All Submission Categories

Some New Collatz-like Sequences: If Odd Add d, if Even Divide by 2

Authors: Julian Beauchamp
Comments: 4 Pages. (Note by viXra Admin: Author name is required in the article; please cite and list scientific references)

In this paper, we describe what seems to be a new Collatz-like ("if odd/if even") function, and propose some related conjectures. For any arbitrary positive number, x, iterative operations can be made such that, when even, x is divided by two, and when odd, it is added to odd integer, d. It appears that when x = 1, after sufficient iterations, the sequence always reaches 1, creating a loop. The iterative function can be stated as follows: f(x) = x/2 if x is even, x+d if x is odd.
Category: Number Theory

Relative Set Theory: Definitions of Finite and Infinite Sets

Authors: Wenjie Wu
Comments: 18 Pages. In Chinese (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

In response to Russell's Paradox, which arises from the a priori assumption of actual infinity and the unrestricted comprehension principle in classical set theory, this paper proposes a novel foundational framework: Relative Set Theory. Taking the concept of potential infinity as its ontological core, this theory strictly defines finite sets from the bottom up based on the dynamic generation logic of determined elements, and abolishes the absolute universal set to eradicate the logical root of the paradox. On this basis, the paper innovatively and uniformly defines an infinite set as the "limit of a strictly increasing sequence of finite sets," pointing out that static infinity divorced from a specific evolutionary process lacks logical validity. By introducing an algebra of relative magnitudes benchmarked against the standard sequence of natural numbers, this theory establishes the "principle of relativity" for infinite metrics, revealing that the size of an infinite set is essentially equivalent to the asymptotic growth rate of its generating sequence. This framework not only resolves the counterintuitive dilemmas of classical equipotence theory at the algebraic level but also provides a rigorous and self-consistent relativistic new paradigm for fundamentally circumventing the third foundational crisis of mathematics and re-examining the concept of infinity in mathematical philosophy.
Category: Set Theory and Logic

Theory of Matrix and Graph Combination ("matregraph")

Authors: Abdoul Kader Adamou
Comments: 96 Pages. In French; Licence: CC BY-SA 4.0 (Note by viXra.org Admin: Please cite listed scientific references)

This new word "matregraph" comes from the combination of two terms already known in the field of mathematics which are: matrix and graph. A "matregraph" is precisely u200bu200ba new mathematical tool with several functions that assemble, rank and perform arithmetical calculations between real numbers (IR) in order to reach to a general result located in the structure of this "matregraph" at the place of n-line and n-column. It’s an algorithm that is able to select some values among a lot of values reducing consequently a long calculation by getting quickly a result. This new theory may be used in many fields such as physics, chemistry, computer science, telecommunications, electricity, cryptography, mechanics, transportation ...etc. Finally, "matregraph" is u200bu200ba mathematical model that is flexible and may help us solve many problems of science and engineering.
Category: General Mathematics

Mechanical, Topological, and Quantum Theory in the Universe of Natural Numbers

Authors: Abdoul Kader Adamou
Comments: 36 Pages. In French; Licence: CC BY-SA 4.0 (Note by viXra.org Admin: Please cite listed scientific references)

Natural numbers used here in mechanics, topology and quantum context is a new branch of modern mathematics whose deep abstraction and revolutionary nature make a great change in our underderstanding of mathematics field’s fundamental knowledge. This new theory applies principles from mechanics, topology and quantum field to natural numbers. It invites us to explore a new type of reasoning where we will use new calculation methods with innovative tools that are useful for mathematical research, particularly for complex open problems and likely useful for other fields of science and technology.
Category: General Mathematics

On Centrifugal Forces and Newton's Third Law of Mechanics

Authors: Antonio León Sánchez
Comments: 2 Pages.

This article presents two brief arguments regarding the reality of centrifugal forces: the first based on Newton’s Third Law of Mechanics, and the second on the Law of Dimensional Homogeneity. As a consequence, either centrifugal forces are real, or both the Law of Action and Reaction and the Law of Dimensional Homogeneity are not universal laws.
Category: Classical Physics

An Observational Study of Localized Optical Intensity Features Under Natural Environmental Conditions

Authors: Yelda Davran
Comments: 7 Pages. 4 figures (Note by viXra Admin: Author name is required in the article after the article title)

Although the particle nature of light has long been established through phenomena such as Compton scattering and double-slit experiments, there are relatively few reports of its direct observability under natural environmental conditions. In this work, we report a novel observational phenomenon suggestive of particle-like behavior of light occurring in a natural outdoor setting. The observations were conducted during the winter of 2020 in Ağrı, Türkiye, at an altitude of 1,640 m and ambient temperatures ranging between −10 °C and −20 °C. During afternoon hours, within deeply shadowed regions formed by surrounding buildings, bright, point-like micro-flashes resembling scattered water droplets were observed impinging on the ground and exhibiting multidirectional dispersion. These features were not detected in areas directly exposed to sunlight. It is suggested that the combination of extreme cold climatic conditions, reduced atmospheric pressure associated with high altitude, dark ground surfaces, and strong shadow—contrast conditions contributes to the enhanced visibility of particle-like optical effects. The observed micro-flashes are interpreted as a phenomenon in which localized light intensity features become macroscopically distinguishable under specific environmental conditions, representing a rare natural observational instance relevant to discussions of the wave—particle duality of light.
Category: Classical Physics

Volume of General Spherical Wedges

Authors: Richard J. Mathar
Comments: 26 pages, including 13 pages of a C++ listing.

