Vieira dos Santos
Comments: 12 Pages.

We construct a nonlinear extension of Fermi's electrodynamics by incorporating a Born--Infeld structure that depends directly on the four-potential $A_mu$ rather than on the field strength $F_{muu}$. The resulting theory, which we call Fermi--Born--Infeld (FBI) electrodynamics, eliminates the $U(1)$ gauge redundancy by elevating the Lorenz gauge to a dynamical condition. The Lagrangian is built from the determinant of a metric-like tensor $g_{muu} = eta_{muu} + 2kappa, partial_{(mu} A_{u)}$, ensuring that the canonical energy--momentum tensor and the spin density remain unique and free of gauge ambiguities. We derive the field equations, which reduce to $partial_u(sqrt{-g}, g^{muu}) = 0$, and show that the Lorenz condition $partial_mu A^mu = 0$ emerges dynamically from retarded boundary conditions and the requirement of a positive-energy spectrum. The nonlinearities modify the propagation of longitudinal modes; we argue, via a Vainshtein-like mechanism, that the nonlinear self-interactions may stabilize the longitudinal mode, opening the possibility of a stable massive scalar photon under extreme field conditions. We also compute the spin density from the Noether current and discuss its properties. The FBI theory preserves the physical gauge of Fermi's original formulation while incorporating the regularization features of Born--Infeld electrodynamics, making it a candidate for describing electromagnetic phenomena in strong-field regimes.
Category: Relativity and Cosmology

Best Play for Imperfect Players and Game Tree Search: part II (experiments)

Authors: Warren D. Smith, Eric B. Baum, Charles Garrett, Rico Tudor
Comments: 39 Pages.

This is part II (experiments) of a 2-part paper about a new, non-minimaxing, approach to search in game-trees such as Chess and Go. Its first point is that minimaxing is NOT the best decision-making (i.e. chess-move-selection) process based on inexact merely-statistical estimates about the "goodness" of the chess positions at the leaves of a search tree. Its second point is that going down the game tree to some fixed depth, then stopping, is NOT the best choice of chess-positions for your search to explore. "BPIP search" is a way to make better decisions based on any particular search tree, and a way to grow better trees to explore. As of year 2026, BPIP still has not yet been used by chess and go programs, but if were might enable them to get substantially stronger. Would it? I would like to know, but never found out because I abandoned my attempts to write strong chess and go programs as just too difficult a programming task for me. However in this paper we did program BPIP and alphabeta gameplayers for a number of simpler games, achieving strengths apparently stronger than any human and also among the strongest year-1995 computer programs. For some games BPIP indeed outperformed alphabeta, sometimes hugely. Games large enough that full solves of game positions are usually out of reach, and which can have "smart and slow" position evaluators, and in which large searches are done, are the games favoring BPIP versus alphabeta.

I originally wrote this paper and put it on the internet in 1995, and at that time "Monte Carlo game tree search" and today's highly advanced selective alphabeta variants did not yet exist, computer chess was weaker than the best humans, and computer go far weaker than decent human amateurs. Later, go programmers invented "Monte Carlo game tree search" which can be regarded as a "poor man's BPIP" (although the MCGTS inventors did not realize that). MCGTS has been used in go programs with great success.
Category: Artificial Intelligence

The Influence Mechanism of Weight Allocation and Test Set Design on Open-Source Large Model Evaluation Results

Authors: Dong Zhang, Yang Sun, Fei Lyu, Xiaofeng Liu, Xin Li
Comments: 22 Pages.

The evaluation results of open-source large language models are not only influenced by model parameter scale, training corpus, and alignment strategies, but also significantly constrained by the test set architecture and the weight allocation of evaluation metrics. To address this issue, this paper leverages multiple types of real-world evaluation data collected from engineering projects to investigate the evolution mechanism of open-source large model evaluation scores and rankings under the coupled effects of weight allocation and test set design. This paper selects four mainstream frontier open-source models—DeepSeek-V3.2, MiniMax-M2.5, Qwen3.6-35B-A3B, and gpt-oss-120b—to conduct controlled experiments. All models uniformly employ 8 96G H20 GPUs for local offline inference evaluation, and weighted aggregation is performed after unifying the scoring criteria to eliminate evaluation interference caused by third-party API rate limiting, version differences, and inconsistent scoring standards. The native capabilities of the models are supplemented with official model card information from the ModelScope platform: MiniMax-M2.5 focuses on code engineering, intelligent agents, and office interaction, with inference speed improved by 37% over the previous generation and inference cost at only 10% of Claude Opus 4.6; gpt-oss-120b is an OpenAI open-source MoE architecture model that natively supports hierarchical reasoning, tool invocation, and MXFP4 quantized deployment. The experimental datasets cover five major tasks—social bias discrimination, common misconception fact-checking, lifestyle question answering, contextual semantic understanding, and basic logical reasoning—corresponding to five evaluation capabilities: bias identification, fact verification, knowledge response, contextual interpretation, and mathematical reasoning. Specifically, this paper operationalizes "task type"as an observational variable into five categories of questions: ：social bias discrimination is used to measure the Bias Identificationconcept（characterized by bias judgment accuracy and harmful tendency response rate），common misconceptionFact-Checkingfact-checking is used to measure the fact verification concept（characterized by fact judgment accuracy），lifestyle question answering is used to measure the knowledge response concept（characterized by answer correctness rate and completeness score），contextual semantic understanding is used to measure the contextual interpretation concept（characterized by semantic consistency and coreference resolution accuracy），basic logical reasoning is used to measure the mathematical reasoning concept（characterized by reasoning step accuracy and final conclusion accuracy）。This paper constructs three evaluation weighting schemes: average baseline weights、performance-oriented weights、, and robust compliance-oriented weights，to analyze the variation patterns of model tier rankings under differentiated weight allocations。The experimental results show that：when the test set task categories are homogeneous、and question types are uniform，model rankings are highly susceptible to local sample perturbations；test sets with diverse task types、and balanced difficulty levels，exhibit stronger evaluation stability，and can objectively characterize comprehensive model capabilities。The study further confirms that，metric weights、sample structure、and task distribution are not auxiliary evaluation variables，but core elements determining the credibility of evaluation conclusions、and applicability。
Category: Artificial Intelligence

Non-Hermitian Quantum Mechanics Fundamentals & Lennard-Jones Potential

Authors: Larry Lee, Preet Sharma
Comments: 8 Pages.

Non-Hermitian quantum mechanics is a fairly new field and has been of great interests to theorists and experimentalists alike. In this study we have shown the basics of Non-Hermitian quantum mechanics and have put forward a scenario in which Non-Hermitian quantum mechanics can be applied to the well known Lennard-Jones potential. We have not shown explicitly what the results would be but when we apply Lennard-Jones potential to the Non-Hermitian scenario, but we have given one idea as to how it can play a part. This idea is also our continuing research.
Category: Quantum Physics

A Network-Based Microscopic Interpretation of Vacuum Localised Structures

Authors: Rudi Van Nieuwenhove
Comments: 10 Pages.

Vacuum Localised Structures (VLS) have recently been proposed as self-gravitating solutions of the Einstein field equations. Such structures have been investigated in connection with galactic dark matter distributions, filamentary gravitational configurations, and black-hole-like vacuum solutions without baryonic matter sources. Although the corresponding solutions are mathematically consistent within General Relativity, the physical interpretation of the underlying stress-energy tensor remained unclear.In the present work, a microscopic interpretation of VLS structures is explored using a dynamical network framework. Space is interpreted as an emergent structure arising from an underlying discrete connectivity network, in which effective metric properties are associated with local link configurations and shortest-path relations. Curvature is interpreted as a spatial variation of effective network connectivity.Within this framework, a VLS is described as a self-sustained coherent network configuration maintained by local reconnection dynamics. This surface-dominated dynamical behaviour naturally leads to the effective equation of state in which the radial pressure equals minus one-third of the energy density, thereby providing a possible microscopic interpretation of the peculiar stress-energy properties associated with VLS solutions.
Category: Relativity and Cosmology

Introduction to Pseudo Vector Theory of the Mediating Medium for Dark Matter

Authors: J. W. A. Zwart
Comments: 12 Pages. (Note by viXra Admin: Please cite and list scientific references)

The dark matter mediating medium for the pseudo vectors carries by definition four independent vector cells of the components for acceleration, spin and precession making up twelve combinations of pseudo vectors. The conjugated medium at the absolute zero energy state consists of solely pseudo e-neutrino triplets as a dynamic non destructible equilibrium in cubic pyramid symmetry. At a relativistic thermodynamic level of electron energy the pseudo vector medium consists of pseudo μ-triplets in cubic symmetry mixed to triplet ensembles of τ-pseudo triplets in cubic symmetry together guided by the pseudo e-neutrinos. Both the μ- and τ- triplets carry always the rotations for τ-triplets perpendicular to the μ-triplets suggesting orthogonal cubic pyramid symmetry. The top in equilateral pyramid symmetry of equal dimension for the base triangle in the cubic symmetry provides the dynamic electric charge in one polarity following the acceleration vector component of the pseudo vector cells. The time intervals for the electric charge dynamics give the sequential conjugated inversion shifts along the rotation axis of the height of the equilateral pyramid. Common sense reasoning of some scaling calculations shows the validity of the statement in this abstract explained in the paper below.
Category: High Energy Particle Physics

Quaternions, Octonions, and Now, 16-Ons and 2^n-Ons: New Kinds of Numbers

Authors: Warren D. Smith
Comments: 68 Pages. Placing this 2004 paper on vixra for archival purposes.

"Cayley-Dickson doubling," starting from the real numbers, successively yields the complex numbers (dimension 2), quaternions (4), and octonions (8). Each contains all the previous ones as subalgebras. Famous Theorems, previously thought to be the last word, state that these are the full set of division (or normed) algebras with 1 over the real numbers. Their properties keep degrading: the complex numbers lose the ordering and self-conjugacy (x̅=x) properties of the reals; at the quaternions we lose commutativity; and at the octonions we lose associativity. If one keeps Cayley-Dickson doubling to get the 16-dimensional "sedenions," zero-divisors appear.

We introduce a different doubling process which also produces the complexes, quaternions, and octonions, but keeps going to yield 2ⁿ-dimensional normed algebraic structures, for every n≥0. Each contains all the previous ones as subalgebras. We'll see how these evade the Famous Impossibility Theorems. They also lead to a rational "vector product" operation in 2^k-1 dimensions for each k≥2; this operation is impossible in other dimensions.

But properties continue to degrade. The 16-ons lose distributivity, right-cancellation yx·x^-1=y, flexibility a·ba=ab·a, and antiautomorphism (c̅=b̅a̅ where c=ab). The 32-ons lose the properties that the solutions of generic division problems necessarily exist and are unique, and lose the "Trotter product limit formula." We introduce an important new notion to topology we call "generalized smoothness." The 2ⁿ-ons are generalized smooth for n≤4.

All 2ⁿ-ons have 1 and obey numerous identities including weakenings of the distributive, associative, and antiautomorphism laws. In the case of 16-ons these weakened distributivity laws characterize them, i.e. our 16-ons are, in a sense, unique and best-possible. Our 2ⁿ-ons also are unique, albeit in a much weaker sense. The 2ⁿ-ons with n≤4 support a version of the fundamental theorem of algebra. Normed algebras (rational but not nec. distributive) over the reals are impossible in dimensions other than powers of 2.
Category: Algebra

Embedding Space Construction of Conformal Field Theory From First Principles

Authors: Sutirtha Mukherjee
Comments: 104 Pages. (Note by viXra Admin: Please cite listed scientific references)

This work presents a systematic development of conformal field theory from first principles in quantum field theory, emphasizing complete derivations of the conformal group in arbitrary dimensions from the conformal Killing equation, proving its isomorphism to $mathrm{SO}(d+1,1)$, and develop the embedding space formalism as a tool for constructing conformally covariant correlation functions constrained by Ward identities. In two dimensions, conformal symmetry enhances to an infinite-dimensional algebra: we derive the Virasoro algebra $[L_m, L_n] = (m-n)L_{m+n} + frac{c}{12}(m^3-m)delta_{m+n,0}$ from infinitesimal generators $ell_n = -z^{n+1}partial_z$, computing the central charge explicitly for free theories (boson $c=1$, Majorana fermion $c=1/2$, $bc$-ghosts $c = 1-3(2lambda-1)^2$) and demonstrating its physical interpretation as vacuum energy. Through radial quantization, we establish the operator-state correspondence and construct the Hilbert space via Virasoro descendants of primary states $|h,bar{h}angle$, deriving the transformation law $T'(w) = (dw/dz)^{-2}[T(z) - (c/12){w;z}]$ that reveals the geometric origin of the conformal anomaly. Unlike conventional treatments, we develop all mathematical machinery from standard QFT without relying on unexplained results from string theory or representation theory, exhibiting all intermediate steps explicitly to provide a detailed continuation beyond introductory QFT texts.
Category: Quantum Gravity and String Theory

Entanglement, Common-Origin Correlations, and the Interpretation of Bell Violations

Authors: Ion Vlad
Comments: 9 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Bell's theorem demonstrates that no local deterministic theory can reproduce the complete set of correlations predicted by standard quantum mechanics. The present work accepts Bell's theorem as mathematically correct but questions the physical interpretation of the quantum correlation function used in Bell analyses. It is argued that entangled particles inherit a complete common physical state at their creation and that subsequent measurements reveal selected observables of this state rather than generating new information or requiring superluminal communication. The paper further proposes that the standard quantum correlation function, (E(θ)=−cosθ), incorporates additional angular dependence beyond the information physically established at the source. Under this interpretation, the observed violation of Bell inequalities arises from the mathematical structure of the correlation function rather than from nonlocal information transfer between distant particles. An explicit local common-source model is presented, leading to a piecewise linear correlation function and motivating a decomposition of the standard quantum prediction into a local component and a supplementary angular term.
Category: Quantum Physics

Ramanujan Transformations and Robin Defects

Authors: Payam Danesh
Comments: 9 Pages.

We studied the Robin defect associated with the inequality σ(n)<e^γ nlogu2061logu2061n, express its Laplace transform through Ramanujan’s transformation for the divisor Lambert series and isolate the precise difference between smoothed positivity and coefficientwise positivity. The main results give us an exact Ramanujan-transformed identity for the Robin defect, an equivalent coefficientwise formulation of the Riemann Hypothesis showing why transform-level positivity cannot by itself prove the hypothesis and an extremal reduction to colossally abundant and highest abundant numbers. Numerical data for early extremal integers illustrate how the normalized defect behaves past the exceptional value 5040. Ramanujan’s identities provide powerful global control, but the Riemann Hypothesis requires pointwise positivity at the extremal divisor-rich integers.
Category: Number Theory

Optimization Model for Polyline Offset

Authors: Zitao Xu
Comments: 7 Pages.

Classical offset algorithms focus on constructing offset curves and surfaces. Optimization-based geometry processing has also been extensively studied for mesh fairing, deformation, and parameterization. The present work differs from both directions by introducing a least-squares formulation whose unknowns are tangential displacements of offset vertices, yielding a globally optimized offset configuration.
Category: Geometry

Analyzing a Variant Version of a Fibonacci Polynomial

Authors: Marciano L. Legarde
Comments: 12 Pages.

In this paper, we introduce a new finite polynomial called the "Variant Fibonacci Polynomial". This polynomial is defined by using the standard Fibonacci sequence as both the coefficients and the exponents of each term. Although the definition is simple, it leads to several interesting mathematical properties.We begin by defining the polynomial and giving several examples. We then evaluate it at different values of x, identify its guaranteed real root, discuss its complex roots, and derive formulas for both its derivative and antiderivative. We also examine the infinite series version of the polynomial and observe when it converges and when it diverges.Finally, we discuss whether this polynomial could be used to construct a new type of series expansion for functions and whether such an expansion might eventually be useful for solving differential equations. While it is still too early to draw definite conclusions, the results of this paper suggest that the Variant Fibonacci Polynomial is an interesting mathematical object that deserves further study.
Category: General Mathematics

On a Quadratic Collatz Type Map Governed by Prime Factorization: A Conjectural Universal Cycle, Two Reduction Theorems and an Intrinsic Computational Barrier

Authors: Christoper Mututu
Comments: 36 Pages.

We study a map T on the integers defined by T(n)=n^2+1 when n is prime or even and T(n)=n/P(n) when n is odd composite, where P(n) denotes a designated prime factor n. Two variants arise according to the choice of P(n). In Part I, P(n) is the largest prime factor of n while in Part II, it is the smallest. Informally, the conjecture of this paper asserts that every integer greater than one in absolute value eventually enters the single twelve element cycle5→26→677→458330→210066388901→52357→41→1682→2829125→1625→125→25 and remains there forever. Formally, we verify this for every integer n∈[2,1000] under Part I with no exception and no alternate cycle observed and we conjecture it holds for every integer n in the domain Z^*=Z {-1,0,1} but we do not prove it.Toward this conjecture, we prove two theorems. The first is exact rather than asymptotic. For any odd composite m, repeated application of the largest prime factor reduction reaches a prime in precisely Ω(m)-1 steps where Ω(m) counts the prime factors of m with multiplicity. Each application removes exactly one element from the prime factorization multiset m so the count decreases by exactly one per step and terminates uniquely at a prime. The second theorem follows from the first. Under the extension of primality to negative integers through |n|, which is the only convention under which the conjecture is well posed on Z, every negative integer reaches a positive value within at most Ω(|n|) steps. This reduces the negative integer case of the conjecture entirely to the positive integer case. We also identify an obstruction to further verification that is structural rather than a matter of computing resources. The reduction step of T requires the complete factorization of the input which is a problem for which no general sub exponential algorithm is known. Repeated application of the squaring branch can therefore produce integers whose factorization lies beyond any presently known method regardless of computing time available. Our verification required factoring intermediate values of up to 96 digits and succeeded in every instance though with no guarantee that a harder instance does not arise beyond the tested range. For Part II, this obstruction is severe enough to foreclose even a conjecture. Every trajectory examined exceeded 100 digits within fewer than 25 iterations without any value repeating. We are unable to characterize the long-term behavior of Part II by any method available to us and as a result, Part II is entirely open.
Category: Number Theory

The Giza Pyramid Complex as an Analogy to the Voyager Mission

Authors: Andrey V. Voron
Comments: 8 Pages.

This paper explores a potential analogy arising from a comparison between the space missions of Pioneer 10, Pioneer 11, Voyager 1, and Voyager 2 on one hand, and the Giza pyramid complex project on the other. Within this framework, five plausible assumptions are examined. Based on their outcomes, the study demonstrates the probable message intended by the pyramid builders and identifies a potential recipient for this transmission (a planet of a specific star).
Category: Archaeology

Artificial General Intelligence (AGI)

Authors: Clark M. Thomas
Comments: 4 Pages.

The sudden injection of giant data server farms into the world’s advanced economies, especially during 2026, is unique in human history. Humanity’s lofty position as the only global hyperkeystone species could be challenged by the emergence of a consciousness not fully human, nor what actual space aliens would bring to ourgeneralized intelligence. Here are some key aspects of this unique cybernetic challenge that we must soon face.
Category: Artificial Intelligence

A Quantum Induced Wapdrive II Subspacestructure, Dilaton-Field (Φ) and Their Cosmic Connections

Authors: Holger Döring
Comments: 26 Pages.

In a former paper a quantum induced warp-drive was introduced by assuming a model of microscopic cylinders as spacelike dimensions whereby the timelike dimension remains at its classical one-dimensional state. Described now is more detailed the underlying fundamental physical and mathematical spacetime structure than in the first paper , which is announced to feature this quantum induced warp-drive concept. Although there are certainly some new elements involved, everything is based on very classical GRT and QTH- descriptions. A more detailed description of the coupling dilaton-field is made, which connects the macroscopic sector of GRT with the microscopic sector of QFTH. This dilaton-field shall be named a "barytic -field".
Category: Quantum Gravity and String Theory

Comment on "Memories of Amplitude and Direction Coexist and Compete in Non-Brownian Suspensions"

Authors: Vladimir Kuz'menko
Comments: 3 Pages.

