All Submission Categories

Extended Diophantine Equation

Authors: Dinh Van Tien
Comments: 54 Pages.

This paper presents a comprehensive overview of extended Diophantine equations—high-degree equations that admit infinitely many solution sets, with each set comprising infinitely many elements. We focus on the effective application of the formula: ab = k(a+b) + c, where a, b, k, and c are integers, to transform complex equations into symmetric forms. This transformation facilitates the derivation of polynomial expansions and enables the systematic construction of solution sets with distinct and primitive elements.
Category: Number Theory

[Speculation on the] Development of a Yeast-Expressed Oral Avian Influenza Vaccine Incorporating Conserved HA and NA Antigens and a PltB Adjuvant

Authors: Hyunho Shin
Comments: 14 Pages.

Background: The ongoing spread of avian influenza (AI) in poultry has led to severe losses. In the United States, H5N1 outbreaks by early 2025 necessitated the culling of roughly 148 million laying hens, causing egg shortages and price spikesu200b. Although AI vaccines exist, their use in U.S. poultry has been minimal due to practical and economic barriers, including trade restrictions and vaccination. Objective: This study introduces a novel oral AI vaccine strategy using genetically engineered Saccharomyces cerevisiae (baker’s yeast) to deliver conserved antigenic fragments of the H5N1 hemagglutinin (HA) and neuraminidase (NA) proteins, together with a Salmonella-derived Pertussis-like toxin B subunit (PltB) as a mucosal. The goal is to stimulate protective mucosal immunity via feed-based administration, providing a cost-effective and scalable alternative to injectable vaccines. Methods: Conserved epitopes — specifically the HA2 subunit fusion peptide region (amino acids 1—78 of H5) and a portion of the NA1 head domain (amino acids 220—290) — were identified based on high cross-strain conservation and immunogenic. Genes encoding these segments were fused in-frame with the Salmonella PltB gene, separated by flexible linkers, under control of a yeast expression system. The recombinant yeast was grown, inactivated, and formulated into a dry powder to mix with poultry feed. Protein expression and folding were confirmed by Western blot and structural modeling.
Category: Physics of Biology

Resolution of the Abraham—Minkowsli Controversy

Authors: Andrew T. Hamilton
Comments: 3 Pages.

The Abraham—Minkowski controversy has arisen because the Minkowski stress-energy tensor for the electromagnetic field in polarized and magnetized matter is not symmetric. This note proposes an alternative that is both symmetric and traceless.
Category: Classical Physics

About the Gravitational Wake of the Galaxy

Authors: A. V. Antipin
Comments: 14 Pages. In Russian

Wake gravitational waves are a supposed phenomenon resulting from the movement of material bodies in the Absolute Space-Time of the universe as a whole.Thus, Wake gravitational waves are a test that, if positive, will provide clear, indisputable arguments in favor of the existence of a dedicated (absolute) frame of reference. This article is devoted to the consideration of the Wake gravitational waves of the Galaxy. It follows an article that examined the Wake gravitational waves of the Sun and Moon. Estimates of the physical and geometric characteristics of the Galactic Gravitational Wake are presented here. Their calculated impact on the Solar System turned out to be insignificant.

Кильватерные гравитационные волны - это предполагаемое явление, возникающее в результате движения материальных тел в Абсолютном Пространстве-Времени — Вселенной, как целое. Т.о., Кильватерные гравитационные волны является тестом, который, в случае положительного результата, даст ясные, неоспоримые аргументы в пользу существования выделенной (абсолютной) системы отсчёта. Данная статья посвящена рассмотрению Кильватерных гравитационных волн Галактики. Она следует за статьёй, в которой рассматривались Кильватерные гравитационные волны Солнца и Луны. Здесь представлены оценки физических и геометрических характеристик Кильватерных гравитационных волн Галактики. Их расчётное воздействие на Солнечную систему оказалось незначительным.
Category: Relativity and Cosmology

Digital Information is Volatile, so We Need Its Preservation

Authors: Stefano Cariolato
Comments: 26 Pages. (Note by viXra Admin: An abstract in the article is required)

This article is destined for social sciences, humanities and science researchers, in addition to general public: it is not a technical paper and it is understandable by anyone. Today the digital revolution is almost completed and information of any kind (texts, images, video clips and TV broadcasts, music and songs, WEB pages) is now recorded and disseminated in digital format rather than with a traditional media (paper, film, magnetic tape), with a change that concern all human activities of any type, both collective and individual. Moreover, also archived printed records are increasingly transformed into digital format, both for diminishing their volume and for having faster search procedures, while the new information is only directly generated in the electronic form. Besides those other recordings are also volatile by their very nature, such as e-mails or WEB pages, but they could host information of value in the future and they equally may deserve conservation. Starting with paleolithic graffiti engraved in caves, followed by inscriptions on stones, cuneiform scripts on clay tablets, texts on vellum or silk and papyrus rolls, ending with paper, ever information has been registered in a persistent form visible and immediately readable by a human being knowing that type of writing. But while a book or a letter can immediately be read even centuries after its writing, if its physical support has withstood the time passing, digital information has a shorter life, even in the absence of deterioration of the used media. That because of the same technological development that makes quickly obsolete any recording by irreversibly mutating both the reading hardware and software. Finally digital recordings are carried out in a great variety of different formats, sometimes incompatible with each other or subject themselves to obsolescence, thus unnecessarily complicating the task of preserving the digital document content. If humanity does not find the way and the will to preserve the content of digital documents, similarly to what was done in the past with paper documents, gradually the culture generated in each period will decrease until it shall disappear. A story without a future would create a future without history.
Category: Social Science

SunQM-9s1: Updates and Corrections for the SunQM Series Articles (Part-1)

Authors: Yi Cao
Comments: 29 Pages.

This is not a research article, but a collection of updates, corrections, terminology normalizations, and questions/answers (Q/A) for my 37 of SunQM series articles that have been posted at the preprint server viXra.org (from April 2018 to February 2025). ... During my ~10 years (2014 ~ 2025) closed-door development on the {N,n} QM (through the "global energy minimization" kind of research), some of my early stage work lacks of consistency with the late stage work, and thus needs to be updated and corrected. Those important updates and corrections have mostly been presented in the late stage SunQM articles. The current paper includes the rest updates and corrections (that may be less important). The current paper (SunQM-9s1: Update u2026 (part-1)) covers the updates for SunQM-1, 1s1, 1s2, 1s3, 2, 3, 3s1, 3s2, 3s6, 3s7, 3s8, 3s3, 3s9, 3s4, 3s10, 3s11, 4, 4s1, 4s2, 5, 5s1, and 5s2. The next paper (SunQM-9s2: Update u2026 (part-2)) covers the updates for SunQM-7, 6, 6s1, 6s2, 6s3, 6s4, 6s5, 6s6, 6s7, 6s8, 6s10, 6s10, 6s11, 7s1, and 7s2. I also wish that the {N,n} QM (or any fragment of it) can be the useful building material for the scientific community to build the more completed QM.The previous copyright "© All rights reserved" that was written in the original 37 SunQM series articles is abolished now. Here I grant the new copyright "CC BY-NC-SA 4.0" to each individua of 37 SunQM series articles (including SunQM-1, 1s1, 1s2, 1s3, 2, 3, 3s1, 3s2, 3s6, 3s7, 3s8, 3s3, 3s9, 3s4, 3s10, 3s11, 4, 4s1, 4s2, 5, 5s1, 5s2, 7, 6, 6s1, 6s2, 6s3, 6s4, 6s5, 6s6, 6s7, 6s8, 6s10, 6s10, 6s11, 7s1, and 7s2), (started from today 3/24/2025).
Category: Quantum Physics