A sphere cap is constructed by slicing a sphere with a plane. Slicing a sphere cap again with a second plane splits it into a pair of spherical wedges.This work evaluates spherical wedge volumes, i.e., the triple integrals over essentially the intersection of the two sphere caps established by the two cut planes. The integrals are closed forms of square roots and inverse sines as a function of sphere radius, heights of the sphere caps, and dihedral angle between the cut planes.
Category: Geometry

A Modular Structure Theorem for Goldbach Representations and a Computational Study of Shift-propagating Prime Pairs in the Arithmetic Progression N≡8 (Mod 30)

Authors: Christoper Mututu
Comments: 25 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We study a structural property of Goldbach representations which are expressions of even integers as sums of two primes within two specific arithmetic progressions modulo 30.We prove the following theorem by elementary modular arithmetic alone requiring no unproven hypothesis and no computation.Theorem. Let n≡8 (mod 30) with n≥38. Then every Goldbach pair (p,q) with p+q=n and p,q prime satisfies p≡q≡1 (mod 6). Furthermore, for any n≡28 (mod 30) within n≥28, every Goldbach pair (p,q) of n satisfies p≡q≡2 (mod 3) which forces both p+10 and q+10 to be divisible by 3 and therefore composite.As a consequence, no Goldbach pair of any n≡28 (mod 30) can produce a Goldbach pair of n+10 via the shift (p,q)↦(p+10,q+10).We then investigate the coupled pairs (n,n+20) where n≡8 (mod 30) observing that n+20≡28 (mod 30) always. For such a coupled pair, the shift (p,q)↦(p+10,q+10) maps a Goldbach pair of n to a Goldbach pair of n+20 automatically in terms of the sum since (p+10)+(q+10)=n+20 provided both p+10 and q+10 are prime.We define the shift-propagation count,R(n)=#{p≤n/2 ∶p prime,n-p prime,p+10 prime,n-p+10 prime}and present the following conjecture supported by extensive computation.Conjecture. For every even integer n≡8 (mod 30) with n≥38, we have R(n)≥1. That is, at least one Goldbach pair of n always shifts by +10 to produce a Goldbach pair of n+20.We verify this conjecture computationally for all 33,332 values of n≡8 (mod 30) in the range38≤n≤999,980 finding zero exceptions. The minimum value R(n)=1 occurs only at n=128 across this entire range and the average value of R(n) grows consistently with the scale of n from an average of 2.00 at the smallest values to an average of 197.69 across the full range to 10^6.We present the modular structure theorem with complete proof, state the conjecture precisely and provide full computational verification. We make no claim of proving Goldbach’s conjecture. We propose that this modular structure and the coupled pair phenomenon may serve as a foundation for future analytic work toward Goldbach’s conjecture.
Category: Number Theory

An Elementary Proof of the Infinitude of Twin Primes Based on Interwoven Mersenne Chains

Authors: Defeng Han
Comments: 6 Pages. In Chinese (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

This paper constructs three classes of deeply intertwined recursive sequences for Mersenne primes, encompassing all Mersenne-type core structures of the forms 2p-3, 2p-1, and 2p+3. These three classes of sequences share a common pool of prime exponents and serve as mutual recursive foundations for one another, thereby forming an organically unified recursive network. The derivations are rigorously established by relying on elementary modular arithmetic, Fermat's Little Theorem, and the $6n pm 1$ prime configuration, combined with mathematical induction and the Fundamental Theorem of Arithmetic. The terms of these sequences naturally differ by 2 from their respective "plus-two" counterparts, thereby constituting candidates for twin primes. By demonstrating the super-exponential growth property of this recursive network, the interchange of infinite quantifiers is rigorously executed within an elementary framework; this establishes the existence of a unified steady-state time and, consequently, proves the infinitude of twin primes. Simultaneously, the standard Mersenne recursive chain itself directly generates an infinite number of Mersenne primes, thereby synchronously resolving the conjecture regarding the infinitude of Mersenne primes. The entire process employs exclusively elementary number theory tools—eschewing analytic number theory and advanced sieve methods—and is logically self-consistent, free of logical gaps or leaps, and fully compliant with the axiomatic system of elementary number theory.
Category: Number Theory

Behavior of a Decimal-Parity-Based 3n+1 Mapping

Authors: J. Adnan, S. A. Dar
Comments: 9 Pages. Licensed under CC BY 4.0 (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

In this paper, we investigate and evaluate the Collatz conjecture, traditionally based on positive integers, under a suitable convergence condition in which the numbers converge towards one. In our derivations, we extend the 3n+1 problem to the decimal values via a scaling factor, for showing behaviour of the last decimal digit, either even or odd. Where the numbers diverges to infinity (∞). From which it follows that between zero and one, the sequence diverges such that its limit approaches infinity.
Category: Number Theory

From Rényi Entropy to the Feynman Path Integral

Authors: Ervin Goldfain
Comments: 17 Pages.

In this sequel to [17 - 18], we argue that Rényi Entropy is organically tied to the FeynmanPath Integral formalism of Quantum Field Theory (QFT).
Category: Quantum Physics

Dynamic Gravitational Field and Its Attributes

Authors: Pavlo Danylchenko
Comments: 19 Pages.

The correspondence of the parameter b of the Schwarzschild solution of the gravitational field equationsto the square of the relative frequency of electromagnetic interaction of micro-objects of a stationarymatter and its equivalence to the square of the maximum possible (limit) velocity of this matter on asingular surface are substantiated. The error in linking the parameter b with the coordinate velocity oflight of the General Relativity (GR) has been exposed. It has been proven that GR can correspond toreality only if it uses a dynamic gravitational field, which ensures the invariance of the flow of the propertime of matter during its inertial motion, instead of a static one. The necessity of using in physics ofrelativistically invariant Newtonians of the free inert rest energy of matter and Keplerians of the ordinaryrest energy of matter, respectively, instead of relativistically non-invariant Hamiltonians and Lagrangians,has been justified. It has been proven that the thing inherent to the Lorentz transformations is not theredshift, but the blueshift of the frequency of centripetal radiation from matter that is at rest in thepeople’s world and is evolutionarily self-contracting in the frame of references of spatial coordinate andtime comoving with the expanding Universe (CFREU). The suitability of Lorentz transformations for thepeople’s world is justified only for the quasi-equilibrium motion of micro-objects of gradually coolingmatter. Ordinary synchronization-compensation transformations of increments of spatial coordinate andtime (OSCT) are provided. They, unlike Lorentz transformations, allow proportional synchronization ofall clocks moving in a gravitational field by inertia and provide compensation (by the motion by inertia)of the concomitant change in the gravitational deceleration of the flow of time counted by these movingclocks. The redshift of the frequency of radiation from distant galaxies that are at rest in the CFREU isindeed inherent exactly to OSCT. And this is in good agreement not only with relativistically invariantthermodynamics, but also with the equations of the dynamic gravitational field of both the Solar Systemand flat galaxies. Newton’s law of gravity is obtained directly from the condition of no change in the flowof the proper time of matter during its inertial motion in a gravitational field. The fallacy of ignoring thecompensation for comoving changes in gravitational dilation of time by the inertial motion of matter ismost thoroughly substantiated. Based on the analysis of the motion of the planets, the compensation bythe centrifugal pseudo-force of inertia not only of the gravitational pseudo-force, but also of the pseudoforceof evolutionary self-contraction of the matter to the center of gravity is confirmed.
Category: Relativity and Cosmology

Hilbert’s 6th Problem New re-Interpretation

Authors: Payam Danesh, Raoul Bianchetti
Comments: 26 Pages.