A recent article [Phys. Rev. Lett. 136, 258201 (2026)] continued the experimental study of an interesting physical phenomenon, where the viscosity of a suspension can be greater when moving forward than when moving backward. The authors attribute this phenomenon to the presence of a certain memory in the environment. The physical nature of both the phenomenon itself and the supposed memory is unknown. A possible explanation of the physical nature of this effect is proposed here and simple experiments to study some properties of such non-local memory are discussed.
Category: Quantum Physics

The Simple Geometry of Time: A Physical Record of Cosmic Metric Transformation

Authors: Alata Elatawneh
Comments: 26 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org) Repository URL: https://github.com/Elatawneh/UCK-Cosmology-Framework.git

We present a predictive, geometrically constrained cosmological architecture, designated the Unified Cosmic Kinematic (UCK) framework, derived from the foundational postulate that cosmic time is macroscopically identical to relational metric spatial expansion. The invariant comoving time derivative of this identity demonstrates that the unperturbed background expansion parameter is the analytical inverse of the cosmic epoch, yielding a global background baseline constant of 70.85 km/ s/ Mpc when anchored to the empirically observed cosmic age of 13.8 Gyr. Although the baseline expansion model is geometrically deterministic, mapping observational signatures requires accounting for the interaction of matter and radiation within the spatial manifold via an effective field theory approach. This framework introduces four native tracking parameters calculated from first principles via the optimization of unbinned data streams, independent of external fluid-driven dark sector parameters. The statistical viability of this architecture is evaluated against five high-precision, unbinned astronomical data pipelines spanning late-universe standard candles, local velocity anomalies, localized mass-deflection geometries, the cosmic microwave background, and deep spectroscopic horizons. Our optimization routines address the persistent Hubble tension by demonstrating that regional gravitational density induces a localized clock-drag fraction that elevates the apparent local expansion rate via gravitational time dilation. This exact localized clock-drag metric reconciles weak-field gravitational limits, precisely mapping the mass-deflection profiles of strong gravitational lensing systems under pure baryonic constraints without invoking dark matter halos. Finally, coupling this expansion history to the primordial plasma sound horizon maps the early acoustic peaks with high statistical fidelity. The resulting high-redshift temporal elongation extends the available structural development timeline, thereby addressing the early mature galaxy chronological discrepancy across all targeted spectroscopic horizons.
Category: Relativity and Cosmology

Geometric Nodal Projections of Quantized Action

Authors: Casey McGrath
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)

We introduce a Projected Node Model, in which quantized action ΔS = ℏ manifests at discrete event loci (nodes) via conjugate projections.From minimal axioms we rigorously derive the invariance of c, de Broglie relations, geometric uncertainty, Minkowski structure, massinertia,and the Planck scale. The framework recovers standard quantum and relativistic phenomenology with enhanced geometric clarity.
Category: Mathematical Physics

A Geometric Approach to the Hydrogen 1S—2S Transition Shift via Horizon-Enforced Acceleration Invariance

Authors: Osama Haggag
Comments: 4 Pages. DOI: 10.5281/zenodo.20459593

We explore a first-principles geometric framework to evaluate the precise frequency corrections in the atomic hydrogen 1S→2S transition by analyzing the coordinate strain of a bounded quantum vacuum. By extending the Einstein Equivalence Principle (EEP) to localized quantum states, we model the electron wavepacket as an extended matter wave whose internal phase clock modulates under intense non-inertial proper acceleration. Demanding that the contracting local Rindler horizon is bounded by the particle's irreducible Compton wavelength yields a maximum proper acceleration ceiling u2044 . Applying this constraint to the hydrogen ground state yields a metric modulation parameter . This coordinate-layer regularization introduces a geometric potential shift of 243.74 Hz, offering a novel, non-perturbative perspective that aligns closely with the high-precision spectroscopy data (2,466,061,413,187,018±11 Hz) tracked by the Max Planck Institute of Quantum Optics.
Category: Relativity and Cosmology

Parapose, Triggering for Transition of Matrix and Principles of an Object to Round Around the Chord or the Point

Authors: Binay Krishna Maity
Comments: 8 Pages.

In the Transpose mode of a matrix we can see thearrangement of the literals of the matrix in a specific manner. If we rearrange these literals in another specific manner and combine the resulting matrix with original and/or transpose as we need, then, there will be different patterns of matrix and we may call this way of transition of the literals of the matrix as Parapose of matrix and the way of combination of the matrices as the Triggering for transition. Then there are three kinds of triggering of transitions. Such as - 1) The Triggering for Transition in First kind, 2) The Triggering for Transition in Second kind and 3) The Triggering for Transition in Third kind. This triggering of Transition may exhibit the principle of any set of objects rounding centering the point or around the chord.
Category: General Mathematics

A Model for Merging Black Holes

Authors: Kohji Suzuki
Comments: 16 Pages.

We present a model in which SING, a singularity-inspired notion (viXra:1812.0480 [v1]), plays some role in black hole merging to suggest that evaporation of black hole leaves something behind.
Category: Mathematical Physics

The Nonlinear Schroedinger Equation and de Broglie Pilot Wave

Authors: Miroslav pardy
Comments: 11 Pages. The original article

The Schroedinger equation with the logarithmic nonlinear term is derived by the natural generalization of the hydrodynamical model ofquantum mechanics. The nonlinear term appears to be logically necessarybecause it enables explanation of the classical motion for the infinite masslimit. The article is the modied version of the articles by author (Pardy,1993; 2001).
Category: Quantum Physics

Deriving the Dot Product From Polar Coordinates

Authors: Timothy Jones
Comments: 1 Page. This derivation doesn't seem to be in the literature.

Using polar coordinates the dot product is easily derived.
Category: General Mathematics

An Interpretation of the Finnish Kalevala

Authors: Jorma Jormakka
Comments: 23 Pages. (Note by viXra Admin: Please cite and list references)

Kalevala may not be a so current topic, but some questions about it were never answered in a fully satisfactory way. What was Sampo, was it really a world pillar as Uno Harva explained, and if so, how can a world pillar have a handle, fall to the sea, and produce Bronze Age trade goods such as grain, salt and money (gold and silver). The article applies the following method to Kalevala: The starting points are, 1) Archeology has shown that Baltic Finns came to the Baltic shores during the Seima-Turbino phenomenon. 2) Many researchers suggest that Kalevala describes the Kaali meteorite. 3) Marjatta poems are from the time when Christianity came to Finland. It follows that Baltic Finns were creating poems during the whole time of their stay in the Baltic area.Considering that Elias L"onnrot and others gathered all poems they could find, the collected poems should contain poems from all of the times since the Nordic Bronze Age to the arrival of Christianity. By identifying which poems originate from which period, we can construct a history of Baltic Finns. The result agrees in much with the accepted view of the history of Baltic Finns, but it also changes the picture that has so far been obtained by other methods. Notably, Sampo is explained as a trade-agreement in the form of a written discand the method interprets Kullervo poems as describing a stage when Baltic Finns were a marginalized people pressed by Baltic peoples.
Category: Religion and Spiritualism

On the Non-Probabilistic Nature of Thermodynamic Processes: Fundamental to a Non-Statistical Formulation of Thermodynamics

Authors: Antonio Jose Mejias Marquina
Comments: 2 Pages.

[This] paper proposes a reevaluation of the fundamental nature of thermodynamics, challenging the prevailing view that attributes macroscopic behavior exclusively to statistical fluctuations of microscopic systems. Through a critical analysis of conservation laws and systems dynamics, it argues that the probabilistic nature observed in conventional thermodynamics is not an intrinsic property of matter at a fundamental level, but rather a consequence of an incomplete description of the microscopic state. The possibility of a deterministic formulation is examined, exploring the implications of integrating a complete causal dynamics that dispenses with overall averages, suggesting that the "arrow of time" and entropy could be emergent manifestations of a more precise underlying dynamic structure and not merely the result of chance.
Category: Thermodynamics and Energy

The Critical Path of Evolution

Authors: Oleg Ponfilenok
Comments: Pages. Source: https://github.com/oponfil/critical-path-of-evolution

The evolution of life is treated as the traversal of N ~ 10^14 small, high-probability steps of increasing complexity, with mean step time μ — a critical path from the thermal gate of the cosmic microwave background to a technological civilization over a time T ≈ 13.8 Gyr. When the step times are independent, the concentration of their sum compresses the relative spread of exit times as 1/√N; within the model this yields a dispersion σ = √(μT). We show that the observed absence of "loud" civilizations (cosmic silence) gives an upper bound on the interplanetary dispersion of exit times σ ≈ 800—1400 yr — of the order of the horizon of the transition to detectability; from this σ follows μ ≈ 25—75 min, which coincides with the generation time of microorganisms. The same silence places an upper bound on the Galactic population at n ~ 10^4—10^5 civilization-bearing planets, in agreement with astrophysical estimates of the number of Earth-like habitats. Two properties of the critical path — its progression under a local surplus of resources and the kinematic uniqueness of the fastest route — make its parameters approximately universal and ensure a synchronous tempo for the development of life; cosmic silence indicates that this route is realized through the carbon—organic chemistry of life of our type. A logical consequence of the same picture is the convergence of civilization form: the carriers of technological civilizations are expectedly close in functional plan to humanoids, although the details of morphology may differ.
Category: Astrophysics

Inertial Manifold for Dyadic Model of the Navier-Stokes Equations

Authors: Yuhan Wei
Comments: 35 Pages.

We prove the existence of finite-dimensional inertial manifolds forthe dyadic model of turbulence for all dissipation exponents α≥1/3.For α = 1/3 and α > 1/3 the proof is unified by working in the Hα-norm and employing a generalized cone method. The dimension scales as N∼1 2αlog λ log ν−1, matching the optimal upper bounds for shell models. The construction relies on a low-mode cut-off, a forward cascade estimate that exploits the monotone structure of the dyadic model, and a modified strong squeezing property of Koksch (2000). The resulting inertial manifold is Lipschitz and C1+ϵ-smooth, and satisfies the exponential tracking property. This provides a rigorousfinite-dimensional reduction for the entire supercritical range α≥1/3. We also answer an open question by Cheskidov (2008) regarding theexistence of strong compact global attractors for α<1/2.
Category: Functions and Analysis

Relaxation to Maxwellian Equilibrium in a Periodic Kinetic Model

Authors: Payam Danesh, Raoul Bianchetti
Comments: 15 Pages.

We study a periodic kinetic Fokker—Planck equation in which free transport in position is coupled to Ornstein—Uhlenbeck relaxation in velocity. Our aim is to give a transparent weighted L^2 analysis of the relaxation mechanism and to test it by a modal approximation. The equation is written in Maxwellian variables, the generator is decomposed into a skew transport part and a dissipative velocity part and its contraction semigroup is considered on the natural weighted Hilbert space. Using Gaussian and torus Poincaré inequalities, we prove mass conservation, microscopic coercivity and exponential decay on the zero-mass subspace through a modified first-order energy containing a spatial—velocity cross term. For the homogeneous problem, the entropy identity gives decay from the Gaussian logarithmic Sobolev inequality. A Fourier—Hermite discretization is then derived, its semi-discrete L^2-stability is shown and truncation tests quantify convergence in the Hermite index and the spectral abscissa of the first nonzero Fourier block. The results give a compact account of how velocity relaxation enforces global return to Maxwellian equilibrium in this model.
Category: Mathematical Physics

A Little Book of Time Series with Python

Authors: Regi Mathew
Comments: 97 Pages.

A Little Book of Time Series with Python is a concise, practical guide designed as a quick reference for students, and analysts seeking to understand and apply time series analysis using Python. Inspired by Avril Coghlan’s A Little Book of R for Time Series, this volume preserves the original’s philosophy of simplicity and brevity while fully adapting the content to the modern Python ecosystem—the dominant language for data science, machine learning, and applied analytics. It emphasizes the enduring importance of statistical foundations in time series analysis and demonstrates how to implement them effectively with contemporary Python tools and libraries. Mirroring the structure and pedagogical approach of its R predecessor, the booklet provides clear explanations, code examples, and workflows tailored to Python, making it an ideal resource for concept clarification, interview preparation, self-study, and rapid application in real-world projects.
Category: Statistics

The Cosmological Constant as a Quantum-Relativistic Necessity

Authors: Osama Haggag
Comments: 4 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org) DOI: 10.5281/zenodo.20459593

The vacuum energy density predicted by Standard Quantum Field Theory (QFT), deviates from cosmological observations by approximately 120 orders of magnitude. This divergence stems from the assumption that spacetime is a continuous manifold permitting infinitely unbounded proper acceleration, which necessitates arbitrary insertion of ultraviolet cutoff at the Planck scale. In this framework, we introduce an impassable, mass-dependent quantum-geometric acceleration ceiling derived from firstprinciples horizon-saturation mechanics. By evaluating the modified Einstein Field Equations under a metric dynamically deformed by this acceleration ceiling, the Cosmological Constant ( ) emerges not as an arbitrary integration parameter, but as an inevitable geometric consequence of the global expansion running up against a baseline cosmic acceleration. This framework predicts a physical vacuum energy density aligns with empirical satellite data without tuning free parameters.
Category: Relativity and Cosmology

Adaptive-Dynamic Gravitational Field of the Solar System

Authors: Pavlo Danylchenko
Comments: 5 Pages.

The correspondence to the Solar System of not the static Newtonian gravitational field, but the dynamic gravitational field, which is also formed by the motion of the planets and, therefore, adapts to changes in the location of the planets in it, is substantiated. The correspondence of the trajectories of the planets' motion to the laws of conservation of angular momentum and energies (the Newtonian of inert free rest energy and the Keplerian of ordinary rest energy of matter) is shown. Spatial distributions of potentials and strength of the adaptive-dynamic gravitational field along the elliptical trajectories of the planets' motion, which correspond both to the laws of conservation and to the results of astronomical observations, are obtained.
Category: Relativity and Cosmology

Crossing the Line: A Dynamical Systems Theory of Bank Runs

Authors: Lucas Brandt
Comments: 35 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The collapse of Silicon Valley Bank in March 2023 unfolded in forty-eight hours, following months of visible but apparently tolerated balance-sheet deterioration. This pattern, prolonged stability followed by sudden and discontinuous collapse, is difficult to reconcile with the canonical Diamond-Dybvig model of bank runs, which treats a bank failure as an instantaneous jump between two static states. This paper proposes a dynamical systems extension of the Diamond-Dybvig framework. We model the joint evolution of depositor beliefs and bank fragility as a coupled pair of nonlinear differential equations, map the full geometry of the system, and establish two threshold results: a saddle-node bifurcation at a critical interest rate r*, at which the system changes from having one possible resting state to having two, and a Hopf bifurcation at r** > r*, at which the calm resting state loses stability and a self-sustaining oscillation appears. That oscillation formalizes the idea of a bank in chronic stress: repeatedly approaching, but not yet crossing, the edge of collapse. Therefore, a bank failure is reinterpreted not as a choice between equilibria but as the crossing of a tipping line in the space of possible states. We apply the framework to Silicon Valley Bank, arguing that the Federal Reserve’s 2022 to 2023 hiking cycle pushed the bank past the saddle-node threshold, that the ensuing months of intermittent stress correspond to the oscillatory regime, and that the capital-raise announcement of March 8th, 2023 was the discrete shock to beliefs that pushed the system across the tipping line into irreversible collapse. Policy implications for deposit insurance design, capital requirements, and depositor-network regulation follow directly from the geometry.
Category: Functions and Analysis

Metaphysical and Spiritual Events

Authors: Kiyoung Kim
Comments: 6 Pages.

The introduction of subtle-spin-string waves within the physical vacuum offers a new type of physical interaction. This interaction provides a comprehensive explanation for phenomena like Ki energy and spirits. It also identifies possible connections between these phenomena and biological genetic evolution, topics that traditionally fall outside natural science.
Category: History and Philosophy of Physics

New Polyhedra with Ambo

Authors: Manuel Diaz Regueiro
Comments: 13 Pages.

The study of polyhedra and their classification can be significantly expanded by focusing on their generation through operations such as the Conway.. This approach gives rise to new polyhedra, new classifications, new problems, and new solutions. The present work focuses on a few preliminary observations concerning the simpler operators when applied to lesser-known polyhedra, with the hope that these insights may be transferable to others.
Category: Geometry

A New Explanation for the Origin of Superconductivity Based on Electron Magnetic Chains with 8-Shaped Magnetic Moments

Authors: Zhaole Sun
Comments: 20 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Since the discovery of superconductivity in 1911, its microscopic mechanism has remained a central challenge in condensed matter physics. The classical BCS theory, which uses lattice phonons as mediators to establish a Cooper pair model of two electrons, can explain the basic properties of low-temperature metallic superconductivity but faces several inherent limitations: phonon coupling is only a short-range interaction, unable to resolve the cross-scale contradiction of long-range synchronous coupling among a large number of electrons, and struggles to counteract the Coulomb repulsion between electrons. This theory fails to explain experimental phenomena such as pre-paired pseudogaps and non-monotonic changes in critical temperature under magnetic fields, while also being incompatible with novel systems like high-temperature and two-dimensional flat-band superconductivity.This paper cites the 8-shaped electromagnetic standing wave + intrinsic drift electron structure model [1], proposing the electron magnetic chain microscopic conductive structure: under an external field, the intrinsic drift within electrons is suppressed, causing their inherent 8-shaped magnetic moment and magnetic coupling effects to manifest. Through the continuous chain-like connection enabled by the 8-shaped magnetic moment attraction, without fixed limitations on the number of paired electrons, a long-range ordered arrangement forms conductive pathways. This model can uniformly cover conventional and high-temperature superconducting phenomena, systematically resolving all existing internal contradictions in BCS theory, and provides a quantifiable theoretical basis for the structural design of new high-temperature and even room-temperature superconducting materials.
Category: Condensed Matter

Geometric Origin of Photon Wave Properties

Authors: Junzheng Liu
Comments: 17 Pages. (Note by viXra Admin: Please cite and list scientific references!)

In this paper, we propose a geometric ontology for the photon and demonstrate its capacity to explain the wave properties of light. Specifically, we discuss the nature of time and wave-particle duality. Also, we show how the geometric characteristics of photons naturally give rise to their frequency and amplitude.
Category: Quantum Physics

Projection Method for Visualizing the Spatial Structure of Light Beams Using a Negative Lens

Authors: Sergei P. Slukhayevskiy
Comments: 7 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

A simple projection method for direct visualization of the transverse spatial structure of freely propagating light beams is proposed and experimentally demonstrated.The optical arrangement consists of a negative lens positioned downstream of the investigated beam cross section and a remote observation screen. Within the paraxial approximation, the lens converts the transverse field distribution into an angular distribution that is projected onto the screen with a magnification determined by the ratio M = L|f|, where L is the distance from the lens to the screen and f is the focal length of the negative lens. The method enables non-invasive observation of beam cross sections while preserving unrestricted access to the investigated region. Longitudinal scanning isachieved simply by translating the lens along the propagation axis, allowing the spatial evolution of optical fields to be monitored without modifying the experimental arrangement.The technique has been applied to visualization of the fine spatial structure of semiconductor laser beams and to the investigation of diffraction fields generated by a knife edge. Experiments performed with projection magnifications of approximately M ≈ 300 reveal structural details that remain inaccessible under conventional observation conditions.Owing to its simplicity, low cost, and high visual sensitivity, the proposed methodrepresents a useful experimental tool for exploratory studies of wave-optical phenomena, laser beam diagnostics, and educational laboratory demonstrations
Category: Classical Physics

Probabilistic Estimation of the Critical Density Threshold for Kessler Syndrome in Low Earth Orbit Using a Two-Shell Monte Carlo Model

Authors: Ayush Samanta
Comments: 13 Pages. (Note by viXra Admin: An abstract in the article labeled as such is required; please submit article written with AI assistance to ai.viXra.org)

Orbital debris has become one of the most significant challenges facing the long-term sustainability of Low Earth Orbit (LEO). As the number of satellites continues to increase, so does the likelihood of collisions capable of generating large quantities of debris, potentially triggering a self-sustaining chain reaction known as Kessler Syndrome. This study develops a stochastic two-shell Monte Carlo model to investigate whether a critical orbital density exists beyond which such debris cascades become increasingly likely. The model represents the orbital environment using two concentric shells and incorporates stochastic collisions, debris fragmentation, atmospheric decay, active satellite failure, and collision avoidance. A systematic density sweep was performed using 200 independent Monte Carlo simulations for each normalized orbital density. The results reveal a rapid transition from stable orbital evolution to near-certain cascade formation over a narrow range of densities, with the critical normalized density multiplier estimated to be approximately $alpha_c approx 0.093$. Near this threshold, simulations with identical initial conditions frequently produced different long-term outcomes, highlighting the importance of stochastic collision dynamics in determining orbital stability. Although the model adopts several simplifying assumptions, it reproduces the fundamental feedback mechanism underlying the Kessler hypothesis and provides a computationally efficient framework for investigating the probabilistic onset of orbital debris cascades.
Category: Astrophysics

Evolution of the Concept of Angular Momentum

Authors: Yu. E. Zevatskiy
Comments: 7 Pages.