Applications of Mathematics in Supervised Learning

Authors: Alinda Rolland Mucunguzi, Laure Gouba
Comments: 22 Pages. 3 figures

In this work, we explore some applications of mathematics in the development and usage of supervised learning algorithms with a strong focus on linear regression models. Subsequently, we look at the mathematical foundations essential for supervised learning, which include linear algebra, probability theory, calculus, optimization, statistics, and geometry. For a concrete illustration of the applications of mathematics in supervised learning, this work employs simple and multiple linear regression models using data that is about pH of pure water. Through these examples, we demonstrate how mathematical techniques are applied in formulating, estimating and evaluating linear regression models. Key processes such as least squares estimation and statistical inference are highlighted to show their critical application in parameter estimation and model validation. The findings underscore the importance of mathematical rigor in ensuring accuracy and interpretability of supervised learning models.
Category: General Mathematics

F(U)-Gravity: A Unified Framework for Singularity Resolution, Dark Matter, and Quantum Gravity

Authors: Vivan Mirchandani
Comments: 13 Pages.

I introduce F(U)-gravity, a modified gravitational framework extending Einstein’s theory by incorporating an energy-dependent curvature function F(U). This approach addresses fundamental issues in cosmology and quantum gravity, including singularity resolution, the nature of dark matter, and deviations from standard general relativity. By modifying the Einstein-Hilbert action, I derive new field equations and examine their thermodynamic and observational consequences. My theoretical predictions suggest distinct signatures in gravitational wave echoes and cosmic microwave background anomalies, which could provide experimental validation through upcoming LIGO and LISA observations. This work builds upon approaches such as those proposed by Rosen [Phys. Rev. 57, 147 (1940)] and Stelle [Phys. Rev. D 16, 953 (1977)], offering a novel perspective on the quantum nature of spacetime.
Category: Quantum Gravity and String Theory

The Method of Dividing the 60° Angle Into Three Equal Parts

Authors: Hongfa Zi, Hongyun Zi
Comments: 5 Pages.

The problem of dividing a 60 ° angle into three equal parts in modern mathematics has not yet been solved. This involves the infinite extension of this trigonometric function in a generalized perspective. After research, it was found that the solution is located between r and two-thirds of r. The former represents a curve, while the latter represents a horizontal line. This article aims to utilize the relationships between various shapes to divide the 60 ° angle into three equal parts, which can then be extended to any angle less than 180 ° between r and two-thirds of r.
Category: Geometry

Verification Experiment of Faraday's Law of Electromagnetic Induction Based on a RF Alternating Magnetic Field

Authors: Hongyuan Ye
Comments: 6 Pages.

As one of the three fundamental universal laws of electromagnetism, Faraday's law of electromagnetic induction reveals that the induced voltage generated in a metal coil is proportional to the number of turns of the coil and the rate of change of the magnetic flux passing through a single turn of the coil. New research indicates that Faraday's law of electromagnetic induction is only an engineering approximation formula, and Lorentz's magnetic field force theorem is the microscopic physical essence of the electromagnetic induction. This verification experiment utilizes two induction coils CA and CB with identical structure and dimensions. CA is wound uniformly with 15 turns in a single layer, and CB is wound densely with 30 turns in a single layer. The ratio of the number of turns between CB and CA is 2. The two coils CA and CB are sequentially placed in sinusoidal alternating magnetic fields with frequencies of 200Hz, 50MHz and 100MHz, respectively. The experiment demonstrates that at a low frequency of 200Hz, the ratio of the induced voltages of CB and CA is approximately 2, which is proportional to the number of turns of two coils. Under low-frequency conditions, Faraday's law of electromagnetic induction and the experimental results are well approximated and consistent. At a radio frequency of 50MHz, the ratio of the induced voltages of coil CB and coil CA is 1.52, which significantly deviates from the ratio of the number of turns of coil CB and coil CA, which is 2. Faraday's law of electromagnetic induction and the experimental results are clearly inconsistent. At a radio frequency of 100MHz, the ratio of the induced voltages of coil CB and coil CA is 0.83, with the induced voltage of the 30-turn induction coil CB being smaller than that of the 15-turn coil CA. Faraday's law of electromagnetic induction and the experimental results are completely opposite. The reason is that Faraday's law of electromagnetic induction does not take into account the electromagnetic radiation of the induction coil, and assumes that the propagation speed of the electromagnetic field is infinite. Faraday's law of electromagnetic induction is one of the two necessary conditions of the "electromagnetic wave" theory. Faraday's law of electromagnetic induction does not hold true in the RF "electromagnetic wave", which further proves that the "electromagnetic wave" theory is incorrect. There is no an "electromagnetic wave" in the objective physical world, and it is an independent electric field wave that realizes wireless communication.
Category: Classical Physics

Possible Evidences from $H(z)$ Parameter Data for Physics Beyond Lambda CDM

Authors: Rong-Jia Yang
Comments: 7 Pages.

We analyse $H(z)$ parameter data with some conditions by using Lagrange mean value theorem in Calculus. We find that: (1) there exists decelerated phase at 1 $sigma$ confidence level in the redshift range $(0.38, 0.59)$; (2) the equation of state of dark energy may be less than $-1$ at 1 $sigma$ confidence level at some redshifts in the redshift range $(1.3, 1.53)$; (3) there exists accelerated phase at 1 $sigma$ confidence level in the redshift range $(1.037, 1.944)$. These results may provide possible evidences for physics beyond $Lambda$CDM.
Category: Relativity and Cosmology

The Universe Circulation System

Authors: Ichiro Nakayama
Comments: 8 Pages. (Note by viXra Admin: For the last time, please cite and list scientific references!)