The axiomatization of physics, particularly the connection between microscopic dynamics and macroscopic laws, remains a central challenge of Hilbert’s Sixth Problem. A persistent conceptual gap in this program is that probability is typically introduced as a fundamental assumption rather than derived from physical evolution itself. To close this gap, we develop Viscous Time Theory (VTT), an evolutionary framework structured around admissibility, coherence, and recoverability. When paired with an informational action principle, VTT allows probability to emerge naturally as an induced statistical measure over bundles of admissible trajectories. To test this proposed mechanism, we analyze a viscous-time kinetic transport operator, establishing its contraction semigroup structure, spectral gap, and hypocoercive convergence. We then extend the model to nonlinear interaction kernels and evaluate its hydrodynamic scaling limit. The analysis proves that this diffusion-driven operator achieves strict spectral stability, exponential entropy decay, and global nonlinear stability, with the macroscopic scaling limit rigorously yielding nonlinear diffusion dynamics for the coherence density. By providing an analytically tractable layer between microscopic and macroscopic behavior, this work demonstrates how probability, irreversibility, and transport laws can cohesively emerge from informational geometry.
Category: Mathematical Physics

Initial Velocities of Hydrated Ions Under an Electropotential Field, Their Molar Masses, and Total Hydration Numbers

Authors: Ikechukwu Iloh Udema
Comments: 17 Pages. License: CCBY-NC-ND

The inner hydration shell, where water is electrostricted, has always been the main area of study. But it appears that the bulk water, which is affected by the ion electric field, is not given the same degree of attention. This largely theoretical study aims to develop equation-based models that can be used to calculate the initial velocities of ions when an electrical potential gradient is applied, as well as the total number of water molecules pulled to the ions and their molar masses (including the mass of the electrostricted water). Theoretical and computational approaches were employed to analyze literature-based data. The initial velocity was approximately 3.8 exp. (—8) m/s for cobalt ions and 26 exp. (—8) m/s for oxonium ions. The equivalent total hydration number ranged from 4 for oxonium ions to 60 for cobalt ions. Initial velocities ranged from 1.65 exp. (—8) m/s for epinephrine to 2.88 exp. (—8) m/s for glycinate, and the corresponding total hydration number ranged from 38 for glycinate to 64 for epinephrine. The molar masses of the hydrated ions ranged from 765 g/mol for glycinate to 1,333 g/mol for epinephrine and from 85.81 g/mol for oxonium ions to 1,137.8 g/mol for cobalt ions. The trajectory and biological function of biomolecules can be impacted by their hydrated mass. The lowest and highest velocities are associated with the highest and lowest total hydration numbers per unit charge. Future research could focus on determining the electrophoretic mobilities of all physiologically active biomolecules at physiological pH and body temperature.
Category: Condensed Matter

The Vortex of Consciousness: The Physical Origin of Subjective Experience

Authors: Zhaole Sun
Comments: 8 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

How neural activity generates subjective experience—the "hard problem" of consciousness—remains unresolved [1]. This paper proposes the Consciousness Flow Vortex Model Hypothesis(CFVM-H), positing that subjective experience arises from vortex dynamics formed by closedrecursive structures in the thalamocortical loop. This vortex exhibits three core characteristics:closed-loop circulation, vortex core focusing, and global synchronization. These featuresdirectly map to three fundamental elements of subjective experience: self-boundary, firstperson perspective, and a unified field of sensation. CFVM-H provides a testable, physicsbased framework for the "hard problem" of consciousness, defining subjective experience asan inevitable product of vortex structure rather than a mysterious emergent property
Category: General Science and Philosophy

The Classical Electromagnetic Standing Wave Model of the Electron: Energy Self-Consistency and Implications for the Mass—Energy Relation

Authors: Chunshu Li
Comments: 5 Pages.

Within the framework of classical electrodynamics, a spherical electromagnetic standing-wave model is constructed. Based on Maxwell equations in vacuum, the lowest-order transverse electric (TE) mode with l=1 in spherical coordinates is adopted, and the half-wave standing-wave condition kru2091=π is imposed as the geometric constraint. Integrating the electromagnetic energy density over the whole domain yields a total field energy exactly equal to the electron rest energy, with the ratio precisely 1.000000. The model gives the fine-structure constant α=ru2091/λc=0.00729735 from geometric relations, consistent with experimental values. No free parameters are introduced; the derivation relies entirely on classical electromagnetic theory. The results show that a self-confined, localized field configuration exists in the solution space of classical electrodynamics, whose numerical characteristics match the known properties of the electron with high fidelity.
Category: Mathematical Physics

Emergent Spacetime and Protomatter from Ollivier-Ricci Flow with Discrete Cartan Torsion