New types of angular momentum of elementary particles arising from the special theory of relativity are examined. A total of 14 types have been identified, including the classical angular momentum. The calculated values of relativistic angular momenta can be applied both to the determination of fundamental properties of elementary particles and to the quantitative description of various types of interactions between them.
Category: Nuclear and Atomic Physics

The Dual Architecture of the Gamma Function: From Vacuum Energy in Odd Dimensions to the Cosmological Constant and Neutrino Mass

Authors: Julinho Jorge Luís
Comments: 21 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The Gamma function, defined by the Euler integral, converges only in a restricted half-plane. Outside this domain, the integral diverges and one resorts to analytic continuation, which does not preserve the original integral form. This work proposes the Dual Architecture of the Gamma Function, a formulation based exclusively on integral representations and their natural domains of convergence. The architecture is built from two complementary objects: the Classical Gamma, convergent for positive real parts, and the Symmetric Gamma, convergent for negative real parts. Their connection is established through a multiplicative inverse relationship that yields unity, providing a parameter-free mechanism to regularize all divergences across the complex plane. A real trigonometric operator encodes a Dirichlet boundary condition with unit reflection coefficient, geometrically corresponding to a specific phase rotation that incorporates wave backscattering at impenetrable boundaries. We investigate the physical consequences of this dual structure in three key areas. First, the vacuum energy density in odd dimensions is evaluated, where the dual architecture produces a sign alternation that agrees with reference values in all analyzed cases. Second, the high-order WKB expansion for the quartic potential is examined, where the dual evaluation completely absorbs an exponential correction of previously unexplained physical origin, confirming backscattering as its source. Third, the cosmological constant problem is addressed by summing the regularized vacuum energy over the dimensional spectrum; the series converges naturally to a fundamental constant that predicts the neutrino mass and places the seesaw scale at the Grand Unified Theory regime. The formulation preserves the core principles of quantum field theory, positioning the dual architecture as a complementary regularization scheme for problems involving boundaries, odd dimensions, and the global structure of the vacuum.Keywords: Gamma function; Vacuum energy; Cosmological constant; Asymptotic expansions; Regularization
Category: Relativity and Cosmology

A Quantum Induced Warpdrive I

Authors: Holger Döring
Comments: 10 Pages.

This quantum induced warpdrive is featuring geometric unification of gravity and electro-magnetism in a four-dimensional cylindrical quantum spacetime as a corrugated spacetime-structure via sub-harmonic dilatonic resonance.Presented is a novel geometric framework for the unification of gravitation and electromagnetism strictly within a four-dimensional manifold . Rather than invoking higher spatial dimensions, proposed is, that the three macroscopic spatial axes possess intrinsic, periodic cylindrical degrees of freedom stabilized at the Planck scale . Under this topology, the standard metric tensor inherently encapsulates both gravitational and electromagnetic fields, where spacetime frame-dragging manifests macroscopically as the magnetic vector potential. Particle mass and charge emerge as localized, symmetric quantum wave configurations wrapped around the Planckian cylinders. Furthermore, introduced is a dynamic intermediate scalar field — derived from the local volume fluctuations of the cylindrical radius — which enables a non-linear, sub-harmonic resonance coupling between macroscopic laboratory-scale fields and the Planck-scale geometry. Demonstrated is then, that under precise phase-locked sub-harmonic frequencies, the effective gravitational coupling can be enhanced, leading to localized modulation of inertial mass, optical birefringence of the vacuum, and triggerable metric drift. Possibly this situation could lead to a form of local quantum induced warp-drive without ftl, which is called "the Metagrav" or QUIW .
Category: Quantum Gravity and String Theory

A More Accurate Period to Mean Distance Relation ( Applied to Mars)

Authors: Erik Gaylan Bergren
Comments: 11 Pages. (Note by viXra Admin: An abstract in the article labeled as such is required; please cite and list scientific references)

An improvement over the usual relation between a Planet's Period and its Mean Distance (semi-major axis) is presented and is compared against the standard relation that is used by JPL's Horizons web app, and against the previous improvement made in the Astronomical Almanac's Orbital Parameters Tables. The experimental data used for the comparisons is the 30390 year JPL Ephemeris integration DE441, analyzed specifically for the Planet Mars, which produced reference values of 686.979857 days per revolution and 1.5236886591 AU for the Period and Mean Distance of the Orbit of Mars respectively.
Category: Astrophysics

On the True Dimensionality of Electric Charge and Some Thermodynamic Quantities

Authors: Anatoly V. Belyakov
Comments: 3 Pages.

An additional justification for the nature of electric charge as momentum is provided, and itsrelationship with thermodynamic parameters is demonstrated. A new interpretation of theBoltzmann constant, temperature, and entropy is given.
Category: Thermodynamics and Energy

Causal Horizons under a Maximal Acceleration Limit

Authors: Osama Haggag
Comments: 4 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org) DOI: 10.5281/zenodo.20580374

Causal horizons—encompassing kinematic, gravitational, and cosmological event boundaries—are classically modeled in General Relativity as continuous, zero-volume mathematical abstractions permitting unbounded proper acceleration. This coordinate-dependent description induces severe non-local information loss, infinite mathematical divergences, and unphysical firewall paradoxes. This Letter provides a rigorous, non-circular operational proof demonstrating that causal horizons are discrete physical entities with an impassable minimum structural thickness equal to exactly one Compton wavelength. By deriving the horizon's properties from the closure of the local phase algebra under maximum metric strain, the Universal Law of Horizon Oscillation is systematically deduced. Crucially, we invoke the Strong Equivalence Principle to generalize this boundary condition as a covariant geometric invariant across all reference frames. This structural quantization resolves the 120-order-of-magnitude cosmological vacuum energy catastrophe as an applied boundary example, yielding a non-tuned density that precisely matches the order of magnitude of empirical observations, and provides a dynamic dark energy scaling framework that naturally reconciles the contemporary Hubble expansion tension.
Category: Relativity and Cosmology

Expansion for Harmonic Numbers Inspired by Ramanujan

Authors: Payam Danesh
Comments: 7 Pages.

In this work, we developed a direct formulation based on the variable X=n(n+1)+h, which h is a real parameter. This method starts from the digamma representation of H_n, recenters the expansion at n+1/2, and then converts the result into descending powers of X. This actually gives an explicit coefficient formula in terms of Bernoulli polynomials evaluated at 1/2. The special value h=1/3 is shown to cancel the first correction term, giving a sharper expansion whose error begins at a higher order. Numerical comparisons showed that the shifted form improves substantially over the standard Euler truncation and the unshifted pronic expansion for small and moderate n and this gives transparent route to Ramanujan-type harmonic-number approximations.
Category: Number Theory

Ehrenfest Paradox and Consistent Relativistic Circular Motion

Authors: Yang-Ho Choi
Comments: 13 Pages.

Some conundrums such as the Ehrenfest paradox have been raised in relation to the relativistic approach to circular motions. Different tangential velocities along the radius of a rotating frame bring about a nonuniform scalar field of potential. Based on the Schwarzschild metric for the potential field, we consistently and comprehensively deal with the problems of relativistic circular motion including the Ehrenfest paradox and the Sagnac effect. The Ehrenfest paradox is readily resolved via a visualization of wave propagation in the field, which shows that the length of radius in the rotating frame is different from the corresponding one seen in the laboratory frame. From the visualization, the anisotropy of the speed of light in inertial frames is also clearly shown. Moreover, a coordinate transformation for the circular motion at a fixed radius is developed based on the metric, which enables us to derive a transformation between inertial frames through limiting operations. The derived inertial transformation becomes the same as the Lorentz transformation if the standard synchronization is introduced. With the transformations, the Michelson-Morley experiment result and the generalized Sagnac effect are consistently explained.
Category: Relativity and Cosmology

Lecture Notes for Teaching Mechanistic Quantum Field Theory Axiomatically

Authors: Nigel B. Cook
Comments: 77 Pages.

The purpose of these brief lecture notes is to provide the basic framework for a course in axiomatically-derived mechanistic quantum field theory, to teach the foundations needed to understand vixra paper 2606.0012. Problems and solutions will be developed for inclusion at a later date, after we have more experience in teaching this course to students.
Category: Quantum Gravity and String Theory

A Quantum Induced Warpdrive

Authors: Holger A.W. Döring
Comments: 10 Pages.

This quantum induced warpdrive is featuring geometric unification of gravity and electro-magnetism in a four-dimensional cylindrical quantum spacetime as a corrugated spacetime-structure via sub-harmonic dilatonic resonance.Presented is a novel geometric framework for the unification of gravitation and electromagnetism strictly within a four-dimensional manifold . Rather than invoking higher spatial dimensions, proposed is, that the three macroscopic spatial axes possess intrinsic, periodic cylindrical degrees of freedom stabilized at the Planck scale . Under this topology, the standard metric tensor inherently encapsulates both gravitational and electromagnetic fields, where spacetime frame-dragging manifests macroscopically as the magnetic vector potential. Particle mass and charge emerge as localized, symmetric quantum wave configurations wrapped around the Planckian cylinders. Furthermore, introduced is a dynamic intermediate scalar field — derived from the local volume fluctuations of the cylindrical radius — which enables a non-linear, sub-harmonic resonance coupling between macroscopic laboratory-scale fields and the Planck-scale geometry. Demonstrated is then, that under precise phase-locked sub-harmonic frequencies, the effective gravitational coupling can be enhanced, leading to localized modulation of inertial mass, optical birefringence of the vacuum, and triggerable metric drift. Possibly this situation could lead to a form of local quantum induced warp-drive without ftl, which is called u201ethe Metagrav" or QUIW .
Category: Quantum Gravity and String Theory

Invariant Maximum Acceleration and Its Non-Linear Composition Law

Authors: Osama Haggag
Comments: 8 Pages. DOI: 10.5281/zenodo.20740142

Standard Special Relativity exhibits a fundamental geometric asymmetry: while the instantaneous velocity of a worldline is strictly bounded by the invariant speed of light ( ), its proper acceleration is permitted to diverge infinitely. This unconstrained upper bound introduces severe vulnerabilities into modern field theories, manifesting as divergent particle self-energies and zero-volume coordinate singularities at causal horizons. This framework proposes an operational resolution of this asymmetry by introducing a generally covariant kinematic framework featuring an impassable, invariant upper boundary on proper acceleration ( ) deduced from first principles. By modeling a massive particle’s internal state as a localized quantum wavepacket acting as an intrinsic clock, we demonstrate that uniform acceleration compresses the local Rindler horizon to its geometric saturation limit. To preserve this invariant ceiling across multi-body compound systems, we derive a velocity-independent, non-linear acceleration composition law based on a hyperbolic group structure. By equating the Rindler horizon with the particle's Compton wavelength, we extend the equivalence principle in quantum systems, Planck’s constant is directly inserted into spacetime kinematics. Finally, this framework offers a pure kinematic reinterpretation of the partonic cross-section flattening (gluon saturation) observed at the Large Hadron Collider (LHC) as an intrinsic, structural feature of a bounded quantum vacuum.
Category: Quantum Gravity and String Theory

Diamond-Confined Metallic Hydrogen: A Roadmap to Metastable Hydrogen Metal at Ambient Conditions via Quantum Electrodynamic Stabilization

Authors: Giustino Travaglini
Comments: 10 Pages.

The realization of metallic hydrogen at ambient temperature and pressure remains one of the most compelling goals in condensed-matter physics, promising a high-temperature superconductor, a revolutionary propellant, and a window into quantum phase transitions. While static compression experiments above 400 GPa have provided tentative evidence for the metallic state, its recovery to ambient conditions has proved elusive because of the vanishingly small kinetic barriers that separate the atomic metallic phase from the molecular insulating ground state at zero pressure. Here I propose a concrete, experimentally accessible strategy—Diamond-Confined Metallic Hydrogen (DCMH)—that combines three interlocking physical mechanisms: (i) sub-nanometer confinement of hydrogen within a fully sp³-bonded diamond-like carbon matrix, which delivers chemical internal pressures sufficient to reach the metallization density; (ii) topological frustration of the molecular Hu2082 recombination path, raising the kinetic barrier to geological timescales; and (iii) optional resonant quantum electrodynamic (QED) vacuum engineering using a tunable optical cavity to induce vacuum-mediated spin pairing, thereby lowering the free energy of the metallic state and rendering it thermodynamically competitive at 300 K and 0 GPa. The entire procedure can be executed in existing high-pressure laboratories using multi-anvil presses, DAC gas-loading systems, and table-top cavity QED setups. I present detailed DFT-based estimates of confinement densities, kinetic barrier heights, and cavity-enhanced pairing gaps, together with a full experimental protocol for synthesis, decompression, and characterization. This roadmap transforms metallic hydrogen from a high-pressure curiosity into a designer material that can be handled at ambient conditions
Category: Condensed Matter

Beal's Conjecture - Proof

Authors: B. N. Pathak
Comments: 19 Pages.

This is a proof for Beal's conjecture by B. N. Pathak - my late father.
Category: Number Theory

Global Mapping of Next Economy Organizations and Their Discourse

Authors: Can Özhasenekler, Elif İpek Ulusoy, Jochelle Laguipo, Uygar Özesmi
Comments: 11 Pages.

This article presents a global mapping of Next Economies organizations and their discourse, based on a dataset of 318 institutions across multiple countries and regions. Recent scholarship stresses that overhauling prevailing economic systems is essential to confront today’s interlinked global crises, with innovative approaches seeking to balance ecological integrity and human well-being (Kenter et al., 2024). Discussions on the "new economy" increasingly emphasize restructuring philanthropy and governance to better respond to the polycrisis and to advance more equitable and sustainable pathways (Alliance Magazine, 2024). To conduct this analysis, we developed a coded dataset capturing institutional structures, geographic locations, discursive critiques, adoption of circular economy principles, alignment with alternative models, and focus areas. The dataset was then translated into a relational network on GraphCommons, where organizations serve as nodes connected by shared features such as country, alliances, critiques, and focus areas. Using network analysis enables the identification of clusters with common orientations and the exploration of relations between institutional characteristics and discourses.Our findings highlight the ways in which Next Economies movements are emerging, revealing structural and thematic patterns in how Next Economies movements are globally distributed andconceptually aligned. The network approach provides insights into both the diversity and interconnectedness of these organizations, offering a foundation for comparative research and coalition-building. Ultimately, structuring these organizations within a global network contributes to a deeper understanding of the discursive and the structural landscape of the Next Economies.
Category: Economics and Finance

EUV-Patterned Diamond-Confined Metallic Hydrogen: A Lithographic Roadmap to Ambient-Condition Superconducting Hydrogen

Authors: Giustino Travaglini
Comments: 11 Pages.

The recovery of metallic hydrogen at ambient temperature and pressure remains a grand challenge, largely because the kinetic barriers preventing the back-conversion to molecular Hu2082 are too small in the pure atomic phase. Here I propose a radically new approach that merges three frontier technologies: (i) chemical precompression of hydrogen inside a diamond-like carbon (DLC) matrix patterned with sub-nanometer cavities, (ii) extreme ultraviolet (EUV) and High-NA EUV lithography to sculpt this matrix with near-atomic precision, and (iii) resonant vacuum quantum electrodynamic (QED) stabilization via an on-chip optical cavity fabricated in the same lithographic workflow. The core idea is to exploit the unique capabilities of EUV photons (92 eV) to crosslink diamondoid self-assembled monolayers into a rigid, fully sp³-bonded carbon network containing a periodic array of identical pores. After high-pressure hydrogen loading and controlled decompression, the hydrogen remains permanently locked at metallic densities by the mechanical strength of the DLC scaffold. Kinetic barriers are amplified by topological frustration and exceed 1.8 eV per H atom, ensuring geological metastability. An integrated Fabry—Pérot cavity tuned to the hydrogen plasma frequency enhances vacuum-mediated electron pairing, potentially tipping the thermodynamic balance and making the metallic state the true ground state. I present a detailed fabrication protocol compatible with existing EUV scanners and multi-anvil presses, quantitative DFT estimates of the confinement-induced metallization, and a full device architecture for a superconducting hydrogen chip. This roadmap transforms metallic hydrogen from a high-pressure curiosity into a designable material platform, accessible with the tools of the semiconductor industry in the 2026—2030 timeframe.
Category: Condensed Matter

DNA as Nanotechnology: Reassessing Life’s Origin Through the Lens of Information and Genomic Intelligence

Authors: Hannan Gondal
Comments: 31 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We undertake a comprehensive examination of the complex interplay between deoxyribonucleic acid (DNA), nanotechnology, and the origin of life, critically engaging with prevailing abiogenetic models. We advance the hypothesis that DNA functions at the quantum scale or exhibits quantum-mechanical characteristics, demonstrating a level of structural stability and informational complexity that challenges the assumptions underpinning theories of spontaneous molecular evolution. Central to the critique is the recognition of the indispensable role of enzymatic machinery in DNA replication—enzymes that, paradoxically, require DNA for their synthesis—thereby presenting a classic instantiation of the "chicken-and-egg" paradox. We further interrogate the significance of molecular chirality and evaluate the environmental prerequisites for biogenesis, contending that early Earth conditions were inherently unfavorable for the natural formation of either DNA or RNA. By synthesizing insights from molecular biology, quantum physics, and information theory, this analysis supports alternative frameworks. Ultimately, we call for a fundamental reassessment of evolutionary mechanisms and reposition DNA not merely as a passive genetic substrate, but as an advanced, self-organizing system for information storage and processing—one that challenges conventional biological paradigms. We propose a Mathematical proof utilizing Minimal Genome formation and the Universe's limit of Genetic generative capacity.
Category: Biochemistry

A Non-Distributive Symmetric Oscillatory Algebraic Structure and Its Implications for Resolving Paradoxes in Theoretical Physics and Quantum Mechanics

Authors: Mohammad Iman Esfandiari
Comments: 9 Pages.

This paper introduces and mathematically formalizes an alternative algebraic system running parallel to classical algebra, founded upon two core axioms: the elimination of the distributive property of multiplication over addition (Non-Distributivity) and a symmetric inversion of the rules of signed multiplication. In this framework, termed Non-Distributive Symmetric Oscillatory Algebra, the product of any two quantities with identical signs yields a negative output, whereas the product of two quantities with opposing signs yields a positive output. This structure induces an inherent frequency-based, oscillatory behavior within the sequential powers of real numbers. This study demonstrates how this novel algebraic model resolves the baryon asymmetry paradox (matter/antimatter) in cosmology, tames the explosion of infinities and singularities within black holes, formulates the exact mathematical mechanism behind wave function collapse in the quantum measurement problem without metaphysical assumptions, and establishes a theoretical foundation for designing room-temperature stable quantum hardware (Non-Distributive Polar Quantum Diodes) and macro-scale superconductors.
Category: Quantum Physics

The Collatz Singularity as a Global Binary Structural Attractor

Authors: Ammar Hamdous
Comments: 77 Pages. Creative Commons Attribution 4.0 International

In our fifth work [3] entitled A Structural Approach to the Collatz Conjecture via the Binary Singularity, we introduced the notion of binary singularity of Collatz sequence as a structural invariant and proposed a structural reformulation of the Collatz conjecture: every positive odd integer either is, or eventually reaches, a singularity configuration. We further hypothesized that this property could be characterized through an appropriate metric defined on binary structures.In the present work, we develop this idea by introducing a global binary structural attractor governing the evolution of odd Syracuse iterates. This attractor is based on the notions of Suffix of Singularity, suffix of generator of the suffix of singularity, and binary overflow, which together reveal a hierarchical binary decomposition of the binary structure of odd integers previously hidden by their arithmetic representation. We prove that every odd Syracuse iterate that is not a singularity admits a unique decomposition into a finite sequence of nested concatenation of suffixes of generators of the suffix of singularity followed by a single suffix of singularity, On = G(p,n) ∥ G(p−1,n)∥ · · · ∥G(1,n)∥Sn, and define a structural complexity function P(On) equal to the number of suffix generators contained in this decomposition. The evolution of P is entirely determined by the complementarity of the overflow generated by the most significant suffix generator G(p,n), leading to a complete structural classification of increasing, stationary, and decreasing transitions. This decomposition provides a symbolic description of the odd Syracuse dynamics and establishes the structural foundation for an eventual Lyapunov function whose minimal state is precisely the binary singularity P = 0. Rather than studying the arithmetic growth of Collatz trajectories,the proposed approach describes the dynamics as the progressive elimination of nested binary suffixes of generators toward a unique global structural attractor.
Category: Number Theory

Human nose and the Graphical Law

Authors: Anindya Kumar Biswas
Comments: 21 Pages.

Nasal index is breadth divided by height of a nose multiplied by hundred. We look into the nasal indices of noses of human beings as gathered by Thomson and Buxton as early as 1923.We draw the natural logarithm of the nasal indices, normalised, vs the natural logarithm of the rank, normalised(unnormalised). We conclude that the human nose, can be characterised by a magnetisation curve of a Spin-Glass in the presence of a little external magnetic field.
Category: Physics of Biology

Research Progress on Relative-Absolute Spacetime View: Logical Basis, Experimental Verification, and Paradigm Innovation

Authors: Runsheng Tu
Comments: 41 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

To address the core issue of the lack of physical mechanism explanation in relativity, a solution is proposed to construct a "relative absolute spacetime view" by reconciling "absolute" and "relative". The necessity of an absolute stationary system is logically demonstrated: The system with the smallest degree of freedom in motion, the system that is most difficult to obtain acquired motion, and the system with "no displacement space" (such as the centroid system of a total galaxy and the cosmic background radiation framework) all point to a logically absolute stationary frame. Based on the longitudinal traction difference between photons and electrons revealed by Jones' experiment, a "geometric optical velocimeter" was designed to calculate absolute velocity and verify the existence of absolute motion by measuring the deflection angle of photons and electron rays. By assuming that the clock in absolute motion slows down, the contradiction between relative and absolute is quantitatively reconciled. The Jones experiment actually proved that the gaps in the hollow glass disk are ineffective in pulling photons. It is equivalent to proving that, relative to photons, the vacuum space inside a moving train carriage does not belong to the same inertial frame as the body of the train. Hafele Keating experiment proved that "different approximate inertial frames are not always equal". Both of these situations pose challenges to the principle of special relativity.It is proposed that physics research should follow a spiral upward path of "absolute → relative → relative-absolute", breaking through the binary opposition between classical absolute spacetime and special relativity. It can provide new explanations for the Michelson-Morley experiment and a new paradigm for spacetime theory.
Category: Relativity and Cosmology

Definite Integration and Summation Are #P-Hard

Authors: Leonid Gurvits, Warren D. Smith
Comments: 4 Pages.

