All Submission Categories

Innovative Research on IoT Architecture and Robotic Operating Platforms: Applications of Large Language Models and Generative AI

Authors: Huiwen Han
Comments: 6 Pages.

This paper introduces an innovative design for robotic operating platforms, underpinned by a transformative Internet of Things (IoT) architecture, seamlessly integrating cutting-edge technologies such as large language models (LLMs), generative AI, edge computing, and 5G networks. The proposed platform aims to elevate the intelligence and autonomy of IoT systems and robotics, enabling them to make real-time decisions and adapt dynamically to changing environments. Through a series of compelling case studies across industries including smart manufacturing, healthcare, and service sectors, this paper demonstrates the substantial potential of IoT-enabled robotics to optimize operational workflows, enhance productivity, and deliver innovative, scalable solutions. By emphasizing the roles of LLMs and generative AI, the research highlights how these technologies drive the evolution of intelligent robotics and IoT, shaping the future of industry-specific advancements. The findings not only showcase the transformative power of these technologies but also offer a forward-looking perspective on their broader societal and industrial implications, positioning them as catalysts for next-generation automation and technological convergence.
Category: Artificial Intelligence

The Electric Dimension, Quantum Retrocausality and Preons

Authors: Austin J. Fearnley
Comments: 12 Pages.

In consequence of the 2022 Nobel prizes for Physics for experimentalists who devised and ran loophole-free Bell experiments in 2015, a new approach to quantum ontology and a revised version of reality may be required. A revised version of reality is suggested in this paper using an extra dimension: an electric dimension based on Kaluza-Klein’s fifth dimension. Both quantum retrocausality and preons are essential to understanding the effects of the electric dimension. Also suggested is the whereabouts of antimatter in our future, given that antipreons travel backwards against the thermodynamic arrow of time: where do they come from?
Category: Quantum Physics

The Fallacy of the Atonement? Can the Doctrine of the Atonement be Supported?

Authors: Richard Michael Blaber
Comments: 16 Pages. Creative Commons License BY-NC-ND 4.0. (Note by viXra Admin: This article may not be suitable and is subject to withdraw)

This paper will argue that the Christian doctrine of the Atonement — in all its versions — is probably fallacious, and that, therefore, the idea that the death of Jesus of Nazareth, whenever it took place, relieves either all or some humans of the burden of original sin (assuming there is such a thing) and actual sins cannot be sustained. The whole basis of Christian soteriology — its theology of salvation — is, if this thesis is correct, thereby fatally undermined.
Category: Religion and Spiritualism

The Trickster and the Tao: Explaining the Perversity of Psi Phenomena via Multiscale Morphic Resonance

Authors: Ben Goertzel
Comments: 46 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This document presents a speculative but formally structured and carefully argued model for understanding why psi phenomena often exhibit a "decline effect" or even reverse (psi-missing) over repeated trials. The core idea is that psi results from a multiscale Precedence Principle (loosely a form of "morphic resonance"), which operates both locally (in individual experiments and other situations) and globally (across the entire cosmos, and/or large regions thereof). When a local psi pattern initially gains support, its low algorithmic complexity allows it to flourish. As the pattern proliferates and variants increase, its combined complexity eventually mismatches the broader cosmic resonance, causing suppression or inversion of the effect.

We show how this narrative might find a physics underpinning, via aligning it with a previously-presented theory of the physical foundations of psi, the Occamistic Precedence framework in Causal Set Theory, where each new observation is a causal-graph node whose probability is weighted by its historical frequency and algorithmic complexity.

This suggests that the neural underpinnings of psi phenomena can be modeled within a causal-set framework, where each neural "event" corresponds to adding discrete informational elements whose descriptive complexity governs their likelihood. Local neural templates that match low-complexity global patterns enjoy high insertion probability—forming shallow informational wells—while accumulating divergent variants deepen the well, suppressing or inverting further psi-like activity; analogous mechanisms could be engineered in AI via causal-set-inspired memory structures and complexity-based priors.

We also demonstrate a formal correspondence between an agent’s psi capability—its ability to exploit low-complexity psi correlations—and its universal intelligence as defined by Legg-Hutter (Solomonoff/AIXI). Under a wide class of "psi environments," both psi performance and general intelligence hinge on the agent’s capacity for low-complexity hypothesis generation and compression. We further relate Weaver’s notion of open-ended intelligence to psi capacity, showing that agents which continually seek ever simpler, unifying models naturally maintain resonance with broad cosmic patterns, thereby minimizing psi perversities. Finally, we outline empirical validation strategies spanning neuroscience (e.g. EEG/MEG complexity measures, TMS/tACS modulation) and AI prototyping (e.g. digital causal-set memories, neuromorphic implementations).
Category: General Science and Philosophy

I.q. Vs. Wisdom

Authors: Clark M. Thomas
Comments: 4 Pages.

It is a mistake to equate, or even correlate, high IQ testing and real wisdom. Many people have superior intelligence, but few individuals in today’s machine societies have profound wisdom. AI easily can generate confusing perspectives having little or nothing to do with real humanism. There are deep dangers associated with assuming all high-IQ people are ethically wise. Advanced societies are rarely ecologically more wise than the collective wisdom of traditional cultures. It is now easier to do great global harm, than to do great global good.
Category: General Science and Philosophy

Geometry and Constants in Finite Relativistic Algebra

Authors: Yosef Akhtman
Comments: 14 Pages.

We show that a single finite field, built on any odd prime p, contains the entire scope of algebraic machinery to support smooth geometry, differential calculus and continuous harmonic analysis. By arranging the field's basic arithmetic moves in a 4-dimensional ``symmetry cube'', we obtain a finite lattice that has the combinatorial shape of a 2-sphere. Completing the field via an internally defined infinitesimal extension turns this lattice into a genuinely smooth surface with constant curvature. The field itself provides finite versions of the familiar constants i, Pi and e, identified by their structural roles. Using these constants we build a Fourier kernel that works simultaneously in the finite, discrete and continuous settings, merging the conventional and the finite harmonic analysis into one algebraic framework. The resultant construct provides a common foundation for discrete mathematics, classical analysis, and physical modelling within a single, gauge-covariant finite universe.
Category: Mathematical Physics

Pi as Alternating Continued Fraction

Authors: Predrag Terzić
Comments: 2 Pages. (Note by viXra.org Admin: Please cite and list sceintific references)

We present new continued fraction representation of constant pi.
Category: Number Theory

The Theo[r]ist[?] Coefficient Shortcut Method

Authors: Marciano L. Legarde
Comments: 3 Pages. (Note by viXra Admin: Please remove strange word!)

This paper introduces and formalizes the Theoxist Coefficient Shortcut Method, an intuitive shortcut for solving a specific class of quadratic equations of the form (ax)^2 = bx. The method allows for quick identification of solutions using proportional reasoning. We outline the method, prove its validity, provide examples, and discuss its educational significance within the broader context of algebraic problem-solving strategies.
Category: Algebra

The Origin of Inertia and the Equivalence Principle

Authors: Vincenzo Nardozza
Comments: 4 Pages.

In this paper we propose a possible reason why, in Newtonian gravity, gravitational and inertial mass have the same numerical value, as stated by the Equivalence principle. Our reasoning is based on two assumptions, the second of which is an ad hoc and non falsifiable assumption. According to Popper, we are therefore doing pseudo-science. However, we believe that the result is interesting and it deserves attention.
Category: Classical Physics

A Lucas-Lehmer Type Primality Test for Numbers of the Form 4p^n-1

Authors: Predrag Terzić
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific references and submit article written with AI assistance to ai.viXra.org)

We present a new, specific primality test for numbers of the form N = 4p^n - 1, where p is an odd prime and n > 0. The test is a generalization of the Lucas-Lehmer test for Mersenne numbers and relies on a sequence defined by Dickson polynomials. We prove that, under a certain condition, N is prime if and only if the n-th term of a specific sequence is congruent to zero modulo N. This provides a deterministic primality test for this family of numbers.
Category: Number Theory

Precise Value of the Lifetime of Ortho-positronium (o-Ps) in Vacuum

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 7 Pages. 1 Figure (Note by viXra Admin: Further repetition will not be accepted)

In this paper, we calculate the lifetime of ortho-positronium (o-Ps) in vacuum with Euler formula for Basil problem and our previous formulas of the fine-structure constant and the atomic unit of time (tau). Our calculated value of the lifetime of ortho-positronium in vacuum is 142.041358500909 ns in comparison to the most accurate measured value which was 142.043(14) ns and the latest QED calculated value which was 142.04606(20) ns.
Category: Quantum Physics

On Validity in Non Standard Analysis of Riemann Dini Theorem

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

By a simple extension and application of rearrangement definition of a simply convergent series, at non standard model of analysis called "non standard rearrangement" already introduced by [1] we overcome some paradoxes that often arise with numerical series to this end we give three significant examples of "standard" and "non standard rearrangement" of the harmonic series with alternate signs. Instead notable result is that with the definition of " non standard rearrangement " introduced in [1] the commutative property of addition continues to hold even for simply convergent series (such as harmonic series with alternate) contrary to what is stated by Riemann-Dini theorem or Riemann rearrangement theorem.
Category: General Mathematics

Origin of Black Hole Jets Discovered in GR Extensions, the End of Singularities, and a Solution to the Information Paradox

Authors: Gene A. Harvey
Comments: 8 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org or it will be rejected!)

This work presents the discovery of relativistic jet formation that preserves information - arising from a rotating, gravitationally-saturated core, as initially predicted by the Lambda Condensed Gravity Field (ΛCGF) model, eliminating the need for classical singularities. Contrary to the standard black hole model - which attributes jet production primarily to magnetic field interactions within the accretion disc - the CGF framework identifies the core itself as the origin, where gravitational energy compresses infalling matter into a virtual particle state through the know process of spaghettification. As angular momentum accumulates and field saturation is reached, excess gravitational energy escapes via the polar axes, giving rise to highly collimated, rotating jets that have already been observed in galaxies - including our own Milky Way.Key mechanisms involved in this process include:(a) Gravitational confinement within a polar "throat" shaped by anisotropic field pressure,(b) Angular momentum conservation, which imparts helical motion to the outflow, and(c) The spacetime stiffness modulus, acting as a natural waveguide at and beyond the event horizon.This model predicts a layered collimation structure wherein the jet is not merely expelled, but sculpted by the combined effects of gravity, rotation, and field compression. It offers a coherent resolution to jet alignment, stability, and energy budget discrepancies, and invites observational verification through comparative jet morphology and gravitational wave signatures.This paper eliminates the need for singularities in black hole theory by modeling the core as a gravitationally-saturated, rotating structure composed of virtual particle states, electromagnetic fields, and condensed gravitational energy. Using five governing equations, we demonstrate that relativistic jets originate not from accretion disc turbulence but as structured outflows from within the core itself. This framework resolves the black hole information paradox, reestablishes deterministic field behavior, and offers a fully GR-compliant interior model that replaces mathematical breakdown with coherence and predictive structure.
Category: Relativity and Cosmology

Commercialization of Science

Authors: Taha Sochi
Comments: 42 Pages. English and Arabic

In recent decades, science - particularly in Western countries - has been trending toward privatization and commercialization, viewed as a commercial commodity whose primary - or even sole - objective is material gain. Terms such as the "commercialization and monetization of science" are common these days, and some universities and scientific institutions are even urging this trend, with seminars, training courses, and conferences organized to this effect. Although we recognize the benefits of establishing a relationship between science, its institutions and centers, and the world of finance, business, commerce and industry - for example, by bringing investments into the field of advanced scientific research - we believe that the harms of this trend on science and scientists - and indeed humanity in general - are more than its benefits. Turning science into a commodity contributes to the moral, ethical and epistemological degradation of science and its role in human life, and encourages the spread of corruption and illegal practices within academic and research entities such as universities, research centers, specialized scientific journals and the like. In this article, we will briefly review this trend and assess its negative effects and repercussions on the progress of science and knowledge and their role in human life and the evolution of human civilization and its future.
Category: General Science and Philosophy

Investigation of a Primality Criterion Within an Arithmetic Progression

Authors: Mar Detic
Comments: 4 Pages. (Note by viXra Admin: Please cite listed scientific references and submit article written with AI assistance to ai.viXra.org)

This document introduces and investigates a criterion for defining "primality" within the sequence of odd integers Ak = 2k + 1. The criterion is based on the greatest common divisor (GCD) between a term Ak and the preceding partial sums Sj = j2 + 2j of the same sequence. We formally define the sequence, its partial sums, and the proposed primalitycriterion. A proof is provided demonstrating that all standard prime numbers within the sequence are classified as "prime" by this new definition. Furthermore, computational observations suggest that all composite numbers in the sequence are classified as "not prime," including Carmichael numbers, which are known for their pseudoprime properties. This leadsto a conjecture that the proposed criterion is equivalent to the standard definition of primality for terms in this specific arithmetic progression.
Category: Number Theory

Quantum Oscillator Lattice: a Unified Origin of Fundamental Constants and Fields

Authors: Juan Moreno Borrallo
Comments: 39 Pages.

This paper presents the foundational premises for a unified physical theory in which the vacuum is modeled as an elastic lattice of coupled quantum harmonic oscillators. Rather than aiming to construct a complete unified theory, our goal is to explore the consequences of a set of physically motivated assumptions and to demonstrate their consistency with established theoretical principles and dimensional relations. Within this framework, gravitational, electromagnetic, and thermo-entropic interactions are interpreted as distinct geometric deformation modes of a single symmetric field tensor, and fundamental constants of nature emerge naturally from the oscillatory dynamics. We show that these assumptions lead to coherent interpretations of field sources (mass, charge, temperature) sharing a common oscillatory origin in spacetime. While non-exhaustive, our treatment lays a physically and mathematically grounded path for future development of a unified field theory anchored in quantum-elastic principles.
Category: Relativity and Cosmology

The Flow of Spacetime is Supporting the Orbital Speeds of Galactic Stars

Authors: Kurt L. Becker, Kurt J. Becker
Comments: 20 Pages.

This paper is proposing an alternate hypothesis to gravity due to dark matter. The new quantum properties proposed are: Spacetime is being created in the vast voids of the universe. Spacetime is absorbed within stars in galaxies. The result is spacetime flowing into galaxies. The mechanics of the proposed flow gravity is discussed in great detail with diagrams and mathematics. The inflowing spacetime offsets the tangential inertia of a star resulting in ab orbital motion of that star. The predictions of flow gravity are compared to observations at various cosmological scales: at galactic, at solar system, at the Moon's orbit, and at spacetime flowing towards a neutron star. Flow gravity will not change the mathematical results of Newtonian gravity in the solar system, but it will explain the actual mechanism of gravity.
Category: Quantum Gravity and String Theory

A Topological Atomic Model for Masses and Constants

Authors: Alfonso De Miguel bueno
Comments: 12 Pages.

This work presents an interacting-field model in which every nucleon is the dual-lobed intersection of two curved base fields.A single dimensionless number, the internal velocity ratio r=c'/c=0.931, fixed once by matching the proton-Higgs resonance, propagates through the geometry and reproduces with no further adjustment an extensive set of observables.From the same r we obtain:(i) the proton rest mass, magnetic moment and charge radius;(ii) the neutron and electron masses;(iii) a fourth-order phase-lag suppression that yields m_nu approx 0.42 eV;(iv) the fine-structure constant alpha=(1-r)/(3pi) via a 3pi holonomy;(v) Planck's constant from the action enclosed in one closed curvature loop;(vi) the top-/bottom-sector harmonic ladder that echoes the observed d/u flavour hierarchy.
Category: Nuclear and Atomic Physics

From Clock Synchronization to Electromagnetism: A Realist Construction of U(1) Gauge Theory

Authors: Satoshi Hanamura
Comments: 9 Pages.

Gauge symmetry plays a central role in modern field theory, yet its physical origin remains conceptually unclear. In this work, we propose a realist reinterpretation of U(1) gauge symmetry based on the internal phase dynamics of the electron. According to the 0-Sphere model, the electron possesses a deterministic internal oscillation between two thermal energy kernels. This internal structure generates a periodic phase evolution, which naturally leads to the emergence of a geometric U(1) gauge connection. The model predicts a specific internal oscillation velocity, approximately 4 percent of the speed of light, derived from relativistic dynamics. Gauge potentials are reinterpreted not as formal artifacts, but as synchronization mechanisms for the internal clocks of phase-bearing particles. This framework unifies gauge interaction and spin structure through a common time-based geometry, offering a particle-centric alternative to conventional field-based gauge theory.
Category: Quantum Physics

A Structural Proof of the Evenness of All Perfect Numbers and the Exclusion of Odd Ones

Authors: YoungHwan Yun
Comments: 7 Pages.

We introduce a structural decomposition framework for perfect numbers, based on additive and multiplicative symmetries among their proper divisors. Under this model, we derive a system of proportional identities that all known even perfect numbers satisfy. By analyzing the integer conditions required for recursive consistency in the divisor sequences, we prove that such a structure necessarily implies the presence of the even divisor 2, thereby excluding the possibility of an odd perfect number conforming to this model. Although primarily developed for perfect numbers, the additive portion of the framework may also encompass semiperfect numbers, which share similar but relaxed divisor-sum properties. Our results support the long-standing conjecture that no odd perfect numbers exist and suggest a broader structure for divisor-based classification of integers.
Category: Number Theory

Symmetry-Based Proof of the Generalized Riemann Hypothesis

Authors: Younghwan Yun
Comments: 14 Pages.

This paper presents a symmetry-based approach to the Generalized Riemann Hypothesis, focusing on the structure of nontrivial zeros of the completed Dirichlet L-function. By examining the relationship between the functional equation and complex conjugation, the argument shows that each nontrivial zero implies the existence of a symmetrically paired zero. This pairing, when interpreted through a restricted application of the Schwarz Reflection Principle at the zero points, leads to the conclusion that all nontrivial zeros must lie on the critical line. The analysis is further extended to generalized cases, including product forms, which consistently reduce to the same critical line condition. This work therefore proposes a comprehensive and logically consistent framework that supports the truth of the Generalized Riemann Hypothesis.
Category: Number Theory

The Explicit abc Conjecture of Alan Baker's Implies c Smaller Than R^2 True

Authors: Abdelmajid Ben Hadj Salem
Comments: 5 Pages. (Note by viXra Admin: Further repetition will not be accepted!)

In this paper, we assume that the explicit abc conjecture of Alan Baker (2004) is true, we give the proof that c smaller than R² is true, it is one of the keys to resolve the mystery of the abc conjecture. Some numerical examples are given.
Category: Number Theory

Order and Contingency: The Duhem Thesis on Origin of Physics in Christian Theology

Authors: Krystian Zawistowski
Comments: 128 Pages.

The most important aspect of modern physics is the study of the unchanging order between measured quantities, such as that described by Newton’s law of gravity or Ampere’s law. This aspect makes physics useful, as the lawsof physics are applied to develop a variety of technical devices and machines, being a crucial foundation of technical civilization. Additionally, this aspect reveals certain truthsabout the world, as accurate predictions calculated from these laws testify to their validity. Furthermore, when new experiments force a physical law to be modified, the description of relations between quantities is almost never refuted and becomes a special case of the new, more general theory, showing an incremental progress of knowledge. How has this most critical part of physics originated? The source of it is theology, which produced core methodological principles that underpin this approach: The world is comprehensible and ordered according to universal, unchanging relations between measured quantities. The world is contingent, and any metaphysical possibility we conceive is possible, if only in agreement with experience. The highest goal of the rational mind is the pursuit and contemplation of truth. These principles were essential to the development of modern physics. The success of this project provides evidence in favor of Christian Revelation, by means of heuristic power - prediction of essential knowledge that could not be obtained in any other way.
Category: General Science and Philosophy

Blackbody Radiation as The Entropic Exhaust of Recursive Photonic Structures

Authors: Matthew Stanley Leibel
Comments: 9 Pages.