Authors: Fabrizio Vassallo
Comments: 38 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We propose a discrete geometric model in which classical spacetime and matter emerge from a discrete random network equipped with two combinatorial structures: Ollivier-Ricci curvature (ORC), a metric-free notion of curvature defined via optimal transport on the network, and discrete Cartan torsion, a 2-cochain on a weighted simplicial complex measuring holonomy defects of parallel transport around elementary triangles. Both structures are intrinsically combinatorial and require no background geometry; classical geometry is an output, not an input, of the model. Building on Trugenberger's ORC-based network model, which exhibits a phase transition between a random hyperbolic phase and a geometric phase, we augment the Ricci flow with a nonlinear torsion coupling and demonstrate, in an explicit four-node toy model, that the resulting dynamical system possesses two distinct basins of attraction whose separation is topologically robust and independent of the specific toy model chosen. Regions of the network with vanishing torsion condense into a one-dimensional geometric phase (embryonic spacetime), while regions with non-vanishing torsion condense into a localized, topologically non-trivial configuration identified as a torsion defect carrying all quantum numbers equal to zero. A key structural result is that the torsion-bearing fixed point P T is a saddle point of the linearized discrete flow, with one expanding and one contracting direction in the (w, T) plane. The Jacobian entry J T w = 8λ/9 > 0 is derived exactly from the Wasserstein optimal transport, yielding real eigenvalues µ = 1 ± 8λη sech 2 (T *)/9 and a determinant det(J) = 1 − (8λη/9) sech 2 (T *) < 1. We conjecture-as a structural analogy motivated by the geometry of Einstein-Cartan theory, but not derivable from the linearized dynamics-that this fixed point is geometrically associated with the parametrization of the Cartan helix. This conjecture motivates, but does not rigorously imply, the hierarchical level model introduced in Section 7, in which the rotation angle and expansion factor of the helix are tentatively associated with spin halving and mass scaling between levels. We further propose a hierarchical particle spectrum-the level model-in which each level is characterized by doubled spacetime dimension, halved spin, and mass scaling by a factor 4α, where α is the 1 electromagnetic fine-structure constant and δ F ≈ 4.6692 is the Feigenbaum period-doubling constant. The conservative flow has a saddle-like structure at P T and cannot produce a Feigenbaum period-doubling cascade. We introduce a physically motivated dissipative extension of the torsion equation-a −ξ sin(T) restoring term-and show that the resulting effective torsion dynamics reduces, in the strongly dissipative limit, to the sine mapT → ξ sin(T) on [0, π], which belongs to the Feigenbaum universality class. The Feigenbaum constant δ F ≈ 4.6692 therefore emerges dynamically from the flow, and the empirical relation α ≈ 1/(2πδ 2 F) is found to be numerically consistent with this scaling, with the factor 2/π from the sine map amplitude. The physical origin of the dissipation is the geometric coarse-graining at each RG step: information is globally conserved, but the geometric distinguishabil-ity of sub-Planckian torsion configurations is reduced, creating equivalence classes in the sense of 't Hooft's dissipative quantum gravity program [82]. Our results and 't Hooft's program converge toward the same conceptual conclusion by independent routes: quantum-mechanical behavior can emerge from an effectively dissipative underlying structure, with information globally conserved. The continuum limit of the full construction is argued to reproduce Einstein-Cartan gravity in four dimensions. Falsifiable numerical predictions are formulated for simulation on synthetic networks.
Category: High Energy Particle Physics

Problems with Nontrivial Symmetrizations of Hamiltonian Operators

Authors: Jouni Puuronen
Comments: 11 Pages.

We discover an example of an infinite collection of simple quantum systems that all have the same classical limit, and recognize this as a problem, because the correct quantization of the example classical system is then not known. Our example contradicts Born-Jordan quantization theory, meaning that at least other one must contain a mistake. We discuss the related possible difficulties with the quantum mechanical description of a charged particle in a magnetic field, but eventually conclude that these difficulties maybe are not so severe after all.
Category: Quantum Physics

Analysis of Solution of Equations for Magnetic Field of Rotating Ball Using Polynomials

Authors: Sergey G. Fedosin
Comments: 62 Pages.

The exact form of the solution for the vector potential and magnetic field of a rotating uniformly charged ball is explicitly found. Expressions for specific vector spherical polynomials associated with the corresponding components of the potential are used to represent the solution. Inside and outside a charged ball uniformly rotating around its axis, the components of the potential and magnetic field are determined up to terms containing the sixth power of the speed of light in the denominator. To do this, it was necessary to use spherical coordinates and eight polynomials of each type. In addition, the solutions inside and outside the ball were equated to each other on the surface of the ball, taking into account the symmetry of the ball. The accuracy of the approach used can be increased, since it is determined only by the number of polynomials used, whose contribution to solutions decreases rapidly as the degree of the polynomials increases. To calculate the vector potential and magnetic field of a rotating ball within the framework of special relativity, it is sufficient to substitute the coordinates of the observation point, the invariant volumetric charge density, the angular velocity of rotation and the radius of the ball into the formulas.
Category: Classical Physics

A Simple 2 X 2 Neural Network with Linear Algebra, by Hand

Authors: Han de Bruijn
Comments: 5 Pages.

An extremely simple single-layer feedforward 2 x 2 neural network is the subject of this article. Because I feel it is important to understand some essential features of neural networks without the help of a computer. The network at hand can be completely described, mathematically, by elementary linear algebra. A working example with two inputs and one output is leading to the general case. A counter example with two outputs instead of one is presented as well. It is concluded that the network with one output has learning capability and the network with two outputs has not. The behaviour of the first network can be formulated in geometric terms: all points on a straight line through two given points in the input plane give the desired output. There are no other inputs that do the job. The network with two outputs, on the contrary, is not able to make any generalization. It does not learn from experience, so to speak. It's kind of surprising that the more intelligent network is characterized by a singular matrix, and the dumber network by a regular matrix of weights.
Category: Artificial Intelligence

Much Ado About Nothing When it Comes to Fractional Energy Levels: is Coulomb Law in Conflict?