The currently mainstream standard cosmology has many problems to be solved, such as dark matter and dark energy. Inflation theory is also difficult to believe. The Energy Body Theory has elucidated the cause of the rotation speed of spiral galaxies, which is the basis for the existence of dark matter. And it has also revealed what dark energy is and showed the reason why galaxies move away isotropically and acceleratingly. This time, I propose that the entire universe is one energy body, and the uneven distribution of energy generated in the energy body forms positive energy of stars and gravitational fields, and the formations of them are accompanied by the formations of dark energy fields, and further throughout the universe, positive energy of stars and gravitational fields circulate by exchanging energy with negative energy of dark energy. This system is called the universe circulation system. The universe exists in eternal time that is not expanding.
Category: Astrophysics

The Light Interaction With Light

Authors: Miroslav Pardy
Comments: 7 Pages. Original article

The scattering of light by light is considered in case where the internalparticles of this process have spin zero. The original calculation of this process wasperformed by Karplus et al. (1950). The pedagogical explanation of this proceswas realized for instance by Akhiezer et al. (1965), or, by Beresteteskii etal. (1982). We use here the model with the Green function for the spin zero particles. The article is written with the mathematical simplicity and the Schwinger pedagogical clarity
Category: High Energy Particle Physics

Permutation Rotations

Authors: Bassam Abdul-Baki
Comments: 7 Pages.

In this paper, we discuss certain properties of permutation rotations on each other.
Category: Combinatorics and Graph Theory

A Small Contribution to Ross-Littlewood Paradox

Authors: Marko V. Jankovic
Comments: 6 Pages.

In this paper Ross-Littlewood paradox is going to be analyzed. Two new experiments were proposed and it will be argued that number of balls at the end of experiment is infinite.
Category: General Mathematics

Solving Recurrence Relations Using Generating Functions

Authors: Harry Willow
Comments: 7 Pages.

This paper explores the applications of generating functions in solving various recurrence relations. We present the explicit formulas for recurrence relations of different forms, demonstrating step-by-step transformations and manipulations using generating functions. Several cases are examined, including linear and nonlinear recurrences, factorial-based sequences, and Fibonacci-related expressions. The derivations leverage algebraic techniques and characteristic equations to obtain closed-form solutions. The results highlight the power of generating functions in simplifying complex recurrence relations and deriving explicit formulas efficiently.
Category: Functions and Analysis

Artificial Prime Numbers Primality Assessment and Analysis in Specific Contexts

Authors: Jose Acevedo Jimenez
Comments: 5 Pages. In Spanish (Note by viXra Admin: Listed scientific references should be cited in the article)

This article explores the concept of artificial prime numbers, defined within specific sets of integers. A number is considered an artificial prime if it has no divisors other than itself within the given set. Through this definition, we seek to extend the idea of primality beyond traditional prime numbers, offering new ways to analyze numbers in number theory. Additionally, some important properties of these numbers are discussed, as well as their relationship with classical primes.
Category: Number Theory

A Transcausal Theory of Quantum Gravity and Map to UFT

Authors: Jennifer Lorraine Nielsen
Comments: 35 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

This paper presents a novel quantum gravity framework within a 6-dimensional spacetimeS^3 × R × C_τ , aiming to unify the four fundamental forces via geometric and transcausalstructures. The 3-sphere S^3 provides spatial topology, R a real-time axis, and Cτ a complexblock-time plane hosting transcausal effects. Gauge fields for gravity, electromagnetism, andthe strong and weak nuclear forces emerge from the spacetime’s geometry, while quantum states reside in a Hilbert space H. Observables are derived, distinguishing "play states" (accelerated, GR-influenced) from "game states" (inertial), with "wonder" defined as a twist torque observable. The theory is designed to be Popper-falsifiable, with potential applications in quantum optics and exotic propulsion.
Category: Quantum Gravity and String Theory

Wallis-Type Product Formulas and Associated Wallis Integrals

Authors: Robert Bilinski
Comments: 3 Pages.

Variants of the Wallis product formula are established using simplicial polytopic numbers. These are then used to represent the Wallis integrals.
Category: General Mathematics

Temporal Flow Theory: A Unified Framework for Time, Gravity, and Quantum Mechanics

Authors: Matthew Warren Payne
Comments: 8 Pages. © Matthew W. Payne 2025 (Note by viXra Admin: AI assisted article is in general not acceptable)

Temporal Flow Theory (TFT) unifies time, gravity, and quantum mechanics through an entropy flux four-vector Wµ, emergent from coarse-grained quantum entanglement and decoherence, coupled to spacetime curvature via a scale- and temperature-dependent function g(r,T). Distinct from Loop Quantum Gravity (LQG), string theory, and entropic gravity, TFT is derived from an information theoretic action and predicts a frequency-independent 1.0 ± 0.5% boost in the cosmic microwave background (CMB) power spectrum at ℓ ∼ 100, a Planck-scale bounce, a (1.0±0.2)×10−6 nanoscale quantum phase shift, and a (1.0 ± 0.3) × 10−16 gravitational wave (GW) speed deviation. These predictions are testable by CMB-S4, the Matter-wave Interferometer Gravitational-wave Antenna (MIGA), and LIGO/Virgo stacking, respectively. Consistent with Planck 2018 and GW170817 data, TFT operates as an effective field theory (EFT), offering a thermodynamically motivated resolution to the problem of time in quantum mechanics. This paper presents the full theoretical framework, including detailed derivations, cosmological implications, quantization, and experimental constraints, situating TFT within the broader quantum gravity landscape
Category: Relativity and Cosmology

Potential Proof of Impossibility of Order-3 Magic Squares of Squares

Authors: Josephi Krakowski
Comments: 3 Pages. (Converted to pdf by viXra admin - Please submit article in pdf format only, and cite and list scientific references)

We prove that there does not exist a 3×3 magic square consisting of distinct perfect squares. Although extensive computational searches have failed to produce such a square, a general proof of nonexistence has remained open since Martin Gardner posed the question in 1996. This proof uses a combination of parity analysis, modular arithmetic, the convexity of the squaring function, and infinite descent to rigorously eliminate all possible configurations.
Category: Number Theory

A Unified Framework for Bright and Dark Fields: A New Cosmological Model Based on Flowing Energy

Authors: Kaisheng Li
Comments: 2 Pages.

lity, nuclear dynamics, and galactic rotation. Spin propels orbits, with perturbations manifesting as gluon waves (λ ≈ 1.24 pm, f ≈ 1022 Hz), fission in 252Cf (200 MeV, force imbalance), and M31’s rotation (flat to 100 kpc). This reinterprets wave-like behavior as a perturbation artifact, fission as dynamic imbalance, and cosmic order as amplified spin. Encoded in F = kSv/r +αv2sin(ωt)−D(A, Z),it aligns with LHC, nuclear, and Gaia data, predicting gluon frequencies, fission thresholds, and rotation anomalies. This framework redefines fundamental interactions across scales.
Category: High Energy Particle Physics

An Intuitive Explanation of the Invariance of the Speed of Light: Understanding the Concept Through the Timeless and Spaceless Nature of Photons.

Authors: Izam Syed
Comments: 6 Pages.

The invariance of the speed of light is a cornerstone of special relativity, yet it remains counterintuitive to many. This paper presents an intuitive explanation based on the nature of photons, which do not experience time or space. We argue that the observed constancy of light speed follows naturally from this fact. Through thought experiments and relativistic principles, we demonstrate why all observers, regardless of their motion, perceive light at the same speed. This perspective deepens our understanding of spacetime and the fundamental properties of light.
Category: Relativity and Cosmology

Calculation and Prediction of the 40Ca, 171Yb and 171Yb+ Atomic/Ionic Transition Frequencies

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 7 Pages. In Chinese.