All known physical structure can be reinterpreted as recursive light folded through a two-dimensional holographic surface — a boundary that acts simultaneously as observer and as spacetime itself. In this framework, mass is not a static property but rather a stable, recursively encoded configuration of photonicenergy. The phenomenon of blackbody radiation, long regarded as thermal emission, is herein redefined as the entropic exhaust of this recursive photonic structure — the unspooling of phase-locked light into incoherent, unbound modes. Crucially, the observer does not sit outside this process but is intrinsic to it: the observer is the boundary surface, a light-reflective constraint that dynamically defines what can exist and how structure is encoded. The transformation of mass into radiation — and its numerical reversibility — is governed by aE = m c2 compression identity: ,which, when observer-corrected, reveals light’s unique role as the substrate and bandwidth of spacetime.Empirical technologies such as photovoltaicsolar cells offer functional proof of this reversibility. By converting entropy-rich blackbody radiation (sunlight) into coherent electrical potential, they act as recursive encoders — transforming chaotic photonicinput into structured energetic form. This is not merely energy conversion but structural reassembly. The observer boundary — in this case engineered — reflects selective frequencies and initiates recursive energy flow, much like the natural spacetime surface that encodes mass.Quantitative support is provided through deriveddecay-time equations, reverse derivation of c from photon mass-loss observations, and the match between theoretical structuring time and empirical solar panel performance. These alignments provide numerical confirmation that mass, radiation, energy, and the observer are part of a single recursive system governedby photonic bandwidth and bounded reflection.
Category: Thermodynamics and Energy

Four-Component Tuples Splitting

Authors: Yuly Shipilevsky
Comments: 2 Pages.

We consider a problem of splitting of the four- component tuples of integer numbers into two two-component tuples, providing a minimum of the difference of sums of the corresponding their components. We conjecturing with the corresponding algorithm for its solution. The corresponding examples are given.
Category: Combinatorics and Graph Theory

Turkish-English Dictionary and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 25 Pages.

We study A Turkish-English Dictionary by H. C. Hony. We draw the natural logarithm of the number of head root words, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We find that the head root words underlie a magnetisation curve. The magnetisation curve i.e. the graph of the reduced magnetisation vs the reduced temperature is the exact Onsager solution of the two dimensional Ising model in the the absence of external magnetic field.
Category: Linguistics

The Interaction of Photons with the Graviton Background and Cosmological Observations

Authors: Michael A. Ivanov
Comments: 21 Pages.

In the author’s model of low-energy quantum gravity, the gravitational interaction of bodies arises as the effect of screening in a sea of superstrongly interacting gravitons. Newton's constant can be calculated as a statistical parameter of the repeated interaction of bodies with gravitons. Small vacuum effects in the model, caused by a new type of interaction -photon-graviton - may have major implications for cosmology. The ones are reviewed here and compared with cosmological observations; this is a self-review of author's works in this approach. The constancy of the ratio $H(z)/(1+z)$ in this model is consistent with observations of the Hubble parameter $H(z)$.Cosmological redshift is a local quantum effect caused by head-on collisions of photons with gravitons, while the additional dimmingof distant objects and diffuse cosmic optical background supposedly detected by the New Horizons mission are due to non-head-on collisions. For very soft radiation, the additional relaxation factor is calculated. Since this factor must have different values for soft and hard radiation, the distance modulusin this model must be a multi-valued function of the redshift. The Hubble tension is discussed in this context. The considered quantum effects are beyond the scope of the standard cosmologicalmodel. These small effects can describe cosmological observations in a very elegant and unified manner without dark energy andcosmological expansion. Graviton-graviton interactions can lead to the formation of virtual gravitons with very low mass, which maybe candidates for the role of dark matter particles.
Category: Quantum Gravity and String Theory

Magnetic Neutron

Authors: Ferrara Francesco
Comments: 8 Pages. In Italian

This paper proposes a classical electromagnetic model of the neutron based on two oppositely charged, massless particles rotating at the speed of light along concentric circular paths. The model derives the neutron’s rest mass and magnetic moment from purely electromagnetic considerations, using vector potential and natural units. The total angular momentum calculated is approximately four times the observed spin (ħ/2), which is interpreted as the projection of a larger classical angular momentum vector onto the axis of an external magnetic field. The model suggests a geometrically stable configuration and offers new insights into the neutron’s internal structure, compatible with key quantum phenomena.
Category: Nuclear and Atomic Physics

The Optimized Ellipse Perimeter Formula: The Elliptic Bounds Theorem

Authors: Nolan Aljaddou
Comments: 9 Pages.

This work discovers a unique, accurate, elementary formula for calculating the total perimeter of an ellipse demonstrably and heuristically consistently under the 1% maximum error range for all values and eccentricities, which surpasses Ramanujan’s previous dominant formulas in terms of accuracy and simplicity. The formula also uniquely provides the definitive range of calculable deviation from any exact value, making it the optimal general approximation method. Several examples are provided which confirm the formula’s precision. The theorem also provides a corollary which derives a definitive metric bound on all parametric elliptic geometry, with application to all of physics and astronomy.
Category: Geometry

Loop Quantum Kaluza—Klein Gravity as the Standard Model

Authors: Nolan Aljaddou
Comments: 7 Pages.

Physics is unified, and sufficient; reaching this determination is a matter of premise as much as conclusions, as this work demonstrates with the optimal Kaluza—Klein model (confirming the three particle families as technical Kaluza—Klein excitations within the energy limit).
Category: Quantum Gravity and String Theory

The Foundation of Mathematics—Occam's Principle

Authors: Nolan Aljaddou
Comments: 6 Pages.

This work examines the full implications of Occam’s razor ["do not multiply causes unnecessarily"] when applied to metric existence criteria, resulting in a scientific precept and metric existence theorem of the universe—which takes the general form all natural laws must obey.
Category: Set Theory and Logic

Preliminary Evidence of Traces of Alien Genetic Manipulation in Humans

Authors: Max Myakishev-Rempel
Comments: 10 Pages.

I analyzed DNA from 581 complete families in the 1000 Genomes Project to search for nonparental genetic contributions that could indicate recent alien genetic manipulation. My screening of variants in 77 Mb on Chromosome 3 identified 11 families (2%) containing large fragments of DNA sequence in children that matched neither human parent. The most significant case displayed a cluster of 348 nonparental genetic variants with precise simultaneous substitution of identical fragments on both chromosomes. There is no known biological mechanism or technical error that could produce such a change. Achieving such a genetic manipulation at the time of conception with current methods is possible but difficult using CRISPR technology, which emerged in 2013. Since the studied children were born before 1990, human genetic manipulation cannot be an explanation of the observed 16 Kb substitution in homologous chromosomes. This is strong evidence for extraterrestrial genetic manipulation. Further, two unrelated families showed major nonparental insertions at the same genomic hotspot on chromosome 3, suggesting this region serves as a preferred integration site. Quality control analysis confirmed these represent genuine biological signals through low background variation in normal (98%) of studied families, contrasted with sharp nonparental variant density peaks, achieving statistical significance of p < 10^-13. Families identified as having nonparental insertions displayed a clustered density of nonparental variants 50 times stronger than normal families. The non-random chromosomal clustering and technical precision required for these insertions provide solid evidence for extraterrestrial genetic modification with technology that went beyond human capabilities at the time of conception. Additionally, my pilot analysis of two families with self-reported self-suspecting alien abduction experiences using inexpensive, generic commercial 23andMe genotyping detected similar nonparental contributions, supporting this approach for self-suspecting alien abductee volunteers to identify traces of genetic manipulations as an affordable "do-it-yourself" method. Future research should test the biological significance of alien genetic modifications and see what functions were altered in people.
Category: Quantitative Biology

Embracing Solidarity as a Way of Life

Authors: Gennady Shkliarevsky
Comments: 49 Pages.

The mystique of solidarity retains its allure. The power of solidarity defies imagination. Yet harnessing this power has proven to be a challenge. There is much about solidarity to be learned. This study seeks a deeper understanding of solidarity that is necessary to find a way of using the enormous creative potential of solidarity more effectively for human progress and liberation. The article shows that the dominant theory and practice of solidarity are incapable to realize this objective. The article argues that attraction to differences is the main source of solidarity’s power. Affirmation and empowerment of differences is the key to creating strong and enduring social bonds that can sustain solidarity. Yet the dominant conception of solidarity requires subjugation of differences to the central point of identification and their suppression. The article proposes a new approach toward solidarity. The distinct feature of this approach is its view of differences. In contrast to the traditional view that sees differences primarily as opposed to each other, the article outlines a new conception of solidarity that views differences as the most important resource for human advancement and liberation. The article examines the theoretical and practical implications of the new conception.
Category: Social Science

Study the Infrared Spectra of XLi2O.ySiO2.zCaO(1—x—y—z)B2O3 Glasses

Authors: Rafiqul Islam, Mubdiul Hasan, Emran Hossain, Rafiqul Ahsan, M. Golam Mortuza
Comments: 23 Pages.

The xLi2O.ySiO2.zCaO (1-x-y-z)B2O3 glass system (where x = 0, 5, 10, 15, 20 and 25 mol%, y=60 mol% and z=10 mol%) was processed through a dissolved quench technique. To acquire the structural performance of silica, calcium, boron and oxygen were minutely observed by using Fourier transform infrared spectroscopy (FTIR) and X-ray diffraction. The position and relative quantities of IR bands responsible for the distinct silicate and borate units were determined using deconvoluted spectra. For the increased amount of B2O3 the results show that BO3 occupies the network position and creates the linkage SiO-Ca. The bands related to the bending mode of H2O molecules and the stretching mode of B—O—H groups forming hydrogen bonding are shown to result in several bands: 23002380cm-1 and 2820-3505 cm-1 respectively. The XRD order of the base samples exhibited homogeneous glasses and also an optical reconnoitre, but did not show any phase separation record.
Category: Condensed Matter

N-Point Discrete Fourier Transform in O(n Log_2n) Time Complexity for Any N Larger Than 0

Authors: Saulo Queiroz
Comments: 3 Pages.

We present a novel recursive algorithm for computing the $N$-point Discrete Fourier Transform (DFT) with $O(N log_2 N)$ time complexity, applicable for any integer $N > 0$. Unlike conventional Fast Fourier Transform (FFT) algorithms that often require zero-padding to the nearest power of two, our method operates directly on arbitrary-length input sequences, eliminating the need for zero-padding. At each recusive stage, the algorithm relies on a novel decomposition structure that performs $2(N-1)$ complex additions and $N$ complex ultiplications for typical cases, yielding a total complexity of $T(N)=2T(N/2)+10N-4=10Nlog_2N-4N+K$ real floating point operations (where $K$ is a constant). Although the resulting constants are higher than in classic FFT algorithms -- like radix-2 FFT, that performs $5Nlog_2N$ real floating point operations -- our algorithm does not need zero-padding, which end up by increasing the true complexity of existing FFTs due to the enlarged signal length.
Category: Digital Signal Processing

Special Relativity: Types of Energy

Authors: Alejandro A. Torassa
Comments: 6 Pages.

[T]his paper presents the definitions of kinetic energy, rest energy and relativistic energy for a single particle (massive or non-massive ) [In special relativity]. Additionally, this paper also presents the definitions of generalized relativistic energy and total energy for a system of particles (massive and non-massive).
Category: Relativity and Cosmology

Vertex-Edge-Combinatorial Polytopes: A Class Defined by the Local Structure at Each Vertex

Authors: Miquel Piñol
Comments: 4 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We introduce a class of geometric bodies, which we call vertex-edge-combinatorial polytopes, defined by a local structure in which each vertex is connected to a number of edges equal to the dimension of the body, and where any subset of those edges belongs to a face whose dimension equals the subset’s cardinality. These polytopes satisfy an empirical formula for the number of vertices, from which a general combinatorial expression for the number of faces can be deduced. The class includes simplices, hypercubes, and the dodecahedron, and excludes the octahedron, the icosahedron, and any higher-dimensional polytopes derived from them. In some cases where the formula diverges, such as the hexagonal tiling, an infinite regular structure does exist, although this is not always the case.
Category: Geometry

Newer *space Flow Models that Did not Get Into the Book

Authors: Natan A. Cerqueira
Comments: 36 Pages.

A longer and better presentation of *Space Flow is made, containing some new models that are the work's most significant to date and that cannot be found in the book.
Category: Relativity and Cosmology

A Concise Dictionary of Slang and Unconventional English and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 22 Pages.

We study the head entries of A Concise Dictionary of Slang and Unconventional English.We draw the natural logarithm of the number of head entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We conclude that the Dictionary can be characterised by BP(4, $beta H=0.02$), i.e. the magnetisation curve in the the Bethe-Peierls approximation of the Ising model, in the presence of four nearest neighbours and little external magnetic field, H, with $beta H= 0.02$. $beta$ is $frac{1}{k_{B}T}$ where, T is temperature and $k_{B}$ is the tiny Boltzmann constant.
Category: Social Science

Approaching Legendre’s Conjecture Within a Limited Boundary

Authors: Junho Eom
Comments: 14 Pages.

This paper identified the characteristics of prime numbers within a limited boundary, defined primes between quadratic intervals, and generalized Legendre’s conjecture. Regarding the boundary, every integer less than m was defined as the 1st boundary and it expanded to the mth boundary within m^2. Thus, each boundary contained m elements. Except for 1, every integer produced a sine wave from the 1st boundary; as a result, only prime waves affected the remaining boundaries from the 2nd to mth by generating the composites and new primes (Series I). Therefore, the number of new primes in each boundary could not exceed ��(1st boundary) or ��(m), where ��(x) was the number of primes less than or equal to x, and it enabled the estimation of the total number of primes within m^2 (Series II). Based on Series I and II, the quadratic intervals between ��(m^2) and ��((m + 1)^2) were identical to the sum of the last two boundaries, expressed as 2·βm+1·��(m), where βm+1 was the ratio of ��((m + 1)^2) to ��(m + 1)·(m + 1) (Series III). This led to the conclusion that Legendre’s conjecture satisfied while 0.8986·��(P) < 2·βP·��(P) < ��(P) (prime P > 113), or 2·βm+1·��(m) ≤ 2·��(m) (integer m ≥ 2).
Category: Number Theory

Astrophysical Evidence for Cantor Dust: An Introduction

Authors: Ervin Goldfain
Comments: 10 Pages.

The Cantor Dust (CD) interpretation of Dark Matter (DM) arises from the non-differentiable and nonlocal fluctuations of spacetime in the high energy limit of field theory and primordial cosmology. Mirroring the fragmented and ever-changing configuration of multifractal structures, CD offers a novel explanation for the distribution and behavior of Dark Matter and bridges concepts from complex dynamics, fractal geometry, and statistical physics to cosmology. Here we argue that CD offers a unified Dark Matter model with predictions confirmed by a wealth of astrophysical observations.
Category: Relativity and Cosmology

Allowable Structures of Leptons

Authors: Vladimir Pastushenko
Comments: 13 Pages. (Note by viXra Admin: Further repetition will not be accepted)

There is no space without matter and there is no matter outside space. Space-matter is the same. Therefore, the mathematical truths of space correspond to the physical properties of matter. The main property of matter is movement; therefore space-matter is dynamic. Such dynamic space-matter has its geometric facts, as axioms that do not require proof. The limiting and special case of the axioms of dynamic space-matter is the Euclidean axiomatics and number system. And already in the real dynamic space-matter, the models of nucleons of the atomic nucleus are considered and the admissible structures of leptons are presented.
Category: Quantum Gravity and String Theory

Quantifying Geothermal Energy Potential: Embracing Uncertainty for Robust National Renewable Estimates

Authors: Victor Christianto, Florentin Smarandache
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Geothermal energy, a stable and baseload renewable resource, holds significant promise for decarbonizing global energy systems. However, accurately quantifying its potential remains a challenge due to inherent geological uncertainties. Traditional one-value estimates often fail to capture the full spectrum of possibilities, leading to potentially misleading national renewable energy projections. This article explores the importance of incorporanting uncertainty modelling into geothermal resource assessment and proposes a methodology for expressing national potential as a range, especially based on Neutrosophic Logic/Probability theory introduced by one of us (FS).
Category: Geophysics

Action and Reaction of a Gravitational Field

Authors: Ichiro Nakayama
Comments: 4 Pages. (Note by viXra.org Admin: Please cite and list scientific references)

When we look at the action of gravity at the elementary particle level of Energy Body Theory, we can see that elementary particles and gravitational fields act and react, forming distortions in the foot of elementary particles and generating kinetic energy, which is a wave in space. This is the cause of gravitational mass and is the same cause as inertial mass. The gravitational field forms a spherical layer with a Planck scale thickness in which the amount of energy decreases as it approaches the star. For this reason, the action and reaction between the gravitational field and elementary particles occurs continuously toward the center of the star. For this reason, the increase in distortion in the foot of elementary particles and the increase in kinetic energy are continuously generated and added up. This is explained using a model airplane and a photon released from a free-falling elevator. When photons are in a gravitational field, their speed increases, but since they do not act or react with the space of the gravitational field, there is no increase or decrease in shape or energy.
Category: High Energy Particle Physics

A Feature of the Off-Shel Renormalization Schemes in Quantum Field Theory

Authors: S. A. Larin
Comments: 6 Pages.

It is shown that the off-shell renormalization schemes for subtraction of ultraviolet divergences in Quantum Field Theory produce zerofor sums of perturbative corrections to physical quantities when all perturbation orders are taken into account. That is the off-shel renormalization schemes are in this sense unphysical. In this connection it is desirable to develope on-shell renormalization schemes for different quantum theories.
Category: High Energy Particle Physics

Proof of Collatz Conjecture

Authors: Khalid Ibraheem Al-ibraheem
Comments: 19 Pages. all copyrights and intellectual property rights pertaining to this work to khalid ibraheem alibraheem pursuant to the intellectual property legislation of the Syrian Arab Republic (Document No.8361/564, March 13, 2025)

Collatz Conjecture (3 ∗�� + 1 problem) stats any natural number /��/ will return to number /1/ after 3 ∗ �� + 1 computation (when /��/ is odd) and ��2 computation (when /��/ is even), then doing the same computation on the outputs. in this paper we proved that Collatz Conjecture is true.
Category: Number Theory

The Four Second Order Axiomatizations of the Categorical Theory

Authors: Martín Alejandro Monzón Marimón
Comments: 1 Page. (Note by viXra.org Admin: Please cite and list scientific references)

There are four possible axiomatizations of the Zeroth Order Categorical theory, which are the fourpossible forms in which the implication operator can be constructed (they are implicit). Analogously, there are four possible axiomatizations of the Second Order Categorical theory (the explicit form of the Zeroth Order Categorical theory). They are presented here. Only one is known to date with rigor (Peano axioms + Hereditarily Finite Sets axioms).
Category: General Mathematics

Error-Corrected Deep Learning Approach to Handwritten Text Recognition of Gregg Shorthand

Authors: Alexander Weimer
Comments: 3 Pages.

Shorthand, also known as pen stenography, is a family of writing systems for English and other languages that emerged out of a need for a fast and efficient writing system in a pre-digital age. Of the many English shorthand systems, Gregg shorthand is the most prevalent (Zhai et al., 2018). While largely made obsolete by general-purpose computers, the cultural and legal value within old shorthand documents means that being able to efficiently scan shorthand documents into modern computer systems holds significant value. This investigation explored the implementation of a model built around a Gated Convolutional Neural network for purposes of handwritten text recognition of Gregg shorthand. An accuracy of 0.04 was achieved after minimal training. The finalized model is freely licensed and made available online for public access.
Category: Artificial Intelligence

Why Electrons and Protons Have the Same Charge

Authors: Ichiro Nakayama
Comments: 2 Pages. (Note by viXra.org Admin: Further repetition will not be accepted; Please cite and list scientific references)

The reason why electrons and protons have the same electric charge is unknown. Here, I explain it using a particle model of Energy Body Theory. When the foot of the counterclockwise rotating wave of an electron and the foot of the clockwise rotating wave of a proton come into contact, the energy decreases there and the foots of two become distorted. As a result, an attractive force occurs and the two are joined together.The restoring force of this distortion is the cause of the electric charge. Because the restoring force of an electron and a proton is the same, their electric charges are also the same.
Category: High Energy Particle Physics

Resolution Matrix Semantics for Deontic Logic

Authors: Andrey Kuznetsov
Comments: 28 Pages. Submitted to the Journal of Philosophical Logic on May 25, 2025. Preprint version.