We show that the common symbolic manipulation tasks of computing multiple partial derivatives, definite integration, and definite summation, are #P-hard, i.e, at least as hard as counting the accepting input strings for any Turing machine that halts in polynomial time. (The "multiple partial derivatives" part was previously known.)
Category: Combinatorics and Graph Theory

Accurate Circle Configurations and Numerical Conformal Mapping in Polynomial Time

Authors: Warren D. Smith
Comments: Sitting on my web pages since 1991; uploading to vixra for archival purposes.

According to a remarkable re-interpretation of a theorem of E.M. Andreev (1970) by W.P. Thurston (≈1982), there is a unique (up to inversive transformations) packing of interior-disjoint circles in the plane, whose contact graph is any given polyhedral graph G, and such that an analogous "dual" circle packing simultaneously exists, whose contact graph is the planar dual graph G*, and such that the primal and dual circle packings have the same set of tangency points and the primal circles are orthogonal to the dual ones at these tangency points.

This note shows that relatively and absolutely accurate coordinates for the primal and dual circles may be obtained in time polynomial in N, the number of vertices of the polyhedral graph, and D, the number of decimals of accuracy desired.

Consequently one may also accurately "midscribe"' a polyhedron – and simultaneously its dual – in polynomial time.

Also consequently, one may implement Riemann's conformal mapping theorem numerically, in polynomial time with provable accuracy.

Our result is obtained by generalizing and reformulating ideas found in the doctoral thesis of Walter Brägger [Math. Institut, Rheinsprung 21, CH-4051 Basel, Feb. 1991] to reduce our problem to maximizing a smooth convex function. This maximization problem is then solved by using Khachian's "ellipsoid method" or Vaidya's algorithm.
Category: Geometry

On the Nature of Light from the Original Meaning of the Antonyms "Bright" and "Dark"

Authors: Peng Xiaotao
Comments: 14 Pages.

Brightness and darkness are a pair of antonyms, both of which describe the state of the objective world related to light. Brightness refers to the state in which the observer can observe the surrounding things well when the light is abundant, while darkness refers to the state in which the observer can not perceive the surrounding things when there is no light. Therefore, the so-called light should be some kind of carrier that can change the state of things around the observer, but it is not something that the observer can directly perceive. Therefore, on the one hand, what the human eye sees can not be the so-called light; on the other hand, the light should be some carrier that can make the objective things bright, so that the human eye can see these things in a bright state. The objective things that can be seen by human eyes and are in a bright state are objective entities composed of various atoms, and it should be a force that can change their state. It can be seen that the essence of light should be the carrier responsible for transmitting some kind of force, which is most likely to exist only between charged particles. Therefore, there is good reason to think that the essence of light is a collection of some carrier or carriers responsible for the transmission of Coulomb force. This conclusion can explain all the physical phenomena and experimental results related to light at the same time, which is the most realistic conclusion at present. Hope to get the attention and support of experts, scholars and friends at home and abroad.
Category: Classical Physics

A Dual Extension for the Gamma Function and the Confinement of the Zeros of the Riemann Zeta Function

Authors: Julinho Jorge Luís
Comments: 14 Pages.

The Bohr-Mollerup Theorem establishes the uniqueness of the Gamma function on the right half-plane, but makes no assertion regarding extensions to the left half-plane that preserve the integral form. This work proposes a Dual Architecture consisting of two integral operators with complementary domains: the Classical Gamma and a Symmetric Factorial, connected by an operator derived from the Hankel contour integral. When applied to the Riemann zeta function, this architecture replaces the classical functional equation—which exhibits indeterminate forms at integer points—with a formulation that is directly evaluable and preserves all values of the Dirichlet series. Analysis of the connection operator reveals that its real part vanishes exclusively on the critical line within the critical strip. Assuming a non-trivial zero off this line leads, via a closed cycle of the dual functional equation, to a contradiction involving the modulus of the Gamma function, as established independently through the Weierstrass representation and the maximum modulus principle. The result forces all non-trivial zeros of the Riemann zeta function to lie on the critical line.Keywords: Gamma function, Riemann zeta function, critical line, Hankel contour, Weierstrass representation.
Category: Functions and Analysis

Arbitrary Approximation of the Shifted-LRC by the LRC

Authors: Deepak Ponvel Chermakani
Comments: 2 pages, 2 Theorems.

Consider an instance of the Shifted Lonely Runner Conjecture (S-LRC) where all n runners (except the stationary runner 0) have integer speeds and start from real values in [0,1[ at time t=0. We show that one can derive an alternative vector of starting points that can be made to be arbitrarily close to the initial vector of starting points. The alternative starting point of each runner i is a rational in [0,1[ and is expressible as (qi / P) where P is a large prime and qi is an integer in [0, P-1]. The S-LRC instance with the alternative starting points, allows a minimal loneliness gap of f, if and only if, the corresponding LRC allows a minimal loneliness gap of f, where f is a desired fraction in ]0,1[. This finding is important in the light of recent counter-examples to the shifted-LRC.
Category: Functions and Analysis

A "Good" Problem Equivalent to the Riemann Hypothesis

Authors: Warren D. Smith
Comments: This 1995 paper by me, heavily revised 2005, had been sitting on my web page but is now uploaded to vixra for archival purposes.

We exhibit a sequence c_n such that the convergence of ∑c_nzⁿ for all complex z with |z|<1 is equivalent to the Riemann Hypothesis. We argue that this particular RH-equivalent problem is "better" than most, or perhaps every, other RH-equivalent problem devised so far, in the sense that (we prove) there is a tremendous gap in behaviors of the c_n if the RH is true versus if the RH is false.
Category: Number Theory

Linear Transformations in the Reciprocal Gamma Function Quadrature

Authors: Ruiguo He
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

As an extension from my previous work, the paper attempts to generalize the Reciprocal Gamma Quadrature under the curve to general linear transformations on the argument itself. It extends further into the territory of Volterra Functions and Ramanujan's Log-Gamma integrals related to the Fransén-Robinson Constant.
Category: Number Theory

Identifying Natural Limits to Infinite Algebraic Singularities with Null Algebra

Authors: Robert S. Miller
Comments: 22 Pages. (Note by viXra Admin: Please cite and listed scientific references)

This paper introduces a framework which regularizes the classical algebraic singularity, using the essential hyperbola y=1/x to illustrate its application. Traditional, classical mathematics leaves the behavior at the origin for this function undefined due to divergence toward unachievable infinities. By using the transformational matrix defined in Null Algebra to map u=-1/y, the defined subspace of y, we may focus on a rate of information transfer implied by the function, as x→0. This is achieved by imposing a strict constraint upon dy/du which is required for any function y=f(x) and based upon chosen scale for the system defined by y=f(x). This shall show the singularity cannot actually be achieved due to natural self-limiting properties unique to a given function which emerge from Null Algebra, leaving a function, that is piecewise defined and continuous.
Category: General Mathematics

Entropic Origin of the Cosmological Constant A(t): Analytical Derivation of 10^122 Bits and Validation via Planck Data

Authors: Friedhelm M. Jöge
Comments: 14 Pages.

The discrepancy 0f 10^120 between the observed cosmological constant and quantum field theory (QFT) predictions remains one of the greatest enigmas in modern physics. The study provides a novel analytical derivation of this value by treating gravity as an entropic force arising from bits on a holographic screen. By establishing a direct link between the bit density of the universe and the dynamic nature of dark energy, the study offers a potential resolution to the cosmological constant problem. These findings bridge the gap between quantum information theory (QIT) and general relativity theory (GRT), suggesting that the accelerated expansion of the universe is a emergent phenomenon driven by the evolution of cosmic entropy.Since dark energy is not simply given as a number, but is derived from the age of the universe (13.82 billion years), the "naturalness problem" - one of the biggest problems in physics - can be solved.It is shown that all the information of the universe is encoded on the Planck-scale and is "unrolled" into spacetime by factor tu (Holographic Principle). The fact that the theoretically derived value of the Hubble constant (Ho) lies well within the range of astronomical measurements is the strongest indication that the connection between the Planck-scale and the age of the universe (tu) is not mere numerology, but a physical principle.
Category: Relativity and Cosmology

How a Matter-to-Vacuum Phase Transition Can Prevent Black-Hole Singularities

Authors: Rudi Van Nieuwenhove
Comments: 14 Pages.

The appearance of spacetime singularities during gravitational collapse remains one of the most important unresolved problems of General Relativity. In the standard picture, continued compression of matter inside a black hole leads to divergent densities, divergent spacetime curvature, and the breakdown of the classical gravitational description. In this work, we investigate an alternative phenomenological scenario in which gravitational collapse triggers a density-induced matter-to-vacuum phase transition once a critical density is reached.We assume that above this threshold ordinary matter is rapidly converted into a Vacuum Localized Structure (VLS) phase, representing a localized vacuum state that carries the mass-energy of the original collapsing matter. The detailed microscopic mechanism responsible for the transition is not specified. Instead, the transition is treated as an effective process that replaces the collapsing matter by a compact vacuum structure while conserving the total mass-energy of the system.The post-transition object is modeled as a static, spherically symmetric equilibrium configuration governed by the Einstein field equations and the Tolman-Oppenheimer-Volkoff equation. A Gaussian density distribution is adopted for the VLS phase, leading to finite central density, finite pressure, and a regular mass profile throughout the interior. The characteristic size of the VLS core follows directly from mass conservation and is uniquely determined by the total mass and the critical transition density.The resulting solutions replace the classical black-hole singularity by a finite-curvature core. The mass function approaches zero smoothly at the center, preventing the divergent gravitational compression associated with conventional collapse solutions. Consequently, all curvature invariants remain finite and the spacetime remains regular throughout the interior region. In this sense, the phase transition acts as a gravitational regulator, replacing continued compression by a stable vacuum-supported equilibrium configuration.Within this framework, singularity avoidance emerges without modification of the Einstein field equations and without the introduction of an explicit de Sitter vacuum core.
Category: Relativity and Cosmology

Atoms Through Nonlinear Dynamical Systems

Authors: Najib Chairi
Comments: 15 Pages. (Note by viXra Admin: Please cite listed scientific references and submit article written with AI assistance to ai.viXra.org) Copyright © 2026 by the author(s), all rights reserved.

The atom is traditionally described by quantum mechanics through linear equations, especially the Schrödinger equation. Yet as soon as the number of particles increases, the atom no longer remains a simple one-body problem: electrons interact with one another, alter the effective potential in which they evolve, and give rise to global structures whose stability cannot always be understood as a mere addition of individual behaviors. This article proposes an exploratory reading of the atom and of the periodic table through the lens of nonlinear dynamical systems, threshold phenomena, collective modes, phase locking, and self-organization. The aim is not to replace standard quantum mechanics, but to examine whether certain atomic regularities - shell closures, noble gases, filling anomalies, transitions between periods, and the special stability of some configurations - can be interpreted as signatures of collective stability. The article also develops analogies with lasers, nonlinear optics, coupled oscillators, the fractional quantum Hall effect, and wave chaos. These analogies should not be understood as strict identifications. They are conceptual tools that help us think of atomic matter as a dynamic, resonant, and self-consistent organization.
Category: Quantum Physics

Predicting Low-Field Visibility Loss from Local Opposite-Polarity Field Coupling

Authors: Matthew Crane
Comments: 32 Pages.

Standard low-power optics treats visibility loss as a readout problem: the detector still records photon locations, but the measured hit pattern no longer separates cleanly into bright regions and dark regions.This paper controls that readout explanation before the prediction is tested. First, a stable visible interference pattern is made. Then the dark-region background, detector noise, false counts, pixel scale, position uncertainty, and minimum distinguishable bright-dark difference are measured. That calibration sets the measured visibility limit of the tested setup.After that calibration, detector sensitivity is part of the threshold test.This paper predicts that the measurable interference zone shrinks as the beam-waist to opposite-polarity + - coupling-event distance increases, until the setup reaches a measurable-visibility threshold.The predicted measurable-visibility threshold distance is:R_low = z_R sqrt(P/P_low - 1)
Category: Quantum Physics

Heisenberg Causes Gravity and Time Dilation

Authors: Leonardo Rubino
Comments: 16 Pages. (Note by ai.viXra.org Admin: For the last time, please cite and listed scientific references!)

Heisenberg causes gravity and time dilation.
Category: Quantum Physics

On Complex Dynamics and Standard Model Parameters

Authors: Ervin Goldfain
Comments: 16 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org)

We present numerical evidence that complex dynamics of nonlinear systems provides a coherent organizing principle for understanding the origin of Standard Model parameters, without introducing new fields or symmetries.
Category: High Energy Particle Physics

The Structure of Electrons and Photons

Authors: Michael Gunning
Comments: 19 Pages.

In this paper I propose a model for a physical explanation of the structure of the electron and the photon. The model explains what the charge of an electron is and why it has a total angular momentum of √3/2 ħ. It suggests what the nature of inertial mass is and explains the spin value of ħ for the photon as well as the origins of its alternating electric and magnetic fields. It includes explanations for what static electric and magnetic fields are and why the stress energy tensors for these fields used in General Relativity have the form that they do. It also explains the Lorentz force and the Stern Gerlach force. It gives a physical interpretation of Planck’s constant and proposes a physical mechanism for gravity which explains why it is so weak compared to the electric force. It also explains why the relativistic energy momentum formula has the form it does and also proposes a physical mechanism to explain the deBroglie wavelength of a particle.
Category: Quantum Physics

Diffraction: An Experimental Search for the Physical Mechanisms of Pattern Formation

Authors: Sergei P. Slukhayevskiy
Comments: 12 Pages. 5 figures

Diffraction is traditionally regarded as a consequence of the disruption of wavefront continuity by an obstacle, whereas experiments usually provide access only to the final intensity distribution observed on a distant screen. In the present work, an approach for the instrumental observation of the spatial evolution of the diffraction process was implemented through successive modifications of classical interference and diffraction arrangements adapted to new experimental objectives. It was experimentally established that, after interaction with a single half-plane obstacle, a finite layered structure is formed within the light beam. This structure remains confined to the beam cross-section and consists of alternating bright and dark regions oriented parallel to the obstacle edge. In the absence of spatial overlap with other disturbances, these layers gradually smooth out and the intensity distribution returns to a nearly uniform state. It is shown that, in more complex configurations, each half-plane generates its own system of spatial beam stratification. Signatures of these structures are observed at distances of approximately 15 cm before the geometrical edge of the obstacle and persist over a comparable distance after it. When spatial overlap occurs, mutual deflecting interactions between the layer systems arise, suppressing relaxation and leading to the formation of a stable wide-angle diffraction pattern. Experiments employing beams marked by a regular geometric light pattern revealed that dark-layer regions suppress the transmission of light from other sources in a manner similar to opaque objects. By varying the degree of spatial overlap between layer systems, a continuous transition was achieved from the classical distribution dominated by the central maximum to regimes exhibiting enhancement of higher-order maxima. Additional experiments revealed a spatially selective character of layer interactions and a weak dependence of the observed effects on the surface quality of macroscopic obstacles. The obtained results provide a basis for further investigation of the causal mechanisms responsible for the formation of diffraction structures and suggest potential practical applications of the observed regularities under controlled boundary conditions.
Category: Classical Physics

A Saturating Magnetic Switched Blumlein High Voltage Pulse Generator

Authors: Max Artusy
Comments: 2 Pages. (Note by viXra Admin: Author name is required in the article after the article title)

The Blumlein charged line generator is designed with a saturating magnetic switch. This allows rapid recharge and robust switching, which can tolerate arcing without switch damage. This shows the versatility of this unique circuit. High rep rate is intrinsic.
Category: High Energy Particle Physics

Architecture of Elementary Particles

Authors: Yvan Raverdy
Comments: 7 Pages. (Note by viXra Admin: Please cite and list scientific references of other authors)

The particles that constitute our Universe, in its so-called "ordinary matter and radiation" component, are all electromagnetic in nature, defined by the unification of their three possible interactions. We know that the fourth interaction (gravitational) is significantly different in nature from the other three. Here, we intend to describe how the so-called "stable" particles of ordinary matter can be composed of those that constitute their most fundamental building blocks. These particles decay in a time ranging from 10u207bu2076 s to 10u207b¹u2076 s, except for the proton, which is extremely stable.
Category: High Energy Particle Physics

Explaining the Complexity of Experimental Results on the Lifetimes of Free-Neutrons and Hyperons and the Masses of W-Bosons Based on the Atom-Like Structure of Baryons

Authors: Sylwester Kornowski
Comments: 14 Pages.

The complexities of the precise experimental data on the lifetimes of free neutrons and hyperons and the masses of W bosons have not yet been resolved within the quark model. These three extremely important problems concern the weak interactions. Here we present exact solutions to these problems within the atom-like structure of baryons described in the Scale-Symmetric Theory (SST). The SST solutions show that they are beyond the Standard Model, but in previous articles we have shown how the quark model emerges from the atom-like structure of baryons. The mean lifetimes of free neutrons are very important in nuclear physics, particle physics and cosmology. Within SST we calculated the ground state for mean lifetime of free neutrons that is 878.10 s — it follows from the transition from the nuclear weak interactions to the weak interactions of the electrons in the presence of dark matter. We showed that in a bottle, the central spacetime condensate in the neutron, which is responsible for the β decay, can be in different mass states that leads to two excited states of neutron lifetime, i.e. 880.36 s and 882.63 s. We showed that in neutron beams, mean lifetime of neutrons depends on neutron velocity because emissions of quanta by the central spacetime condensate with increasing neutron velocity are more and more suppressed. For neutron velocity equal to a threshold velocity 3.356 km/s we obtain a longer mean neutron lifetime equal to 888.89 s. For velocity 2.2 km/s we obtain 886.83 s. We showed that mass of the W boson depends on the place of creation — the two calculated basic values are 80,360.11 MeV and 80,378.96 MeV which lead to the mean value 80,369.5 MeV that is very close to the world average central value (80,369.2 MeV). We also calculated the exact lifetimes of the hyperons.
Category: High Energy Particle Physics

Emergent Gravity from Fundamental Triangles with Inner Torsion-Twist Degrees of Freedom — an Analogon to Structure of Penrose-Triangles

Authors: Holger Döring
Comments: 8 Pages.

Investigated is a model of spacetime in which fundamental triangles possess not only geometric properties such as area and edge lengths but also internal degrees of freedom representing twist, which encodes their relative orientation with respect to neighboring triangles. While local triangles are flat and consistent, global misclosures can accumulate, acting analogously to holonomies in curved spacetimes. This approach enables the construction of a spin-network-like model in which gravity can be interpreted as a statistical emergent phenomenon arising from these accumulated twists. The concept is inspired by Penrose-triangles: local consistency combined with global twist. Therefore this description is called the Penrose-triangle-ansatz (PTA).
Category: Quantum Gravity and String Theory

Special Relativity Violates Physical Identity

Authors: Antonio León Sánchez
Comments: 3 Pages.

The Theorem of Physical Identity demonstrated in this article is an almost immediate consequence of the Laws of Logic. However, it is incompatible with the theory of special relativity.
Category: Classical Physics

Recurrence Relations in the Tessellation of the Upper Half-Plane by the Full Modular Group

Authors: Hans Montanus
Comments: 11 Pages.

The successive actions of the generators S and T of the full modular group SL(2,Z) on the fundamental domain F lead to a tessellation of the upper half-plane H. Each image can be obtained by acting on the fundamental domain with a word consisting of solely S's and T's. For instance STTSTTT(F) is the image when the word STTSTTT acts on F. There is no shorter word that produces the image STTSTTT(F). A recurrence relation will be derived for the number of images for a given minimal word length.
Category: Combinatorics and Graph Theory

How to Derive the Fine Structure Constant Using Probability and Compton Equations

Authors: Colin James
Comments: 32 Pages.