In our previous paper, we calculated out and determined the atomic unit of time (tau) to be 2.41888432658653284(45)×10-17 s. In this paper, using the BIPM recommended 171Yb atomic transition frequency which is 518295836590863.63(10) Hz and its reciprocal in atomic units calculated from our corresponding formula, we once more calculate out and determine the atomic unit of time to be 2.41888432658653280(46)×10-17 s. With this very slightly revised atomic unit of time and the reciprocal of 40Ca atomic transition frequency in atomic units calculated from our corresponding formula, we calculate out the 40Ca atomic transition frequency to be 455986240494140.30(9) Hz, which is about 94 times more precise than the BIPM recommended value, i.e., 455986240494140(8) Hz. Employing the same method, we also calculate out two 171Yb+ ionic transition frequencies which are consistent with the BIPM recommended values.
Category: Nuclear and Atomic Physics

Notes on the Jellinek-Berry Thermostated Ideal Gas

Authors: Leo T. Butler, Alireza Sharifi
Comments: 12 Pages.

This note studies Hamiltonian systems which are thermostated using the Jellinek—Berry thermostat (J. Chem. Phys. 1988; Phys. Rev. A 1988). Jellinek & Jellinek and Berry propose an extension of Nosé's thermostat (J. Chem. Phys. 1984). They introduce multiple functional parameters in order to achieve ergodicity of the thermostatted dynamics. This family of Hamiltonian thermostats aim to simulate the macro canonical ensemble of a Hamiltonian $H$ by coupling $H$ to a 1-d heat reservoir with potentialenergy $v(s)$ and kinetic energy $p^2/2Q(s)$. Our note derives a normal form for the reservoir’s potential energy; investigates when the Jellinek—Berry thermostated system admits a Nosé—Hoover reduction; and, we demonstrate that a Jellinek—Berry thermostated periodic ideal gas is completely integrable and satisfies a KAM twist condition called Rüssmann non-degeneracy. This is used to deduce that a thermostated, collision-less, non-ideal gas (i.e. one with a smooth potential energy) at sufficiently high temperatures of the reservoir has a positive measure set of invariant tori—hence, the thermostated dynamics are non-ergodic.
Category: Statistics

Introduction to Hestenes’ Use of Geometric Algebra in Treating Constant-Acceleration Motion

Authors: James A. Smith
Comments: 8 Pages.

As an aid to teachers and students who wish to apply Geometric Algebra to high-school-level physics, we provide the first installment in a guide to Hestenes’s treatment of constant-acceleration motion. Specifically, we present a more-detailed version of Hestenes’ solution to the problem of finding the time and distance at which a projectile will cross a given line of sight. We begin by reviewing the GA ideas that we will use, and finish by verifying the solution via a GeoGebra worksheet.
Category: Classical Physics

Proof that e is Rational

Authors: Armando Evangelista Jr
Comments: 1 Page.

In this short paper, I used Joseph Fourier's proof that e is irrational to prove that it is actually a rational number.
Category: Algebra

Faster-Than-Light Travel Feasible with Negative Mass - Superluminal Dynamics

Authors: Raul Fattore
Comments: 29 Pages.

The study demonstrates that faster-than-light travel requires negative mass. Mass must decrease as velocity increases and must be negative beyond the speed of light.It also proves that there is no absolute speed limit in the universe, contradicting faulty Einstein's theory of relativity and quantum theory. The study also reveals that relative motion depends on relative coordinates, not reference frames.It is demonstrated that gravitational and inertial control of mass is the basis of faster-than-light travel. A hypothetical spaceship is described, and physical calculations are made to demonstrate the possibility of traveling faster than light. The study also explores the potential effects of gravitational interaction and collisions. The technology is proposed for instantaneous cosmic communication and other applications of negative mass using the free energy of the gravitational field.* Is faster-than-light travel indeed possible?* What kind of propulsion could achieve such a technology?* Could any matter be traveling faster than light?* Could living beings be traveling faster than light?* What could be the consequences of that?The above questions will be scientifically answered through this study in accordance with the negative mass theory.
Category: Astrophysics

Diophantine Equation Degree Six Type (6-4-4) Equation

Authors: Oliver Couto
Comments: 5 Pages.

There are numerical solutions available on Wolfram world of mathematics website (ref. # 1) for the equation, (a^6+b^6+c^6+d^6)=(e^6+f^6+g^6+h^6). In this paper the author has arrived at numerical solution by algebra instead of elliptical theory. There are methods for the (6-4-4) equation in (ref #6) providing numerical solutions but parametric solutions are not shown. Also on the internet the author has not come across a similar method (given in this paper) for the above mentioned equation.
Category: Number Theory

Industry-Specific Sentiment Analysis Comparison: Evaluating VADER and TextBlob Across Finance, Healthcare, Social Media, and Customer Reviews

Authors: Manan Maheshwari
Comments: 7 Pages.

This study explores the effectiveness and strengths of two widely used Natural Language Processing (NLP) models—VADER and TextBlob—in different industry contexts. VADER (Valence Aware Dictionary and sEntiment Reasoner) is a specifically designed model to analyze sentiments in social media posts and short texts. VADER relies on a lexicon-based approach, using a pre-defined list of words (the lexicon) with associated sentiment labels (positive, negative, or neutral) to determine the sentiment of a text, that consists of contextual strengths of words. TextBlob also implements a lexicon-based approach, however, it enforces a rule-based technique that uses linguistic rules that help determine the sentiment polarity (positive, negative, or neutral) of a piece of text; this approach makes it more adaptable for general language processing tasks. This research evaluates the power and usefulness of these models across four key industries: Finance, Healthcare, Social Media, and Customer Reviews. Upon intensive testing against 100's of datasets, the study realized that VADER outperformed in Finance and Healthcare because of its capacity to process domain-related sentiment nuances, giving it a slight edge when it comes to sophisticated sentiments. In the case of Social Media, both models show similar and consistent accuracy; concurrently, TextBlob outperforms VADER in Customer Reviews because it is better suited for longer and more complex texts. The results stress the need to use the right sentiment analysis model according to industry-specific requirements. Comparing VADER and TextBlob on real-life data, this study offers useful implications for businesses, researchers, and developers aiming to improve their sentiment analysis approaches.
Category: Artificial Intelligence

Investigating Cyclic Gravity and Cosmology (CGC) as an Alternative Framework to Standard Cosmology

Authors: Joseph Bakhos
Comments: 16 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