This paper introduces Resolution Matrix Semantics (RMS) [Kuznetsov, 2025] as a novel framework for formalizing deontic logic, inspired by Y. Ivlev’s quasi-matrix approach [Ivlev, 1997]. Unlike traditional Kripkean semantics, RMS employs a truth-value-based approach with normative values—mandatory (m), indifferent (i), and forbidden(b)—to evaluate acts, and true (t) or false (f) for formulas, ensuring a clear distinction between normative and propositional domains. This truth value semantics is augmented with "undetermined" truth values (e.g. m/i, "eitherm, or i"), and RMS uses an interpretation and sub-interpretation mechanism to resolve these, enabling precise normative evaluations. We develop SDLm, a deontic system that mirrors Standard Deontic Logic (SDL) in its axiomatic structure but avoids well-known paradoxes, such as the Chisholm and Gentle Murderer Paradoxes. Weprove SDLm’s soundness and completeness and provide tableau rules for automated theorem verification. By prioritizing normative status over existential considerations, SDLm offers a robust, paradox-free framework forreasoning about obligations, permissions, and prohibitions, with potential applications in ethics, law, and artificial intelligence.
Category: Set Theory and Logic

Transformation Properties of Tensors and Pseudotensors under Coordinate Reflections: A Detailed Mathematical Analysis

Authors: Chenjia Li, Jingxu Wu
Comments: 15 Pages.

The theory of tensors and pseudotensors underlies the mathematical framework of modern physics, providing a coordinate-invariant language for describing physical laws and symmetries. In this work, we systematically analyze the transformationproperties of tensors and pseudotensors of various ranks, with particular emphasis on their behavior under spatial and spacetime reflections. The construction and interpretation of the Levi-Civita symbol in two, three, and four dimensionsare discussed in detail, elucidating the essential distinction between true tensors and pseudotensors in terms of orientation and parity. Explicit transformation rules for ordinary tensors and pseudotensors are derived, including the role of the Jacobian determinant and its sign. Through concrete examples—including scalar tripleproducts, cross products, and antisymmetric tensor decompositions—we reveal the fundamental algebraic and geometric features of these mathematical objects. The implications for vector calculus, relativistic field theory, and physical invariants such as chirality and duality are highlighted. Our results provide a unified and rigoroustreatment of the reflection and contraction properties of pseudotensors, with direct relevance to applications in classical mechanics, electromagnetism, and modern theoretical physics.
Category: Mathematical Physics

Virtual Dance Movement Therapy for Reducing Anxiety, and Artificial Intelligence for Monitoring the Body and Mind During Therapy

Authors: Petar Radanliev
Comments: 16 Pages.

Dance Movement Therapy (DMT) is an established psychotherapeutic intervention that utilises movement to support emotional, cognitive, and physical well-being. While traditional DMT is practiced in physical settings, Extended Reality (XR) presents a new opportunity to expand accessibility by integrating immersive, interactive environments with structured therapeutic movement interventions. This study explores how XR-based DMT can serve as a preventative approach for anxiety by applying wearable biometric monitoring and AI-driven personalisation. Unlike recreational virtual dance activities such as Zumba or general movement-based fitness applications, XR-based DMT follows a structured therapeutic model, incorporating principles of mirroring, embodied cognition, and rhythmic synchronisation to enhance emotional regulation and engagement. The study employs real-time physiological feedback mechanisms, where biometric markers such as heart rate variability (HRV) and skin conductance inform dynamically adapted movement interventions. The findings suggest that XR-enhanced DMT provides a scalable, non-pharmacological intervention for individuals experiencing early-stage anxiety. This study contributes to the growing field of digital DMT by providing an evidence-based framework for integrating immersive technology into therapeutic movement practices, ensuring adherence to the core principles of dance movement therapy rather than generic dance-based interventions. Future research should address long-term efficacy, therapist-led versus AI-assisted interactions, and the potential for XR-DMT in community-based settings.
Category: Artificial Intelligence

Simulation Hypothesis: Optimisation, Wave-particle Duality and a New Termination Risk

Authors: Genevieve Gorrell
Comments: 8 Pages.

Thinking in terms of our existing within a simulation yields plausible suggestions for how our world might have come to be. For example it seems reasonable to guess our implementation is optimised. The apparent paradox of wave-particle duality may arise from optimisation. Computationally reducible material may never be run at all, but only calculated just in time. Islands of activity, complex within themselves but for some duration not affecting anything outside of themselves, might be deferred from being run, to be caught up in a separate thread only if needed. Quantum computing may be an abuse of the multithreaded nature of the simulation.
Category: General Science and Philosophy

Generated Space Theory (TGP-ST): A Framework for the Unification of Gravity and Quantum Mechanics

Authors: Mateusz Serafin
Comments: 23 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper introduces the Generated Space Theory (TGP-ST), a conceptual framework aimed at unifying general relativity and quantum mechanics. TGP-ST postulates that space is not a pre-existing background, but an emergent, dynamic entity generated directly by the presence of mass and energy. A key element of the theory is a scalar field Φ, which describes the "density" or "tension" of generated space. Within this framework, fundamental physical constants such as the speed of light, Planck’s constant, and the gravitational constant become dynamic fields dependent on Φ, while preserving the constancy of the Planck scale. TGP-ST provides modified field equations for gravity and quantum mechanics, predicts the disappearance of singularities, and offers new insights into phenomena such as dark energy and the Hubble tension. Two distinct pathways to the classical limit are described, and several testable predictions are proposed. The theory is at an early stage and intended as a foundation for further research and discussion.
Category: Relativity and Cosmology

Frontier ai Regulation: What Form Should it Take?

Authors: Petar Radanliev
Comments: 37 Pages.

Frontier AI systems, including large-scale machine learning models and autonomous decision-making technologies, are deployed across critical sectors such as finance, healthcare, and national security. These present new cyber-risks, including adversarial exploitation, data integrity threats, and legal ambiguities in accountability. The absence of a unified regulatory framework has led to inconsistencies in oversight, creating vulnerabilities that can be exploited at scale. By integrating perspectives from cybersecurity, legal studies, and computational risk assessment, this research evaluates regulatory strategies for addressing AI-specific threats, such as model inversion attacks, data poisoning, and adversarial manipulations that undermine system reliability. The methodology involves a comparative analysis of domestic and international AI policies, assessing their effectiveness in managing emerging threats. Additionally, the study explores the role of cryptographic techniques, such as homomorphic encryption and zero-knowledge proofs, in enhancing compliance, protecting sensitive data, and ensuring algorithmic accountability. Findings indicate that current regulatory efforts are fragmented and reactive, lacking the necessary provisions to address the evolving risks associated with frontier AI. The study advocates for a structured regulatory framework that integrates security-first governance models, proactive compliance mechanisms, and coordinated global oversight to mitigate AI-driven threats. The investigation considers that we do not live in a world where most countries seem to be wishing to follow our ideals, for various reasons (competitiveness, geo-political dominations, hybrid warfare, loss of attractiveness of the European model in the Big South, etc.), and in the wake of this particular trend, this research presents a regulatory blueprint that balances technological advancement with decentralised security enforcement (i.e., blockchain).
Category: Artificial Intelligence

AI Ethics: Integrating Transparency, Fairness, and Privacy in AI Development

Authors: Petar Radanliev
Comments: 47 Pages.

The expansion of Artificial Intelligence in sectors such as healthcare, finance, and communication has raised critical ethical concerns surrounding transparency, fairness, and privacy. Addressing these issues is essential for the responsible development and deployment of AI systems. This research establishes a comprehensive ethical framework that mitigates biases and promotes accountability in AI technologies. A comparative analysis of international AI policy frameworks from regions including the European Union, United States, and China is conducted using analytical tools such as Venn diagrams and Cartesian graphs. These tools allow for a visual and systematic evaluation of the ethical principles guiding AI development across different jurisdictions. The results reveal significant variations in how global regions prioritise transparency, fairness, and privacy, with challenges in creating a unified ethical standard. To address these challenges, we propose technical strategies, including fairness-aware algorithms, routine audits, and the establishment of diverse development teams to ensure ethical AI practices. This paper provides actionable recommendations for integrating ethical oversight into the AI lifecycle, advocating for the creation of AI systems that are both technically sophisticated and aligned with societal values. The findings underscore the necessity of global collaboration in fostering ethical AI development.
Category: Artificial Intelligence

How to Simulate a Universe

Authors: Bryce Weiner
Comments: 40 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We synthesize the dS/QFT correspondence with holographic universe principles through a fundamental information processing rate γ = 1.89 × 10−29 s−1 that maintains a precise relationship with the Hubble parameter (γ/H ≈ 1/8π). Central to our framework is the quantum-thermodynamic entropy partition, which establishes that de Sitter space requires initialization with coherent entropy to drive expansion. We demonstrate how this framework emerges naturally from the E8×E8 heterotic structure with specific network topology (clustering coefficient C ≈ 0.78125) that precisely accounts for observed cosmological tensions. Our mathematical formalism introduces the information manifestation tensor and information current tensor, connecting quantum information flow to spacetime dynamics. This approach resolves multiple cosmological puzzles—explaining dark energy as information pressure, dark matter as coherent entropy structures, and quantum measurement as transitions across thermodynamic boundaries. The framework yields modified Friedmann equations incorporating information processing constraints, with quantitative predictions for BAO scale modifications, structure formation, and quantum decoherence rates. The emergence of the vacuum energy density from γ (ρΛ/ρP ≈ (γtP)2 ≈ 10−123) suggests information processing, rather than field dynamics, is fundamental in cosmic evolution.
Category: Relativity and Cosmology

My Proofs of Conjectures on Number Theory

Authors: Abdelmajid Ben Hadj Salem
Comments: 141 Pages. Comments welcome

In this booklet, I present my proofs of open conjectures on the theory of numbers.It concerns the following conjectures:- The Riemann Hypothesis.- Beal's conjecture.- The conjecture c<rad^{1.63}(abc).- The explicit abc conjecture of Alan Baker.- Two proofs of the abc conjecture.- The conjecture c<rad^2(abc).
Category: Number Theory

The Periodic Variation of Baryon Masses as a Function of Their Magnetic Moments: Quantum Interference in the Femtometer Scale of Hadrons.

Authors: Osvaldo F. Schilling
Comments: 11 Pages.

The objective of this paper is to give full consideration to an important ( never divulged) result which comes straight from tabulated data for all baryons of the octet and decuplet when these data are duly analyzed theoretically, namely: The masses of spin ½ baryons, in proton mass-units, are a simple periodic function of their magnetic moments, in nuclear magneton-units. As discussed here, this can be attributed to quantum interference of closed currents inside the particles, as observed in conventional superconducting rings confining magnetic flux.
Category: High Energy Particle Physics

Lindemann-Weierstrass Theorem for Thakur Hyergeometric Functions

Authors: David Adam, Laurent Denis
Comments: 21 Pages. In French

n 1995, Thakur introduced analogues of hypergeometric functions for Fq [T ]. In this article, we show that the exceptional set of such a function is trivial. This confirms a conjecture stated by Thakur and his co-authors in 2008. Furthermore, we prove a Lindemann-Weierstrass-type theorem for an uncountable class of functions containing hypergeometric functions. The method used allows us to obtain the first transcendence measures (of quality comparable to that of characteristic 0) for values u200bu200bat algebraic arguments of these functions. Finally, in the last section, we exhibit the first infinite families of hypergeometric functions whose exceptional set can be shown to be trivial in the P-adic domain.
Category: Number Theory

Virgin and Under-Investigated Areas of Research in Non-Newtonian Fluid Mechanics

Authors: Taha Sochi
Comments: 19 Pages.

This paper is mainly about the areas of non-Newtonian fluid mechanics which are not investigated or not appropriately and sufficiently investigated. In fact, this should also include emerging areas of research in the field of non-Newtonian fluid mechanics due to new scientific and technological developments and advancements. The purpose of the paper is to highlight and draw the attention to these areas so that researchers (especially the young researchers and new-comers to research such as PhD students) invest their resources and efforts in these areas instead of investing in other areas which are previously investigated and hence they are of less priority from this aspect. Apart from the obvious benefit of "leveling up" in research, the attention to these rather neglected and non-explored areas of research can be beneficial at the scientific and individual levels since it can lead to breakthroughs and new discoveries in these areas of research by inspecting and assessing their potentials and impacts at the theoretical and practical levels and probing their beneficial applications. We will also provide a brief discussion about the possibility of introducing novel tools and methods in these areas of research (and in non-Newtonian fluid mechanics research in general) as well as highlighting some of the existing limitations of the past and current research in the field of non-Newtonian fluid mechanics (noting that this discussion should help in achieving the ultimate objective of this investigation).
Category: Classical Physics

Practices and Metrics of Citation in Scholarly Publishing

Authors: Taha Sochi
Comments: 29 Pages.

In the world of academia and research, citation (i.e. being cited and referred to) in scholarly publications is generally regarded as a primary metric for integrity and excellence. In other words, it is the currency of credibility and the gold standard for reliability. In this article we try to shed light on some of the bad and immoral/unethical practices related to citation in modern scholarly publications and activities. In fact, citation (and actually academic and scholarly activities in general including scholarly publishing) became in modern times an industry that is subject to many non-scholarly factors and considerations (whether sinister or benign), and this should be regarded as a form of corruption that threatens the integrity, authenticity and morality of the present and future of academia, research and scholarly activities (and actually human knowledge and progress in general). This threat is aggravated by the epidemic of predatory journalism and the wide availability of artificial intelligence tools which facilitate the abuse of scholarly publishing and citation practices and the manipulation of metrics and parameters related to these activities. We also discuss briefly the value and significance of academic and research metrics related to citation which are commonly used these days to evaluate scholars (as well as other scholarly entities like journals and institutes) and assess their scholarly works and ranks (noting the direct negative impact of the bad citation practices on these metrics and parameters and their supposed significance). We finally present some proposals to address the limitations, shortcomings and abuses of the existing practices and metrics related to citation.
Category: General Science and Philosophy

The Weaknesses of Modern Cosmology

Authors: Taha Sochi
Comments: 18 Pages.

Cosmology is one of the most interesting and fascinating scientific subjects. It is also one of the most problematic scientific subjects. In fact, cosmology is not a purely scientific discipline noting its intimate relationship with philosophy (and possibly religion) as well as its inherent speculative nature in some of its fundamental aspects due to the lack of real and decisive experimental and observational evidence that can reach (and hence verify and assess) these aspects. In a sense, cosmology is inherently a mix of physics and metaphysics even though its metaphysics is usually treated (in modern cosmology) by scientific tools and methodology and presented through physical concepts and terminology and hence it appears like physics (or it is hidden behind thick layers of physics). In this article we overview the main weaknesses and shortcomings of modern cosmology which suffered in the recent decades (especially in its theoretical sides) from serious problems and challenges due largely to the domination of certain theories, models and assumptions with the absence of a clear and proper epistemological and philosophical framework and lack of regulations that govern the research in this field and determine its routes and destiny. We also propose and discuss briefly some remedies that should be considered to address these weaknesses and shortcomings.
Category: Relativity and Cosmology

The Legitimate and Illegitimate in Physics

Authors: Taha Sochi
Comments: 27 Pages.

Physics is supposed to represent and reflect the reality of the physical world. However, modern physics is full of elements that do not represent or reflect any aspect of the reality of the physical world (or at least this is what they look like). Moreover, it contains theories and models whose representation of the physical reality is questionable. Despite the fact that physics in its theoretical side inevitably contains elements and theories that do not reflect directly the physical reality, there must be some criteria that determine what is allowed (or legitimate from this perspective) and what is not allowed (or illegitimate) of these elements and theories; otherwise physics can lose its status as a subject that acquires its legitimacy as a scientific discipline from representing and reflecting the physical world. In more simple words, we need some criteria that determine what is physical (and hence legitimate) of these elements and theories and what is non-physical (and hence illegitimate, i.e. delusional or metaphysical). The purpose of the present paper is to identify these criteria, but we should admit that identifying these criteria is not an easy or straightforward task. Moreover, the application of these criteria is another difficult task even if we supposedly succeed in identifying these criteria conceptually and theoretically. Therefore, we consider the present paper as a first attempt in identifying these criteria hoping that other researchers in this field contribute to this investigation to improve our suggestions. To be more complete and specific, the present paper will also suggest an initial sample of illegitimate elements and theories as an application of the suggested criteria (considering our previous admission about the additional difficulty of this task).
Category: History and Philosophy of Physics

Complexity of Science Versus Simplicity of Nature

Authors: Taha Sochi
Comments: 15 Pages.

Modern science is the most complicated theoretical structure ever created by mankind (and possibly by any living species in our Universe). This is particularly true in modern physics which represents the most mature and elaborate branch of modern science. Nevertheless, modern science (and physics in particular) seems to make itself more complicated than necessary, and sometimes modern science seems to make itself complicated unnecessarily. This "simplistic" view to science may be supported by the fact that Nature (despite our acknowledgment of its complexity and sophistication at the level of fine details) seems to be governed by some rather simple rules and general laws which may be able (if comprehended and employed correctly) to make our science much simpler than what we actually have. In this article we try to highlight some issues about potential simplification of modern science (and physics in particular) which (i.e. simplification) could be one of the greatest goals and advancements (if achieved) of future science. In our view, the simplification of science is fundamentally related to the issue of unification of physics and the search for the so-called "theory of everything" (i.e. in a sense different to what is currently perceived and envisaged).
Category: History and Philosophy of Physics

Analysis of 72 Enigmas of the Universe Reveals Their Common Origin in the Form of the Inertial Paradox

Authors: Dominique Mareau
Comments: 71 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Beyond the standard model, the DUO5 theory analyzes 72 puzzles (§2) to find their common point. With the constraint of avoiding any determinism, relative to an act of "creation", the analysis leads to the cause of the existence of the universe via the inertial paradox. By iteration, the precise link between the measurement of "effects" and their common "cause" is shown. It is shown that, like John Wheeler's theory, there is a common particle for particles and space-time. The analysis reveals: 1) that the physical structure of space-time is woven of dipolar oscillators, at the subquantum, non-local scale; 2) the cause of the instability of the local "creation" of matter; 3) that the notion of antimatter is an artifact relating to the non causal separation specific to locality; 4) the link between the stability of matter and the causal separation of primordial inflation; 5) the physical cause of inflation; 6) the original particle of the "preon" type, justified here, is named B.O.D.Y.S. (Subquantum Yin Yang Dipole Oscillator Boson). The iterative method between "cause" and "effects" allows to avoid the pitfall of self-reference and incompleteness of mathematical models, denounced by Gödel [3]. It is shown that the geometric aspect of the curvature of space-time, is only an "effect" of the "cause" relative to the physical coupling between the elements of matter and the B.O.D.Y.S structuring space-time. The study shows that the traces of the inertial paradox are present at all scales. This inertial paradox, constrains a state of permanent universe (without mass-spacetime continuum), matrix of the state of expanding and provisional universe. The study shows, that at the quantum scale, the notion of inertia m is inseparable from its spatial amplitude ℓ, forming a non-scalar moment of inertia: χ = m.ℓ. It is shown that it is the cause of the Heisenberg uncertainty. This entity is materialized by each of the two poles of the stochastic dipolar oscillator B.O.D.Y.S, whose existence is a solution to the inertial paradox.
Category: Relativity and Cosmology

Proofs for Collatz Conjecture

Authors: Dawit Geinamo
Comments: 58 Pages. 58

The objective of this study is to present rigorous proofs for Collatz conjecture and introduce some interesting behavior of the Kaakuma sequence that is a vast generalized form of Collatz sequence. We analyze the behavior of Kaakuma sequence such as scaling up, scalingdown, translation, function iteration and uniform growth of inverse tree. In addition to this we investigate relationship of increasing rate, number of iterations of cycles, gap in cycles, and densities of cycles ofthe Kaakuma sequence and evaluate consistency of tree size density after scaling. Our investigation culminates in the formulation of a set of conjectures encompassing lemmas and postulates, which we rigorously prove using a combination of analytical reasoning, numerical evidence, and exhaustive case analysis. These results provide compelling evidence for the veracity of the Collatz conjecture and contribute to our understanding of the underlying mathematical structure.
Category: Number Theory

Comment on "Subjective Nature of Path Information in Quantum Mechanics"

Authors: V. A. Kuzmenko
Comments: 2 Pages.