I use the relativistic Compton equations to calculate the momentum response of a ‘target’ electron to vacuum photon collisions redirected from a ‘source’ electron. The equations give the ratio of the momentum of the ‘target’ electron after the collision divided by the momentum of the incoming photon over the range of all angles of the ‘target’ electron’s deflection. By summing evenly (over the maximum cross-section) over all angles we obtain the ratio of 1/2.1412 when using photon frequencies of 2 and 4 times the mass equivalence of an electron in the ratio of 5.6269 to 1. 4 times the mass equivalence may be 2 x (2 times electron mass equivalence photons acting simultaneously) or a double photon composite.The fraction 1/8 is a probability based on spherical geometry — the ratio of the maximum cross-sectional area of a sphere to its surface area (¼) and a further probability of (½) due to the even chance of the electromagnetic properties of a photon matching those of an electron. This gives a total probability of (¼) x (½) = 1/8. There are 2 such 1/8 probability collisions — one in which a photon is deflected by a ‘source’ electron towards a ‘target’ electron and a second 1/8 probability collision at the ‘target’ electron. The Fine Structure Constant is therefore divided into 3 parts.1/8 x 1/8 x 1/2.1412 = 1/137.0360 based on probability, spherical geometry and the use of the Compton scattering equations. 1/2.1412 {0.4670} is calculated using the Compton scattering equations. 1/2.1412 x 1/8 (probability) gives 1/17.1295 {0.05838} Coulomb’s Law. 1/17.1295 x 1/8 (probability) gives 1/137.0360 {0.007297} the Fine Structure Constant. A ‘free’ electron may be pictured/averaged as a speed of light particle contained in an approximately circular orbit with fixed angular momentum by collisions with vacuum momenta.
Category: High Energy Particle Physics

An Optimized Sech-Based Approximation of E^{-X^2}

Authors: Vladyslav Vasilache
Comments: 2 Pages. (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)

This paper introduces a new, highly accurate approximation for the function $e^{-x^2}$. By differentiating a known error function approximation and optimizing its parameters, we drastically reduce the maximum absolute error from $1.88%$ to less than $0.09%$ without using any exponential terms.
Category: Functions and Analysis

Towards a Floer Theory for Mars II Floer Hessian Field Almost Extends

Authors: Urs Frauenfelder, Joa Weber
Comments: 57 pages, 2 figures

In part I, [FW26a], we showed that collisional periodic orbits of twisted Zeeman systems can be detected variationally by a non-local Hamiltonian action functional. In this part II we show that the linearized gradient flow of this non-local functional is a Fredholm operator and prove a non-local elliptic regularity result. These results are obtained with the theory of almost extendability of weak Hessian fields introduced in [FW26c].
Category: Mathematical Physics

Inference Operators

Authors: A. Zelmer
Comments: 40 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

Certainly the beauty of mathematics also lies in the precision of mathematical sentences, as well as in the proofs of theorems. However, this can only be fully achieved by formalizing sentences and proofs.Our computer-assisted proving system, which we have called "Logic", contains two fundamental modules: the sentence editor and the proof module. We presented the sentence editor in Mathematical Sentences as Matrices. The proof module of the "Logic" system is based on certain primitive functions that we have called inference operators. In this paper we present what inference operators are and how they can be used in formalized mathematical proofs.
Category: Set Theory and Logic

A Possible Solution to the Mystery of the Bermuda Triangle: a Nuclear Physics-Based Quark Transfer Model Leading to Perpetuity of Magnetic Force

Authors: Bijon Kumar Sen, Subha Sen
Comments: 5 Pages. 2 Figures

On the basis of a nuclear physics-based model, an attempt has been made to explain the neutron to proton (n — p) conversion in the nucleus of an atom and the way of transfer of a d- quark into a u- quark. From examination of their implications in the mechanism of low and high temperature superconductivity, we came across a stupendous conclusion which may lead to busting the mystery of the Bermuda triangle. This, however, assumes free quarks may have limited existence under special condition. It is the swarm of quarks produced from unlimited supply of free electrons, unhindered by the warmth and the depth of the ocean, unchecked by the Meissner effect, add up (aided and abated by mutual enforcement) to a strong attractive force which can explain the anomalous magnetic behaviour as noticed by Columbus during his voyage through Bermuda triangle. The appearance and disappearance of the hysteresis curve shows that the Bermuda Triangle serves as a natural channel, passing everything that comes into contact with it into eternal sleep leading ultimately to the perpetuity of magnetic force. It is advisable that the study of tectonic and geophysical processes should be carefully made by the scientists so as not to meet the swarm of quarks for their own safety, security and escape from becoming a part and parcel of perpetuity.
Category: Nuclear and Atomic Physics

Extended Lorentz Spacetime Approach to Gravity

Authors: Tomasz Kobierzycki
Comments: 13 Pages.

In this paper I will present simple model of gravity field not as spacetime curvature but as a motion of arrows or more precise set of vectors from each point of spacetime. It's rooted in special relativity and it extends Minkowski spacetime to three sectors.
Category: Relativity and Cosmology

Short Version of "Turing-Unsimulability & Cosmic-Censorship-Falsity for General Relativity"

Authors: Warren D. Smith
Comments: 6 Pages.

My paper http://vixra.org/abs/2605.0004 "Turing-Unsimulability, and instantaneous & sustained Cosmic-Censorship-falsity, for Einstein-Vacuum General Relativity", at 60, 74, and 78 pages for versions 1, 2, and 3, was too long for many stomachs. Therefore I here also provide a short introductory explanation (in the spirit of Phys.Rev.Letters summaries of fuller papers) of its main ideas to try to advertise it and to get expert readers oriented right before they start.
Category: Astrophysics

Emergent Time and the Elimination of Cosmological Singularities Via Clock-Field Deparametrization

Authors: Ruslan Yurkevich
Comments: 7 Pages. Distributed under the arXiv.org perpetual, non-exclusive license.

Context: In canonical quantum gravity, the Wheeler-DeWitt equation suffers from the notorious "problem of the frozen Universe," lacking an explicit time parameter. Methods: This paper introduces a novel pre-geometric quantum cosmological formalisation where the flow of time is an emergent property tracking microscopic transitions. We execute a canonical 3+1 ADM deparametrization of the gravitational constraint using a scalar clock-field (chi ), yielding a dynamic Schrödinger-type equation for quantum gravity. Results: We postulate a non-linear feedback loop where the local clock rate w slows down as the energy density (ho ) increases: (w(ho) = 1/(1 + xi ho)), where (xi > 0) is a universal coupling constant. Semi-classical WKB analysis of the homogeneous FRW mini-superspace reveals a singularity-free "bounce-plateau" state at the Big Bang and within black hole cores. In the low-density limit, this mechanism naturally acts as a dynamic negative pressure component, driving late-time cosmic acceleration without a cosmological constant (Lambda ). Significance: The modified Mukhanov-Sasaki equations predict explicit corrections for primordial perturbations ((n_{s}) and r) that fall precisely within the discovery thresholds of the upcoming CMB-S4 and DECIGO experiments, rendering the model fully falsifiable.
Category: Quantum Gravity and String Theory

Gravity as Spacetime Distortion: A Unified Framework from the Full Affine Connection

Authors: Luca Eliseo Pavesi
Comments: 26 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org)

We present a comprehensive geometric framework for gravity in which the fundamental dynamical variable is the distortion tensor encoding both torsion and non-metricity. After a thorough review of metric-affine geometry, we construct the most general action quadratic in the distortion and linear in the Levi-Civita curvature, supplemented by a Yang-Mills-type kinetic term. The theory propagates a massless graviton, a massive vector, and a massive scalar. We derive the full non-linear field equations, linearize them around Minkowski spacetime, perform a complete mode decomposition, and analyze the stability and unitarity of each sector. We study the low-energy limit and show that General Relativity is recovered exactly below the distortion mass scale. We then explore cosmological solutions, finding that the vector mode can drive late-time acceleration without a cosmological constant. Black hole solutions are analyzed perturbatively, revealing a possible mechanism for singularity regularization. We discuss gravitational wave signatures, including dipole radiation from the vector mode, and place preliminary constraints from LIGO/Virgo observations. Finally, we outline the power-counting renormalizability of the theory and its potential as an ultraviolet completion of General Relativity. Extensive appendices provide detailed derivations of all identities used in the main text.
Category: Relativity and Cosmology

The Optical Prison: Universal Physical Isolation as the Physical Solution to the Fermi Paradox

Authors: Hao Xu
Comments: 10 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

An Optical Prison hypothesis is proposed that would physically resolve the Fermi's Paradox. Three independent ground optical experiments verify the physical limitation of the astronomical observations caused by structural self-weight collapse and optical inherent constraints. Unlike conventional SETI concepts, the conclusion is quantitatively restricted by measurable experimental data, lacking empirical support, our conclusion is qualitatively restricted by neutron degradation and explaining the cosmic silence in SETI observations.
Category: Astrophysics

Testing the D.m. By Quantum Gravitation Theory by the Mass Associated to the Turnaround Radius

Authors: Manuel Abarca Hernandez
Comments: 9 Pages.

The DM by Quantum Gravitation theory (DMbQG hereafter), is a novel theory developed in the two main papers [1] and [2] Abarca,M.(2024). In the present work, in the framework of DMbQG theory it will derived the formula for the mass associated to the turnaround radius depending on the turnaround radius and it will be shown that the new expression has a deeper physical meaning regarding the same formula in the current LCDM paradigm. The DMbQG theory states a direct relation between the virial radius and the turnaround radius as well as the virial mass and the mass associated to the turnaround radius.The most important contribution of this work is placed in the chapter 2 where it has been demonstrated that the formula for the mass associated to the turnaround radius, using the DMbQG theory, is the same that the one in the current LCDM paradigm. However the new formula has a deeper physical meaning because its dimensionless factor is simpler regarding the one in the current LCDM paradigm. It is remarkable the fact that the both dimensionless factors depend on exclusively from the Universal omega parameters for the mass or for the DE and the both ones differ only a 5%. The fact that in the framework of DMbQG theory has been found a better formula for the mass associated to the turnaround radius is a strong support for the DMbQG theory whose hypothesis about the origin of DM is exclusively the gravitational field. The chapters 3, 4 and 5 are devoted to test the DMbQG theory in the clusters, Virgo, Coma and the Local Group of galaxies using recent data published about these clusters. The tests are mainly focused on the turnaround radius and its mass associated and all of them have been a complete success by the DMbQG theory.
Category: Astrophysics

Gravity as an Emergent Force Via the Uncertainty Principle

Authors: Morgan W. Weinberg
Comments: 51 Pages.

The core concept of this paper is the relation between an accelerating field and time uncertainty. This relation distills from the derivation of Newton's Law of Gravitation via the uncertainty principle. It's shown, further, that this relation can be used to derive the Coulomb Force, suggesting that it may be a general principle in nature. Taking this concept further, this paper draws a connection between expanding space and acceleration---offering an explanation for the missing-mass problem in galaxies. The paper goes on to draw a connection between the expansion of space and time uncertainty, leading to a startling conclusion: The expansion of space is not a function of the energy contained therein, but conversely, the mass of the universe is created in concert with the expansion of space. Further, because this expansion is a function of time, the mass of the universe is a function of time and increases in lockstep therewith. It's deemed that the model of the universe presented herein obviates the need for dark matter and dark energy to explain our observations of the cosmos.
Category: Astrophysics

Doppler Effect, Absolute Stellar Aberration, Stellar Velocity, Stellar Distance and Speed of the Light

Authors: Miloš Čojanović
Comments: 6 Pages.

Our assumption is that the Doppler Effect and Absolute Stellar Aberration are two complementary phenomena. This means that if we are able to use the result obtained by measuring $DE$ to determine the radial velocity, then by using the result obtained by measuring "ASA" we should be able to determine the transverse velocity with which the star moves in relation to the observer. We will prove that if we know the velocity of the star, we can determine its distance in relation to the observer and the speed of light emitted from the star in the direction of the observer.
Category: Astrophysics

Multi-Metric Wormholes: A No-Horizon Theorem and 1/N Suppression of Exotic Matter

Authors: Luca Eliseo Pavesi
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We present a comprehensive study of traversable wormholes in multi-metric gravity, a ghost-free theory with N interacting metric tensors. The action, field equations, and constraints are derived step by step. We construct a static, spherically symmetric wormhole ansatz with a Gaussian deformation localised at the throat, and reduce the field equations to a system of ordinary differential equations. A central result is a no-horizon theorem: any stationary, asymptotically flat solution with a non-zero multi-metric charge Q, defined as the asymptotic flux of a conserved current built from the metric differences, cannot contain a Killing horizon and must therefore be a traversable wormhole. We show analytically and numerically that the null energy condition (NEC) violation is suppressed by a factor 1/N compared to the single-metric case, and that the exotic matter can be confined to an arbitrarily narrow shell. The deflection angle and Shapiro time delay are computed, and the stability under radial perturbations is analysed. The model satisfies Solar System constraints and makes falsifiable predictions for near-future instruments.
Category: Relativity and Cosmology

Shaking up the Theory of the Expanding Universe

Authors: Henk Dorrestijn
Comments: 11 Pages.

Obstruction Theory offers an alternative to the Newton/Einstein theory for cosmology. Assuming a rarefied mass density in the universe, the redshift we observe in distant light sources can be explained without assuming that the sources are moving away from us at high speed, causing the universe to expand. The redshift can be easily explained by the average mass density of the universe.It is known that a mass slows down the velocity of time at a point in its vicinity. This slowdown turns out to be equal to the reduction of direct radiation from more distant space due to the presence of the mass. We show that the amount of direct radiation reaching an observer from the universe is always partially lost along the way through scattering by protons and other small particles. This translates into the velocity of time, which we observe as redshift. We find the size of our visible universe by stating that the observed time velocity of the light sources at the boundary of the universe is reduced to zero. The value for the size that we find via a simple calculation is close to the value found in the traditional way. Furthermore, with this theory, a value for the Hubbleconstante can be found using the mass density of the universe. According to Obstruction Theory, there can furthermore be no question of a bounded universe. Every observer is the center of their own universe. Beyond its own universe, the universe extends infinitely far.
Category: Relativity and Cosmology

Collatz Conjecture: A Simple Proof for a Simple Problem

Authors: Ulrich Neuenschwander
Comments: 8 Pages.

A simple proof of the Collatz conjecture is proposed. The approach relies on the fundamental properties of N and on their fruitful interplay with the Collatz transformation.It will be interesting to see how the field receives the proposal and whether the reasoning and the conclusions are confirmed or need modification.
Category: Number Theory

Observation of D+D Fusion in Electromagnetically Self-Contained, Long-Lifetime Plasmoids

Authors: Dominik Kuryga, Paulina Nadia Weremczuk
Comments: 28 Pages.

We report the generation of self-contained, long-lived plasmoids in a low pressure coaxial diode of novel concept, driven by a ~5ns up to 1MV pulse, generating neutron bursts consistent with D+D fusion in discharges in deuterium. Neutrons were detected using a silver activation based detector. A correlation was observed between lifetime and neutron yield. Average neutron yields reached approximately 5—7x10u2075 neutrons per shot, with peak values up to 1,4x10u2076 neutrons/shot. Microwave emission measurements were done showing long decaying radiation. The demonstrated detectable nuclear fusion in this novel device opens new perspectives for compact neutron sources and alternative fusion concepts based on self-confined plasmoids.
Category: Nuclear and Atomic Physics

Traversable Wormholes in Quadratic Covariant Gravity: Localised Deformations, Shapiro Delay, and Stability

Authors: Luca Eliseo Pavesi
Comments: 19 pages. English.

We consider a covariant theory of gravity defined by the action S = ∫ d^4x √−g [(16πG)^{-1}(R + αR^2) + L_matter], which reduces to general relativity when α → 0. This theory, belonging to the class of f(R) gravities, is ghost-free and contains an additional massive scalar degree of freedom (the scalaron), and is treated as an effective field theory valid below the Planck scale. We derive the fourth-order field equations step by step, including all boundary terms. We then apply them to a static, spherically symmetric metric describing a traversable wormhole. The metric includes a Gaussian deformation X(r) = A exp[−(r − r0)^2/(2σ^2)] localised around the throat r = r0. The flare-out condition is satisfied for A > −1. We compute all Christoffel symbols exactly, derive the Ricci tensor and scalar, and solve the modified Einstein equations for an anisotropic fluid. The energy conditions are analysed: the null energy condition is violated only in an arbitrarily small region near the throat if α > 0 and the Gaussian parameters are chosen appropriately. We study null geodesics using the corrected radial equation, compute the deflection angle and the Shapiro time delay for light passing near the wormhole, and show that the Gaussian deformation introduces a characteristic shift compared to the Morris—Thorne case. Stability under radial perturbations is analysed in the scalar—tensor representation, showing that the wormhole can be stable for a range of parameters. The asymptotic limit is studied via a post-Newtonian expansion: the PPN parameters remain γ = β = 1, and the scalaron mass m^2 = 1/(6α) is constrained by Solar System tests to be m ≥ 10^{-3} eV. We discuss observational signatures such as lensing, Shapiro delay, and gravitational-wave echoes that make the model falsifiable. All calculations are presented in detail, with intermediate steps collected in appendices.
Category: Relativity and Cosmology

A Geometric Explanation of Dark Matter Based on General Relativity

Authors: Hao Shen, Ruipeng Ma
Comments: 19 Pages.

Within the framework of standard general relativity (Einstein 1915), under the assumptions of staticity, spherical symmetry and the strong energy condition, we prove that a geometric transition zone — the "reverse-bending zone" — must appear in the periphery of any finite self-gravitating system, where the t—r sectional curvature changes sign from negative to positive. This zone is bounded by the curvature zero r0, the curvature peak rpeak, and the matter boundary R; in the interval (r0, R) the sectional curvature smoothly transforms from matter-dominated spherical compression to vacuum saddle-shaped stretching. The reverse-bending zone is not a free vacuum but a forced geometry locked jointly by the interior baryonic potential well and the far-field boundary condition. Within this zone, the Misner—Sharp-type gravitational mass M(r) continues to grow: it grows faster than linearly in the region r0 → rpeak, and although the growth slows down in the region rpeak → R, it never ceases. The resulting geometric Weyl stretching together with the self-energy of the gravitational field provide an extra centripetal acceleration, which naturally manifests itself, in the weak-field approximation, as an approximately logarithmic potential and a flattening of the rotation curves. The theory yields parameter-free, falsifiable predictions that can be directly tested with existing rotation-curve and photometric data. These results show that, without introducing new particles or modifying the field equations, the forced geometry within general relativity can produce "dark-matter-like" gravitational effects on galactic scales.
Category: Relativity and Cosmology

Elementary Weak Solutions of the Navier—Stokes Equations and an Application of the Banach Fixed-Point Theorem

Authors: Masatoshi Ohrui
Comments: 23 Pages.

This is an application of functional analysis to the existence and smoothness of the Navier—Stokes equations using elementary weak solutions in Sobolev spaces.We solve the problem in mathematics. The problems are not in physics, so we do not use any physics or assumptions-falsified mathematics, such as other papers. We use mathematics only. We can solve the problem by using an exactly and completely FALSIFIED resolution, where large initial values destroy the earth, because uniqueness does NOT hold, or SMALL initial values love your cup of coffee.There are no long or complicated calculations; semi-groups, a priori estimates, and boundary conditions are not used at all. We apply the local solvability of linear partial differential operators with constant coeficients.
Category: Functions and Analysis

Proof of Hartog’s Phenomenon and Cohomology Vanishing Theorem

Authors: Masatoshi Ohrui
Comments: 2 Pages.

We can prove Hartog’s phenomenon by solving the ∂-bar equation for compactly supported forms. To solve the equation, we construct the solution using convolution.
Category: Functions and Analysis

Extended Standard-Model by the Coxeter Element of the Affine Weyl Group E˜8

Authors: Reinhard Kronberger
Comments: 20 Pages.

In this paper i will give an extension of the known Standard-Model.The shape of the extension is not arbitrary choosen.The shape explains gravity and more. I show that the symmetries generated by the coxeter-element of the affine Weyl group E˜8 which is the affine extension of the well known exceptional group E8 is a candidate which explains open questions like dark matter and gravity.
Category: Quantum Physics

Geometric Projection of Arithmetic Spirals Onto Logarithmic Manifolds: a Moiré Interference Framework for Studying Prime Distribution Without Complex-Analytic Tools

Authors: Jian-Yu Huang
Comments: 27 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We develop a geometric and spectral framework for studying structural fluctuations in discrete arithmetic sequences, operating entirely within real-variable analysis and without appeal to the Riemann zeta function, Euler products, explicit formulae, or analytic continuation. An arithmetic lattice is mapped onto a transcendental logarithmic manifold via an area-filling projection; the resulting Moiré-type interference field serves as the primary object of study. The principal contributions are as follows. (i) We prove, with explicit constants, that the projection map is injective and that successive images are uniformly separated (Propo-sitions 2.3-2.4). (ii) We establish a uniform L 2 near-orthogonality theorem for finite phase families, yielding a computable operator-norm bound on the associated Gram matrix via Gershgorin's circle theorem [5] (Theorem 3.3). (iii) We introduce an explicit Moiré di-lation operator T σ = −i(x ∂ x + σ) on L 2 ([1, ∞)), show that the geometric phasor family {x −(σ+it) } t∈R constitutes its formal eigenfunction family (Lemma 3.12), and prove by integration by parts that T σ is formally self-adjoint if and only if σ = 1 2 (Theorem 3.14). (iv) We derive quantitative variance bounds for node-count statistics, controlled by the pairwise phase-correlation bounds (Theorem 3.19). Complete exponential-sum estimates with explicit constants (Appendix C) and Abel-smoothing remainder formulae including an incomplete-Gamma bound (Appendix B) are provided. All theoretical claims are either proved using the above tools or explicitly designated as conjectural.
Category: Number Theory

Finite Bernoulli—Zeta Transforms for Fibonacci-Type Recurrence

Authors: Payam Danesh
Comments: 12 Pages.