Authors: Udema Ikechukwu Iloh
Comments: 14 Pages. License: CCBY-NC-ND

From a theoretical viewpoint, this investigation examined fractional energy levels and velocities that surpass the speed of light in a vacuum. These phenomena have received limited attention. Using a classical framework, the study aims to validate these phenomena by computing relevant parameters using fundamental constants and their multiples in derived equations. The presence of fractional energy levels and superluminal velocities (SVs) is validated within a classical framework aligned with the mass-energy equivalence principle. SVs are directly proportional to the masses of fundamental and baryonic particles when the first energy level is set to one. Conversely, if a constant luminal velocity is considered, the irrational energy levels (n_i) are proportional to the square of the particles' masses. For example, the values for the proton and the top quark are 3.022436467 exp. (+8) and 556.3297886 exp. (+8) m/s, respectively. The corresponding energy levels are 1.0164718078 and 34,436.83251, respectively. With the first atomic energy level, the energy levels are equal to the corresponding atomic numbers. For each atomic number, the fractional energy levels are inversely related to the subluminal kinetic energy. From Z=1 to Z=4, however, the energy levels showed an increasing trend. Even though the classical theoretical framework considers the distance between two centers of mass, determining the mass radius of the proton remains a possibility at specific fractional energy levels for certain atomic numbers. Future research may explore achieving the proton's mass radius at higher atomic numbers and lower fractional energy levels (below 0.1).
Category: Nuclear and Atomic Physics

SignaVision (Sign Language Interpreter)

Authors: Aashraya Man Singh, Bhuvanesh S, Tanikanti Dinesh Babu
Comments: 5 Pages.

This report presents the design and implementation of a real-time American Sign Language (ASL) recognition system using computer vision and deep learning techniques. We use MediaPipe for hand landmark detection, OpenCV for image pre-processing and a Convolution Neural Network (CNN) for gesture classification. The system provides a solution to bridge the communication gap between sign language users and non-signers by converting hand gestures into text and speech output in an accessible and affordable way.The project presents a lightweight webcam-based solution that does not require any specialized hardware like sensor gloves or depth cameras. The system uses skeletal hand landmark rendering to improve robustness and accuracy, reducing the effect of background noise and lighting changes. Experiments show that the method has high recognition accuracy and efficient real-time performance, which makes it applicable to practical applications such as educational support, assistive communication, and public service interaction. This work showcases the promise of the integration of artificial intelligence, computer vision and human-computer interaction technologies for the development of scalable and inclusive communication systems. The report also discusses system limitations and future enhancements, including dynamic gesture recognition, sentence-level translation, and deployment on mobile and embedded platforms.
Category: Digital Signal Processing

Longitudinally Polarized Same-Sign W Boson Pairs Scattering and Noncontractibility of the Physical Space

Authors: Davor Palle
Comments: 8 Pages.

The production of the longitudinally polarized same-sign W boson pairs at the LHCpp collisions presents the unique opportunity to study and verify in detail the mechanism ofthe symmetry breaking in the Standard Model and beyond.We compare at leading order the electroweak contribution to this productionin the Standard Model and in the theory of the noncontractible space containing the zero-normmassless zeta particle. It appears that the difference between differential cross sectionsis huge with the possibility to measure it in Run 3 and high-luminosity runs of the LHC.
Category: High Energy Particle Physics

On the Nature of the Superfluid Phase in Liquid He4

Authors: Alekseenko Viktor Viktorovich
Comments: 14 Pages.

A hypothesis on the physical nature of the superfluid phase in liquid helium is presented. It is shown that atomic delocalization is possible only along one coordinate, rather than along three, as is currently accepted in classical concepts of helium's transition to a superfluid state. Filamentous coherent states of atoms form the basis of the superfluid component of liquid helium. The hypothesis is supported by the justification of the critical velocity during rotation of cylindrical vessels and thermodynamic calculations.
Category: Condensed Matter

An Alternative to Light's Limiting Speed

Authors: Ken Gonder
Comments: 10 Pages, 1 Diagram

Another perplexing dilemma in special relativity has recently emerged. Under ordinary conditions, multiple objects/reference frames with different relative motion would cause an unresolvable conflict in their motion-created mass. This article elaborates on the finding, suggesting an explanation for the disparity while providing a realistic resolution.
Category: Relativity and Cosmology

The Speed Limit for a Rotating Object

Authors: Yannan Yang
Comments: 4 Pages.

This paper presents a new kinematic analysis of relativistic rotating objects within the framework of special relativity. By examining the Lorentz contraction of concentric circumferences on a spinning disk, we show that when the edge speed approaches the speed of light, the outer circumference may paradoxically become shorter than the inner one. To eliminate this geometric inconsistency, we derive a strict upper speed limit for rotating bodies: the linear velocity of any point must not exceed the speed of light divided by the square root of 2. This constraint arises purely from special relativistic kinematics, independent of material strength or mechanical properties, offering a novel resolution to the Ehrenfest paradox complementary to existing approaches.
Category: Relativity and Cosmology

On Gravitational Binding Energy Evaluation

Authors: Nicolas Poupart
Comments: 19 Pages.

We develop a hierarchical formulation for evaluating gravitational binding energy from the internal organization of matter, volume conservation, and mass--energy equivalence. Rather than relying only on pairwise interaction terms defined relative to infinity, the proposed estimator assigns an intrinsic energy scale to compact configurations of matter. We then test whether the corresponding mass-equivalent contribution can reproduce the effective dark mass inferred in galaxies.We test this formulation using SPARC rotation-curve data together with independent GALEX and SDSS photometric observations. Stellar population mixtures are reconstructed from dynamical information alone, without using photometric data as input, and are then used to predict integrated galaxy colors. The resulting colors show significant correlations with observations, indicating that the reconstructed populations encode non-trivial information about stellar structure.A systematic exploration of the estimator reveals structured regions of high-quality solutions in parameter space. In particular, the results favor a hierarchical recursive interpretation in which class-level binding energies are preserved, while the global heterogeneous aggregate may contribute with an effective virial factor. The dynamical reconstruction varies only weakly across a broad range of parameters, whereas the photometric constraints provide greater discrimination between candidate forms.These results suggest that gravitational binding energy provides a physically motivated contribution to the effective dark mass inferred in galaxies, while also explaining why dynamical information can encode stellar population structure.
Category: Astrophysics

Asymptotic Regularization of Poles and Closed-Form Generalization for Arithmetic Progressions in the Gamma Function

Authors: Julinho Jorge Luís
Comments: 25 Pages.