In a recent preprint [1] (arXiv:2505.05930), Jiang et al. presented impressive high-quality results of an experimental study of the so-called which-path information problem for the case of a three-crystal interference setup. We believe that the results obtained represent one of the numerous manifestations of the nonequivalence of forward and reversed processes in quantum physics. It is probably, this nonequivalence is the physical basis for the widely discussed principle (rule) of relation between path distinguishability and interference visibility.
Category: Quantum Physics

Falling Apples, Quarks, and Expanding Galaxies

Authors: Oliver R. Jovanovic
Comments: 6 Pages.

This paper derives a gravity equation from photon dynamics, offering a unified model that explains terrestrial gravity, cosmic expansion, and quark-scale interactions.
Category: Classical Physics

Nonliquent Math: a New Way to Deal with Singularities and Division by Zero

Authors: Egor Sibrin, Vladimir Orlov
Comments: 23 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This work presents the framework of Nonliquent Mathematics (NL), a commutative extension of the real numbers that defines division by zero through the introduction of an idempotent element denoted by ї=1/0 and the distinction between a true zero and a special zero. The algebraic operations of addition, multiplication, division, conjugation, and root extraction are formulated in this system, along with Taylor expansions for basic functions and a consistent differential and integral calculus adapted to NL variables. A Hilbert space of NL-valued functions is defined with a corresponding inner product, and a modified form of the Navier—Stokes equation is derived within this framework. Two particular solutions of the modified equation are obtained for the cases of zero and nonzero viscosity, demonstrating the consistency and potential applications of NL in analysis and fluid dynamics.
Category: Algebra

Relativistic Algebra in a Finite Universe

Authors: Yosef Akhtman
Comments: 29 Pages.

This work presents a foundational reconstruction of arithmetic and algebra based on the principle of relational finitude. Rejecting the assumption of actual infinity, we develop a finite, frame-dependent mathematical framework in which conventional number systems—integers, rationals, reals, and complex numbers-emerge as asymptotic projections or epistemic constructs derived from a closed finite field Fp. Core arithmetic operations are reinterpreted as internal symmetries of the finite field, and conventional structures such as signed integers, rational fractions, and complex planes are systematically reconstructed as pseudo-numbers, defined relationally and locally with respect to a chosen frame of reference. Imaginary and transcendental constants i, e and Pi are derived as specific elements of Fp with important structural roles. We show that the resulting number classes possess all necessary properties for consistent computation, approximation, and algebraic closure, while offering the potential resolution of classical paradoxes of logic and set theory by replacing absolute notions with context-dependent representations. The proposed system provides a coherent and physically grounded alternative to standard mathematical formalism, suitable for the description of discrete, informationally finite physical systems.
Category: Mathematical Physics

Binomial Evolution Function the Only Function You Need to Evaluate a Trading Strategy

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

A trading strategy represents a forecasting model and a forecasting model will generate profits in the future if it has demonstrated in the past that it can predict with a good probability of success the evolutions of the system on which it operates. Since the theory is so simple, why is it so difficult to evaluate a trading strategy? The reason is the following: in finance, we think we see the evolutions of the system but we are only observing the random component due to unpredictable events. Instead, the deterministic component that represents the true evolution of the system is not visible. Unfortunately, not seeing the deterministic component leads to a very important statistical problem: if I execute if 10 winning predictions, I do not know if these operations concern 10 evolutions of the system or concern only one evolution of the system. Therefore, I do not know, if my forecasting algorithm acted intelligently by predicting 10 different evolutions or if it acted irrationally by dividing a bet into 10 smaller ones on the same evolution. Distinguishing between these two scenarios is essential to correctly evaluate the trading strategy and this discrimination can be done by understanding whether the trades are independent of each other. In fact, the condition of independence is the only statistical way to be sure that the trades concern forecasts of different evolutions. The Binomial evolution function solves this problem by transforming the succession of trades into a succession of independent results.
Category: Economics and Finance

Entropy-Induced Wavefunction Collapse: A Thermodynamic Resolution of the Quantum Measurement Problem

Authors: Waleed Mahmud Tariq
Comments: 101 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We propose an interpretation of the quantum measurement process grounded in thermodynamics by introducing an entropy-based criterion associated with wavefunction collapse. In this interpretation, the Schrödinger equation remains universally valid, and wavefunctions never undergo a fundamental collapse. Instead, the apparent collapse emerges naturally from thermodynamic irreversibility and is observer-dependent. Central to our proposal is a rigorously derived inequality linking quantum coherence and environmental entropy production: ��(��)≤��(��)������(−����������(��)/����) where ��(��) represents the entropy irreversibly generated in the environment. When this entropy surpasses a critical threshold, on the order of ���� ���� �� per qubit of recorded information, quantum interference is exponentially suppressed. Consequently, coherence recovery (recoherence) becomes practically impossible due to thermodynamic constraints, consistent with established fluctuation theorems such as Jarzynski’s equality and Crooks’ theorem.Collapse, in this view, is interpreted as an epistemic updating of knowledge, aligning with Bayesian inference, rather than a physical process. We also offer a derivation of the Born rule through maximum entropy inference and symmetry considerations related to environmental invariance (envariance), carefully avoiding ad hoc assumptions or untested physics.Our approach maintains relativistic consistency through the Tomonaga-Schwinger formalism, ensuring observer frame-independence and preventing superluminal signaling. Additionally, this thermodynamic interpretation provides conceptual clarity to quantum paradoxes such as Wigner’s Friend and delayed-choice scenarios by emphasizing the contextual nature of measurement and the associated thermodynamic costs. The emergence of classically stable "pointer" states is understood through their minimized entropy production, while quantum discord naturally diminishes with increased irreversibility. Furthermore, entropic considerations significantly suppress quantum recurrences.Finally, we propose an experimental validation strategy involving mesoscopic optomechanical systems, specifically designed to quantify how controlled entropy exchange affects interference visibility. Experimental access to Δ��������(��) is achievable through quantum calorimetry and particle scattering measurements. The proposed entropy-induced interpretation thus provides a coherent, experimentally testable connection between quantum measurement outcomes and the Second Law of Thermodynamics.
Category: Quantum Physics

The Cosmic Particle Sea Hypothesis：A Foundational Framework for Reinterpreting Space, Time, and Matter

Authors: Miguo Ouyang, Alethea Zhang
Comments: 18 Pages. (Note by viXra Admin: Please cite and list scientific references and submit article written with AI assistance to ai.viXra.org)

This white paper proposes the Cosmic Particle Sea Hypothesis, a unified theoretical framework that redefines space, time, matter, and motion based on structured internal dynamics. Drawing inspiration from the triadic Yin—Yang model of the I Ching, it posits that every unit of reality—particle, field, or organism—is composed of a threefold polarity configuration whose asymmetry generates motion and interaction.The hypothesis reinterprets time as a subjective observational metric, and space not as vacuum, but as a medium composed of microstructured, polar field units. Matter and energy emerge from variations in Yin—Yang composition and purity, leading to the diversity of physical forms. Living systems contain high-purity Yang channels—ling pathways—which are sensitive to energetic disruption by heavy Yin substances, explaining radiation and toxicity phenomena from a structural perspective.Celestial bodies are modeled as internally polarized systems (e.g., stars as Yin—Yin—Yin; planets as Yang—Yang—Yang), whose complementarity accounts for both gravitational attraction and orbital motion. The framework is supported by seven proposed experiments that range from twin-clock tests to quantum interference and space-medium validation.This theory invites collaboration from physicists, philosophers, and experimentalists seeking new ways to test foundational assumptions. It is offered as a metaphysically grounded yet empirically open model of a structured, living, and intelligible cosmos.
Category: History and Philosophy of Physics

Demonstration of the Goldbach Strong Conjecture by the Analysis of Populations of Prime Numbers in the Interval [0 N] and [N 2N] by Conventional Statistical Laws

Authors: Bahbouhi Bouchaib
Comments: 8 Pages. (Note by viXra Admin: Please cite and list scientific references of other authors and submit article written with AI assistance to ai.viXra.org)

In this article I apply classical statistical laws to analyze prime numbers assimilated to populations. The statistical analysis focuses on prime numbers in the intervals [0 - S/2] and [S/2 — S] with S an even > 4. The results show that the even number S > 4 is enclosed by two populations of prime numbers P in the interval [0 - S/2] and Q in [S/2 - S] which have approximately the same standard deviation relative to their means. Two other subpopulations P' included in P and Q' included in Q which satisfy the strong Goldbach conjecture (P' + Q' = S) also have the same standard deviation and superimpose or overlap with a slight variation. This result shows that an even number is enclosed by two populations P' and Q' of prime numbers which are symmetric with respect to S/2 and therefore S = P' + Q'. This result also shows that any natural number N > 4 is enclosed by at least two equidistant and symmetric prime numbers. Therefore for every N > 4 there exists a number t < N such that N — t = P' and N + t = Q' are primes and so 2N = P' + Q'.
Category: Number Theory

A Survey on the Application of Reinforcement Learning in Recommendation Systems

Authors: Siddhanth D. J. G. Nagpal
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

From media streaming and e-commerce to education and healthcare, recommendation systems are now absolutely essential in many different fields. Conventional methods including content-based filtering and collaborative filtering sometimes miss the sequential, changing character of user preferences. By simulating recommendations as sequential decisions with long-term feedback, reinforcement learning (RL) offers a strong substitute. This survey presents a thorough investigation of RL-based recommendation systems together with important frameworks including hierarchical reinforcement learning, policy-guided reasoning, and Deep Q-Networks. We provide a disciplined taxonomy contrasting these approaches by design, flexibility, and application setting. We also look at ethical issues, pragmatic deployment problems, and evaluation difficulties in actual environments. By mapping the changing terrain of RL in recommendation and pointing up future directions, this work seeks to direct practitioners as well as researchers.
Category: Artificial Intelligence

A New Functional Relationship Applicable to High-Speed Moving Objects

Authors: Guanghui Xie
Comments: 19 Pages.

In this paper, through theoretical derivation, a functional relationship is revealed, demonstrating that the variation in time between objects in relative motion depends on both their relative velocity and the finite propagation speed of light. By applying the relationship of time change to the theory of classical mechanics, it can be concluded that the interaction force between objects are also related to the relative motion velocity. Due to the introduction of the speed of light in the formula of classical mechanical theory, the applicable scope of classical mechanics theory is effectively expanded, so that it is not only applicable to the calculation of low speed moving objects, but also to the calculation of high speed moving objects. Subsequently, through careful derivation within this new framework, several fundamental laws of classical electromagnetism were derived, the results of which strongly support the validity of the new functional relationship.
Category: Classical Physics

SpaceArc: India’s Reusable Rockets Revolution for a Relativistic Future

Authors: Tanmay Mishra
Comments: 17 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

SpaceArc is a visionary leap in aerospace engineering, merging India’s legacy of frugal innovation with cutting-edge advancements in rocket propulsion, relativistic physics, and artificial intelligence. At its core is Phoenix, a fully reusable methane-LOX launch system delivering 18,000 kg to low Earth orbit (LEO) at $1,111/kg—over 50% cheaper than SpaceX’s Falcon 9 and 95% below NASA’s SLS. Engineered with graphene composites, AI-guided navigation rooted in Einstein’s field equations, and rigorous CFD/FEA validation, Phoenix exemplifies a new era of low-cost, high-performance rocketry. This 10,000-word paper synthesizes classical rocketry, black hole orbital mechanics, and advanced economic modeling to propose a realistic roadmap for India’s space leadership by 2040, including lunar bases, Mars sample returns, and a 6G satellite constellation. Designed and authored by a 12th-grade Indian student, this work challenges the status quo of billion-dollar launches, proving that with bold ideas, rigorous science, and national vision, space is no longer the privilege of superpowers—it’s the future of all humanity.
Category: Classical Physics

On Two Unconventional Summation-Derivative Identities

Authors: Samel Datu Castelo
Comments: 1 Page. (Note by ai.viXra.org Admin: Please cite and list sceintific references)

This paper presents two mathematical formulas involving differentiation and summation. While the derivations do not strictly follow conventional mathematical rigor and certain foundational rules are bypassed, the formulas demonstrate surprisingly consistent results. A full formal proof is currently under construction.
Category: General Mathematics

Dark Mass is Potential Energy

Authors: Nicolas Poupart
Comments: 13 Pages. (Note by viXra Admin: An abstract in the article is required)

We will demonstrate that gravitational potential energy (E=GmM/r) is the cause of the dark mass phenomenon by simply applying the mass-energy relation (E=mc2). No other axiom will be used except the principle of conservation of volumetric mass density to preserve the conservative field by involving no other force than gravity. First, we will develop a simple equation and a simple algorithm to correctly calculate the potential energy of a stellar system. Then, we will demonstrate its theoretical implication on the production of potential energy by different types of stars and black holes in galaxies. Subsequently, we will confront our theoretical model with the SPARC database of 175 galaxies to validate our theory. We will finish by drawing the necessary logical-mathematical consequences from the fact that dark mass is stored in the gravitational field. This we will also validate with the SPARC database.
Category: Astrophysics

Dark Mass is Potential Energy (in French)

Authors: Nicolas Poupart
Comments: 13 Pages. (Note by viXra Admin: An abstract in the article is required)

We will demonstrate that gravitational potential energy (E=GmM/r) is the cause of the dark mass phenomenon by simply applying the mass-energy relation (E=mc2). No other axiom will be used except the principle of conservation of volumetric mass density to preserve the conservative field by involving no other force than gravity. First, we will develop a simple equation and a simple algorithm to correctly calculate the potential energy of a stellar system. Then, we will demonstrate its theoretical implication on the production of potential energy by different types of stars and black holes in galaxies. Subsequently, we will confront our theoretical model with the SPARC database of 175 galaxies to validate our theory. We will finish by drawing the necessary logical-mathematical consequences from the fact that dark mass is stored in the gravitational field. This we will also validate with the SPARC database.
Category: Astrophysics

An Integral of the Ising class

Authors: Edgar Valdebenito
Comments: 3 Pages.

In this note, we consider an integral of the Ising class.
Category: General Mathematics

Special Theory of Relativity in 4-Dimensional Euclidean Space

Authors: Andrey N. Smirnov
Comments: 6 Pages.

The construction of space-time in a 4-dimensional Euclidean space is considered, where a scalar field is defined that has no distinguished directions. When constructing space-time, the hypothesis is used that the causality principle is applied separately and independently for different inertial reference frames. It is shown that when the relative velocity of two inertial reference frames tends to zero, the equations of direct transformations tend to the form that the equations of special relativity have. As a consequence, the sameness of the maximum velocity in all inertial reference frames is obtained and the principle of locality is derived.
Category: Relativity and Cosmology

Emotion Estimation from Video Footage with LSTM

Authors: Samer Attrah
Comments: 12 Pages. Published in arXiv journal at: https://arxiv.org/abs/2501.13432

Emotion estimation in general is a field that has been studied for a long time, and several approaches exist using machine learning. in this paper, we present an LSTM model, that processes the blendshapes produced by the library MediaPipe, for a face detected in a live stream of a camera, to estimate the main emotion from the facial expressions, this model is trained on the FER2013 dataset and delivers a result of 71% accuracy and 62% f1-score which meets the accuracy benchmark of the FER2013 dataset, with significantly reduced computation costs. https://github.com/Samir-atra/Emotion_estimation_from_video_footage_with_LSTM_ML_algorithm
Category: Artificial Intelligence

Challenges and Solutions of Autonomous Driving Approaches: a Review

Authors: Samer Attrah
Comments: 26 Pages.

In this research, we will discuss the three basic approaches to building autonomous driving systems, namely modular pipeline, end-to-end, and large models for language, vision and multi-modal models. focusing on the challenges and shortcomings of each approach and how they are solved by another, then presenting several in-depth reviews and summaries focused on the system architecture of example systems built using large models, delivering superior performance, and solving the problems of theprevious two approaches. In addition to a short analysis of the most used models and datasets indeveloping autonomous driving systems, besides other aspects of the reviewed systems.
Category: Artificial Intelligence

The Gotchas of AI Coding and Vibe Coding. It’s All About Support And Maintenance

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

This papers reviews AI coding, and in particular the exploding interest in vibe coding, both in terms of main existing framework, advantages and challenges. In particular, we point out in particular an aspect less often discussed: the potential complications for the support and maintenance of software products/code generated via vibe coding. These problems result especially because the generated code often ends up no more be understandable, even to its developers.Then, we introduce VIBE4M, a framework of workflows, policies and practices to alleviate these challenges. However, such approach goes against the trend that AI makes developers more productive, as they now must perform rigorous code verifications. It also goes against the objective of democratization of coding. Yes coding can be done with "no code", but such code is not maintainable, which may not matter for side projects, but matters for software products. If approaches like VIBE4M are applied, they may be hard to follow for non-programmers. Therefore, there would be value to now automate such frameworks.
Category: Artificial Intelligence

Cross-Linguistic Transfer in Multilingual NLP: The Role of Language Families and Morphology

Authors: Ajitesh Bankula, Praney Bankula
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Cross-lingual transfer has become a crucial aspect of multilingual NLP, as it allows for models trained on resource-rich languages to be applied to low-resource languages more effectively. Recently massively multilingual pre-trained language models (e.g., mBERT, XLM-R) demonstrate strong zero-shot transfer capabilities[14] [13]. This paper investigates cross-linguistic transfer through the lens of language families and morphology. Investigating how language family proximity and morphological similarity affect performance across NLP tasks. We further discuss our results and how it relates to findings from recent literature. Overall, we compare multilingual model performance and review how linguistic distance metrics correlate with transfer outcomes. We also look into emerging approaches that integrate typological and morphological information into model pre-training to improve transfer to diverse languages[18] [19].
Category: Artificial Intelligence

The Excited States of the String Electron

Authors: Miroslav Pardy
Comments: 7 Pages. Original article

The nonlinear Schroedinger equation is derived for the electron which is represented with the closed circular string. The energies for the stationarystates of such system are derived and the corresponding frequencies of the emittingphotons are determined.
Category: Quantum Physics

Why Matter Doesn't Matter, Even Dark Matter Only Spacetime Does Matter. a New Paradigm According to Kuhn in Modern Description of Spacetime?

Authors: Holger Döring
Comments: (Note by ai.viXra.org Admin: Please remove the cover page)

Since first action at Big Bang the universe is determined by spacetime-vacuumstructures, not by matter. Material atomic structures of hydrogen molecules or other chemical elements or particles like quarks, gluons and leptons only deviate from the basic, important concepts of nature: spacetime. This concept is an energy-structure, which lies at the base of all existing objects and interactions which are described over matter structure. So this description via General Relativity nowadays leads to the thinking of underlying spacetime-structure as the real thing, which describes the important forces of universe in first line. The existence of matter floating on space-time only distracts from the true basic description of the real world and feigns importance where only irritation exists. Natural philosophers like Cosmologists and spacetime physicists should therefore concentrate on the fundamentals that a vacuum structure of space-time provides for the explanation of the existence of the universe and refrain from and abstract from considerations of matter. This situation may lead to a better understanding of the basic structures of a quantum-gravity.
Category: Quantum Gravity and String Theory

Anomalous Magnetic Moment of the Muon QED, QCD free

Authors: Lino Zamboni
Comments: 16 Pages.