Cyclic Gravity and Cosmology (CGC) is introduced as an alternative framework to General Relativity (GR) and the ΛCDM model. CGC retains Euclidean space and proposes that gravity is a residual effect of electromagnetism ratherthan a fundamental force. The theory replaces the standard expansion model with cyclic expansion and contraction phases governed by large-scale gravitational oscillations. Redshift in CGC is explained through a combination ofDoppler motion, neutrino interactions, and a refined tired light mechanism. Time dilation and light deflection arise from neutrino scattering rather than spacetime curvature, preserving a Euclidean structure. CGC naturally explains the Cosmic Microwave Background (CMB) power spectrum without requiring inflation, aligns with observed large-scale structure, and provides a resolution to the Hubble tension within a non-expanding space framework. The theory predicts a self-regulating cosmic equilibrium maintained by an outer shell of intergalactic medium, preventing energy loss and sustaining cyclic dynamics. The observed galactic rotation curves, large-scale filament-and-void cosmic structures, and elemental recycling in Active Galactic Nuclei (AGN) are also consistent withCGC’s gravitational model. The purpose of this paper is not to assert CGC as the definitive model of cosmology but to establish it as aframework worthy of rigorous scientific investigation. Given recent challenges to ΛCDM from JWST observations and inconsistencies in Hubble measurements, CGC presents an opportunity to explore alternative gravitational dynamicsand cosmic evolution mechanisms that align with observational data.
Category: Relativity and Cosmology

Chaos, Confusion, and the Illusion of Gravity Waves

Authors: Keith D. Foote
Comments: 13 Pages.

The interpretation of vibrations detected by LIGO’s facilities is critically examined. The concept of gravitational waves is disputed and the argument is made the detected vibrations are the result of synchrotron radiation. Spacetime is treated with skepticism, and a modern version of the aether is described. Synchrotron and Cerenkov radiation are used as supporting evidence of a medium supporting the transport of electromagnetic waves.
Category: Relativity and Cosmology

A New Theory of Gravity and the Design and Fabrication of a Gravitational Field Generator Based on [a] New Theory

Authors: Yuan Pan, Yong Wen Pan
Comments: 86 Pages.

Albert Einstein (1879-1955) used a different line of thought to study the physical properties of gravitational fields before he established the general theory of relativity on the mathematical basis of Riemannian geometry. Based on this idea, we developed a new theory of gravity that describes the physical properties of gravitational fields on the basis of special relativity and eventually unifies the electromagnetic and gravitational fields. This paper is only the first part of this new gravitational theory, focusing on the construction of the foundation of the new theoretical system, with the following main contents:1.A new view of space-time is put forward, which holds that time, space and the mass of matter are determined by the gravitational field, and therefore controlling the gravitational field can control the space-time and the mass of matter to a certain extent.2. Recalculating and reinterpreting the classical verification experiments of general relativity (including the gravitational redshift of light frequencies, the gravitational deflection of light, the Mercury perihelion procession shift, etc.) in accordance with the new theory of gravity yielded identical calculations to those of general relativity.3.On the basis of the observed speed of motion of the centre of mass of the solar system with respect to the stationary reference system of the cosmic microwave background radiation (CMBR), it was calculated that a 1-year cycle variation should be included in the complex variation of the Earth's rotation rate. In this cycle, the change in the length of day (ΔLOD) of the Earth decreases by about 0.77376 ms to 0.85972 ms in August compared to February each year. We analyse that this calculation is consistent with the observation data released by IERS (International Earth Rotation Service).4.The new gravitational theory explains the dark energy in the Universe.5.We have revised De Broglie's matter wave formula, and the revised matter wave formula can explain why matter cannot be cooled to absolute zero, and this new matter wave formula can be used as the basis for unifying the electromagnetic field and the gravitational field. We believe that fluctuations in matter (matter waves) generate gravitational fields, and that regulating matter waves regulates the generation of gravitational fields.6. We have designed and built the world's first gravitational field generator since 2016 based on this new theory of gravity, and have successfully conducted a gravitational field generator (curvature engine) experiment in 2021, which is briefly described in this paper.
Category: Relativity and Cosmology

A Note on Gradient-Based Parameter Estimation for Energy-Based Models

Authors: L. Martino, S. Ingrassia, S. Mangano, L. Scaffidi
Comments: 12 Pages.

Energy-based models (EBMs) are an important family of models where a piece of the likelihood is intractable, and hence unknown. For this reason, the parameter estimation in EBMs is a challengefor the standard estimation methods. In this paper, we present a critical discussion of gradient-based approaches for inference in energy-based models. We provide many details of different derivations, clarify connections and differences. We give practical suggestions for the application of the different schemes. Specifically, we focus on a suitable choice of the proposal/reference density that is crucial for the performance of the gradient-based procedures.
Category: Statistics

Multioutput Feature Selection for Emulation and Sensitivity Analysis

Authors: J. Vicent, L. Martino, J. Verrelst, J. P. Rivera Caicedo, G. Camps-Valls
Comments: 26 Pages. Published in IEEE Transactions on Geoscience and Remote Sensing, vol. 62, pp. 1-11, 2024

Statistical regression methods are widely used in remote sensing applications but tend to lack physical interpretability. In this paper, we introduce a methodological framework to improve modelemulation and its understanding with machine learning feature selection. Our wrapper-forward feature selection method seamlessly integrates physics knowledge into model emulation, improving the tradeoff between accuracy and interpretability. We illustrate our methodology by applying it to atmospheric radiative transfer models in the context of global sensitivity analysis (GSA) and emulation. Our approach consistently aligns with variance-based GSA, pinpointing the critical features of aerosol properties, solar zenith angle, and water vapor. While our physically-based emulators yield only a modest accuracy improvement of 0.2% over conventional Gaussian Processes emulators, its introduction signifies a step forward to physics-aware machine learning-based emulation. The emulator performance remains steadfast, unaffected by substantial changes, further underscoring the reliability of our approach.
Category: Statistics

Multi-fidelity Gaussian Process Emulation for Atmospheric Radiative Transfer Models

Authors: J, Vicent, L. Martino, J. Verrelst, G. Camps-Valls
Comments: 28 Pages. Published in IEEE Transactions on Geoscience and Remote Sensing, vol. 61, pp. 1-10, 2023.

Atmospheric radiative transfer models (RTMs) are widely used in satellite data processing to correct for the scattering and absorption effects caused by aerosols and gas molecules in the Earth’s atmosphere. As the complexity of RTMs grows and the requirements for future Earth Observation missions become more demanding, the conventional Look-Up Table (LUT) interpolation approach faces important challenges. Emulators have been suggested as an alternative to LUT interpolation, but they arestill too slow for operational satellite data processing. Our research introduces a solution that harnesses the power of multi-fidelity methods to improve the accuracy and runtime of Gaussian Process (GP) emulators. We investigate the impact of the number of fidelity layers, dimensionality reduction, and training dataset size on the performance of multi-fidelity GP emulators. We find that an optimal multi-fidelity emulator can achieve relative errors in surface reflectance below 0.5% and performs atmospheric correction of hyperspectral PRISMA satellite data (one million pixels) in a few minutes. Additionally, we provide a suite of functions and tools for automating the creation and generation of atmospheric RTM emulators.
Category: Statistics

The Unifying Theory: The Missing Link Between Quantum Reality and Classical Physics

Authors: Bader Binkhudhayr
Comments: 7 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