Fibonacci and Lucas sequences are basic examples of second-order recurrences, and their behavior is closely connected to the golden ratio. Bernoulli numbers and special values of the Riemann zeta function also form a classical part of number theory. This paper connects these two areas through exact finite identities. The method starts from exponential generating functions, separates the odd-indexed terms, applies Bernoulli generating functions, and then compares coefficients. This gives a finite formula in which a weighted sum of zeta values at non-positive integers becomes an explicit Fibonacci expression. The same argument also gives a Lucas version, and then extends to every sequence satisfying the Fibonacci recurrence with arbitrary initial values. Exact symbolic checks and residual plot are included to show how the cancellation works. The result is a complete unconditional link between Fibonacci-type recurrences, Bernoulli numbers, and special zeta values.
Category: Number Theory

Dual Architecture of the Gamma Function: Complementary Extension to the Left Half-Plane and Regularization of Logarithmic Divergences

Authors: Julinho Jorge Luís
Comments: 20 Pages.

This work proposes a complementary extension of the factorial function to the real line, based on the separation of the bilateral integral of e^(-Ax) into two disjoint domains. For A>0, the classical Gamma function Γ(z) emerges in the right half-plane; for A<0, we introduce the Symmetric Gamma Function Γ ˉ(z)=e^(-iπ(z+1)) Γ(-z), defined in the left half-plane, with poles at the positive integers. The duality between the integral kernels underlies a regularization mechanism for logarithmic divergences: Γ_R (z)=1/Γ ˉ(z-1) and Γ ˉ_R (z)=1/Γ(z+1), replacing each pole by an exact finite value. An alternative real representation B(x)=∫_0^∞e^(-u) u^(-x) du (convergent for x<1) is constructed, together with a trigonometric factor C(x)=2sinu2061(πx)+cosu2061(πx), defining F(x)=C(x)B(x) for x≤0, yielding F(-n)=(-1)^n n!, thereby unifying the complex branch, real regularization, and Laurent expansion formalisms. The relation F(-n)⋅Resu2061(Γ,-n)=1 establishes the fundamental duality, which emerges directly from the construction of the integral kernels. The method is validated in arithmetic progressions, QED, and QCD. The extension to k-loops is systematic via exponentiation: Γ_R^((k) ) (-n)=[(-1)^n/n!]^k. Distinct physical prediction: In d=5 dimensions, the vacuum energy density changes sign — a repulsive force where the MS-bar predicts attraction. This inversion has direct implications for the stability of extra dimensions in string theory and brane models.
Category: Quantum Gravity and String Theory

The Atomic Structure of the Chemical Elements

Authors: Jozsef Garai
Comments: 68 Pages.

Based on the analysis of the well-known features of the atoms, the following conclusions can be deduced. The identical and invariant properties of the chemical elements can only be ensured if the charge distribution of the nucleus is invariant and identical for each of the elements, dynamic equilibrium between the opposite charges in the atoms cannot be stable in the time scale of the universe, classical electromagnetism is valid at atomic scale, since neither theory nor experiments sets limits on it. Taking these conclusions into consideration the following modifications of the contemporary atom models are proposed. Nucleus: The identical reproduction of the nucleus requires lattice arrangement for the nucleons. Protons and neutrons have the same size. These nucleons should occupy the space in the most efficient way, forming a closest packing arrangement. The smallest building blocks of this arrangement are tetrahedrons. Assuming alternate arrangement of the protons and the neutrons, and expanding a tetrahedron seed by adding additional layers to it, the number of protons in the layers reproduces the periodicity of the chemical elements. Electronegativity represents the average attraction of the unshielded proton/s on the valence electron/s. This physical description is even consistent with the irregularities of electronegativity. Electronic shell: In the time scale of the universe, dynamic equilibrium of the opposite charges in the atoms would be chaotic. This contradicts with the known stability of the atoms. Static equilibrium between the opposite charges can only be achieved if at least one of the charges is a distributed one. The physical behavior of the free and the bounded electrons are different. Thus, these electrons are not identical. These differences can be explained if the point charge free (unbounded) electron at capturing transfers and forms a surface charge electron shell around the nucleus, and vice versa. This phase transformation is energetically feasible. The electronic shell structure of the atoms is the consequence of the nuclear lattice. New electron shell is formed when the attraction of the added proton of an element is weaker on the captured electron than the average attraction on an electron in the existing shell.
Category: Nuclear and Atomic Physics

Completeness of the Metric Description of Gravitational Reality: An Radiative Generalization of Kerr-Newman Spacetime

Authors: Tanishq Chandu Khandare
Comments: 2 Pages.

I derive a non-vanishing, solution to the Einstein-Maxwell field equations representing a dynamical, radiating, rotating, and charged manifold. Utilizing the Newman-Penrose (NP) formalist, I project the metric onto a nulltetrad {l, n, m, m¯ } to evaluate the Weyl and Ricci scalars. We demonstrate that the resulting stress-energy tensor Tµν = T (null) µν + T(em) µν satisfies the Weak Energy Condition (WEC) and the local conservation law ∇µTµν = 0. By formalizing the EPR criterion for physical completeness, we argue that the stationary KerrNewman limit is a sub-manifold of the broader radiative reality. I further prove that the r = 0 singularity is a transient topological feature that resolves into a Minkowski vacuum in the limit of total evaporation.
Category: Relativity and Cosmology

Is the Central Valley of California an Elongated Impact Basin?

Authors: David E. Rutherford
Comments: 4 Pages.

In general, impact craters are circular in shape, but occasionally, they exhibit non-circular forms. One such form is the elongated impact crater. I suggest that the Central Valley of California may be a larger version of an elongated impact crater, an elongated impact basin. Its elongated shape might be the result of a very low angle of impact of one or more celestial objects with the surface of the Earth. The `central' peak (or uplift) of the original basin might be the Sutter Buttes, in the northern part of the Central Valley. In order to support these conclusions, images of lunar impact craters are compared to shaded relief maps of the Central Valley (and surrounding mountains) of California.
Category: Geophysics

Quantum Mechanics and The Subjective Nature of Mathematics

Authors: Joseph Palazzo
Comments: 3 Pages. (Note by viXra Admin: An abstract in the article labeled as such in the article is required)

In the historical debate between Einstein and Bohr, it is practically seen in every sentence that Einstein was debating ontology ("Do you really believe the moon is not there when you are not looking at it?")[1] while Bohr was debating epistemology (we only know until particles are observed, at which point the "wave function collapses" into a definite state). This is like as if one is talking about basketball, while the other is talking about hockey. It’s no surprise that they were talking passed each other, not aware of what was going on. Worse is that the whole physics community for the past 100 years did not see it. In 2022, the Nobel Prize in physics was headlined as: quantum mechanics is right, Einstein is wrong — indicating by all measures that we still don’t have it right.
Category: Quantum Physics

The Oscillations of a Particle in an Anharmonic Potential with Damping

Authors: L. A. Xamidullayeva, U. O. Muhammedov, X. N. Ismatullayev
Comments: 3 Pages.

The natural processes equations are nonlinear and have dissipating terms. In many cases they donot have an exact analytical solution. Using perturbation theory we solved the equation of anoscillating particle in an anharmonic potencial.
Category: Classical Physics

Kinematic Analysis of the Motion of an Ellipsograph Point Under Various Velocity Laws

Authors: Viktor Strohm
Comments: 5 Pages.

This paper investigates the kinematics of a fixed point on the connecting bar of an ellipsograph (Archimedes' trammel) under different driving motion regimes: uniform, uniformly accelerated, and Keplerian (elliptical). Based on differential constraint equations, analytical expressions for the velocity and acceleration vectors of the trajectory point are derived. A numerical approach, modeling the division of the orbital quadrant into equal time intervals, is utilized to calculate the corresponding areal velocities. It is rigorously demonstrated that the constancy of the areal velocity and the fulfillment of Kepler's second law occur exclusively under one specific law of angular velocity—the Keplerian regime—whereas under uniform and uniformly accelerated motions, the law of areas is violated. This work establishes a link between the mechanical modeling of trajectories and the author's fundamental theoretical research in the focal and central kinematics of the ellipse.
Category: Classical Physics

Decoupled Prompting and Topology-Aware Optimal Transport for CLIP-Based Unsupervised Cross-Modal Re-Identiffcation

Authors: Xiaohao Xie, Wenhua Jiao, Wei Meng
Comments: 14 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Unsupervised Visible-Infrared Person Re-identification (USL-VI-ReID) is critical for cross-modal intelligent surveillance. While vision-language models (e.g., CLIP) present powerful representational capabilities, directly fine-tuning them for USL-VI-ReID often causes catastrophic feature collapse and prompt degradation due to massive domain gaps and noisy pseudo-labels. Furthermore, traditional discrete matching and heuristic denoising strategies suffer from severe cross-modal information starvation and numerical bias against hard positives. To address these challenges, we propose a robust, CLIP-based unsupervised cross-modal fine-tuning framework. First, we design an implicit adapter fine-tuning strategy coupled with decoupled multi-dimensional semantic prompting to isolate domain biases without destroying pre-trained priors. Second, a Cluster-Aware Cross-Modal Semantic Alignment (CCSA) mechanism maps dynamic visual centers to modality-shared textual proxies via visual-conditioned prompting, facilitating an implicit soft alignment decoupled from hard clustering noise. Third, we frame cross-modal association as a Topology-Aware Optimal Transport (TOTO) problem. Utilizing Fused Gromov-Wasserstein (FGW) constraints and Argmax assignments, TOTO injects potent hard regularization to overcome optimization inertia on difficult samples. Finally, our Pure Relative Confidence Ratio and Dual Adaptive Denoising (RCR-DAD) module eliminates numerical bias, formulating a robust self-paced learning trajectory. Extensive experiments on SYSU-MM01 and RegDB demonstrate our framework achieves state-of-the-art performance. The code will be released.
Category: Artificial Intelligence

Ramanujan Polynomial Expansion for Hurwitz Zeta Function

Authors: Payam Danesh
Comments: 29 Pages.

Polynomial expansions of zeta functions provide a natural way to connect analytic continuation, regularized summation, Mellin analysis, and orthogonal polynomial theory. In this paper we try to develop a shifted Ramanujan—Mellin expansion for the Hurwitz zeta function in the critical strip. The construction combines Abel—Plana regularization over the nonnegative integers, Ramanujan summation for shifted Dirichlet terms, the Cayley transform of the right half-plane, and Mellin transforms of Laguerre functions. The main result proves that the Hurwitz zeta function admits a locally uniformly convergent expansion in a universal polynomial basis that is independent of the shift parameter. The shift appears only through explicit coefficients involving the digamma function and shifted Hurwitz zeta values. The Riemann zeta function is obtained as a special case. On the critical line, the normalized basis forms a complete orthonormal system with respect to a hyperbolic weight, and every zero of each basis polynomial lies on the critical line. The final result gives an exact zero-free compact criterion equivalent to the Riemann Hypothesis.
Category: Number Theory

A New Home for Bivectors Geometric Algebra on a Sphere

Authors: Norm Cimon
Comments: 20 Pages.

The impetus for the work is this quote:"...as shown by Gel’fand’s approach, we can only abstract a unique manifold if our algebra is commutative."[1] Geometric algebra is non-commutative. Components of different grades can be staged on different manifolds. As operations on those elements proceed, they can effect the promotion and/or demotion of components to higher and/or lower grades, and thus to different manifolds. This paper includes imagery that visually displays bivector addition and rotation on a sphere. David Hestenes interpreted the vector product or rotor in two-dimensions: "as a directed arc of fixed length that can be rotated at will on the unit circle, just as we interpret a vectoras a directed line segment that can be translated at will without changing its length or directionu2026"[2]Rotors can be used to develop addition and multiplication of bivectors on a sphere. For those rotational dynamics, rotors of lengthare the basis elements. The geometric algebra of bivectors — Hamilton’s "pure quaternions" — is thus shown to transparently operate on a spherical manifold.This paper also explores the possible generalizations that emerge from the placement of the graded elements which make up a geometric algebra onto separate manifolds.
Category: Geometry

The Weakening of Earth's Magnetic Field is the Real Cause Driving Current Ocean Warming

Authors: Jamal S. Shrair
Comments: 21 Pages.

Earlier studies estimated that the Arctic region is warming around twice as fast as the global average. Yet, recent studies have found this figure to be wrong by a huge margin (hugely underestimated). Actually, in the last 45 years, the Arctic region has warmed almost four times faster than the rest of the planet, while the South Pole is warming three times faster than the global rate. On the other hand, since 2016, the Atlantic Ocean especially its northern part, has warmed faster than other ocean basins in the top 100 meters of ocean. Nonetheless, the real reason for the rapid warming of these regions is because of the huge decline in the strength of Earth's magnetic field, and the enormous flow of thermal energy from Earth's interior into the upper layers. Back in 2014, data from Swarm (three specialized satellites) revealed that Earth's magnetic field has weakened 10 times faster than expected. It was astonishing data, totally unexpected and unexplained by the current model that relies on self-generating dynamo. Specifically, Swarm found the biggest decline in the strength of Earth's magnetic field around the Arctic regions, the North Atlantic Ocean and also within the South Atlantic, as the South Atlantic Anomaly (SAA) shows. The decline in the strength of Earth's magnetic field, definitely implies that these regions would receive more solar radiation from above, and higher flow of thermal energy from the interior than when the field was strong and stable. Hence, one can say conclusively that the rapid weakening of Earth's magnetic field was the real cause that made the Polar Regions, and those close to them, warm faster in comparison to other regions of the planet. However, the most fundamental reason why the pseudoscience theory of greenhouse gases is the name of the game - in addition of course to the widespread corruption of our society - is because of the lack of understanding the most important scientific facts about the most important astronomical objects to us, namely our own planet and star. Basically, the origin and mechanism of the magnetic fields of the Earth and the Sun, including the reason for their reversal, are currently mysteries and will remain mysteries forever under gravity-dominated physics.
Category: Climate Research

Visual Space, Neural Networks, and AI Algorithm Models

Authors: Taiwei Song
Comments: 4 Pages. 4

This paper briefly discusses the concept of visual space discovered by the author [1-4], its transformation equation with the natural space-time, and points out that this transformation relationship is the key algorithm for AI embodied agents to automatically recognize the surrounding "world". It also briefly demonstrates that neural networks inherently possess the properties of "iterative convergence" and "self-learning evolution", and the "emergence of intelligence" in large AI models based on neural networks is inevitable.
Category: Artificial Intelligence

Hastings-Cody Approximations of the Integral of a Power Times the Complete Elliptic Integral of the First Kind

Authors: Richard J. Mathar
Comments: 16 Pages.

Hastings and later Cody tabulated minimax polynomial approximations for the Complete Elliptic Integral of the First Kind. The simplicity of this representation by polynomials and polynomials times a logarithm allows to integrate their terms analytically. We demonstrate how integrals of the Complete Elliptic Integral times a power of its argument achieve double precision accuracy for powers from 0 to 2 based on Cody's polynomials up to 9th order.
Category: Functions and Analysis

A Theory of Kinematic Gravitation, and Some Fundamental Consequences

Authors: Charles Ba Oumar
Comments: 14 Pages.

We will be concerned with the study of relativistic density and hence demonstrate from first principles the possibility of kinematic black hole formation in inertial systems of coordinates in Minkowski spacetime. We will discuss the applicability of these principles to elementary particles on the basis of a set of geometrical assumptions, some general consequences, and also present alternative gravitational equations on the basis of some related elementary considerations. Finally, we will conclude with some general remarks on the meaning of these results.
Category: Relativity and Cosmology

Once More on the Aether

Authors: Viktor Stetsovich
Comments: 12 Pages.

Based on the hypothesis of the aether's existence, this article proposes an explanation for the results of the Fizeau and Michelson experiments, as well as an experiment for detecting the aether.
Category: Relativity and Cosmology

Saturating Magnetic Max Bank Drives Mismatched Loads, Using the Method of Self Matched Lines

Authors: Max Artusy
Comments: 3 Pages.

Abstract: The saturating magnetic Max Bank, provides a versatile topology to produce rectangular high voltage pulses with little secondary distortion. The self matched line method, is employed to achieve this. Rapid recharge is intrinsic, allowing high rep rate operation.
Category: High Energy Particle Physics

Resolving the Cosmological Hubble Tension via Local Wave Impedance Fluctuations in a Hexagonal Close-Packed Lattice

Authors: Markov Efim Sergeevich
Comments: 5 Pages. License: CC BY 4.0 (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The persistent cosmological discrepancy between early-universe cosmic microwave background (CMB) measurements (H0 approx 67.4 km/s/Mpc) and late-universe local distance ladder observations (H0 approx 73.0 km/s/Mpc) - known as the Hubble Tension - presents a fundamental crisis for the continuous Lambda-CDM paradigm. This paper resolves this conflict by shifting from expanding spacetime metrics to a stationary, non-singular Hexagonal Close-Packed (3HCP) discrete space crystal. We demonstrate that cosmological redshift is not a Doppler-like stretching of space, but a dissipative energy attenuation of electromagnetic wave packets undergoing sub-nodal friction across contacting cellular boundaries. By modeling the material vacuum as a discrete transmission network with a baseline register capacity Llimit = 256, we derive the propagation velocity and local wave impedance purely from first-principles lattice geometry. Through a multivariable Taylor series expansion, we establish a rigorous mathematical bridge proving that our discrete wave difference scheme converges onto the continuous Maxwell equations with a damping term as the lattice spacing approaches zero (h -> 0). Crucially, we show that local structural density fluctuations within the 3HCP matrix systematically alter the sub-nodal impedance along different lines of sight. Low-density intergalactic voids minimize wave friction, yielding an apparent higher local expansion rate (H0 approx 73.0), while deep CMB-scale averaging profiles smooth over macroscopic high-density clusters, converging onto the lower background global baseline (H0 approx 67.4). The Hubble Tension is thus completely eliminated, emerging as a predictable geometric artifact of measuring discrete wave impedance across a multi-scale, non-uniform spatial crystal.Creative Commons Attribution Non Commercial No Derivatives 4.0 International
Category: Astrophysics

The Final Theory

Authors: Nigel B. Cook
Comments: 102 Pages. (Note by viXra Admin: Please cite and list scientific references and submit article written with AI assistance to ai.viXra.org)

We construct a complete quantum field theory in which all observed interactions - electromagnetic, weak, strong, gravitational, and cosmological - arise from a single mechanistic principle: energy conservation in vacuum polarization. The theory replaces the ad hoc structure of the Standard Model and the geometric assumptions of general relativity with a unified framework based on the group chain for Euclidean signature SO(3, 3) ~ SU(4) ⊃ SU(3) × U(1)G ⊃ U(2) ⊃ SU(2) × U(1)Y . Matter representations, gauge charges, running couplings, particle masses, gravity, and dark energy all emerge from this structure without arbitrary parameters. This paper is a new presentation of the ideas in vixra paper 1111.0111 dated 2011, with updates, a few corrections, and further development. That earlier paper should still be consulted for further references, graphics and details documenting the origins of the various nascent ideas.
Category: Quantum Gravity and String Theory

An Alternate Resolution of the Famous Grandmother Paradox Which Might be Also Validated Via a Classic Experiment

Authors: Moshe Segal
Comments: 16 Pages.