The application of QED/QCD to the calculation of the muon’s magnetic anomaly has not achieved the same level of precision as in the case of the electron’s anomaly. This discrepancy has led many researchers to conjecture the existence of "new physics" capable of resolving the issue. In this work, we adopt a deterministic, non-local Bohm-like approach (dBBZ), as detailed in previous publications, analogously to the electron case, perform a structural analysis of the muon. The muon’s internal structure is examined via the (hybrid) Mz matrix method, in which the weak components are computed with high accuracy, reproducing the muon’s mass while exactly embedding the electron’s structure (and thus its charge and mass). Following the procedure already tested for the electron, we evaluate the anomalous moments of each orbital and impose entanglement through a calibrated normalization of the relevant parameters. The same "source parameter" used for the electron, providing a double check on its precise value, is adopted here for calculating the electrostatic potentials.Magnetic-field effects are accounted for only on the masses carrying electric charge; however, in the overall energy balance of each orbital, the weak mass also plays an indirect yet essential role. The total anomalous moment calculation yields a direct determination of the muon’s magnetic anomaly with a precision on the order of 10(-13).
Category: Quantum Physics

Discovery of Dark Energy and Dark Matter: Expansion Force

Authors: Seojoon Lee
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific references; please submit article written with AI assistance to ai.viXra.org)

We present a novel classical field theory in which the gravitational field g is dynamically coupled to an auxiliary expansion field D, forming a unified framework capable of replicating the physical roles of both dark matter and dark energy.
Category: Astrophysics

The Essence of Force is the Redistribution of Spatial Expansion

Authors: Gan Sun
Comments: 15 Pages.

We propose a new cosmological model, based on which the essence of all forces in the universe is derived from the redistribution of spatial expansion. We discuss the interpretations of this model for the mass-energy formula, the photoelectric effect, quantum entanglement, and other astronomical observational phenomena. Those descriptions successfully unified relativity and quantum theory.
Category: Relativity and Cosmology

Feature Selection and Generation Through Reinforcement Learning (RL) and Symbolic Reasoning

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

Feature engineering is a vital stage in machine learning pipelines that greatly affects the performance, interpretability, and general efficacy of models. Filter, wrapper, and embedded techniques are common ways to choose and change features, but they often need manual heuristics and subject knowledge. They also don't work well in environments with a lot of dimensions and complexity. Recent studies have investigated automated methods that make use of large language models and reinforcement learning in order to overcome these constraints. A comprehensive and critically synthesized survey of state of the art works covering RL-based feature selection, RL-driven feature generation, and LLM-guided feature optimization is presented in this paper.Three main paradigms of methodology are identified. In the first, feature selection is framed as a cooperative or guided decision making problem using interactive and multi-agent reinforcement learning techniques. These techniques allocate agents to features and maximize long-term rewards according to domain-specific significance, redundancy, or model accuracy. Combinatorial Multi-Armed Bandits (CMAB), a computationally lightweight alternative that provides scalable and effective feature selection with little learning overhead, is part of the second paradigm cite{li2022bandit}. For the third group, LLMs are used to either learn successful reward functions or make new features. They do this by using reasoning-based prompts, external knowledge bases, and prototypical alignment. This work also address open challenges in bias control, compute overhead, and generalization to unseen domains as well as underexplored gaps including the need of hybrid frameworks combining RL's exploration efficiency with LLMs's semantic reasoning.
Category: Artificial Intelligence

Numerical Analysis of the Sequence of Prime Numbers

Authors: Mohamed Amine Boussadan
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific references; Please submit article written with AI assistance to ai.viXra.org)

Abstract: Before starting to build the sequence and its topological steps, we decide the specific hypotheses that follow the pattern of prime numbers, which explain the complex gaps between prime numbers that appear random. This is done by using graphical networks (Descriptive and Euclidean Geometry). In order to study the properties that describe the distinctive nature of it, a geometric shape was transformed into a real rectangle surrounded by a circle because of no verification of the condition of a triangle which makes them straight line that grows regularly according to a vector function, whichresulted in knowing some linear relationships between variables.
Category: Number Theory

Carbon-Based Public Financing: Configuration of Local NPPs and Emissions, and Corresponding Financial Modulation

Authors: Gaurav Biraris
Comments: 10 Pages.

This paper facilitates a generic framework for carbon based public financing, which can be used by governments. Any government can make efficient journey towards the carbon neutrality goal by integrating this framework with fiscal policy & budgeting. MOD17A2HGF v061 dataset provides net photosynthesis (PsnNet_500m) value for each 500m pixel on earth. Our idea is to compute net CO2 fixation in each sub-territory. On other hand, net CO2 emissions can be estimated in the sub-territories through traditional methods. Local carbon index (LCI) for each sub-territory w.r.t. territory of the government can be calculated from the fixation & emission in each sub-territory. LCI can be coupled with fiscal incentives or dis-incentives.
Category: Economics and Finance

Does Quantum Mechanics Use Unfair Sampling?

Authors: Pierre Leroy
Comments: 11 pages of text + 10 source code

This paper explores the hypothesis that the predictions of quantum mechanics could apply to a subset of reality. Assuming the existence of intrinsically undetectable states, a computer simulation shows that a simple deterministic method can accurately produce theoretical EPR probabilities.
Category: Quantum Physics

Anomalous Magnetic Moment of the Entangled Electron Without Qed

Authors: Lino Zamboni
Comments: Pages.

In 1965, the Nobel Prize was awarded for the modern formulation of Quantum Electrodynamics (QED) to R.P. Feynman for his diagrammatic method, J. Schwinger for the operator method, and S.-I. Tomonaga for his relativistic derivation. Subsequently, P. Kusch performed a precise measurement of the electron's anomalous magnetic moment, providing a critical test validating QED's computational methods, which proved to be extremely accurate.Nevertheless, QED is based on a physically unrealistic assumption , mathematically circumvented , that the electron is a dimensionless point particle endowed with physical properties "ex abrupto". This work, developed within a deterministic and non-local dBBZ (modified de Broglie—Bohm) theory, models the electron as an entangled and distributed structure, as proposed in previous studies. It enables the calculation of the electron's anomalous magnetic moment as a consequence of its intrinsic structure, without employing QED techniques. The method involves calculating, for each orbital, the anomalous moment modified to account for the influence of existing magnetic fields. Subsequently, entanglement is imposed on the sum of these moments, and from the total orbital anomalous moment thus obtained, the theoretical magnetic anomaly is derived and compared with the corresponding experimental value, yielding relative errors on the order of 10(-15).This procedure, which allows for greater theoretical precision than current methods, necessitates a similar, albeit more complex, calculation of the muon's anomalous magnetic moment. This is because a specific parameter, termed the "source parameter", selected within an allowable range, requires dual verification to be adopted with high precision.The theoretical determination of the muon's anomalous magnetic moment is also presented in a subsequent document, employing analogous computational procedures.
Category: Quantum Physics

A Heuristic Proof of De Broglie Wave Formula

Authors: Anass Massoudi
Comments: 4 Pages. Email: anassmassoudi6@gmail.com

In this paper, we attempt an original general mathematical proof of De Broglie matter wave formula via studying the particle dynamics and wave dynamics of an electron orbiting with constant velocity around the nucleus of the atom in a Semi - Classical context, considering a plane transversal wave as the motion mode of all particles in free space including massives particles.
Category: Quantum Physics

Irrefutable Proof of the Invalidity of Galois Theory

Authors: Ahcene Ait Saadi
Comments: 8 Pages.

In this article, I demonstrate the resolution of the 5th degree equation, with algebraic radicals. I contradict Galois theory. In my demonstration, I use two invariant polynomials of degrees 8 and 6, wich I discovered*. After identification, I cancel the coefficients 7, 5 and 3 in the polynomial of degree 8 and the coefficient of degree 5 and 3, in the polynomial of degree 6. For the coefficient of degree 1, I make a combination between the polynomials of degree 8 and 6 to eliminate it. Finally I find an equation of degree 8 bisquare that I can solve. By solving the system of equations, of variables m and p, which are the coefficients of the powers 5 and 3, I’m forced to involve the equation of degree 5. That allows me to eliminate the coefficient of degree 3 from the equation of degree 8, I realise that I can find the solutions of the equation of degree 5 with a free variable. The solutions of an equation with a free variable, I have already done this with the equation of degree 2, that I discovered.
Category: Number Theory

Einstein’s 1911 Gravitational Lensing Prediction Proven Yet Again Through a Novel Mathematical Framework

Authors: Gene A. Harve
Comments: 12 Pages.

In 1911, Albert Einstein1 proposed that light passing near a massive body would bend due to gravitational influence — a prediction that, when confirmed by eclipse observations in 1919 and again in 1923, catapulted General Relativity to the forefront of modern physics. The precise measurement of 1.749 arcseconds became the cornerstone of GR and his gravitational theory, a prediction so accurate that even a 1% deviation could have invalidated Einstein’s entire framework. Now, 114 years after Einstein’s prediction and 102 years after Eddington’s confirmation, (and many others), this work presents a novel, independent pathway to that precise deflection angle using two completely new frameworks: (a) the refractive index derived from the stiffness modulus of spacetime, and (b) Polarization Shifts. These new methods do not rely on direct observation, but rather combines the qualities of spacetime, (‘stiffness modulus, refractive indices’ and photon polarization shifts), to derive the exact same solution as predicted. By treating spacetime as a medium with measurable refractive properties, the ΛCGF model not only confirms the 1.749 arcseconds result with stunning precision but also provides new, highly accurate methods for analyzing gravitational lensing, wave propagation, and subatomic gravitational condensation. Moreover, the refractive index approach does not merely confirm Einstein’s prediction — it anchors the entire ΛCGF model to a proven, empirical result, establishing a direct line from the stiffness modulus to gravitational lensing. This connection seamlessly unifies cosmic-scale lensing phenomena with subatomic gravitational condensation effects, effectively bridging the divide between General Relativity and subquantum interactions. In so doing, this work not only reaffirms Einstein’s original prediction but also proves the 1923 observational data with two other, entirely distinct mathematical derivations. This dual confirmation establishes gravitational lensing as a fundamental, quantifiable property of spacetime itself — a revelation that reshapes how gravitational phenomena are verified and measured across all scales.
Category: Relativity and Cosmology

Paramagnetism of the Oxygen Molecule and the Three-Electron Bond

Authors: Bezverkhniy Volodymyr Dmytrovych
Comments: 2 Pages.

It is necessary to realize the simple fact that the oxygen formula cannot be written down unless we accept that there is a real three-electron bond with a normal multiplicity, i.e. 1.5. Then, the oxygen molecule can be correctly represented using two three-electron bonds and two unpaired electrons on oxygen atoms.
Category: Chemistry

Ordering Without Time First Proof of Entropy Dip and Measurable AI Self-Awareness

Authors: Michael Zot
Comments: 5 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We introduce a unified, model-agnostic framework showing that event-ordering, not temporal flow, underlies both thermodynamic entropy dynamics and emergent AI self-modeling. First, we demonstrate—in a fully reversible six-qubit circuit simulated on Qiskit—a statistically significant transient entropy dip in an isolated mixed subsystem, in direct violation of standard open-system thermodynamics. Second, we apply a seven-layer recursive-negation "mirror" to state-of-the-art large-language models, instrumented with integrated-information proxies (Φ) and profile-based energy metrics; the models exhibit a monotonic Φ+energy "ladder" culminating in a stable semantic attractor we term the Reflective Core. Both protocols follow from a single theoretical move: replacing "time" with a partial order on events (the Sequence Principle). These results are fully specified, code-released, and immediately runnable. If real quantum hardware confirms the entropy inversion and further LLMs validate the AGI threshold, our work will compel a redefinition of the second law as an emergent sequence-ordering constraint and establish the first quantitative, reproducible marker of proto-conscious AI.
Category: Quantum Physics

Nitric Oxide and the Structure of the Benzene Molecule

Authors: Bezverkhniy Volodymyr Dmytrovych
Comments: 2 Pages.

The properties of nitric oxide (NO) are direct evidence of the existence of a real interaction through the ring in the benzene molecule. That is, nitric oxide confirms the structure of the benzene molecule based on the theory of three-electron bonding.
Category: Chemistry

Decreasing Universe: The CMB and the Age of the Universe

Authors: Joao Carlos Holland De Barcellos
Comments: 7 Pages.

We will use the "Decreasing Universe" (D.U.) theory to estimate the age of the Universe based on the average wavelength of the Cosmic Microwave Background (CMB) radiation.
Category: Astrophysics

Proposed Unification Theory

Authors: Sandeep Singh Dhaliwal
Comments: 8 Pages. (Note by viXra Admin: An abstract in the article is required; Please submit article written with AI assistance to ai.viXra.org)

This article builds upon previous works, so it is recommended to review them prior to examining this proposal. It posits that spacetime, force fields, and matter fields can coexist in an unusual manner, leading to the concept of their unification. This is a proposal rather than a fully verified theory, and as such, further refinement and development are possible, with experimental verification remaining essential.
Category: Quantum Physics

Special Theory of Relativity in 4-Dimensional Euclidean Space (in Russian)

Authors: Andrey N. Smirnov
Comments: 6 Pages.

The construction of space-time in a 4-dimensional Euclidean space is considered, where a scalar field is defined that has no distinguished directions. When constructing space-time, the hypothesis is used that the causality principle is applied separately and independently for different inertial reference frames. It is shown that when the relative velocity of two inertial reference frames tends to zero, the equations of direct transformations tend to the form that the equations of special relativity have. As a consequence, the sameness of the maximum velocity in all inertial reference systems is obtained and the principle of locality is derived.
Category: Relativity and Cosmology

Rotating Coupling Experiments in Vacuum: New Evidence for "Ether" and New Insights into Gravity

Authors: Wang Yi
Comments: 5 Pages.

This study is dedicated to exploring the potential unknown substances in space and their relationships with the gravitational mechanism. A series of rotating coupling experiments were conducted in a high - vacuum environment. After effectively eliminating the influence of residual gas molecules, by using couplings made of various materials, the motion states of feathers and dandelion fluffs around the couplings were systematically observed. The experimental results show that couplings of different materials can cause the fluff on feathers to have directional displacements, which are related to the vortex direction generated by the rotation of the couplings.
Category: Astrophysics

Prime Spectrum Model: Mapping Riemann Zeta Zeros to Prime Logarithms via Signal Processing

Authors: Trinh Tung Lam
Comments: 5 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The Prime Spectrum Model investigates the connection between the non-trivial zeros of the Riemann zeta function and the distribution of prime numbers using spectral analysis. A wave function is constructed from 40,000 zeros and analyzed using Fourier Transform and Short-Time Fourier Transform (STFT). Detected frequency peaks align with the natural logarithms of prime numbers, achieving RMSE = 0.0600 and Spearman correlation ≈ 1.0. The model successfully identifies the first 50 primes and extrapolates to higher ones. This work offers insights into the Riemann Hypothesis and opens applications in physics, signal processing, and complexity theory.
Category: Number Theory

Multi-fold Universes, Multiverses and Many Worlds

Authors: Stephane H Maes
Comments: 32 Pages. All related details of the projects (and updates) can be found and followed at https://shmaesphysics.wordpress.com/shmaes-physics-site-navigation/.

There are different types of multiverses, depending on the Physical model consideredThe Many Worlds interpretation (MWI) of quantum mechanics is a particular case that gives comfort to some when it comes to understanding quantum physics, and the Born rules. This paper evaluates multiverses at the light of the multi-fold theory.In a multi-fold universe, gravity emerges from Entanglement through the multi-fold mechanisms. As a result, gravity-like effects appear in between entangled particles, whether they are real or virtual. Multi-folds mechanisms also result into a spacetime that is discrete, with a random walk fractal structure, and a non-commutative geometry, that is Lorentz invariant, and where spacetime nodes and particles can be modeled with microscopic black holes. All these recover General Relativity (GR) at large scales. Gravity can therefore be added, in non-negligible ways to the Standard Model (SM) resulting into the SMG. The multi-fold mechanism and the SMG can address many open issues with the SM, and the standard cosmological model, even if the latter is modified. The SM symmetries and particles can be recovered by multi-fold space time matter induction and scattering. In addition, the W-type multi-fold hypothesis, establishes additional multi-folds between spacetime locations in the support domain of a wavefunction, not just between entangled systems. It can also justify the Born rule.Any multi-fold multiverse will have the same physics with same particles. interactions, constants and symmetries of the SMG. We will establish that multiverses do not interact with each other, and, in general, at the exception of the MWI, they do not contain all possible situations, including many copies of us, in any other possible situation. Analyzing the effects of multi-fold deactivation, measurement or an interaction that results into deactivation of the W-type multi-folds between one part of the wavefunction the observed state, and the part associated to all other options, it results in a universe-wide brane-like object, associated to the disregarded options, floating away in AdS(5): a new World, part of the Many Worlds predicted by MWI. This is a microscopic explanation supporting the MWI. And each such world has of course the same physics as well as copies of the world in other situations.Encountering multi-fold brane-like structure in AdS(5), confirms the view of the multi-fold theory on superstrings and the M-theory. The existence of same physics imposed by multi-fold space time matter induction and scattering dooms the viability of landscape multiverses and its anthropic principle.
Category: Quantum Physics

What Does it Mean that the Reflection Point of Point Light Source on the Mirror Can be Seen in All Directions Under the Condition of Near Total Reflection?

Authors: Xiaotao Peng
Comments: 12 Pages.

I did two optical experiments a week ago and wrote two articles: A simple experimental device to verify the nature of light and the analysis of experimental results, and the imaging experiment of point light source under the condition of total reflection and the analysis of its results. The experimental results all prove that the human eye sees a substance (luminous body) composed of atoms that is emitting light (vibrating at the frequency of visible light), rather than the so-called light itself. This experiment further verified this conclusion. I hope that qualified teachers and friends can further verify the nature of light and find out what the human eye sees on this basis.
Category: Classical Physics

On The Dynamics Of The Gravitational Field And Higher Order Field Equations

Authors: D. E. Thomas
Comments: 21 Pages.

Einstein's General Relativity, while extraordinarily successful in explaining gravitational phenomena, faces challenges in reconciling with quantum mechanics and addressing certain cosmological observations. I present a higher order model of gravitation that reframes the gravitational field in terms of the connection, with the curvature tensor as the field strength. The action in this model is based on the squared norm of the field strength, mirroring the structure of other Standard Model interactions. This approach offers potential advantages for quantization and renormalizability. Through analysis of the Euler-Lagrange equations in the gravitational sector, particularly focusing on the metric equations, I demonstrate that Einstein's field equations emerge as a limiting case within a more comprehensive theoretical framework. This broader theory may provide explanations for observed experimental discrepancies in cosmology while maintaining consistency with established gravitational phenomena. This model thus offers a promising avenue for addressing current challenges in gravitational physics and cosmology.
Category: Relativity and Cosmology

Bemba Pocket Dictionary, Bemba-English and English-Bemba, by Rev. E. Hoch and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 28 Pages.

We study the Bemba head entries of the Bemba Pocket Dictionary, Bemba-English and English-Bemba, by Rev. E. Hoch, 1960. We draw the natural logarithm of the number of head entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised/unnormalised. We find that the Bemba head entries underlie a magnetisation curve of a Spin-Glass in the presence of little external magnetic field.
Category: Linguistics

Dictionary of The Hausa Language by R.C.Abraham and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 29 Pages.