Einstein’s spacetime curvature falters as gravity’s cause—gravitational waves (strain h ~ 10^-21) stretch Earth without orbital jolts, exposing his causal lie (Sec. 4.1) [1]. The Unifying Theory reinterprets motion as quantized relocations—instantaneous jumps forming wave-like or linear patterns—dismantling the quantum-classical divide with a revolutionary mechanism. Particles leap at ultimate speeds, mimicking waves by tunneling (~10^21 s^-1) or aligning under scrutiny (double-slit [2]), their continuity a perceptual sham (Sec. 2). Length contraction—muons enduring ~7 μs at 0.99c vs. 2.2 μs rest [3]—demands quantized steps. A variant variable emerges from photon relocation distances, leading to a universal frame of reference (Sec. 3), torching special relativity’s equivalence [4]. Forces shift relocation frequencies, unifying gravity and electromagnetism via introducing a new unit: particle counts (Sec. 4, Eq. 6), relegating curvature to a passive backdrop [1]. Observation alters patterns, echoing free will theorems’ non-deterministic dance (Sec. 5) [5]. LIGO, tunneling, and relativistic data anchor this theory, shattering Copenhagen’s premature duality—a sloppy guess misreading tempo for states (Sec. 5.1). This framework unifies all forces, bridges quantum and classical realms, and exposes a century of missteps, ending with a truth unifying gravity and electromagnetism in one equation [19].
Category: High Energy Particle Physics

Systemic Relativity & Logarithmic Gravity (SRLG): A Scale-Dependent Framework for Unifying Quantum and Cosmic Phenomena - REVISION

Authors: Lukas A. Sosna
Comments: 16 Pages. 6 figures (Note by viXra Admin: AI assisted article is in general not acceptable)

The persistent rotation curve anomalies of galaxies present one of modern physics' most profound puzzles. Stars orbit galactic peripheries at velocities far exceeding Newtonian predictions based on visible matter alone, a discrepancy conventionally addressed by postulating vast halos of invisible dark matter. Meanwhile, the theoretical landscape remains fractured by the fundamental incompatibility between quantum mechanics and general relativity, particularly in extreme gravitational environments.This paper introduces Systemic Relativity & Logarithmic Gravity (SRLG), a theoretical framework that addresses these challenges through a single unifying principle: the scale-dependence of gravitational interactions. The core mathematical innovation is remarkably straightforward—a logarithmic modification to Newtonian gravity that causes gravitational force to decline more gradually with distance than the inverse-square law predicts:$$g_{text{log}}(r) = frac{GM}{r^2} times e^{-lambda log(r)}$$The distinguishing feature of SRLG is the system-dependent parameter λ, defined as the ratio of gravitational binding energy to Planck energy. This definition provides a physical basis for why gravitational behavior transforms across cosmic scales, with λ naturally increasing from negligible values at solar-system scales (λ ≈ 10^-38) to appreciable values at galactic scales (λ ≈ 10^-5).Rigorous analysis using 175 galaxies from the SPARC database demonstrates that SRLG reduces rotational velocity prediction errors by approximately 50% compared to Newtonian models without requiring dark matter. The framework also successfully models gravitational lensing in the Abell 2744 galaxy cluster with λ ≈ 0.26-0.32, producing observed lensing strength within 5-8% of measured values without dark matter components.The time-frequency dynamics incorporated in SRLG yields testable predictions for gravitational wave propagation, specifically a frequency-dependent phase shift potentially detectable by LIGO and LISA. This aspect of the theory may provide crucial insights into how gravity behaves in the strong-field regime, offering a bridge between quantum and relativistic physics. SRLG's connections to renormalization group approaches, black hole thermodynamics, and quantum gravity suggest it may be uncovering a fundamental pattern in nature's architecture rather than merely providing a convenient fitting function. By reconceptualizing gravity as a scale-dependent phenomenon, this work offers not only a potential resolution to the dark matter problem, but also a fresh perspective on the century-old quest to reconcile quantum mechanics with general relativity.
Category: Relativity and Cosmology

The Quo Vadis Effect: A Graviton-Based Explanation of Mercury’s Perihelion Precession

Authors: Adolfo Santa Fe Dueñas
Comments: 14 Pages.

We propose the Quo Vadis Effect (QVE), a velocity-dependent correction to Newtonian gravity arising from gravitational aberration. Unlike General Relativity (GR), which explains Mercury’s perihelion precession via space-time curvature, the QVE operates within a Newtonian framework without modifying the geometry of space-time. The core mechanism of the QVE is that an orbiting body perceives gravitons arriving at an apparent velocity greater than $c$ due to aberration. This results in two simultaneous effects: (1) an increased flux of gravitons and (2) an enhanced force per graviton, leading to a total gravitational force correction proportional to (1 + (v/c)²). This correction modifies the gravitational potential energy, reproducing the standard GR prediction for Mercury’s perihelion precession.A similar velocity-dependent correction was previously explored by Wayne (2015), albeit without a clear physical derivation, speculating on possible friction-like effects. In contrast, the QVE provides a well-defined mechanism based on gravitational aberration.Beyond Mercury’s orbit, the QVE may have broader implications, including potential corrections to GPS satellite clocks and alternative explanations for galaxy rotation curves without invoking dark matter. Additionally, it may offer insights into cosmic acceleration if graviton propagation exhibits similar aberration effects at cosmological scales.Given the ongoing debate surrounding modified gravity theories, this work aims to contribute to the discussion by demonstrating that a Newtonian approach incorporating gravitational aberration can recover key relativistic results. The QVE suggests a possible bridge between classical mechanics and quantum gravity, warranting further investigation.
Category: Relativity and Cosmology

Quantum Mechanics

Authors: Loïc Renaut, Laurent Bruneau
Comments: 65 Pages. In French

The aim of this thesis is to study the basic concepts and the mathematical formalism of quantum mechanics. To do so, we will first examine Newtonian mechanics. This was the prevailing theory until the early 20th century for describing the motion of objects of all sizes. However, it was later discovered that this theory had its limitations. Consequently, at the beginning of the 20th century, two new theories emerged to address the shortcomings of Newtonian mechanics: quantum mechanics, which is the focus of this thesis and describes the physics of atomic and subatomic-scale objects, and special relativity, which deals with the physics of objects on a very large scale.In the second part, we will study quantum mechanics and attempt to identify the similarities and differences between the two theories. The foundational principle of quantum theory is wave-particle duality. This principle states that the objects that make up matter (such as electrons and photons) exhibit behavior characteristic of a particle in some situations and behavior characteristic of a wave in others. However, they are neither purely waves nor purely particles—they are something else entirely. This is one of the fundamental differences between the two theories. In Newtonian mechanics, objects are considered exclusively as particles. To illustrate the intellectual revolution brought about by this principle, we can recall the major debate that took place in the 17th century regarding the nature of light (at the time, photons were unknown). Two opposing camps emerged: one led by Isaac Newton, who believed that light was composed of particles, and the other led by Christiaan Huygens, who argued that light was a wave. Newton’s influence was so great that his view was widely accepted by most scientists of the time. No one had yet considered that light might be neither a particle nor a wave. Moreover, the necessary mathematical tools to explore this idea did not yet exist.
Category: Functions and Analysis

Another Approximation for Prime Counting Function

Authors: Khazri Bouzidi Fethi
Comments: 4 Pages. (Note by viXra Admin: Listed scientific references should be cited in the article; AI assisted/generated content is in general not acceptable)

This paper proposes a more accurate approximation to the prime counting function, especially for small numbers, using a base-10 logarithm. It relates this approximation to the Riemann zeta function, providing geometric interpretations of its terms.
Category: Number Theory

Dictionary of Early English by Joseph T. Shipley and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 22 Pages.