This paper proposes a novel analytical framework for the Gamma and Factorial functions, extending their consistent application beyond the domain of positive real numbers. Traditionally, these functions encounter singularities (poles) at non-positive integers, limiting their continuity. Through an asymptotic regularization method, this work demonstrates that the ratio of Gamma functions can yield finite and unique values at these critical points, effectively bypassing traditional meromorphic constraints.The core contribution is the derivation of a universal closed-form formula for the product of arithmetic progressions, valid across the entire real line without the need for manual domain adjustments. Furthermore, the concept of a "Rising Gamma Function" ($check{Gamma}$) is introduced as a dual operator. By establishing the zero point as an inversion axis, a functional symmetry is revealed, integrating the properties of the function into a complete and continuous structure. This approach provides new insights into analytical continuity and simplifies calculations in complex analysis and number theory.Keywords: Gamma Function, Factorial, Asymptotic Regularization, Arithmetic Progressions, Functional Symmetry, Analytical Continuity.
Category: Functions and Analysis

An Identity with Symmetry in Basic Hypergeometric Series and Its Applications

Authors: Edigles Bezerra Guedes
Comments: 4 Pages. (Note by viXra.org Admin: Please cite listed scientific references)

This paper determines a symmetry relation between basic hypergeometric series that has escaped the scrutiny of other mathematicians.As a direct application of this identity,we derive a double-sum symmetry and present a particular case as an exercise. Theseresults contribute to the understanding of hidden symmetries in ��-series. Moreover, it may be useful in the study of basic hypergeometricfunctions and ��-analogues of special functions.
Category: Number Theory

Mathematical Description of the Oscillations of the Radius Difference Modulus at Symmetrical Orbital Points

Authors: Viktor Strohm
Comments: 11 Pages.

The provided materials demonstrate an empirical study (Figs. 1-12) identifying mysterious "envelope waves" through the analysis of distance differences at symmetrical points of planetary orbits. Additionally, a rigorous kinematic apparatus [2] has been developed to derive a force law applicable not only to closed ellipses but also to precessing orbits (rosettes).Using the kinematic apparatus from work [2], we can construct a mathematical description of the observed oscillations. The key idea is that the envelope wave in the graphs is a direct consequence of orbital precession, "decomposed" through an original methodology of symmetrical differences.
Category: Astrophysics

Horizons in a 3D Alternative and Symmetric Natario Warp Drive Vector Using the Adm-MTW-Alcubierre Formalism

Authors: Fernando Loup
Comments: 96 Pages. complements the developments in viXra:2509.0064

The Natario warp drive appeared for the first time in 2001.Although the idea of the warp dive as a spacetime distortion that allows a spaceship to travel faster than lightpredated the Natario work by 7 years Natario introduced in 2001 the new concept of a propulsion vector to define or to generate a warp drive spacetime.Natario defined a warp drive vector for constant speeds in Polar Coordinates but remember that a real warp drive must accelerate or de-accelerate in order to beaccepted as a physical valid model so it must possesses variable speeds.We developed the extension for a symmetric alternative warpdrive vector that encompasses variable speeds. Also Polar Coordinates uses only two dimensions and we know that a real spaceship is a 3D object inserted inside a 3D warp bubble that must be defined in real 3D Spherical Coordinates.In this work we present the alternative warp drive vector in 3D Spherical Coordinates for variable speeds.One the major drawbacks concerningwarp drives is the problem of the Horizons (causally disconnected portions of spacetime) in which an observer in the center of the bubble cannot signal nor control the front part of the bubble. The behavior of a photon sent to the front of the warp bubble in the case of the alternative warp drive with variable velocity and a lapse function is also one of the main purposes of this work. We present the behavior of a photon sent to the front of the bubblein the alternative warp drive in the 3+1 spacetimes with the lapse function using quadratic forms and the null-like geodesicsds^2=0 of General Relativity and theADM (Arnowitt-Dresner-Misner) formalism equations with the approach of MTW(Misner-Thorne-Wheeler) and Alcubierre.
Category: Relativity and Cosmology

A Complete Proof of the Rational Distance Problem for the Unit Square

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

This paper studies the following classical geometric problem: does there exist a point inside the unit square whose distances to all four vertices are rational? We first prove that if such a point exists, its coordinates must be rational. Through a scaling transformation, the original problem is equivalently reduced to a Diophantine problem involving an integer square with integer coordinates and integer distances. Based on the parity alignment of common legs, we discuss three cases and derive contradictions using the parameterization of primitive Pythagorean triples and parity analysis. Combined with known results for boundary cases, we prove that no such point exists inside the unit square.
Category: Number Theory

The Scholz Conjecture is True for 2^n-1 for Almost All N

Authors: Theophilus Agama
Comments: 9 Pages.

An addition chain of length h that leads to a number n is a sequence of positive integers s_0 = 1, s_1 = 2,. .. , s_h = n such that s_i = s_j + s_k (i > j ≥ k) for each 1 ≤ i ≤ h. A Brauer addition chain is the one where j = i − 1 for each 1 ≤ i ≤ h. Let l(·) and l* (·) denote the minimal length of an addition chain and the Brauer addition chain, respectively, that leads to an integer ·. Applying probabilistic methods to the iterated factor method, we show that l(2^n − 1) ≤ n − 1 + l(n) for almost all positive integers n as n −→ ∞.
Category: Number Theory

An Average Loneliness Gap of 1/n Can Allow a Minimum Loneliness Gap of 1/(2n)

Authors: Deepak Ponvel Chermakani
Comments: 6 Pages. 7 Theorems and 2 Algorithms

Consider n runners R0, R1, ... Rn-1, with distinct constant integer speeds S0, S1, ... Sn-1 respectively, where S0=0, running around the circumference of a circle of unit circumferential length from arbitrary starting points at time t=0. At time t, denote gi(t) be the minimum absolute distance along the circumference of Ri from R0. We first use aresult on prime numbers to obtain special cases of runners speeds, for which the Lonely Runner Conjecture (LRC) is true. We then develop an approach to the LRC that derives a time at which, some subset of the runners is placed at the extremities of arcs of sectors ensuring implicit separation from R0, while the remaining runners are directly separated from R0. We use this approach to show that in the general case for large n, there exists a time T at which, gi(T) > 1/(2n) for all integers i in [1,n-1], and (g1(T) + g2(T) + ... + gn-1(T))/(n-1) tends to 1/n.
Category: Number Theory

The Theory of Observational Relativity Serial Report 5: Is the Big Bang a Theory in Scientific Sense?