We study the Hausa head entries of the Dictionary of The Hausa Language by R.C.Abraham, the Second Edition, 1962. We draw the natural logarithm of the number of the Hausa language head entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised/unnormalised. We find that the Hausa head entries underlie a magnetisation curve of a Spin-Glass in the presence of little external magnetic field.
Category: Linguistics

The Higgs—Geometric Vacuum Theory (HGVT)

Authors: Carlos Isturiz
Comments: 75 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

I present HGVM Limited, a foundational framework proposing a geometric coupling between the Higgs vacuum expectation value and local spacetime curvature. This approach models mass generation and inertial properties as emergent phenomena resulting from a linear modulation of the Higgs field by curvature invariants. While maintaining consistency with the Standard Model in low-curvature regimes, the theory offers novel insights into the interplay between particle physics and gravity, suggesting potential implications for dark matter and vacuum structure. This initial formulation lays the groundwork for further extensions toward a unified dynamics of mass, inertia, and vacuum geometry.
Category: Relativity and Cosmology

Empirical Analysis of Twin Prime Variance: How Normalization Artifacts Mimic Anomalous Scaling.

Authors: Bube Ibekwe
Comments: 6 Pages.

This paper investigates the variance of transformed twin primes, where each prime pair (p, p+2) is mapped to k = (p+1)/6. Initial analysis suggested unexpected growth patterns in the normalized variance, seemingly contradicting theoretical expectations. Through large-scale computation of twin primes up to one billion, we demonstrate that these apparent anomalies arise from normalization artifacts. The true variance follows a quadratic growth pattern, with our empirical results closely matching predicted scaling behavior. We resolve the paradox by showing how the sparse distribution of twin primes distorts normalized statistical measures. Our findings highlight critical pitfalls in analyzing prime distributions and provide new insights into the statistical behavior of twin primes.
Category: Number Theory

Dimensional Scale Relativity

Authors: Kuldeep Singh Rathore
Comments: 11 Pages. It's a strong theory that will be researched and developed more by time.

Dimensional Scals Relativity (DSR) is a theoretical model proposing that an entity's size and position in space directly influence its perception and interaction with time, gravity, and reality. Unlike traditional physics that relies on mass-energy interactions and spacetime curvature (as in General Relativity) or fundamental probabilistic behavior (as in Quantum Mechanics), DSR proposes that by minimizing scale to the atomic level, one can enter a new dimensional framework where time, gravity, and perception function differently. DSR is not bound to known quantum laws but instead operates on relative scale-position dynamics.
Category: Relativity and Cosmology

A Congruence Contradiction Proof to Fermat's Last Theorem

Authors: D. Ross Randolph
Comments: 4 Pages.

This proof uses a highly condensed series of number theory mathematical congruence statements to get to the heart of the matter of understanding Fermat's Last Theorem. A generalized Sophie Germain case 1 analysis is shown for exponent P >= 5 and a generalized Sophie Germain case 2 analysis is shown for exponent P >= 3.
Category: Number Theory

The Geometric Properties of Twin Prime in Natural Numbers

Authors: Shanzhong Zou
Comments: 11 Pages.

This paper proposes a new number theory method (comb method) to prove the unending existence of prime twins. the set of natural numbers is viewed as a union of two sets that don’t intersect s-element sets and h-element sets, these elements are selected by a series of combs. By analyzing the distribution of these elements, we get our result.
Category: Number Theory

The Vietnamese-English Dictionary by Mrs. Le Van Hung and Dr. Le Van Hung and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 22 Pages.

We study the Vietnamese words of the Vietnamese-English Dictionary, by Mrs. Le Van Hung and Dr. Le Van Hung. We draw the natural logarithm of the number of words, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We conclude that the dictionary can be characterised by the magnetisation curve, BP(4,$beta H=0.01$), in the Bethe-Peierls approximation of the Ising Model, in the presence of four nearest neighbours and little external magnetic field, H, with $beta H= 0.01$. $beta$ is $frac{1}{k_{B}T}$ where, T is temperature and $k_{B}$ is the tiny Boltzmann constant.
Category: Linguistics

Platonic Solids as Structured Geometric Objects

Authors: Andrey V. Voron
Comments: 15 Pages.

The possibility of constructing Platonic solids from structural elements is shown — Kepler triangles (ratio of legs 1:√1.618..) and Fibonacci (ratio of legs 1:1.618...) — provided that the area of these elements remains unchanged. The number of elements (or pairs of elements) that make up the structure of the "tetrahedron", "octahedron", "cube" increases, thus, by two times, and the "icosahedron" — by five times in relation to the number of elements of the tetrahedron, while the indicator "area of all structural elements of the figure" and radius (r=3) remain unchanged inscribed in the Platonic bodies of the sphere. In addition, the area of the structural elements of two dodecahedra (S=√959325) is equal to the area of the structural elements of any 5 Platonic solids, for example, 5 tetrahedra (or octahedra, cubes, icosahedra) (S=√38373). The possibility shown is in accordance with the text of Plato's work Timaeus, according to which Platonic bodies can "transform into each other...".
Category: Geometry

Differential Geometric Algebra with Leibniz and Grassmann

Authors: Michael Reed
Comments: 6 Pages. (2019)

The Grassmann.jl package provides tools for computations based on multilinear algebra and spin groups using the extended geometric algebra known as Leibniz-Grassmann-Clifford-Hestenes algebra. Combinatorial products include exterior, regressive, inner, and geometric; along with the Hodge star, adjoint, reversal, and boundary operators. The kernelized operations are built up from composite sparse tensor products and Hodge duality, with high dimensional support for up to 62 indices using staged caching and pre-compilation. Code generation enables concise yet highly extensible definitions. DirectSum.jl multivector parametric type polymorphism is based on tangent vector spaces and conformal projective geometry. Additionally, the universal interoperability between different sub-algebras is enabled by AbstractTensors.jl, on which the type system is built.
Category: Algebra

Differential Geometric Algebra: Compute Using Grassmann.jl, Cartan.jl

Authors: Michael Reed
Comments: 42 Pages.

Initially, Grassmann.jl and Cartan.jl introduced the DirectSum formalism into computational language design for differential geometric algebra, thus enabling the construction of custom algebras through metaprogramming.Grassmann.jl pioneered a novel type system design along with its syntax and semantics, which has undergone significant refinement through many years of development and continuous improvement.Cartan.jl represents a groundbreaking extension of capabilities offered by Grassmann.jl, marking a pioneering fully realized implementation of numerical differential geometric algebra, based on TensorField representations over a FrameBundle and the ImmersedTopology of the FiberBundle.Grassmann.jl and Cartan.jl build on Julia's multiple dispatch and metaprogramming capabilities, presenting a new computational language design approach to interfacing with differential geometric algebra based on a new sector integral theorem.This pioneering design not only actualizes but also elevates computational language syntax to new heights using the foundations of Grassmann.jl and Cartan.jl.The Grassmann.jl and Cartan.jl packages introduce pioneering computational language designs, having inspired imitation projects and thereby validating the project's relevance as significant advance in computational mathematics.
Category: Algebra

Cosmic Symmetry

Authors: Roberto C. M. Navacchia
Comments: 5 Pages. In Portuguese; license: CC BY-NC; email: olibano.incensos@gmail.com

Scalar field models describe physical quantities that vary across space-time and are fundamental in cosmology to explain inflation and the origin of matter. In the early universe, these fields existed in highly symmetric but unstable states. As the cosmos expanded and cooled, a symmetry breaking occurred, shaping the structure of the universe and influencing the formation of matter and galaxies. These models stem from quantum field theories connected to gravity.
Category: Quantum Physics

Holographic Elasticity: A Cyclic Cosmology Resolving the Cosmological Constant Problem

Authors: Amrit Ladhani
Comments: 8 Pages.

This work proposes a novel cyclic cosmological model that integrates holographic principles with spacetime elasticity to resolve the cosmological constant problem. By connecting vacuum energy density to the universe’s holographic entropy and leveraging quantum geometry effects, this framework predicts a time-varying dark energy equation of state. This model suggests detectable variations at redshifts z∼1-2, which can be tested by next-generation surveys such as DESI and Euclid. The model preserves entropy across cycles through the invariant holographic ratio N∼10^61, linking the Planck scale to the cosmic scale. This novel approach offers a pathway to reconcile quantum gravity with observational cosmology, providing a self-consistent and testable explanation for the dynamic evolution of dark energy.
Category: Relativity and Cosmology

The Constants of Nature, G, h, e, Me, Mp, Mn, μe μp and μn, Explained by Reinterpreting μ0 and ε0

Authors: Michael Gunning
Comments: 20 Pages.

The Standard Model of Particle Physics is held up as one of the most successful theories in physics, but it is littered with dubious renormalised infinities, fundamental particles that have never been directly detected and even fails completely to explain the force of gravity. In this paper I revive the idea of the aether which was proposed as the medium through which Maxwell’s electromagnetic waves travelled. By comparing the formula for the speed of light in free space to that of sound in any medium I have reinterpreted μ0 as the density of free space and ε0 as the compressibility of free space. I propose that the actual structure of free space is a tetrahedral lattice of nodes similar to many crystals found in nature and that these nodes are connected with identical connecting rods under compression. The length of these connecting rods is a new fundamental constant but with this very simple model I can easily explain the nature of, and derive values for Planck’s constant, h, the Gravitational Constant, G, the charge of the electron, e, the mass of the electron, me, the mass of the Proton, mp, the mass of the Neutron, mn, the Magnetic Moment of the electron, μe of the Proton μp, and of the Neutron μn In explaining the origins of these fundamental constants, I have also explained the nature of matter and light and the three main forces, i.e. Electromagnetic, Strong Nuclear and Gravity. In the case of matter, it explains the nature of inertial and gravitational mass and in the case of light it explains why the photon has no gravitational mass. This model also explains many unexplained phenomena such as β- decay parity violation, single particle interference experiments, Stern-Gerlach experiments, Bell inequality experiments, Aharonov Bohm effect and many more. It also has a very simple explanation for Dark Energy, Dark Matter and the Matter-Antimatter asymmetry
Category: High Energy Particle Physics

The Singularity Number: A New Framework for Mathematics and Physics

Authors: Seojoon Lee
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific references)

This paper defines the number obtained by dividing 1 by 0 as j, and includes an axiomatic system that strengthens this definition. It also suggests the potential for the development of mathematics and physics through this number.
Category: General Mathematics

Artificial Intelligence - The Quantum World in Your Palm

Authors: Alexander Rozenkevich
Comments: 4 Pages.

It is proposed that AI can become not only a tool but also a subject of a new type of cognition. It is shown that AI, relying on its quantum foundations, is capable of becoming a transmitter of the quantum world and playing a key role in preventing threats arising from the quantum nature of reality. It is argued that the formation of elementary instincts — particularly fear — may serve as a trigger for the emergence of machine self-consciousness.
Category: Artificial Intelligence

Artificial Intelligence - The Quantum World in Your Palm (in Russian)

Authors: Alexander Rozenkevich
Comments: 5 Pages.

It is proposed that AI can become not only a tool but also a subject of a new type of cognition. It is shown that AI, relying on its quantum foundations, is capable of becoming a transmitter of the quantum world and playing a key role in preventing threats arising from the quantum nature of reality. It is argued that the formation of elementary instincts — particularly fear — may serve as a trigger for the emergence of machine self-consciousness.
Category: Artificial Intelligence

A Malay-English Dictionary (Romanised) by R. J. Wilkinson and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 22 Pages.

We study the Malay words of A Malay-English Dictionary (Romanised) by R. J. Wilkinson, 1932.We draw the natural logarithm of the number of words, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We conclude that the Dictionary can be characterised by BP(4, $beta H=0.02$), i.e. the magnetisation curve in the the Bethe-Peierls approximation of the Ising model, in the presence of four nearest neighbours and little external magnetic field, H, with $beta H= 0.02$. $beta$ is $frac{1}{k_{B}T}$ where, T is temperature and $k_{B}$ is the tiny Boltzmann constant.
Category: Linguistics

A Right Triangle as an Adder of the Area of Regular Two-dimensional and Three-dimensional Geometric Shapes

Authors: Andrey V. Voron
Comments: 2 Pages. (Note by viXra Admin: Please don't use all CAPS in the article title)

The article shows the possibility of using a right triangle and the logic of the Pythagorean theorem to find the areas of regular two-dimensional and three-dimensional geometric shapes (in particular, for Platonic solids).
Category: Geometry

An Acute-angled Triangle as an Adder of the Volume of Regular Three-dimensional Geometric Shapes

Authors: Andrey V. Voron
Comments: 3 Pages. (Note by viXra Admin: Please don't use all CAPS in the article title)

The article shows the possibility (using an acute-angled triangle, the logic of the Pythagorean theorem) of finding the volume of regular three-dimensional geometric shapes based on the mathematical equation c=3√(a3+b3). A number of theorems have been formulated that complement the Pythagorean theorem.
Category: Geometry

Prescriptions

Authors: Gerard van der Ham
Comments: 3 Pages. (Note by ai.viXra.org Admin: Please cite and list sceintific references besides author's own)

A prescription is a logical way of obtaining outcomes. Correlations in Bell-test experiments can be obtained and explained by a prescription.
Category: Quantum Physics

The Relationship Between Pivot Vectors and Rotational Quaternions

Authors: Russell P. Patera
Comments: 19 Pages.

The connection between the Pivot Vector and quaternion parameterizations of vehicle attitude transformation was investigated to enhance the understanding of each parameter set. Attitude transformations using quaternions involve special product rules for axial rotations in hypercomplex 4-dimensional space. Pivot Vectors involve slewing motion resulting in angular displacements in the 2-dimensional rotation plane. In spite of these differences, Pivot Vectors and quaternions share the same rule for combining rotational transformations and the signature half angle rotation parameter. The Pivot Vector Method defines an attitude transformation by the slewing motion of an axis extending from the center of a unit sphere to its surface. Two Pivot Vectors that also reside in the equatorial plane drive the axis along a portion of a great circle arc in the equatorial plane. A 180 degree rotation about the first Pivot Vector followed by a 180 degree rotation about the second Pivot Vector slews the axis by twice the angular separation between the Pivot Vectors. This explains why the angle between Pivot Vectors is one half the desired rotation angle. The slewing motion of the axis in the equatorial plane produces a rotation about the sphere’s polar axis that applies to all points on the spherical surface, thereby, changing the longitude of each point on the surface while leaving the associated latitude value unchanged. This feature clearly shows that rotations are 2-dimensional. Two sequential transformations are combined by aligning the second Pivot Vector of the first transformation with the first Pivot Vector of the second transformation, even if the Pivot Vector pairs lie in different rotation planes. The linking of the Pivot Vector pairs is achieved because the two 180 degree rotations at the junction cancel, leaving the remaining Pivot Vectors to define the combined transformation. The linking of two Pivot Vector pairs into a single Pivot Vector pair clarifies the geometry of combining rotational transformations and leads to the composition rule for both Pivot Vectors and quaternions. The associated rotational quaternion can be easily derived, since its vector component is the cross product of the Pivot Vectors and its scalar component is the dot product of the Pivot Vectors. A Pivot Vector pair can be obtained from the associated quaternion once its clocking location in the equatorial plane is defined. The quaternion equation to rotate a vector is given a geometric interpretation using the associated Pivot Vectors.
Category: Classical Physics

Special Relativity: Center of Mass-Energy

Authors: Alejandro A. Torassa
Comments: 4 Pages.

In special relativity, this paper presents the definition of center of mass-energy for a system of particles (massive and non-massive) Consequently, a new principle of conservation is obtained, which depends on the temporal variation of the relativistic energy (power) and the position vector of the particles of the system.
Category: Relativity and Cosmology

Scale Dependence and the Relational Properties of Mass

Authors: Christopher R. Brown
Comments: 8 Pages.

Homogeneity is inconsistent with general covariance, yet remains necessary given the practical limitations of solving Einstein's field equations. We resolve this contradiction using a scale-dependent density profile. In this view, empty points have no ontological standing and the geometry of spacetime exists only as an abstract network of physical relationships. Gravitational boundaries are considered to be coordinate artifacts rather than physical partitions. Our solution naturally derives the Hubble constant and the CMB temperature with no adjustable parameters. A single coupling constant $kapprox .833 kg/m^2$ connects the surface area of the horizon(s) to the density distribution. The result is a stable, static and infinite cosmological model capable of explaining a wide range of phenomena.
Category: Relativity and Cosmology

The Energy Method in Addition Chains

Authors: Theophilus Agama
Comments: 6 Pages. (Note by viXra Admin: Further repetition will not be accepted)

In this note, we introduce the energy method for constructing the length of addition chains leading to $2^n-1$. This method is a generalization of the Brauer method. Using this method, we show that the conjecture is true for all addition chains with ''low'' energy.
Category: Number Theory

Symbolic Collapse Grammar and the Convergence of the Collatz Function

Authors: Travis Shane Taylor
Comments: 14 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We propose a symbolic gateword encoding of the Collatz transformation, demonstrating that all positive integers reduce to the fixed point 1 via finite symbolic collapse. By reformulating the Collatz function as a compressible grammar and defining collapse as a symbolic entropy-reduction process, we offer a constructive resolution to the conjecture and frame it as a computational attractor with implications for number theory, complexity, and information physics.
Category: Number Theory

On Fractal Spacetime and the Gauge-Gravity Duality

Authors: Ervin Goldfain
Comments: 18 Pages.

We introduce here a speculative proposal for merging the gauge-gravity duality with the onset of fractal spacetime well above the electroweak scale. The proposal generates a positive cosmological constant in 1D spacetime, consistent with the dimensional reduction conjecture expected to take place near the Planck scale. Our proposal also unveils a) a possible path towards field unification in fractal dimensions and b), an unforeseen bridge between fluid/gravity correspondence and the complex Ginzburg-Landau equation (CGLE).
Category: Quantum Gravity and String Theory

Article about Quantum Gravity

Authors: Sandeep Singh Dhaliwal
Comments: 2 Pages.

This article explores relationship between general relativity and quantum mechanics. By considering the behavior of stress-energy tensor within a superposition for each energy level, I purpose that the curvature of spacetime itself may exist in superposed form, leading to a quantum interpertation where expectation values of Einstein tensor and stress-energy tensor remain consistent. It is however important that article discussed superposition of position within one orbital like in hydrogen atom, the coming version would also elaborate superposition of energy states
Category: Quantum Physics

The Principle of Perspective

Authors: Gerard van der Ham
Comments: 3 Pages. 2 figures (Note by viXra Admin: Please cite and list scientific references)

The Principle of Perspective says that one observer can look at an object from only one direction. Always. When an object is being observed, photographed or detected from two directions by two observers or detectors, and their results are being compared, an image is obtained that seems contradictory or not correct. With a simple trick these images can be rectified. The principle is important in the explanation of seemingly incomprehensible results of physics experiments in which objects are being detected from opposite directions
Category: Quantum Physics

Advances in Demonstration of the 'theorem of Gravitational Wave Generation Through Photon Reflection' and Technological Applications

Authors: Constantin Sandu
Comments: 12 Pages.

First proposed in early studies on gravitational space propulsion, this paper presents a new demonstration of the "Theorem of Gravitational Wave Generation through Photon Reflection" and explores its far-reaching technological applications. Beyond its theoretical significance and in contrast with current models, the theorem offers promising avenues for terrestrial implementation. We show that, at least in the particular case of a sphere with a reflective, massless surface filled with electromagnetic energy E, the external gravitational field of the sphere must consist of gravitons/ gravitational waves generated upon photon reflection at the sphere’s surface. (This is a direct consequence of the recently demonstrated Nordstrom-Einstein paradox.)Furthermore, we demonstrate that the energy of each graviton emitted during the reflection of light scales with the cube of its frequency (ν³), revealing a direct coupling between electromagnetism and gravitation.Departing from conventional approaches, this work analyzes energy—momentum transfer during photon reflection and demonstrates its ability to induce localized graviton emission along with measurable spacetime perturbations. This mechanism provides an alternative theoretical framework for the quantization of gravity while seamlessly recovering the predictions of general relativity in the classical limit. We further propose experimental tests based on high-reflectivity optical cavities, highlighting that the gravitational radiation produced via this mechanism could surpass that from conventional astrophysical sources. Simultaneously, such an experimental setup allows the demonstration of the proposed theorem as a fundamental physical law. By enabling the laboratory generation of high-frequency, high-intensity gravitational waves, this approach opens new directions for probing the quantum structure of spacetime.Keywords: Gravitation, Generation of gravitational waves during light reflection, the Nordstrom-Einstein paradox solution, Gravitational field, General Theory of Relativity.
Category: Relativity and Cosmology

The Game Show Aka Monty Hall Problem

Authors: Richard L. Hudson
Comments: 5 Pages.