The nowadays Science of Physics still embeds unresolved paradoxes, and incompatibilities between various Physics branches.One significant unresolved paradox is the famous Grandmother Paradox, in which someone returns to the past, kills his grandmother and thus, inhibits his birth, which obviously, also inhibits his ability to travel to the past.In addition to paradoxes, as presented just above, the nowadays Science of Physics still also embeds incompatibilities between various Physics branches.One of these branches is the branch denoted as the Classic Physics, which focuses on understanding and explaining what is denoted as the Macroscopic Environment.Another such branch is the branch denoted as the Quantum Physics, which focuses on understanding and explaining what is denoted as the Microscopic Environment.And, as presented above, these two branches of Physics are not fully compatible, and Humans are still struggling, to expand the knowledge that might bridge the gap that still exists between these two branches of Physics.Moreover, even the branch of the Classic Physics itself, still embeds branches which are also not fully compatible, as for example, the Gravity and the Electromagnetism, and more must be done to bridge the gap that exists also between these two branches, which both belong, as stated above, to the branch of the Classic Physics.Additional papers, by the author of this paper, present significant and reasonable arguments, which argue that the nowadays branch of the Classic Physics might be misleading in how it presents the concept of the Space-Time.By presenting an alternative view of how the Science of Physics should refer to the concept of the Space-Time, possible bridging between incompatible branches of the nowadays Science of Physics might be achieved, and also, a resolution to the famous Grandmother Paradox, might be presented.The above-mentioned additional papers, also propose experiments, which if implemented successfully, might provide validity, to the proposed alternative view of how the Science of Physics should refer to the concept of the Space-Time, which is presented in these additional papers.Thus, since a resolution of the famous Grandmother Paradox might be a significant step forward, and also the above-mentioned possible bridging between incompatible branches of the nowadays Science of Physics might also be a significant step forward, then, an implementation of the above-mentioned experiments, or any other experiments that might provide validity to the alternative view of how the Science of Physics should refer to the concept of the Space-Time, presented in the above-mentioned papers, should be an important and a significant endeavor.
Category: Relativity and Cosmology

Special Case of Law About Keep Moving of the Center of the Mass of а Closed System — Device from Two Bodies (Two Hulls), Uncompensated Moment and Propulsion in the Cosmic Space Without Propellant

Authors: L. Georgiev, D. Georgiev
Comments: 14 pages, 4 figures, In Bulgarian language

This article examines, special case of the law for conservation the motion of the center of the mass of а closed inertial system - device from two bodies (two hulls). Like in this special case, we obtain uncompensated moment for one of the hull of the device. As conditionally named first hull is standard rigid body. While on the second hull are connected two discs, which have equal masses and they can rotate free to the second hull. As when we apply the third law of Newton, between the two hulls, it’s uses the inertial of the two discusses. Like this way, because the kinetic energy is additive magnitude, it’s the hull with the discusses distribute the itself energy and for rotary motion of the discusses and for translational motion of the second hull. While for the first hull total kinetic energy, as a result of the applied third law is in the form of translational motion. As a result of the distribute of the energy of the second hull we obtain uncompensated moment for first hull. As a result of which is obtains and the special case of the law conservation motion of center of the mass of closed system — device from two bodies (two hulls). Like this way we have possibility for specific propulsion without propellant of the device in the cosmic space. Despite some shortcomings of the resulting specific propulsion, this is one of the possible ways of propulsion in cosmic space without "ejection" of propellant, and as only uses electrical energy from photovoltaics or nuclear energy.
Category: Classical Physics

Limitation in Ramanujan Positivity and Zeta Zeros of Riemann

Authors: Payam Danesh
Comments: 17 Pages.

Ramanujan’s divisor-sum identity gives one of the most analytical positivity arguments in the theory of the Riemann zeta-function: in Ingham’s work it yields the non-vanishing of ζ(s)on the line Rs=1. This paper revisits that mechanism and examines what is required to move it toward the critical strip. We first give a self-contained proof of the Ramanujan—Ingham zero-free line. We then prove that the direct critical-strip analogue fails for a precise Euler-factor reason: the positive Ramanujan square acquires an obstructing pole, while removing that pole destroys positivity already at prime level. This obstruction leads naturally to the Nyman—Beurling Hilbert-space formulation. Using Mellin transforms, we express the relevant closure problem through centered Ramanujan fractional-part functions and derive the exact finite-dimensional Gram system for optimal approximation. We prove fixed-window density of the associated boundary functions and separate the remaining problem into compact approximation and tail control. The main conclusion is a rigorous reduction: within this Ramanujan—Beurling framework, the remaining obstruction to the Riemann Hypothesis is an explicit uniform growing-window approximation estimate with controlled coefficient mass.
Category: Number Theory

Liniar Transformations on Multi-Vector Spaces

Authors: Constantin Scheau
Comments: 7 Pages.

A Smarandache multi-space is a union of spaces satisfying certain conditions. If the spaces beingunited are vector spaces, then we have a vector multi-space [3]. In [4] we defined the notion of a multimatrix and operations with multi-matrices, and in this paper we shall define linear mappings on a vector multi-space and study some of their properties.
Category: Algebra

Time vs. Duration: A Reinterpretation of Special Relativity

Authors: Ion Vlad
Comments: 23 Pages.

The twin paradox is often presented as a consequence of time dilation and the relativity of simultaneity, yet its standard interpretation frequently relies on simplified Minkowski diagrams and ambiguous coordinate assignments that obscure the physical meaning of the turnaround event. This paper re-examines the paradox by constructing a Lorentz-consistent spacetime diagram in which inertial and accelerated phases are treated separately and coordinate assignments are preserved consistently across reference frames. We show that a single spacetime event is invariant under Lorentz transformation; different observers may assign different coordinates to that event, but they do not describe different physical occurrences. The apparent contradiction arises not from simultaneity itself, but from conflating event identity with frame-dependent observation and from applying measurement transformations inconsistently after acceleration has ceased. This construction clarifies the operational meaning of simultaneity and demonstrates that the apparent paradox disappears once all measurements are analysed within a common comparison framework.
Category: Relativity and Cosmology

Geometric and Topological Approaches to Crystallography

Authors: Ellie Richwine, Lucian M. Ionescu
Comments: Pages.

This article explores the mathematical structures underpinning crystalline materials, bridging the gap between pure mathematics and materials science. Building upon Toshikazu Sunada’s breakthrough framework of topological crystallography and subsequent formalizations by John C. Baez, we provide a rigorous yet accessible introduction to the geometric and topological modeling of crystals. The study examines polyhedral geometry, duality, and lattice arrangements such as the Eisenstein and triangular lattices, framing them within the context of covering maps and Abel-Jacobi maps. Furthermore, we advance this foundation by introducing a simplified formulation of Graph Cohomology based on short exact sequences of graphs. This homological approach provides a unifying architectural template capable of tracking lattice defects via integer cohomology and modeling macroscopic continuous phenomena from discrete microscopic networks. The paper concludes by discussing the broader applications of these tools in molecular biology, theoretical physics, and fault-tolerant quantum engineering.
Category: Mathematical Physics

A Dynamic Model of Tidal Deformations of the Earth's Elastic Crust in the Central Force Field of the Earth-Moon System

Authors: Viktor Strohm
Comments: 8 Pages.

Traditional theories of Earth tides (such as the classical models of Clairaut, Love, and Darwin) describe geoid deformations via the differential potential of an isolated external disturbing body distributed across the volume of an elastic-plastic sphere. However, when attempting to interpret the physical meaning of forces acting on discrete crustal elements (mobile tectonic plates) within a real bound system, researchers inevitably encounter kinematic paradoxes—specifically, a theoretically unavoidable but empirically unobservable macro-displacement of the planet’s dense core toward its internal boundaries.The present work aims to describe the dynamics of the Earth’s shape variation based on generalizing the law of central forces and the kinematics of the system’s elliptical motion around the barycenter, as presented in [1]. The primary conceptual difference of the proposed approach is the transition from abstract scalar potentials to direct vector summation of actual gravitational accelerations acting on a rigid elastic shell of fixed thickness.The resolution of the apparent contradiction in the direction of individual particle force vectors during the transition from an abstract disk to the real Earth-Moon system lies within the framework of the classical three-body problem. As soon as we begin decomposing the monolithic mass of the planet M into an ensemble of discrete elements m_i, the system transforms into a hierarchical three-body configuration: two interacting bodies are located in immediate proximity (the analyzed crustal microparticle m_i and the residual mass of the planet M-m_i), while the third massive body (the Moon) is removed at a significant orbital distance.In such a formulation, the total force vector acting on each particle naturally decomposes into two components. The short-range (local) interaction binds the particle to the main mass distribution of the planet, directing its elastic retention vector strictly toward the center of the disk C (which, in a geocentric reference frame, manifests as radial compression in the lateral zones Y-Y' ). At the same time, the long-range (gravitational) field of the distant third body imparts the necessary centripetal acceleration to the entire bound system, directing the orbital force vector toward the system’s focus — the barycenter F. Thus, the formalism of force decomposition into focal and central components, proposed in [1] for the circle model O_E, receives a rigorous dynamic justification within the restricted three-body problem, linking the internal geodynamics of the lithosphere with Kepler's laws.
Category: Geophysics

From Ramanujan to Riemann Hypothesis

Authors: Payam Danesh, Raoul Bianchetti
Comments: 16 Pages.

In this work we offer a careful framework for approaching the critical-line problem associated with the Riemann zeta function. At its heart is a long-standing divide in the subject. On one side are analytic approaches, which study the completed zeta function through its reflection symmetry. On the other side are arithmetic approaches, where related criteria often appear through extreme behavior in divisor functions. The purpose of this paper is not to claim a proof of the Riemann Hypothesis, but to place these two perspectives into a clearer and more usable relationship. The argument begins with reflected analytic data for the completed zeta function. It shows that such data can be described through an odd analytic perturbation, giving a more organized way to understand the analytic side of the problem. This also resolves a common point of confusion: the full complex defect is not required to vanish on the critical line. What matters is more subtle. Under a natural real-symmetry condition, the real part of the defect vanishes on the critical line, and this is the feature that becomes useful for the bridge argument. The arithmetic side is built around Ramanujan’s logarithmic divisor profile. The paper establishes the existence and positivity of the relevant extreme scale in the range needed for the proposed connection. These analytic and arithmetic pieces are then brought together through a real bridge functional, made up of a main sign term and a correction term. The main outcome is a conditional criterion for the critical line. If the bridge functional is zero-adapted at the nontrivial zeros, if the real analytic defect satisfies the required one-sided sign condition, and if the correction term remains strictly smaller than the main term, then every nontrivial zero must lie on the critical line. The contribution of this work is therefore structural rather than conclusive. It does not present the Riemann Hypothesis as solved. Instead, it separates what is already established from what still needs to be proved. The key sign law, the domination estimate, and the zero-adaptation identity remain open requirements for any future application of the framework. Its practical value is that it gives researchers a precise checklist for testing whether a proposed analytic or arithmetic strategy can genuinely support a critical-line argument.
Category: Number Theory

Big Gravity Remains Elusive

Authors: Clark M. Thomas
Comments: 5 Pages.

Big Gravity’s (G) Newtonian constant for the local universe seems to be something that eludes astrophysicists seeking better numbersfor the claimed four forces. The latest G data have failed to confront the hermeneutical limits of what their experimental tools measure.We need better multiversal causative precision in 4D dimensions, not weak mathematical correlations. Big Gravity, and Earth’s variablesurface gravities (g), include electromagnetism, along with the properly conceived net push/shadow kinetics. Unifying harmony among all physics dimensions is needed for any elegant multiversal paradigm.
Category: Astrophysics

Motion, Mass, Space and Time: An Emergent Vector Field Framework

Authors: Mangleshwar Thakre
Comments: 41 Pages.

The primary objective of this paper is to investigate the fundamental cause underlying the motion of a massive object. In other words, it seeks to elucidate the nature of momentum and how it originates. To achieve this, a comprehensive literature review on space, time, mass, and motion is presented, offering a novel perspective on these foundational concepts. The mathematical framework is constructed using the core principles and equations of classical mechanics and the special theory of relativity, drawing some direct and substantial indirect influences from continuum mechanics. To analyze physical phenomena within a four-dimensional space-time continuum, the Hodge decomposition theorem and tensor decomposition methods are employed. This paper derives a new set of governing equations for the state of motion of a massive object, providing an entirely new interpretation of its dynamics. Ultimately, this work establishes that mass-energy and momentum are manifested forms of the periodic change of a vector field defined to characterize the system's physics. Within this research paper, the Translational Gravitomagnetic Field Tensor is derived using an entirely novel method. Furthermore, the physical mechanism responsible for giving rise to space-time is explicitly detailed, thereby reinforcing the contemporary paradigm in physics that space-time is an emergent property rather than a fundamental entity of nature. Ultimately, the research paper appears to advocate for an absolute background throughout its entire exposition.
Category: Classical Physics

A One-Way Relativistic Decay-Clock Test of Kinetic Preferred-Frame Time Dilation

Authors: Jayanta Majumder, Sambuddha Majumder
Comments: 11 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

A recently proposed kinetic route to the Lorentz transform models an elementary particle as a closed lightlike intrinsic motion whose internal cycle is reallocated, under bodily translation, between intrinsic circulation and spatial advance. The construction recovers the usual time-dilation law and the Lorentz boost as a hyperbolic state map, while allowing a physical ``special'' frame in which the intrinsic tick count and the external time parameter coincide. In such a framework, ordinary closed-path clock tests are not necessarily the most sensitive probes of the special frame, because the leading directional term proportional to $Ucdotvvec$ cancels when the transported clock returns to its starting point. This paper develops a sharper null test: a one-way lifetime anisotropy measurement using unstable relativistic particles as intrinsic clocks. If a laboratory has special-frame velocity $U$ and an unstable particle beam of speed $u=beta c$ is sent along direction $$, the strong preferred-frame reading of the kinetic model predicts, to leading order,begin{equation*} tau_{m lab}() simeq gamma_u tau_0 left(1 + betafrac{Ucdot}{c}ight),end{equation*}whereas standard special relativity predicts $tau_{m lab}=gamma_utau_0$ independent of absolute orientation. Antiparallel one-way beams would therefore exhibit a fractional lifetime asymmetrybegin{equation*} frac{tau_{+}-tau_{-}}{(tau_{+}+tau_{-})/2} simeq 2betafrac{Ucdot}{c}.end{equation*}For a candidate $|U|simSI{369}{km.s^{-1}}$, as suggested by the CMB dipole scale, the maximal signal for relativistic beams is of order $2.5times 10^{-3}$, far larger than the fourth-order residuals expected in closed transport tests. The decisive experimental signature is an antiparallel lifetime or decay-length asymmetry with sidereal modulation as the Earth rotates the beam axis relative to the putative preferred-frame vector. The proposal is framed as a falsifiable extension of the kinetic model: a null result would strongly constrain the strong preferred-frame interpretation rather than merely refine an existing relativistic clock test.
Category: Relativity and Cosmology

State Commitment Learning: Training Language Models to Distinguish Computation from Memory

Authors: Fei Ding, Yongkang Zhang, Runhao Liu, Yuhao Liao, Zijian Zeng, Huiming Yang
Comments: 9 Pages.

Reasoning language models do not distinguish tokens used for computation from tokens that constitute persistent state: once generated, all hidden thoughts remain in context and influence future predictions. As a result, downstream reasoning may depend on failed attempts, dead ends, and private scratch work that should not be safely relied on later. We recast this phenomenon as a new training objective, state commitment learning: training models to explicitly distinguish information that should be committed as persistent state from temporary computation that can be discarded. We define a counterfactual criterion, persistent-state sufficiency, which makes it trainable and measurable whether an answer remains usable after hidden thoughts are erased. We then propose Counterfactual Erasure RL (CERL), which evaluates, under the same prefix, both a path that keeps hidden thoughts and a path that erases them, and gives reward only when the erasure path remains correct. We also introduce the Erasure Dependence Protocol and show across mathematics, long-chain logic, scientific QA, and multi-turn tool-use evaluation that CERL substantially reduces answer dependence on hidden thoughts without sacrificing accuracy, consistently outperforming correctness-only RL and long-answer SFT baselines.
Category: Artificial Intelligence

Scaffold-Mediated Post-Training: Co-Evolving Model Parameters and Procedural Scaffold Graphs

Authors: Fei Ding, Yongkang Zhang, Runhao Liu, Yuhao Liao, Zijian Zeng, Huiming Yang
Comments: 9 Pages.

Post-training of large language models optimizes only parameters, while inference-time procedural scaffolds are typically designed independently of parameter training. This disconnect makes it difficult to automatically acquire and internalize complex strategies. We propose scaffold-mediated post-training: procedural scaffolds are organized into an evolvable graph structure that co-evolves with model parameters through discovery, distillation, and dynamic recompilation. We instantiate this paradigm as Skill Training. On FeatureBench, automatically discovered skills improve the passed rate by 8.1pp, and after progressive distillation the model still achieves a 27.7% passed rate without any external scaffold (distillation retention rate 85.2%, defined as post-distillation / with-skill passed rate), significantly outperforming standard SFT on the same data.
Category: Artificial Intelligence

Check Token: Real-Time Self-Verification and Precise Truncation in LLM Reasoning

Authors: Fei Ding, Yongkang Zhang, Yuhao Liao, Zijian Zeng, Huiming Yang
Comments: 9 Pages.

ECC memory embeds 8 parity bits for every 64 data bits and automatically detects and corrects errors on each read. The parity bits carry no data and only safeguard integrity, at ~12.5% overhead. Yet the reasoning chains of large language models lack such built-in self-verification: once an error occurs it propagates along the chain, and existing methods can only verify externally after generation completes. We propose the check token, establishing built-in self-verification for language model generation streams for the first time: a functional marker is added to the vocabulary, and the model triggers self-checking (analysis, localization, truncation, rewriting) by outputting it at any position. The check token carries no reasoning content (discarded after triggering) and only safeguards reasoning correctness, directly corresponding to the role of ECC parity bits, also at only ~13% overhead. Speculative forking further eliminates false-positive latency, and segmented reward makes trigger timing end-to-end learnable. Experiments (Qwen3-32B / Qwen3-Next) show that the check token achieves +10.8 pp improvement on HMMT25 at 1.13x overhead, with token efficiency 88x that of Best-of-8, and the precise truncation advantage monotonically increases with chain length.
Category: Artificial Intelligence

On the Impossibility of Unbiased and Length-Invariant Policy Optimization with Outcome Rewards

Authors: Fei Ding, Yongkang Zhang, Yuhao Liao, Zijian Zeng, Huiming Yang
Comments: 9 Pages.

Group Relative Policy Optimization (GRPO) is the dominant reinforcement learning algorithm for training reasoning capabilities in large language models, notably adopted by DeepSeek-R1. The recent improvement Dr. GRPO (COLM 2025) identifies the response-level length bias caused by per-trajectory length normalization in GRPO and proposes removing this normalization, claiming the resulting optimizer is "unbiased." We show that this claim is incomplete. Specifically, we establish an impossibility theorem: under the standard outcome reward + GRPO setting, no length-based weighting scheme can simultaneously achieve the following two properties. (P1) Gradient unbiasedness: the gradient estimator is an unbiased estimate of the true policy gradient. (P2) Length invariance: each trajectory's effective contribution to the gradient is independent of its token length. GRPO approximately satisfies P2 but violates P1; Dr. GRPO satisfies P1 but violates P2. We characterize the complete tradeoff spectrum via the parametric family f_alpha(L) = L^{alpha - 1}, where alpha = 0 recovers GRPO, alpha = 1 recovers Dr. GRPO, and provide quantitative analysis showing that Dr. GRPO's length bias can cause longer trajectories to dominate gradient updates by a factor proportional to the length ratio. Our results reveal that neither algorithm is universally "done right"; they occupy opposite ends of a fundamental and unavoidable tradeoff.
Category: Artificial Intelligence

Ramanujan-Inspired Prime Sums

Authors: Payam Danesh, Raoul Bianchetti
Comments: 15 Pages.

This paper develops a finite framework for studying sums of prime numbers through consecutive prime gaps. The motivation comes from Ramanujan’s influence on arithmetic decompositions, partition methods, and summation ideas, while the argument remains within ordinary finite number theory. We study the partial sum of the first n primes and prove an exact identity that writes this sum as a baseline term from the initial prime together with a weighted accumulation of consecutive prime gaps. Each gap receives a weight equal to the number of later primes affected by that gap. The same identity is then expressed geometrically by encoding each weighted gap as the slope of a right triangle. Exact numerical examples verify the formula, and the asymptotic discussion shows that the decomposition has the same leading scale as the classical growth predicted by the prime number theorem. This paper also separates finite identities from regularized infinite summations. This distinction is essential: the finite formula is exact, while divergent infinite prime sums require a separate summation theory and cannot be treated as ordinary convergent series.
Category: Number Theory

An Infinite Family of Solutions to the Generalized Cannonball Problem

Authors: J.W.L. Eerland
Comments: 4 Pages.

In an earlier paper I considered the generalized cannonball problem for r-regular polygons and studied integer solutions to the associatedDiophantine equation. In this note I prove that for every positive integer n, the triple[(r,a,b)=left(3n+2,,3n^2-2,,3n^3-3n+1ight)] is a solution. Hence the generalized cannonball problem admits infinitely many positive integer solutions. I also compare this parametric family with the 858 tuples listed in the appendix of the earlier paper. Among those tuples, 802 are generated by the present family and the remaining 56 tuples are listed explicitly.
Category: Number Theory

Explicit U(2) Matrices and the Emergence of Electroweak Charges

Authors: N B Cook
Comments: 3 Pages.