Authors: Xiaogang Ruan
Comments: 31 Pages.

The theory of Observational Relativity (OR), as a new theory of physics, reports its significant findings and new insights in the form of serial reports in F1000Research. Now, OR Serial Report 5 focuses on the Big Bang theory of modern cosmology. Human beings always believe that the universe was bestowed by the Creator: no matter time or space must have a starting point. So, cosmologists have invented the Big Bang model: the universe that human beings rely on for survival originated from a Big Bang 13.8 billion years ago. Einstein's theory of relativity is the most important theoretical basis of modern cosmology, and the invariance of light speed and the doctrine of spacetime curvature play important roles in the Big Bang theory. The Big Bang theory is not only a product of logical deduction and mathematical formulization, but also has empirical evidences such as cosmic expansion and cosmic microwave background radiation. However, the theory of OR has discovered that the speed of light is not really invariant, and spacetime is not really curved. From the broad perspective of the general observational agent, the theory of OR has clarified that Einstein's theory of relativity, including the special and the general, is that of optical observation adopting the optical agent, which has the observational locality, presenting us with only optical images of the physical world and not representing the objectively physical world. The doctrine of Big Bang, or even the entire modern cosmology, is only a mirage based on such optical images. Since the speed of light is not really invariant, the doctrine of spacetime curvature, the doctrine of cosmic expansion, and Einstein's theory of relativity, including the special and the general, cannot hold true. Can the Big Bang theory still hold up without Einstein's theory of relativity as the theoretical basis? Can the Big Bang theory still hold up without Hubble's doctrine of cosmic expansion as the empirical basis? This article has elucidated for readers from the perspectives of both science and philosophy that the doctrine of Big Bang is not only contrary to science but also contrary to philosophy.
Category: Relativity and Cosmology

Energy-Anti-energy,Matter-AnnihilatingMatter:FoundationalConceptReconstructionandTestableExperimentalSchemes

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

Based on respect for the classical physical conclusion that matter-antimatter annihilation produces photons, this paper redefines the logical boundaries of fundamental concepts such as energy-anti-energy and matter-annihilating matter. Itstrictly distinguishes between two types of physical processes: first, the traditional mass-energy conversion process when matter and antimatter meet, which leaves behind energy and photons; second, the field-configuration-annihilation process proposed herein, which after interaction completely returns to the quantum vacuum ground state, leaving no observablephysical remnants. This paper introduces two hypothetical physical entities — matter-annihilating matter and electron-annihilating electron—and clarifies their symmetric annihilation relationship. Based on the philosophy of binaryopposition and unity, a theoretical framework of Chaos Theory is constructed, proposing three core foundational rules with mathematical expressions. On this basis, two major directions are outlined: experiments feasible with current technology and research directions verifiable with future technology. A set of falsifiable scientific predictions is also proposed. All theoretical inferences are ultimately judged by physical experiments, providing a theoretical reference forfundamental physics and new physics beyond the Standard Model.
Category: Relativity and Cosmology

The Problem of Cosmological Constant Correlation Between Observation and QFT-Measurement as a Fixpoint-Description Spectral Self-Adjustment of the Cosmological Constant from Quantum Vacuum Structure

Authors: Holger A.W. Döring
Comments: 31 Pages.

Discussed is a trying to solve the obvious contradiction in discrepance between the measuring of cosmological constant (CC) from GRT-description and its calculated prediction in classical QFT.Either then the coupling of CC to theory is wrong or the physical and mathematical methods tocalculate CC by QFT in flat Minkowskispace-background are wrong. Tried is a fixpoint-method tocome to a calculated value of CC which better fits to observation. In this context the sum-rules for1-loop/2-loop in BSM-QFT are solved, three new scalarons ("Stooges") and two new heavyfermione ("Tweedles") are introduced to couple matter-field beyond SM to CC and to look atdiscrepances between measuring and calculation in a more consistent way.
Category: Quantum Gravity and String Theory

A Short Formula to Discover the Real Evolution of the Expansion of the Universe

Authors: Dino Bruniera
Comments: 4 Pages. In English and Italian (Note by viXra Admin: Please cite and list scientific references)

A short formula to find the real travel time of photons from Type Ia supernovae and, therefore, the real epoch relative to the scale factor of the expansion of the Universe, indicated by their redshift. This, thanks to the thousands of ob-servations of Type Ia supernovae of all epochs already available, would allow us to obtain a graph showing the real evolution of the expansion of the Universe.
Category: Relativity and Cosmology

For All Hyperoperations, 2^4 = 4^2 is The Only Whole Number Pair Exception to their Anticommutativity

Authors: Anthony Veglia
Comments: 7 Pages.

All higher-order hyperoperations beyond multiplication are anticommutative, featuring a pair of distinct input values being the base and the power, such as x^y. Using real whole numbers, other than the infinite trivial examples where x = y, it has been proven that 2^4 = 4^2 is the only exception to the anticommutativity property of the hyperoperation exponentiation. This proof shows that for all higher-order hyperoperations, including tetration, pentation, and beyond, thatsingular exception, H3(2, 4) = H3(4, 2), remains the sole example of "anti"-anticommutativityusing real whole number inputs.
Category: Number Theory

Eigenvalues of Transpose of a Matrix

Authors: Sanjeev Saxena
Comments: 1 Page.

A proof without using determinants is given to show that the eigenvalues of a square matrix A are the same as those of its transpose A^T. The proof only uses the fact that the row and column ranks of a matrix are same.
Category: Algebra

Turing-Unsimulability, and Instantaneous and Sustained Cosmic-Censorship-Falsity, for Einstein-Vacuum General Relativity

Authors: Warren D. Smith
Comments: 60 Pages.

(I) We construct instantaneous counterexamples to Penrose's "cosmic censorship conjecture" (CCC) in Einstein's vacuum field equations (EVFEs) in general relativity (GR).

(II) We also construct ones that persist for a positive timespan (e.g. 1 million years). More precisely, II demonstrates either (1) the existence of a solution of EVFEs – note, no matter is involved – for a million years, throughout which there are any desired arbitrary number (including infinity as a number") of "naked" point-singularities, or(2) Einstein solutions suddenly stop existing, or(3) solutions of Einstein that ought to be well described by Newton-law dynamics, are not, or(4) "stability" of Newton law solutions does not work the way everybody thought based both on many experiments and KAM/Nekhoroshev mathematical theory.