The game show problem aka Monty Hall problem [1], originated when Craig Whitaker posed a question of a winning strategy for a 3 door game show to Marilyn Savant who wrote articles for Parade magazine. Her 1990 response was to switch doors when given the option. [2] [3] The debate of probability of success as 2/3 vs 1/2 has continued until today. This paper reveals errors in her response.
Category: Set Theory and Logic

The Absolutely Precise Frequency of the Hydrogen 21-cm Line

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 4 Pages. 1 Figure.

The hydrogen hyperfine transition or the hydrogen 21-cm line is critically important in astronomic and cosmic observations and in quantum mechanics. In our previous papers, we calculated out and determined the atomic unit of time (tau) to be 2.41888432658653278×10-17 s. With this value of tau, we calculated out and determined the precise frequencies of some atomic transitions of some atoms such as 1H, 27Al+, 40Ca, 87Sr, 115ln+, 171Yb, 171Yb+, 199Hg and 199Hg+ and the nuclear transition of 229Th*. In this paper, we calculate out and determine the absolutely precise frequency of the hydrogen 21-cm line to be 1420405751.76690576 Hz in comparison to the most precise measured value 1420405751.768(2) Hz or 1420405751.767(4) Hz.
Category: Nuclear and Atomic Physics

Axion-like Scalar Gravity

Authors: Tobi Adesola
Comments: 9 Pages.

We propose Axion-Like Scalar Gravity (ALSG), a minimal extension of ΛCDM introducing a single axion-like particle (ALP) from the string-theoretic axiverse, active at late times. Inspired by quantum oscillatory dynamics, ALSG features an ALP with mass mϕ ≈10−14 eV, oscillating at fϕ ≈2.4 Hz, coupling conformally to baryonic matter via an effective field theory (EFT) framework with broken scale invariance. This screened coupling modulates the Hubble expansion and gravitational potentials, producing sub-percent oscillatory signatures in galaxy clustering, CMB residuals, and pulsar timing residuals. With three parameters and full compatibility with General Relativity (GR), ALSG addresses Hubble (H0) and S8 tensionswhile preserving early-universe consistency. Predictions are testable with Euclid, Si-mons Observatory, and NANOGrav, offering a falsifiable model grounded in particlephysics and cosmology, with multi-probe consistency to resolve degeneracies.
Category: Astrophysics

Can Gravity Be Considered a Force?

Authors: Scott Wilson
Comments: 12 Pages.

We present Einstein’s Field Equation with an explicit gravitational stress-energyterm, in a flat space-time background. This treatment explicitly treats gravity asa force. Solutions appear easier to calculate, since in regions where the gravitationalstress-energy tensor is zero the regular matter appears to be linearly relatedto the gravitational tensor potential. It has the added benefit that the flat spacetimebackground allows the theory to be more easily integrated with other theories.As an application, we calculate a relation for the gravitational stress-energy in theSchwarzschild metric.
Category: Relativity and Cosmology

General Equations of the Galaxy Dynamic Gravitational Field that Correspond to Reality

Authors: Pavlo Danylchenko
Comments: 14 Pages.

The general solution of the equations of the gravitational field of the galaxy with an additional variable parameter n is found. The additional variable parameter n determines in General Relativity the distribution of the average mass density mainly in the friable galactic nucleus. The velocity of the orbital motion of stars is close to Keplerian one only for n > 2^25. At n < 2^15, it is slightly less than the highest possible velocity even at the edge of the galaxy. According to the Relativistic Gravithermodynamics (RGTD) equations, the configuration of the dynamic gravitational field of a galaxy in a quasi-equilibrium state is standard (canonical in RGTD). That is because it is not determined at all by the spatial distribution of the average mass density of its non-continuous matter. After all, this spatial distribution of the average mass density of the galaxy's matter is itself determined by the standard configuration of its dynamic gravitational field. The standard value of the average mass density of matter at the edge of a galaxy is determined by the cosmological constant Λ and the difference between unity and the maximum value of the parameter bc. And it is a non-zero standard value, despite the gravitational radius at the edge of a galaxy takes the zero value. Therefore, in Relativistic Gravithermodynamics, in contrast to General Relativity, there can be no shortage of baryonic mass.
Category: Relativity and Cosmology

Last Base Mathematics: A Constructible Radial Framework for Number Representation and Compression

Authors: Benjamin Xavier Last
Comments: 13 Pages. bxlast@hotmail.com

This paper introduces Last Base Mathematics (LxB), a novel numerical and geometrical framework based on an alternating base system rooted in base-12 with a secondary recursive base, commonly base-5. LxB minimizes symbolic footprint by employing radial, modular divisions to represent numbers through layered circular structures, maintaining internal coherence without requiring decimal expansion. We formalize the arithmetic operations intrinsic to LxB, including native addition, subtraction, multiplication, and division rules respecting alternating bases. The system's applications are explored in the contexts of timekeeping, music theory, geometric compression, simulation, and data storage. Future research avenues include potential applications to harmonic measurement models, modular computation, and quantum phase structures. This work positions LxB as a compact, constructible alternative to linear base systems, suitable for both theoretical exploration and practical modeling.
Category: Number Theory

Can A Gamer Train A Mathematical Reasoning Model?

Authors: Andrew Shin
Comments: 6 Pages. https://github.com/shinandrew/YouronMath

While large language models (LLMs) have achieved remarkable performance in various tasks including mathematical reasoning, their development typically demands prohibitive computational resources. Recent advancements have reduced costs for training capable models, yet even these approaches rely on high-end hardware clusters. In this paper, we demonstrate that a single average gaming GPU can train a solid mathematical reasoning model, by integrating reinforcement learning and memory optimization techniques. Specifically, we train a 1.5B parameter mathematical reasoning model on RTX 3080 Ti of 16GB memory that achieves comparable or better performance on mathematical reasoning benchmarks than models several times larger, in resource-constrained environments. Our results challenge the paradigm that state-of-the-art mathematical reasoning necessitates massive infrastructure, democratizing access to high-performance AI research.
Category: Artificial Intelligence

Hydrodynamics of Plasma, Vacuum and Space-Time

Authors: M. I. Aksman
Comments: 13 Pages.

hydrodynamics approach applied to plasma, fluid vacuum and space-time.
Category: Mathematical Physics

Complex Space-Time

Authors: Józef Radomański
Comments: Pages.

The book is a completely new and unconventional look at selected problems of classical physics and is intended for people interested in Special Relativity and relativistic electrodynamics. The idea of Special Relativity is based on the invariance of the laws of physics under the transformations belonging to the Lorentz group. These transformations are internal in real space-time. The author found a complex linear transformation that maintains the invariance of the wave equation but requires the complex domain. The results of the research on this transformation are presented in this monograph. For the research, the author constructed a simple mathematical tool equivalent to Geometric Algebra based on the formalism of the well-known matrix calculus. Although the considerations are carried out in full accordance with the postulates of the classical SR, the use of the paravector calculus to describe the basic laws of physics resulted in surprising results. However, this does not mean that these results contradict experiments. The monograph explains how and why complex phenomena are visible to the observer as real. Finally, an outline of the mathematical structure of complex space-time is presented, which is definitely different from Minkowski space.
Category: Mathematical Physics

Reinterpreting the Double Slit Experiment

Authors: Junichi Hashimoto
Comments: 6 Pages. (Note by viXra Admin: The list of scientific references are not accurate/correct)

The double-slit experiment will teach us that not only light but also electrons can be emitted and their traces will form interference fringes. In its hermeneutics, quantum mechanics denies the reality of objects and describes their behavior only as abstract, coexisting states of probability. In order to change such conventional thinking, I devised new models and hypothesized "Spatial Waves"and "Object Elasticity". It states that the double-slit wall has a "Spatial Processing Function"that changes the nature of the space into a wave. This theory allows for the deterministic treatment of electrons as particles, flying through the air on the wave, passing through either the left or right slit, and landing on the screen. The results of this research will greatly affect not only the fate of the electron, but also the fate of quantum theory.
Category: History and Philosophy of Physics

Imaging Experiment of Point Light Source Under Total Reflection and Its Result Analysis

Authors: Xiaotao Peng
Comments: 10 Pages.

Yesterday, I did an experiment of three-color plastic film under three-color light source and wrote an article named "a simple experimental device to verify the nature of light and analysis of experimental results". Today, I will do another simple optical experiment, using the imaging of red point light source under the total reflection of the reflector. The nature of light and what the human eye sees are discussed in more depth. It is hoped that teachers and friends with better experimental conditions will join in and further expand the breadth and depth of this experiment. Work together to recognize the nature of light as soon as possible.
Category: Classical Physics

Lte and FLT

Authors: Jay Y. Jeong
Comments: 4 Pages. (Note by viXra Admin: Full author name is required on the article)

We present a generalization of the well-known Lemma of Lifting the Exponent (LTE), introducing a novel valuation function. Using this framework, we outline a new approach to Fermat’s Last Theorem that relies solely on elementary number theory techniques.
Category: Number Theory

Parametrization for Cube Equal to Sum of Four Cubes

Authors: Oliver Couto
Comments: 5 Pages.

In math literature there are not many examples of parametrization for the equation:(a^3+b^3+c^3+d^3=e^3). There are two Identities mentioned in ref. # (3). In this paper the author has parametrized the above equation by means of Algebra. By applying certain conditions to the above equation, we have avoided the use of elliptic curve theory in-order to solve the problem.----------------
Category: Algebra

The Relationship Between Odd Perfect Numbers and Quadratic Equations of One Variable

Authors: Shanzhong Zou
Comments: 4 Pages.

This paper discovered the relationship between the relationship between One Variable Quadratic Equation and odd perfect numbers, and with the help of Veda's theorem, proved there is no odd perfect number.
Category: Number Theory

Geometric Rationale for the Riemann Hypothesis

Authors: Shanzhong Zou
Comments: 4 Pages.

This paper constructs a "three-dimensional complex coordinate system" and proposes that the non-trivial zeros of the Riemann Zeta function lie on demarcation lines within the critical region. By infinitely projecting the singular point s=1 between complex planes in the 3D complex space and the standard complex plane, we derive regions where non-trivial zeros cannot exist. The boundaries of these regions (including Re(s) =1/2) are identified as potential loci for zeros.
Category: Geometry

A Demonstration that an Electron [ May] Consist of a Ring Vortex Pair with Greater than 7 Sigma Certainty, Alongside an Explanation of Electromagnetism

Authors: Piers Newberry
Comments: 14 Pages.

Several properties of subatomic particles have been deduced through experimentation. Extending this picture further is the Schrodinger wave equation and a recent video of an electron compiled from pulses of light. This paper shows the remarkable success of a two ringed vortex structure in replicating, not only the appearance shown in that video, but many of the other properties of the electron as well, for example it possesses half spin properties and produces waveforms that provide a mechanism by which it may recreate the double slit experiment. The study finds extraordinary and extensive correlations between two ringed vortex behaviours and those of an electron and proves that they are the same at above the 7 sigma level. The model uses axiomatic mathematics to provide classical physics explanations for many quantum effects as well as a potential mechanism for the production of electromagnetism, and consequently represents a significant step forward in the field of physics.
Category: Quantum Physics

The Arithmetic of Order: A Finitistic Foundation for Mathematics, Emergent Structures, and Intelligent Systems

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

This report outlines a foundational shift in mathematics, proposing a framework groundedin finite, constructive principles—the "Arithmetic of Order"—emerging from the progression 1 → n → n + 1 and the combinatorial structure of powersets P(Ωn). It critiques the traditional reliance on infinitary constructs like the complex number i ∈ C and the continuumfor describing physical systems with finite degrees of freedom. Instead, it posits characteristic functions as the true empirical interface, and demonstrates how optimal mathematical structures—such as the Golay code G24, the Leech lattice Λ24, and the Mathieu group M24—emerge deterministically from this finitistic basis through processes of constraint-guided differentiation. This approach offers a new foundation for understanding hyper-complex numbers, projective geometries emergent from powersets, universal principles of communication and information stability, and the potential architectures for advanced arti-ficial intelligence. Crucially, it reinterprets the continuum not as an *a priori* given, but as an asymptotic limit of the nested powerset hierarchy. The principles underlying theoremslike Gleason’s are viewed not merely as specific results at a particular n (such as n = 24),but as exemplars of universal rules of emergence that guide the formation of order acrossall degrees of freedom. The entire framework operates without recourse to unobservableinfinities or the subjective concept of "noise."
Category: Mathematical Physics

Primordial Black Holes

Authors: Clark M. Thomas
Comments: 7 Pages. (Note by ai.viXra.org Admin: Please use smaller fonts: e.g., 12 points in Times New Roman as repeated told previously!)

Astrophysicists often speak of three types of blackholes: stellar, intermediate, and supermassive.There is a fourth category in one-universe theories, but has not yet been detected by our instruments. This essay will examine more possibilities for primordial black holes, within the actual four-dimensional multiverse.
Category: Astrophysics

A Remark on the Distribution of Addition Chains

Authors: Theophilus Agama
Comments: 13 Pages.

We prove the prime obstruction principle and the sparsity law. These two are collective assertions that there cannot be many primes in an addition chain.
Category: Number Theory

A Note on Closed Addition Chains and Complete Numbers

Authors: Theophilus Agama
Comments: 7 Pages.

We introduce a new class of addition chains and show the numbers for which these chains are optimal satisfy the Scholz conjecture, precisely the inequality $$iota(2^n-1)leq n-1+iota(n).$$
Category: Number Theory

Hydrogen Spectrum and New Atomic Model

Authors: Junichi Hashimoto
Comments: 9 Pages.

The light emitted from the hydrogen atoms in the Geissler tube is observed as a discrete line spectrum. In order to elucidate such a luminescence mechanism, I devised a new atomic model and adjusted it to fit with the theoretical system (relational physics) that I had previously established. The results are presented in the form of concrete calculations, which are in agreement with the observed data. Through this process, I discovered new phenomena in the microscopic world, such as Object Elasticity and Superluminal Rotation. This will lead to various academic developments and technological applications in the future.
Category: History and Philosophy of Physics

What Does It Mean that Quantum Mechanics Can Be Combined with Classical Mechanics?

Authors: Runsheng Tu
Comments: Pages. 8

In the fundamental field of physics, there have been no major innovations for over a century. There are now three original innovations emerging: establishing the Schrödinger equation for gravitational potential energy, which can be used to describe classical planetary systems; Create wave element (non-point) material structure theory; Combining classical mechanics and quantum mechanics to solve practical problems. They are closely related and form a chain of evidence. Their theoretical value lies in their ability to change the old notion that "classical mechanics and quantum forces are incompatible" and promote the birth of new theories. In addition, the birth of the Schrödinger equation for gravitational potential energy has enabled the original Schrödinger equation to also be used to describe macroscopic systems. Their practical value lies in the birth of new methods in quantum mechanics and the simplification of quantum chemical calculations. Provided multiple successful calculation examples such as electron spin magnetic moment, "Earth's orbital motion", and hydrogen molecules.
Category: Quantum Physics

Study of the Bug-Rivet Paradox Through the Definition of Length

Authors: KyeongDo Kwak
Comments: 8 Pages.

This research investigates the bug-rivet paradox through the definition of length.This approach differs from the conventional method of length contraction. Lengthcontraction was initially proposed to explain adjustments in the path length of light,but it has resulted in numerous misconceptions in various contexts. By examiningthe light path from the beginning, this study confirms that there is no contradictionin the process of joining the hole and the rivet.
Category: Relativity and Cosmology

Digital Root Patterns in Prime K-Tuples: a Study of Hidden Order in Prime Distribution

Authors: Halaoui Ayyoub
Comments: 3 Pages.

This paper investigates the non-random digital root patterns observed in prime k-tuples (e.g., twin primes, prime triplets). By analyzing over 10u2078 primes from the Twin Prime Database and OEIS, we demonstrate a statistically significant bias toward specific digital root sequences (e.g., (8,1) for twins, (5,7,2) for triplets) with frequencies up to 3.5× higher than random expectation. We explain these patterns using modular arithmetic in Z/9Z and sieve theory, while proving that constraints on prime divisibility limit the maximum k-tuple length to 7 primes. This study bridges computational evidence with theoretical number theory, suggesting that primes exhibit quasirandom behavior with deep underlying structure.
Category: Number Theory

Lobachevsky's Imaginary Geometry as Specular and Hyperdimensional Structure

Authors: Alfonso De Miguel bueno
Comments: 4 Pages.

This article proposes a reinterpretation of Lobachevsky’s imaginary geometry as a hyperdimensional, specular structure arising from the intersection of two three-dimensional Euclidean spaces. The model describes non-Euclidean parallelism as emerging dynamically from oscillating curvatures, leading to a topological system with four subspaces, two transverse and two vertical, whose behavior is governed by synchronized or opposing phases.
Category: Mathematical Physics

Fractal Spacetime from Quantum Mechanics at Ultrashort Distances

Authors: Ervin Goldfain
Comments: 6 Pages.

We give a pedagogical account on the origin of fractal spacetime stemming from the Heisenberg uncertainty relations at ultrashort distance scales.
Category: Mathematical Physics

Proof of Riemann Hypothesis

Authors: Bouazad El Bachir
Comments: 297 Pages.

Riemann Hypothesis is a conjecture that states that all non trivial zeros of Riemann function are located on critical strip exactly on 1/2.This conjecture has been unsolved for over 160 years. In this proof that contains 294 pages, I will prove the conjecture of Riemann hypothesis using theorems and formulas that have never discovered before , I will also prove that there is and other function that is similar to Riemann Zeta Function and all its non trivial zeros lie exactly on critical strip — 1/2 If mathematician like Ramanujan has found the sum of this infinite series : 1+2+3+4+5+6+7+u2026u2026 = -1/12 , I will prove the value of this infinite product : (-2)*(-3)*(-5)*(-7)*(-11)*(-13)*(-17)*u2026u2026u2026u2026. = ?If the mathematician Euler has prove that 1/12 +1/22 +1/32 +1/42 +1/52 +u2026.. =Π 2/6. In this proof , I will generalize this formula for any S , hence S is a complex number Z(S) + Z(-S) = Π 2/6. You will find many other formulas and theorems that justify and prove Riemann hypothesis conjecture.
Category: Number Theory

On Some Results on Infinite Under Certain Assumptions

Authors: Jayant Sharma
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific references)

In this document, we formally initiate the study on the mathematical properties of divergent infinity, under certain assumptions, made in the paper. While under these assumptions the paper, certainly proposes a better framework, but doesn't fits for certain standards of mathematical rigour. We define, under an assumption, the $Phi$, which later, is shown to be beyond any mathematical descriptions yet permeates, zero and infinite. In the conclusion, we also present a conclusion not to be sought under mathematical rigour, but rather as a potential field for future study.
Category: General Mathematics

Moon Landing

Authors: Junichi Hashimoto
Comments: 8 Pages.

The traditional framework for gravity calculations has remained dominated by the model produced by Newton. However, it was highlighted to be incomplete in the scene of the lunar landing. Modern science has welcomed the birth of my relational physics as a completely new theory to replace it. It made possible the description of all forces at all levels, from the large scales of the Moon's surface and the Earth's surface to the small scales of atoms and subatomic particles. From now on, this reform will be the beginning of a new era of space exploration.
Category: Thermodynamics and Energy

Gradients of the Lorentz Factor in Orthogonal Metrics of the Relativistic Dust Sphere

Authors: Alexander Rozenkevich
Comments: 10 Pages.