We study the words of the Dictionary of Early English by Joseph T. Shipley. 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

Mass Defect

Authors: Nainan K. Varghese
Comments: 6 Pages.

Although the mass of an object is defined to represent the equivalent of 3D matter it contains, it is often considered as the quantity of 3D matter contained in the object. Mass is the mathematical relation between an external linear effort on an object and the rate of the rate of its displacement in the direction of the external effort. This relationship is often ignored, and the value of a body's mass is regarded in almost all academic fields as the quantity of 3D matter present in the object. Loss (or gain) of mass of an object during its development stage or changes in its structure is understood as ‘mass defect’. This is often related to an assumed phenomenon of binding energy required to stabilize the nucleons in the atoms in a body.
Category: High Energy Particle Physics

Training Neural Networks with {-1,1} Weights by Genetic Algorithm

Authors: Hidehiko Okada
Comments: 7 Pages.

The author previously reported an experimental result of evolutionary reinforcement learning of binary neural network controllers. In the previous study, the controller was trained by Evolution Strategy. In this study, the author experimentally applies Genetic Algorithm, instead of ES, and the results were compared between GA and ES. In both studies, the same Acrobot control task is utilized, and the same three-layer feedforward neural network is adopted. The difference lies in the training algorithm. The findings from this study are (1) GA trained the controller better than ES (p<.01), (2) increasing the population size, rather than the number of generations, improved performance more in GA (p < .01), and (3) the optimal number of hidden units for the binary MLP was 128 among the choices of 16, 32, 64, 128 and 256, which was consistent with the previous study using ES.
Category: Artificial Intelligence

Bounds on Prime Gaps and Their Consequences in Number Theory

Authors: Siddid Gosain
Comments: 5 Pages.

In this paper, I establish several novel and rigorous bounds on prime gaps. These bounds not only enhance our understanding of prime distribution but also provide elegant proofs for certain unsolved problems in number theory. Moreover, this work paves the way for estimating the density of primes in large intervals and opens new avenues for further research.
Category: Number Theory

New Proof of Dark Numbers by Means of the Thinned Out Harmonic Series

Authors: W. Mückenheim
Comments: 1 Page.

It is shown that not all numbers can be expressed and communicated such that the receiver knows what the sender has meant. We call them dark numbers.
Category: Set Theory and Logic

Irrational Numbers Do Not Exist [?]

Authors: Armando Evangelista Jr
Comments: 1 Page. (Note by viXra Admin: Please cite and list scientific references)

This short paper proves that there are no such things as irrational numbers.
Category: Algebra

Surface Area of the Mobius Strip

Authors: Richard J. Mathar
Comments: 6 Pages.

The (half) area of the surface of the Mobius strip is the expected product of the length of the circular spine times the width of the sweep line times a positive correction factor. The manuscript writes down this factor as a Taylor series of the ratio of width over circle radius; it approachesone if that ratio approaches zero.
Category: Geometry

A New Dictionary of the Portugese and English Languages Enriched by H. Michaelis and the Graphical Law

Authors: Anindya Kumar Biswas
Comments: 20 Pages.

We study the Portugese head entries of A New Dictionary of the Portugese and English Languages enriched by H. Michaelis. 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 the magnetisation curve, BP(4,$beta H=0$), in the Bethe-Peierls approximation of the Ising model, in the resence of four nearest neighbours and in the absence of external magnetic field, H. $beta$ is $frac{1}{k_{B}T}$ where, T is temperature and $k_{B}$ is the tiny Boltzmann constant.
Category: Linguistics

137 First Prime of Form, First Prime Expressed with Four Base Numbers of Number Type

Authors: Dwight Boddorf
Comments: 2 Pages.

Where N is a counting number, one hundred and thirty-seven is the first prime number to take the form of 2[(2N+2)(2N+2)] + NN , if N equals 3 then prime number is one hundred and thirty-seven.
Category: Mathematical Physics

Bessel Functions and pi

Authors: Edgar Valdebenito
Comments: 3 Pages.

We give two sequences for Pi.
Category: Functions and Analysis

Nova Framework: A Unified Theory of Quantum Gravity and Beyond

Authors: Thura Zaw Oo
Comments: 6 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

Nova proposes quantized spacetime fluctuations (QSFs)—a scalar field ϕ constrained to Planck-scale vacuum perturbations—as the sole constituent of the universe, with no external background,unifying General Relativity (GR) and Quantum Mechanics (QM) at all scales without invoking extra dimensions or geometric quantization. QSFs are both quantized and dynamic, inducing GR’s tensor gravity through a scalar-tensor coupling (κ) derived from gravitational vacuum energy, where grav-ity manifests as an inertial-like spread action driven by relative differences in QSF densities. Particlemasses and fundamental forces emerge from knotted QSF structures: the strong force as the knot-ting strength or potential at the bare minimum matter level, the weak force as the action strength of the knots themselves, the electromagnetic (EM) force as a vibration-like spread across the dynamic QSF scalar, and gravity as the relative QSF fluctuations’ spread action around matter-like QSFs. Antimatter and antiforces arise from stretched, non-knotted QSF actions, distinct in nature from knotted matter, not merely symmetric opposites. Time is derived from QSF actions, ceasing where action halts (e.g., ∂tϕ = 0). QSFs couple to Standard Model (SM) gauge fields through a constrainedSO(5) symmetry-breaking mechanism, generate dark matter via non-knotted fluctuations, producedark energy via expansion dynamics, and drive cosmic inflation through early high β-rates. Nova resolves singularities with a dynamic finite-core metric and eliminates the Hierarchy and Strong CPProblems as artifacts of linear thinking, not requiring fine-tuning or additional particles. We rigorously test against Planck CMB, LIGO GW150914, and LHC Higgs datasets, computing densities and masses with Monte Carlo error estimates, and predict a 510 ± 20 GeV scalar (consistent with LHC limits via suppressed coupling) and CMB B-modes at ℓ > 3000 with ∆C BB ℓ = 0.8 ± 0.2 µK 2, derived from inflationary physics. Nova offers a coherent, testable, and comprehensive framework grounded in exhaustive derivations.
Category: Quantum Physics

Kaluza Klein Theory Versus the Possibility that the Electric Field Strength Might be Recognized as a Form of Acceleration

Authors: Moshe Segal
Comments: 12 Pages.