Consequently, if Penrose's CCC is physically valid,then the reason is not Einstein gravity alone – some other physics must play a crucial role. The construction for II shows as corollaries that GR can have everywhere non-analytic metrical solutions, maximally-refuting an unfortunately-widely-believed myth; and also indicates that naked singularities arise from generic initial data – at least with some people's notions of the word "generic" (but possibly not yours).

(III) We sketch a proof of the "Turing unsimulability" of EVFEs. More precisely, either (1) the metric of spacetime time-evolves during a finite timespan (e.g. 1 year) in a manner which no Turing machine can simulate to within arbitrary user-specified accuracy bound in any finite timespan, or (cases 2, 3 basically same as in II), or (4) "chaos lifetime" in Newtonian 3-body scenarios behaves very differently than everybody had thought based on extensive experiments. It probably should be possible to get rid of case (4) via a different, chaos-avoiding, proof technique based on more-explicitly defined motions with perturbation bounds devised with computer aid – I sketch how but do not actually do this. The argument also suggests that unsimulability happens with generic initial data, at least with some people's notions of the word "generic" (but possibly not yours). All these scenarios I, II, III involve finite and bounded total mass-energy.

Crucial to I-III is the fact that the EVFEs permit storing an infinitude of information in a compact finite-volume region using finite mass-energy; and furthermore (for III) an infinitude that's dynamically relevant, i.e. changing any single bit of that information will yield an easily-observable macroscopic consequence within a fixed timespan. That mathematical fact probably is unphysical, in which case the EVFEs are not the laws of gravity in our universe, but rather only an approximation to truer (e.g. "quantum gravity") laws.

I believe case 1 is the truth in both theorems II and III; cases 2-4 were added to handle my inability to prove case 1 fully rigorously.(Theorem I, however, is fully rigorous and does not need extra cases.) Key obstacles to rigor: Humankind presently is usually unable to prove eternal existence and uniqueness of solutions to the Einstein equations; and cannot prove or disprove (for any particular N≥3) that a positive-measure set of Newton N-body solutions can exhibit "eternal chaos." And although there has been progress on problems resembling "proving stability of the solar system" for Newton N-body problems (at least in a Nekhoroshev long-time-survival sense), that progress has not yet been good enough to handle N=∞. But regardless of which cases happen, I contend theorems I, II, III signify the failure of the EVFEs as an algorithmic theory of gravitational physics. Some lessons are drawn from that, e.g. everybody trying to combine standard model with GR whilekeeping the latter nonquantum, is misguided. Also includes(a) an introduction reviewing previous works in my "computational complexity status of physics" aka "Church's thesis meets physical law X" research programme;(b) a long survey of useful facts about Newtonian N-body problems, in some respects the best currently available, and highlighting the important open question of whether a positive-measure set of "eternal chaos" N-body solutions exist.
Category: Relativity and Cosmology

Some of the Biggest Problems for the Theory of Relativity

Authors: Lars Frølund Jensen
Comments: 4 Pages.

According to experts in special relativity, it is ‘mathematically self-consistent’, and therefore it should be impossible to demonstrate any inconsistency in the theory. Supposedly, only physical experiments have the possibility of disproving it! — However, I and other researchers have demonstrated several inconsistencies in both the special and general theory of relativity, and in this paper I will show examples that are so simple and clear that experts will easily be able to understand the arguments. So — unless they can demonstrate crucial errors in my argumentation — they will be able to realize that there are serious inconsistencies in the theory of relativity!
Category: Relativity and Cosmology

Pythagorean Theorem: an Alternative Formula

Authors: Muhammad Roy Asrori
Comments: 2 Pages.

In this note we give a formula for the pythagorean theorem.
Category: Number Theory

About Possibilities of Physical Unrealizability of Cosmological and Gravitational Singularities in General Relativity and in Relativistic Gravithermodynamics

Authors: Pavlo Danylchenko
Comments: 34 Pages.

The possibility to avoid physical realizability of cosmological singularity (singularity of Big Bang of the Universe) directly in the orthodoxal general theory of relativity (GR) and in its improved version — the relativistic gravithermodynamics (RGTD) is substantiated. This can take place in the case of counting of cosmological time in frame of reference of coordinates and time (FR) not comoving with matter, in which by the Weyl hypothesis galaxies of the expanding Universe are motionless. The absence of any limitations of the value of mass of astronomical body, which self-contracts in the comoving with expanding Universe FR (CFREU), when it has hollow topological form in the space of CFEU and mirror symmetry of its intrinsic space, is shown. Because of this symmetry, both external and internal boundary surfaces of body are observed as convex. At that, in the "turned inside out" internal part of the intrinsic space (in the Fuller-Wheeler lost antiworld) unlike external part, instead of the phenomenon of expansion phenomenon of contraction of "internal universe" is observed. And there is antimatter instead of matter in this internal part of the space. Inevitability of self-organization in physical vacuum of spiral-wave structural elements, which correspond to elementary quasiparticles, and universal electromagnetic nature of all non-fictive quasiparticles are substantiated. Ultrahigh luminosity of quasars and certain types of supernovas is caused by annihilation of matter and antimatter. It is proved that only in the case of the joint application in the Universe of a physically homogeneous exponential scale of unified gravithermodynamic time and a dynamic gravitational field, which ensure the invariance in space and time of the vacuum velocity of light and the Hubble constant, is it possible to ensure not only the general covariance of all physical laws, but also the gravitational-relativistic invariance of thermodynamic parameters and potentials of matter. Although the use in the Universe of a metrically homogeneous uniform scale of the proper time of matter and of a static gravitational field ensure the eternity of the existence of the Universe and the non-exceeding of the values of the false coordinate velocities of light of the GR by the radial velocities of distant galaxies, it does not ensure both the general covariance of all physical laws and the gravitational-relativistic invariance of thermodynamic parameters and potentials of matter.
Category: Relativity and Cosmology