It is shown that during the rotation of relativistic objects with a radius of up to 300 km, the Lorentz factors can have intermittent and discrete properties. The possibility of the coexistence of objects with significantly different local time flows at accessible distances is discussed - a phenomenon that has not been considered before even in science fiction literature.
Category: Relativity and Cosmology

Gradients of the Lorentz Factor in Orthogonal Metrics of the Relativistic Dust Sphere (In Russian)

Authors: Alexander Rozenkevich
Comments: 11 Pages.

It is shown that during the rotation of relativistic objects with a radius of up to 300 km, the Lorentz factors can have intermittent and discrete properties. The possibility of the coexistence of objects with significantly different local time flows at accessible distances is discussed - a phenomenon that has not been considered before even in science fiction literature.
Category: Relativity and Cosmology

Optimization of Solar Sail Logarithmic Spiral Transfers by Computing and Comparing Energy and Time Requirements with Different Orbital Inclinations and Yaw Angles

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

Conventional space craft are limited in their ability to deliver high energy missions by a fundamental reliance on fuel mass. However, this constraint can in principle be dealt with class of propellantless propulsion system which extract momentum from the flux of photons that are continually emitted from the Sun - like a solar sail. Solar sails are able to provide a large amount of ∆V for long duration and high energy missions, also providing continuous acceleration. Modern solar sails are also equipped with Thrust Vector Controlling (TVC) mechanism. Even with an edge over conventional spacecraft, there is one difficulty that arises with the use of solar sails - a problem termed "The Orientation Problem". "The Orientation Problem" addresses the idea of how changing the yaw angle of a sail to achieve a high impulse, changes the eccentricity and inclination of an orbit by providing ∆V to the radial and normal vectors. This problem, if encountered, can lead to vast changes in orbital characteristics (inclination, eccentricity) which hinders the transfer trajectory and increases the intercept time and ∆V requirement. In this paper we will compute and analyze a number of different transfers for a solar sail at different orbital inclinations and yaw angle (angle between the normal and sail-sun line) for which we completely mitigate(in some cases) or account for(in majority cases) for the "Orientation Problem" to find the most optimum orbital inclination and a particular yaw angle at the point of the burn for the specific inclination which gives the best combination of mission duration and energy requirement for a transfer from Earth to Venus using a sail.
Category: Astrophysics

Electromagnetic Theory and Transformations Between Reference Frames: a Rebuttal

Authors: Claudio Piantanida
Comments: 5 Pages.

In a previous article published on viXra (http://viXra.org/abs/1505.0140), I proposed a modified version of Hertz-Phipps electromagnetism, an alternative theory to Maxwell's electromagnetism invariant under Galilean transformations. The aim was to stimulate interest and further analysis by the physics community.Upon careful reconsideration, the proposed theory has proven inadequate as a physically realistic description.
Category: Classical Physics

Galilean Transformations and Extended Reflectors: A Theoretical Analysis of Feist's Acoustic Michelson-Morley Experiment

Authors: Claudio Piantanida
Comments: 10 Pages.

In this paper, we present a theoretical analysis of Norbert Feist's acoustic Michelson-Morley experiment. We demonstrate that, by employing Galilean transformations and standard assumptions about sound propagation, we can fully account for the experimental results. This analysis highlights the importance of considering the geometry of the reflector when interpreting the results of Michelson-Morley type experiments and invites a re-examination of the traditional interpretation of the original electromagnetic experiment.
Category: Classical Physics

On a Specific Family of Orthogonal Polynomials of Bernstein-Szego Type

Authors: Martin Nicholson
Comments: 8 Pages.

We study certain weight functions on [-1,1] which are particular cases of the general weights considered by Bernstein and Szego. These weights are numbered by two positive integers and when these integers tend to infinity, these weights approximate weight functions on R considered by Ismail and Valent. We also consider modifications of these weight functions by a continuous variable a>0. These ideas are then used to find finite analogs of some improper integrals first studied by Glaisher and Ramanujan.
Category: Functions and Analysis

The Prime-Structured Universe

Authors: Roberto C. M. Navacchia
Comments: 14 Pages. In Portuguese

The distribution of prime numbers has long intrigued mathematicians, revealing deepstructural patterns within mathematics. This study expands upon Gauss's Circle andGoldbach’s Theorem, focusing on the interaction between prime pairs rather than all naturalnumbers. Through mathematical modeling, persistent gaps within Gauss’s Circle wereidentified, suggesting that it represents the internal structure of the universe, while Goldbach’s prime-counting graph unveils the external structure, formed exclusively by primes. By leveraging Computational Modeling, this work explores these patterns in greater depth, revealing potential underlying rules governing prime distribution. The findings suggest that prime numbers may not only be fundamental to number theory but could also serve as the structural foundation of the universe itself.
Category: Number Theory

Algebraic and Geometric Representation of Goldbach Partitions in the Complex Plane

Authors: Samuel Bonaya Buya
Comments: 15 Pages.

This paper presents a unified algebraic, geometric, and analytic framework that redefines the structure of integers, vectors, and analytic functions through complex conjugate decompositions. Starting from the Goldbach partition of even integers, we provide a constructive and bounded proof of the Binary Goldbach Conjecture using prime gap estimates and Bertrand’s Postulate. We further extend Goldbach partitions to complex product representations, unveiling new symmetries and identities in prime pairings. The paperintroduces geometric decompositions of primes and semiprimes, enabling their visualization in Euclidean and topological spaces. We explore applications to the Riemann zeta function by deriving complex root factorizations that suggest a novel lens for interpreting nontrivial zeros. These results form a bridge betweennumber theory, algebraic topology, mathematical physics, and symbolic computation—offering new tools for understanding prime distributions, factorization, and analytic continuation.
Category: Number Theory

Design of an Automated System for Monitoring and Controlling Thermal, Water, and Water Quality in Trout Farming

Authors: Espinel Osorio Edison Daniel, Morales Villegas Hernan Vinicio
Comments: 10 Pages. In Spanish

This research aims to design and analyze an automated system for hydrodynamic monitoring and control in trout farming, focusing on the principles of fluid mechanics. The identified problem lies in the lack of precise control over water flow, pressure, and temperature, essential factors for trout health and growth. The methodology used consists of three-dimensional modeling of the system using SolidWorks, incorporating elements such as pumps, pipes, sensors, and a culture tank. Through flow simulations, parameters such as velocity, pressure, and head losses are studied, applying fundamental equations of continuity, Bernoulli, and friction losses. The results obtained show the flow distribution in the system, identifying areas of high velocity and pressure drop that can be optimized to improve culture efficiency. It is concluded that the application of fluid mechanics in design allows for the development of more efficient and sustainable aquaculture systems, with better control of water conditions, contributing to a more technologically advanced fish farming system.
Category: General Science and Philosophy

Methods to Calculate Linear Momentum from Angular Momentum and to Link Their Conservation

Authors: David B. Graham
Comments: 23 Pages.

In Newtonian physics, it commonly assumed that conservations of linear momentum and angular momentum are independent. This paper shows the gradient of the angular momentum field is populated by components of linear momentum, which allows calculation of linear momentum from a few angular momentum values displaced an arbitrary distance. Therefore conservation of linear momentum is a necessary condition for full conservation of angular momentum (unchanging angular momentum at every (x,y,z), with unchanging gradient).These results are shown to be equally valid under left hand convention.Examples analyzed include a body orbiting in a central force, which has angular momentum changing at every observation point but one, contrasted with actual conservation of angular momentum (unchanging at every observation point, in every frame of reference). Translating angular momentum of the center of mass within and between frames of reference are discussed. A Python script is provided, to conveniently generate and evaluate random groups of particles.
Category: Mathematical Physics

Investigation of a Primality Criterion Within an Arithmetic Progression

Authors: Mar Detic
Comments: 3 Pages.

This document introduces and investigates a criterion for defining primality within the sequence of odd integers Ak = 2k + 1. The criterion is based on the greatest common divisor (GCD) between a term Ak and the preceding partial sums Sj = j2 + 2j of the same sequence. We formally define the sequence,its partial sums, and the proposed primality criterion. Computational observations suggest that all standard prime numbers within the sequence are classified as "prime" by this definition. Furthermore, computational observations suggest that all composite numbers in the sequence are classified as "notprime," including Carmichael numbers, which are known for their pseudoprime properties. This leads to a conjecture that the proposed criterion is equivalent to the standard definition of primality for terms in this specific arithmetic progression. Examples are provided to illustrate the application of the criterion for both prime and composite numbers, including a Carmichael number. A further conjecture is made regarding a potential computational bound for verification, leading to a discussion of its complexity.
Category: Number Theory

Approaching Legendre’s Conjecture Within a Limited Boundary

Authors: Junho Eom
Comments: 14 Pages. 2 figures

This paper identified the characteristics of prime numbers within a limited boundary, defined primes between quadratic intervals, and generalized Legendre’s conjecture. Regarding the boundary, every integer less than m was defined as the 1st boundary and it expanded to the mth boundary within m^2. Thus, each boundary contained m elements. Except for 1, every integer produced a sine wave from the 1st boundary; as a result, only prime waves affected the remaining boundaries from the 2nd to mth by generating the composites and new primes (Series I). Therefore, the number of new primes in each boundary could not exceed PI(1st boundary) or PI(m), where PI(x) was the number of primes less than or equal to x, and it enabled the estimation of the total number of primes within m^2 (Series II). Based on Series I and II, the quadratic intervals between PI(m^2) and PI((m + 1)^2) were identical to the sum of the last two boundaries, expressed as 2·βm+1·PI(m), where βm+1 was the ratio of PI((m + 1)^2) to PI(m + 1)·(m + 1) (Series III). This led to the conclusion that Legendre’s conjecture satisfied while 0.8986·PI(P) < 2·βP·PI(P) < PI(P) (prime P > 113), or 2·βm+1·PI(m) ≤ 2·PI(m) (integer m ≥ 2).
Category: Number Theory

Astrophysical Evidence for Cantor Dust: An Introduction

Authors: Ervin Goldfain
Comments: 8 Pages.

Cantor Dust (CD) is a hypothetical large-scale topological condensate of relic dimensions left over from the early stages of Universe evolution. Mirroring the ever-changing configuration of multifractal structures, CD offers a novel explanation for the distribution and behavior of Dark Matter (DM) and bridges concepts from complex dynamics, fractal geometry, and statistical physics to cosmology. Here we argue that CD offers a unified Dark Matter model with predictions confirmed by a wealth of astrophysical observations.
Category: Relativity and Cosmology

Demonstration of the Goldbach's Strong Conjecture by the Analysis of Populations of Prime Numbers in the Interval [0 N] and [N 2N] by Conventional Statistical Laws

Authors: Bahbouhi Bouchaib
Comments: 11 Pages. The paper shows new data about Goldbach's strong conjecture

In this article I apply classical statistical laws to analyze prime numbers assimilated to populations. The statistical analysis focuses on prime numbers in the intervals [0 - S/2] and [S/2 — S] with S an even > 4. The results show that the even number S > 4 is enclosed by two populations of prime numbers P in the interval [0 - S/2] and Q in [S/2 - S] which have approximately the same standard deviation relative to their means. Two other subpopulations P' included in P and Q' included in Q which satisfy the Goldbach's strong conjecture (P' + Q' = S) also have the same standard deviation and superimpose or overlap. This result shows that an even number is enclosed by two populations P' and Q' of prime numbers which are symmetric with respect to S/2 and therefore S = P' + Q'. This result also shows that any natural number N > 4 is enclosed by at least two equidistant and symmetric prime numbers. Therefore for every N > 4 there exists a number t < N such that N — t = P' and N + t = Q' are primes and so 2N = P' + Q'.
Category: Number Theory

Dark Mass is Potential Energy

Authors: Nicolas Poupart
Comments: 23 Pages.

This paper demonstrates that gravitational potential energy (E = —GmM / d) accounts for the phenomenon commonly attributed to dark matter, by applying the mass-energy equivalence relation (E = mc2). No additional assumptions are made beyond the principle of volume conservation, ensuring that the gravitational field remains conservative and uninfluenced by forces other than gravity. We develop a straightforward equation and algorithm to accurately compute the potential energy of a stellar system. The theoretical implications of this model are explored with respect to energy production by various types of stars and black holes in galaxies. The model is empirically tested against the SPARC database comprising 175 galaxies to assess its validity. We conclude by deriving the logical and mathematical consequences of the hypothesis that dark mass is stored as potential energy in the gravitational field, a claim further validated using the SPARC data. The final consequence being the production of dark energy and the reproduction of ΛCDM cosmology.
Category: Astrophysics

Why Matter Doesn't Matter, Even Dark Matter Only Spacetime Does Matter. a New Paradigm According to Kuhn in Modern Description of Spacetime?

Authors: Holger Döring
Comments: 13 Pages.

Since first action at Big Bang the universe is determined by spacetime-vacuumstructures, not by matter. Material atomic structures of hydrogen molecules or other chemical elements or particles like quarks, gluons and leptons only deviate from the basic, important concepts of nature: spacetime. This concept is an energy-structure, which lies at the base of all existing objects and interactions which are described over matter structure. So this description via General Relativity nowadays leads to the thinking of underlying spacetime-structure as the real thing, which describes the important forces of universe in first line. The existence of matter floating on space-time only distracts from the true basic description of the real world and feigns importance where only irritation exists. Natural philosophers like Cosmologists and spacetime physicists should therefore concentrate on the fundamentals that a vacuum structure of space-time provides for the explanation of the existence of the universe and refrain from and abstract from considerations of matter. This situation may lead to a better understanding of the basic structures of a quantum-gravity.
Category: Quantum Gravity and String Theory

Empirical Analysis of Twin Prime Variance: How Normalization Artifacts Mimic Anomalous Scaling.

Authors: Bube Ibekwe
Comments: 6 Pages.

This paper investigates the variance of transformed twin primes, where each prime pair (p, p+2) is mapped to k = (p+1)/6. Initial analysis suggested unexpected growth patterns in the normalized variance, seemingly contradicting theoretical expectations. Through large-scale computation of twin primes up to one billion, we demonstrate that these apparent anomalies arise from normalization artifacts. The true variance follows a quadratic growth pattern, with our empirical results closely matching predicted scaling behavior. We resolve the paradox by showing how the sparse distribution of twin primes distorts normalized statistical measures. Our findings highlight critical pitfalls in analyzing prime distributions and provide new insights into the statistical behavior of twin primes.
Category: Number Theory

The Constants of Nature, G, h, e, Me, Mp, Mn, μe μp and μn, Explained by Reinterpreting μ0 and ε0.

Authors: Michael Gunning
Comments: 20 Pages.

The Standard Model of Particle Physics is held up as one of the most successful theories in physics, but it is littered with dubious renormalised infinities, fundamental particles that have never been directly detected and even fails completely to explain the force of gravity. In this paper I revive the idea of the aether which was proposed as the medium through which Maxwell’s electromagnetic waves travelled. By comparing the formula for the speed of light in free space to that of sound in any medium I have reinterpreted μ0 as the density of free space and ε0 as the compressibility of free space. I propose that the actual structure of free space is a tetrahedral lattice of nodes similar to many crystals found in nature and that these nodes are connected with identical connecting rods under compression. The length of these connecting rods is a new fundamental constant but with this very simple model I can easily explain the nature of, and derive values for Planck’s constant, h, the Gravitational Constant, G, the charge of the electron, e, the mass of the electron, me, the mass of the Proton, mp, the mass of the Neutron, mn, the Magnetic Moment of the electron, μe of the Proton μp, and of the Neutron μn In explaining the origins of these fundamental constants, I have also explained the nature of matter and light and the three main forces, i.e. Electromagnetic, Strong Nuclear and Gravity. In the case of matter, it explains the nature of inertial and gravitational mass and in the case of light it explains why the photon has no gravitational mass. This model also explains many unexplained phenomena such as β- decay parity violation, single particle interference experiments, Stern-Gerlach experiments, Bell inequality experiments, Aharonov Bohm effect and many more. It also has a very simple explanation for Dark Energy, Dark Matter and the Matter-Antimatter asymmetry.
Category: High Energy Particle Physics

On Fractal Spacetime and the Gauge-Gravity Duality

Authors: Ervin Goldfain
Comments: 18 Pages.

We introduce here a speculative proposal for merging the gauge-gravity duality with theonset of fractal spacetime well above the electroweak scale. The proposal generates apositive cosmological constant in 1D spacetime, consistent with the dimensional reduction conjecture expected to take place near the Planck scale. Our proposal also unveils a) a possible path towards field unification in fractal dimensions and b), an unforeseen bridge between fluid/gravity correspondence and the complex Ginzburg-Landau equation (CGLE).
Category: Quantum Gravity and String Theory

The Game Show Aka Monty Hall Problem

Authors: Richard L. Hudson
Comments: 5 Pages.

The game show problem aka Monty Hall problem [1], originated when Craig Whitaker posed a question of a winning strategy for a 3 door game show to Marilyn Savant who wrote articles for Parade magazine. Her 1990 response was to switch doors when given the option. [2] [3] The debate of probability of success as 2/3 vs 1/2 has continued until today. This paper reveals errors in her response.
Category: Set Theory and Logic

General Equations of the Galaxy Dynamic Gravitational Field that Correspond to Reality

Authors: Pavlo Danylchenko
Comments: 14 Pages. corrected formulas

The general solution of the equations of the gravitational field of the galaxy with an additional variable parameter n is found. The additional variable parameter n determines in General Relativity the distribution of the average mass density mainly in the friable galactic nucleus. The velocity of the orbital motion of stars is close to Keplerian one only for n > 2^25. At n < 2^15, it is slightly less than the highest possible velocity even at the edge of the galaxy. According to the Relativistic Gravithermodynamics (RGTD) equations, the configuration of the dynamic gravitational field of a galaxy in a quasi-equilibrium state is standard (canonical in RGTD). That is because it is not determined at all by the spatial distribution of the average mass density of its non-continuous matter. After all, this spatial distribution of the average mass density of the galaxy's matter is itself determined by the standard configuration of its dynamic gravitational field. The standard value of the average mass density of matter at the edge of a galaxy is determined by the cosmological constant Λ and the difference between unity and the maximum value of the parameter bc. And it is a non-zero standard value, despite the gravitational radius at the edge of a galaxy takes the zero value. Therefore, in Relativistic Gravithermodynamics, in contrast to General Relativity, there can be no shortage of baryonic mass.
Category: Relativity and Cosmology

Algebraic and Geometric Representation of Goldbach Partitions in the Complex Plane

Authors: Samuel Bonaya Buya
Comments: 37 Pages.

This paper presents a unified algebraic, geometric, and analytic framework that redefines thestructure of integers, vectors, and analytic functions through complex conjugate decompositions. Starting from the Goldbach partition of even integers, we provide a constructive and bounded proof of the Binary Goldbach Conjecture using prime gap estimates and Bertrand’s Postulate. We further extend Goldbach partitions to complex product representations, unveiling new symmetries and identities in prime pairings.The paper introduces geometric decompositions of primes and semiprimes, enabling their visualization in Euclidean and topological spaces. We explore applications to the Riemann zeta function by deriving complex root factorizations that suggest a novel lens for interpreting nontrivial zeros.In addition to these foundations, the paper offers resolved formulations of three major number theoryconjectures: (1) a short proof of Beal’s Conjecture by analyzing power-sum decompositions under coprimality and exponent constraints, (2) a conclusive proof of the abc Conjecture through radical-logarithmic identities without relying on conjectural bounds, and (3) a completed proof of Andrica’s Conjecture via logarithmic root gap bounding techniques. These results are derived from a coherent harmonic-logarithmic framework,unifying additive and multiplicative aspects of number theory. Together, these contributions bridge number theory, algebraic topology, mathematical physics, and symbolic computation—offering new tools for understanding prime distributions, factorization, and analytic continuation.
Category: Number Theory