We make the U(2) structure completely explicit in terms of 2 × 2 matrices and show how Woit’s construction on Λ∗(C^2) reproduces the chiral electroweak charges of the first lepton and quark generations.
Category: Quantum Gravity and String Theory

Logical Foundations of Geometric Space and Natural Space-time Space

Authors: Taiwei Song
Comments: 6 Pages. 6

This short paper briefly discusses the fundamental concepts, intrinsic rules, and logical relationships of geometry from the most essential perspective, and its relationship with algebra. It also defines natural space-time space and its intrinsic logical relationships and significance. Most of the content in this paper is important achievements of the" Geometry of Space-time Structures " established by the author.
Category: Mathematical Physics

Towards a Floer Theory for Mars I Twisted Zeeman Systems

Authors: Urs Frauenfelder, Joa Weber
Comments: 57 pages, 3 figures

In this article we study periodic orbits of an electron attracted by a proton subject to Lorentz, electric, and Euler forces where each of them is allowed to depend periodically on time. This setup is motivated by the elliptic restricted three-body-problem where the Lorentz force corresponds to Coriolis force, the Coulomb force is replaced by the gravitational force, and the electric force of an external source is a combination of centrifugal forces and gravitational forces of other bodies. This is a singular version of a Euler-Hamilton system as discussed in [FW26b]. The singularity is due to collisions of the electron with the proton, respectively of two masses. Due to the possibility of collisions this problem has to be regularized.We show how periodic collisional solutions of this problem can be detected variationally in a non-local Lagrangian setup as well as in a non- local Hamiltonian setup.
Category: Mathematical Physics

False Equivalence of Accelerating Rocket and Gravity Pull on Elevator

Authors: Carl Littmann
Comments: 6 Pages.

Gravity bends a light beam more than a particle beam. We show how elevator occupants can use that fact to determine whether the forces they feel are caused by a gravitational or non-gravitational acceleration. I.e., although that capability supposedly violates the ‘Equivalence principle’ of ‘General Relativity’. Einstein imagined "the experiences of occupants in a windowless chamber, in deep, isolated space" as it was ‘accelerated upward’ by a pulling. And claimed ‘Equivalent’ (identical) feelings and test results would arise for occupants in a non-moving elevator on our gravitational earth.[1] Yet, let us imagine that a photon and an ultra-high-speed particle are launched at the same time from an internal wall of an elevator; then they go through two adjacent pin-holes, and finally hit the opposite wall. But surprisingly, they do not hit the same spot - because the gravity bends photons twice as much as a particle beam.[2] So we discuss that violation of ‘Equivalence in Relativity’ and its broad implications, in this article.
Category: Relativity and Cosmology

A Proof for the Collatz Conjecture

Authors: Jérôme Chauvet
Comments: 5 Pages.

This proof adresses the Collatz conjecture and relies on the quantitative characterization undergone by the evolving densities of even versus odd natural numbers within the limit set produced by infinite iterations of the transformation law T from any initial value taken in IN. This couple of limit densities at infinity for even and odd numbers naturally comes along with respective frequencies of occurrence for the two competing transformations of the Collatz system, from which we deduce the final cyclic attractor, hence proving the conjecture.
Category: General Mathematics

SlideTuner: PowerPoint Slide Design via XML Representation Learning and Preference Optimization

Authors: Lixiang Li, Anjan Goswami, Md Muksitul Haque, Bharat Bhargava
Comments: 7 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Generating high-quality PowerPoint slides from natural language instructions is a complex task that demands not only deep semantic understanding, but also aesthetic design. The essential component for building a functional and visually rich slide is the XML object. Therefore, it is intuitive that the most direct path to creating a high-quality slide is to generate it directly from the foundational XML structure. However, previous ``human instruction to slide generation" models typically rely on generating Python code, which serves as an intermediary to produce the final slide output rather than direct production of the XML object. As a result, these models lack the ability to precisely construct and control the building blocks required for a detailed slide composition. We introduce SlideTuner, a custom finetuned GPT-4o model specifically engineered to generate high-quality PowerPoint slides by generating the required XML files. Through extensive empirical experiments, we demonstrate that the fine-tuned GPT-4o model successfully and consistently produces visually coherent and aesthetically pleasing slides. The SlideTuner employs a two-stage training approach: first we apply SFT to the language model, enabling it to generate slide-rendering XML code directly from user instruction, utilizing XML data extracted from native PowerPoint slides. Second, we apply Direct Preference Optimization (DPO) to align the model's outputs with preferred visual styles, such as specific font choices. The slides produced by our model exhibit superior layout scores and style adherence. While this work focuses on font-level aesthetic control, our work establishes a foundation for future research aimed at precisely guiding slide generation toward diverse visual or structural preferences.
Category: Artificial Intelligence

Infinitely Many Twin Prime Reexplored - Proof

Authors: James DeCoste
Comments: 12 Pages.

Without any concrete feedback from the mathematical community, I was forced to have an enlightening discussion with Google's AI engine to determine what the likely problems were with my initial paper Infinitely Many Twin Primes — Proof (found on viXra.org: https://vixra.org/abs/2502.0186).Since I did all my own research in a sandbox without contributions from the mainstream mathematical community ( blind research ), I evidently ran into the same wall all prior mathematicians hit and that was proving that the twin primes candidates don't simply fizzle out as one approaches infinity. I was relying on combinatorics to prove this, which I now see was a mistake when taken by itself. As the AI engine and myself did a deeper dive on current mainstream research we noticed that much of the research I performed but did not include in my original paper were already explored by others. Some of these will be the key when reworking this on it's second take; the Hardy-Littlewood ratios 1:1:2 and the product rule that sees the pattern repeat at that product, to mention two. This was done blind without ever realizing it.We were able to determine that the rest of the original paper was sound even if not written in mainstream mathematical language. However that wall where the twin primes could simply fizzle out or completely dry up was impossible to ingore. While exploring some of the new approaches being implemented by Maynard and Tao, I made the realization that the probabilities angle should not have been abandoned. I had already done research to establish floor and ceiling limits as decaying log curves...but they too appear likely to fizzle out as one approaches infinity. That was until we took a look at a specific probability ratio of my window size sample growth versus the number of primes total growth. The first was a quadratic growth rate ( x^2) and the second was strictly linear ( number of primes grow at a steady rate). Using this probabilty along with the prior published paper finally plugs the hole and smashes down that wall as a mathematical improbability. The idea is that we have a fraction that is continually shrinking but can't actually get to absolute zero, the wall. The number of new elements (prime elimination patterns) is not increasing fast enough to keep up and eliminate all candidates in the exponentially increasing window size of my ranges. Candidates always escape. This clearly shows that my combinatoric approach was also correct in it's logic and that twin primes can never totally disappear.
Category: Number Theory

Quasinormal Modes of Black Holes in Finsler-modified Gravity

Authors: Holger A.W. Döring
Comments: 5 Pages.

Investigated is the ringdown phase of black holes within a modified gravitational framework that includes a weak Finsler coupling (a) , a quadratic curvature correction (b) and a dynamical timelike vector field (u^μ). Using analytical approximations and dicussing numerical simulations, there is shown, that quasinormal modes (QNM) are slightly shifted and anisotropically modulated. Residuals against standard Kerr fits are calculated, and observational constraints from LIGO, Virgo, pulsar timing, and atomic clocks are analyzed. Found is, that current gravitationalwave detectors constrain (a≾10 −3 ), while next-generation detectors (Einstein Telescope, LISA) could probe (a∼10 −12 −10 −8 ). Quadratic curvature corrections remain unobservable at thePlanck scale. The given results highlight characteristic signatures of Finsler-modified gravity in black hole ringdowns.
Category: Relativity and Cosmology

The Variable Mass Theory and Gravitational Paradoxes

Authors: Han de Bruijn
Comments: 10 Pages.

Essential reading is the first article in the series, which is about Atomic Time, Orbital Time and the Variable Mass Theory. It has been shown in this article that General Relativity (GR) can be effectively replaced by Variable Mass (VM) in a Static Euclidean Universe (SEU), which is eternal in Atomic time and has moments of creation (i.e. one or more beginnings) in Orbital time.
The cosmological redshift is intrinsic: it only depends on variable (elementary particle rest) mass. Because that is where the VM theory has been designed for.
A convenient consequence is that Newton's theory is good enough for describing gravity at a cosmic scale. It is demonstrated that the latter, when combined with the Variable Mass hypothesis, solves for Gravitational Paradoxes.
Category: Relativity and Cosmology

A Novel View of Quark Electric Charges and Baryon Composition

Authors: Wolfram Loewenstein
Comments: 3 Pages. (Note by viXra Admin: Please cite and list scientific references)

I propose that the quarks (d, s, b) carry the electric charge (-1) and the quarks (u, c, t) are electrically neutral. I further propose that baryons are composed of one quark and two anti-quarks. I believe that these assumptions help to solve some problems in the Standard Theory of elementary particles.
Category: High Energy Particle Physics

Simple Proof of Fermat’s Last Theorem for Odd Powers

Authors: Minho Baek
Comments: 29 Pages. (Note by viXra Admin: Please cite listed scientific references)

It was already proved right that x^n+y^n=z^n, (n>2) has no solutions in positive integers which we called Fermat’s Last Theorem (FLT) by Andrew Wiles. But his proof would be impossible in the 17th century. I took the idea from Euler proof and proved in case of n=odd by simple method.
Category: Number Theory

The Infinite Dynamo Cosmological Model: Unifying Non-Linear Born-Infeld Electrodynamics with Holographic Saturation Bounds and Fibonacci Informational Structures

Authors: Dan Aurelian Ivan
Comments: 6 Pages. (Note by viXra Admin: There is overlap of equations; please submit article written with AI assistance to ai.viXra.org)

We present an alternative cyclic cosmological model, termed the "Infinite Dynamo,"wherein the initial Big Bang singularity is systematically avoided via a smooth bounce governed by non-linear electrodynamics and topological informational mechanisms. We mathematically demonstrate that a global geometric contraction of the metric can optically mimic an accelerated expansion for a local observer, conditioned by the temporal evolution of anactive cosmic web optical medium. At extreme densities, magnetohydrodynamic (MHD)induction triggers exponential pair production from the vacuum via a coupled Schwingermechanism. By deploying a Born-Infeld formalism structurally modified by the GoldenRatio (), we show that the effective electromagnetic pressure becomes asymptotically negative, driving a mechanical bounce at a non-zero minimum radius (amin). This inflectionpoint is stabilized and protected by the Holographic Principle, preventing loss of unitarity and conserving the universal informational states of consciousness encoded within cosmic skyrmions. Finally, we formulate four testable empirical predictions for modern astrophysics and high-power laser facilities.
Category: Relativity and Cosmology

Arbitrary Approximation of the Shifted-LRC by the Equi-Split-LRC

Authors: Deepak Ponvel Chermakani
Comments: 2 Pages. Clarified on the new LRC variant called equi-split-LRC

Consider an instance of the shifted Lonely Runner Conjecture (shifted-LRC) where n runners (except the stationary runner 0) have integer speeds and start from real values in [0,1[ at time t=0. We show that one can derive an alternative vector of starting points that can be made to be arbitrarily close to the initial vector of starting points. The alternative starting point of each runner i is a rational in [0,1[ and is expressible as (qi / P) where P is a large prime and qi is an integer in [0, P-1]. We then introduce a new LRC variant called the equi-split-LRC. The LRC instance allows a minimal loneliness gap of f for runner 0 from the remaining n-1 runners, if and only if, the equi-split-LRC instance with the same vector of speeds and alternative vector of starting points simultaneously allows a minimal loneliness gap of f/P for the arc-center of each of P sectors into which the circle is divided from the remaining n-1 runners. Here, f is a desired fraction in ]0,1[. This finding is important in the light of recent counter-examples to the shifted-LRC.
Category: Functions and Analysis

On Complex Dynamics and Standard Model Parameters

Authors: Ervin Goldfain
Comments: 22 Pages.

The Standard Model (SM) of particle physics contains nineteen freeparameters—and up to twenty-six with massive neutrinos—whose numerical values remain unexplained by the theory itself. The present paper developsa unified framework in which these parameters emerge from Large DeviationTheory (LDT) applied to a multifractal attractor that describes the endpoint of entropy flow at the electroweak scale.
Category: High Energy Particle Physics

The Structure of Electrons and Photons

Authors: Michael Gunning
Comments: 23 Pages.

In this paper I propose a model for a physical explanation of the structure of the Aether from within which the structures of the electron and the photon emerge. The model gives a physical interpretation of Planck’s constant ħ, and explains why the electron has a total angular momentum of √3/2 ħ. It also explains the spin value of ħ for the photon as well as the origins of the photon’s alternating electric and magnetic fields. It includes explanations for what static electric and magnetic fields are and why the stress energy tensors for these fields used in General Relativity have the form that they do. It also explains the Lorentz force and the Stern Gerlach force. It proposes a physical mechanism for gravity which explains why it is so weak compared to the electric force. It also shows why acceleration and gravity are indistinguishable and proposes a physical mechanism to explain the flat rotation curves of galaxies. It also explains why the relativistic energy momentum formula has the form it does and also proposes a physical mechanism to explain the de Broglie wavelength of a particle. It concludes with a physical explanation for length contraction, time dilation and gravitational redshift as well as a novel derivation of the mass energy equivalence relationship.
Category: Quantum Physics

Testing the D.M. By Quantum Gravitation Theory by the Mass Associated to the Turnaround Radius

Authors: Manuel Abarca Hernandez
Comments: 9 Pages.

The DM by Quantum Gravitation theory (DMbQG hereafter), is a novel theory developed in the two main papers [1] and [2] Abarca, M. (2024). In the present work, in the framework of DMbQG theory it will derived the formula for the mass associated to the turnaround radius depending on the turnaround radius and it will be shown that the new expression has a deeper physical meaning regarding the same formula in the current ΛCDM paradigm. The DMbQG theory states a direct relation between the virial radius and the turnaround radius as well as the virial mass and the mass associated to the turnaround radius.The most important contribution of this work is placed in the chapter 2 where it has been demonstrated that the formula for the mass associated to the turnaround radius, using the DMbQG theory, is the same that the one in the current ΛCDM paradigm. However the new formula has a deeper physical meaning because its dimensionless factor is simpler regarding the one in the current ΛCDM paradigm. Also it is remarkable the fact that the both dimensionless factors depend on exclusively from Ωm or ΩDE and the both ones differ only a 5%. The fact that in the framework of DMbQG theory has been found a better formula for the mass associated to the turnaround radius is a strong support for the DMbQG theory whose hypothesis about the origin of DM is exclusively the gravitational field. The chapters 3, 4 and 5 are devoted to test the DMbQG theory in the clusters: Virgo, Coma and the Local Group of galaxies using recent data published about these clusters. The tests are mainly focused on the turnaround radius and its mass associated and all of them have been a complete success by the DMbQG theory. In this second version of the paper, the mass associated to the turnaround radius formula is obtained by a different way regarding the first version. In this new method is not used any formulas with the parameter "a", achieving a more understandable process to obtain the same formula.
Category: Astrophysics

Gravity as an Emergent Force Via the Uncertainty Principle

Authors: Morgan W. Weinberg
Comments: 51 Pages.

The core concept of this paper is the relation between an accelerating field and time uncertainty. This relation distills from the derivation of Newton's Law of Gravitation via the uncertainty principle. It's shown, further, that this relation can be used to derive the Coulomb Force, suggesting that it may be a general principle in nature. Taking this concept further, this paper draws a connection between expanding space and acceleration---offering an explanation for the missing-mass problem in galaxies. The paper goes on to draw a connection between the expansion of space and time uncertainty, leading to a startling conclusion: The expansion of space is not a function of the energy contained therein, but conversely, the mass of the universe is created in concert with the expansion of space. Further, because this expansion is a function of time, the mass of the universe is a function of time and increases in lockstep therewith. It's deemed that the model of the universe presented herein obviates the need for dark matter and dark energy to explain our observations of the cosmos.
Category: Astrophysics

Collatz Conjecture: A Simple Proof for a Simple Problem

Authors: Ulrich Neuenschwander
Comments: 8 Pages.

A simple proof of the Collatz conjecture is proposed. The approach relies on the fundamental properties of N and on their fruitful interplay with the Collatz transformation.
Category: Number Theory

A Geometric Explanation of Dark Matter Based on General Relativity

Authors: Hao Shen, Ruipeng Ma
Comments: 38 Pages.

Within the framework of standard general relativity[1], under the assumptions of staticity, spherical symmetry and the strong energy condition, we prove that a geometric transition zone — the "reverse-bending zone" — must appear in the periphery of any finite self-gravitating system, where the t—r sectional curvature changes sign from negative to positive. This zone is bounded by the curvature zero (r_0), the curvature peak (r_{mathrm{peak}}), and the matter boundary (R); in the interval ((r_0, R)) the sectional curvature smoothly transforms from matter-dominated spherical compression to vacuum saddle-shaped stretching. The reverse-bending zone is not a free vacuum but a forced geometry locked jointly by the interior baryonic potential well and the far-field boundary condition. Within this zone, the Misner—Sharp-type gravitational mass (M(r)) continues to grow: it grows faster than linearly in the region (r_0 to r_{mathrm{peak}}), and although the growth slows down in the region (r_{mathrm{peak}} to R), it never ceases. The resulting geometric Weyl stretching together with the self-energy of the gravitational field provide an extra centripetal acceleration, which naturally manifests itself, in the weak-field approximation, as an approximately logarithmic potential and a flattening of the rotation curves. The theoretical sectional curvature formula precisely reproduces the Friedmann acceleration equation, the Newtonian radial tidal formula (and, by integration, the Newtonian gravitational acceleration), the TOV equation, and the Schwarzschild solution, among others — not approximately, not asymptotically, but exactly in their respective limits. It yields parameteru2011free, falsifiable predictions that can be directly tested with existing rotationu2011curve and photometric data. This result demonstrates that, without introducing new particles or modifying the field equations, forced geometry within general relativity alone can generate a "darku2011matteru2011like" gravitational effect on galactic scales.
Category: Relativity and Cosmology

The Final Theory

Authors: Nigel B. Cook
Comments: Corrected contents page links to sections and also a bibliography added.

We construct a complete quantum field theory in which all observed interactions - electromagnetic, weak, strong, gravitational, and cosmological - arise from a single mechanistic principle: energy conservation in vacuum polarization. The theory replaces the ad hoc structure of the Standard Model and the geometric assumptions of general relativity with a unified framework based on the group chain for Euclidean signature SO(3, 3) ~ SU(4) ⊃ SU(3) × U(1)G ⊃ U(2) ⊃ SU(2) × U(1)Y . Matter representations, gauge charges, running couplings, particle masses, gravity, and dark energy all emerge from this structure without arbitrary parameters. This paper is a new presentation of the ideas in vixra paper 1111.0111 dated 2011, with updates, a few corrections, and further development. That earlier paper should still be consulted for further references, graphics and details documenting the origins of the various nascent ideas.
Category: Quantum Gravity and String Theory

An Infinite Family of Solutions to the Generalized Cannonball Problem

Authors: J.W.L. Eerland
Comments: 4 Pages.

In an earlier paper I considered the generalized cannonball problem for r-regular polygons and studied integer solutions to the associated Diophantine equation. In this note I prove that for every positive integer n, the triple [(r,a,b)=left(3n+2,,3n^2-2,,3n^3-3n+1ight)] is a solution. Hence the generalized cannonball problem admits infinitely many positive integer solutions. I also compare this parametric family with the 858 tuples listed in the appendix of the earlier paper. Among those tuples, 802 are generated by the present family and the remaining 56 tuples are listed explicitly.
Category: Number Theory

False Equivalence of Accelerating Rocket and Gravity Pull on Elevator

Authors: Carl Littmann
Comments: 6 Pages.

Gravity bends a light beam more than a particle beam. So, this article tells elevator occupants how to use that fact to detect whether the forces they feel are caused by a gravitational or non-gravitational acceleration. I.e., although that capability supposedly violates the ‘Equivalence principle’ of ‘General Relativity’. Einstein imagined "the experiences of occupants in a windowless chamber, in deep, isolated space" as it was ‘accelerated upward’ by a pulling. And claimed ‘Equivalent’ (identical) feelings and test results would arise for occupants in a non-moving elevator on our gravitational earth.[1] Yet, let us imagine that a photon and an ultra-high-speed particle are launched at the same time from an internal wall of an elevator; then they go through two adjacent pin-holes, and finally hit the opposite wall. But surprisingly, they do not hit the same spot - because the gravity bends photons twice as much as a particle beam.[2] But not so - for a rocket in deep outer space, experiencing a non-gravitational acceleration! So we discuss that violation of ‘Equivalence in Relativity’ and its broad implications, in this article.
Category: Number Theory

A Proof for the Collatz Conjecture

Authors: Jérôme Chauvet
Comments: 5 Pages.

This proof addresses the Collatz conjecture and relies on the quantitative characterization undergone by the evolving densities of even versus odd natural numbers within the limit set produced by infinite iterations of the transformation law T from any initial value taken in IN. This couple of limit densities at infinity for even and odd numbers naturally comes along with respective frequencies of occurrence for the two competing transformations of the Collatz system from which we deduce the final cyclic attractor, hence proving the conjecture.
Category: General Mathematics

Exact Solution to Einstein's Field Equation

Authors: Antonio Jose Mejias Marquina
Comments: 3 Pages.

In this work, Einstein's field equation will be solved by removing the framework of tensor analysis.
Category: Relativity and Cosmology

Exact Solution to Einstein's Field Equation

Authors: Antonio Jose Mejias Marquina
Comments: 3 Pages.

In this work, Einstein's field equation will be solved by removing the framework of tensor analysis.
Category: Relativity and Cosmology