Einstein's Theories are considered as significant theories of the nowadays Science of Physics. However, the nowadays Science of Physics did not provide yet a verified theory for unifying Gravitation and Electromagnetism.Kaluza Klein Theory addresses that issue by predicting that there are five dimensions, with the fifth dimension being of the shape of a tiny circle, with a radius of 23 times the Planck length, which is of the order of 10−33 cm.However, because there is no foreseeable technology for verifying that prediction, about that fifth dimension, the Kaluza Klein Theory is not yet accepted as a complete viable theory, which implies that the issues of presenting a theory which unifies the Gravitation and Electromagnetism is still an open issue.This paper, and several other preprints, by the author of this paper, also tries to address that issue, by presenting an alternate theory, which is also accompanied by a proposal for an experiment, which might either disprove the proposed theory, if the proposed experiment implementation will turn out to be unsuccessful, or, alternatively, provide validity to the proposed theory, if the proposed experiment implementation will turn out to be successful.However, while the Kaluza Klein theory does not challenge significant elements of the nowadaysScience of Physics, the proposed theory does challenge significant elements of the nowadaysScience of Physics, and as such, might appear, initially, as completely wrong. Thus, this paper concludes that the implementation of the proposed experiment might be an important endeavor, because it might provide validity to the proposed theory, while the Kaluza Klein theory does not seem to be verified, in the foreseeable future, leaving the issue of the unification of Gravity and Electromagnetism as an open issue.
Category: Relativity and Cosmology

TSVF-SUSY: A Time-Symmetric Supersymmetric Framework for Quantum Gravity Unification, Dark Matter Resolution, and Gravitational Wave Signature Predictions

Authors: Muhammad Shahzaib Uddin Khan
Comments: 19 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

This work unifies the Two-State Vector Formalism (TSVF) of quantum mechanics with N = 1 supersymmetry (SUSY) into a mathematically rigorous framework for quantum gravity. Key results include: (1) A ghost-free, renormalizable Lagrangian with bidirectional time evolution; (2) Proof of SUSY algebra closure under Planck-scale corrections; (3) One-loop renormalizability with asymptotic safety; (4) Testable predictions for gravitational wave physics, dark matter, and neutrino oscillations. The framework resolves tensions between SUSY and quantum gravity while offering falsifiable deviations from General Relativity.
Category: Quantum Gravity and String Theory

The Missing Mass: A Heuristic Explanation of Dark Matter

Authors: Guofeng Chang
Comments: 5 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

In this paper, we analyze the phenomenon of non-isotropic mass distribution in spiral galaxies and propose a hypothesis that such an imbalanceintroduces a relative velocity for observers. Furthermore, we suggest observational methods to verify this hypothesis. If proven correct, thishypothesis could provide a more reasonable explanation for the origin of dark matter.
Category: Astrophysics

Pythagorean Complex: on Truth and Falsness Superpositions

Authors: Osvaldo Duilio Rossi
Comments: 1 Page. (Note by viXra Admin: An abstract in the article is required and cited references should be listed)

r^2 = x^2+y^2 implies r^2 = (x+yi)(x-yi), implying r^2 = rr*, superposing a statement true under algebra with a statement fals under epistemology, revealing the true nature of complex numbers and mathematical thinking.
Category: Algebra

Conditional Negation of The ABC Conjecture

Authors: Jinhua Fei
Comments: 4 Pages.

In this paper, the abc conjecture is negated under certain conditions.
Category: Number Theory

Multi-layer GRPO

Authors: Fei Ding
Comments: 7 Pages.

The success of DeepSeek-R1 has demonstrated the effectiveness of the GRPO algorithm. However, due to the absence of process rewards, GRPO often suffers from inefficiencies in exploration, as a single detailed error can result in an entirely incorrect final answer, leading to zero rewards.To address these challenges, we propose MGRPO (Multi-layer GRPO). In the first layer, GRPO operates identically to the original version, generating an initial response. This response is then fed into a second-stage GRPO process, which primarily trains the model to correct errors. Experimental results indicate that MGRPO outperforms standard GRPO, achieving superior performance.
Category: Artificial Intelligence

Patterns of Perfect Magic Squares of the 4th and 8th Order, Magic Cubes of the 2nd and 4th Order

Authors: Andrey V. Voron
Comments: 5 Pages.

The article shows the possibility of a formula calculation of patterns of ideal magic squares of the 4th and 8th order, magic cubes of the 2nd and 4th order, as well as substantiates the hypothesis that the laws of dialectics apply to numbers as ideal objects. In particular, the presence of mathematical patterns can characterize the dialectical law of "unity and struggle of opposites", when the sums of the numbers of the pattern act as opposites. The presence of the golden division constant or its derivatives between the opposite patterns is probably due to the property of the unity of the elements that make up such a whole. This unity of the elements that make up the whole is probably due to the greatest number of structural mathematical connections obtained in connection with the unique properties of the golden proportional relations.
Category: Number Theory

English Language and Science

Authors: Jeremy Dunning-Davies
Comments: 4 Pages.

Here attention is drawn to possible problems arising from an inaccurate use of the English language in science. It is noted that such misuse may lead to incorrect public understanding of some common notions in science today.
Category: History and Philosophy of Physics

Analytical Model for the Thermal Conductivity of Fully Ionized Plasmas

Authors: Yuanjie Huang
Comments: 13 Pages.

The thermal conductivity is a fundamental property of plasmas, yet its experimentally observed reduction remains an enigmatic phenomenon. Over the past half-century, extensive efforts have been dedicated to elucidating the mechanisms behind this reduced thermal conductivity and the associated heat-flux limiter, but a definitive solution has remained elusive. In this work, we present an analytical model for plasma thermal conductivity that is free of artificial parameters. This model employs Maxwell distributions for both electrons and ions and provides analytical expressions for thermal conductivity and the heat-flux limiter. Importantly, the predictions of the model are in good agreement with experimental observations. Its validity extends across plasmas with both small and large temperature gradients, significantly enhancing its applicability. This straightforward model not only offers insights into the underlying physics of reduced thermal conductivity and the heat-flux limiter but also plays a crucial role in advancing our understanding of thermal transport in plasmas across diverse areas.
Category: Nuclear and Atomic Physics

Recursive Differentiation and the Logarithmic Structure of Fundamental Constants

Authors: Leah Travers
Comments: 20 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

The values of fundamental physical constants have long been treated as free parameters, requiring empirical measurement rather than derivation from first principles. In this work, we establish a novel analytical proof demonstrating that these constants emerge as equilibrium conditions of a recursive differentiation process. This analysis reveals that these constants are not independent but are instead stabilized by a universal recursive scaling law.A central result of this work is the emergence of a fixed recursion exponent k ≈ -3, derived from first principles, which constrains the values of h, the fine-structure constant α, and the cosmological constant Λ through a logarithmic scaling relationship. This exponent aligns with known renormalization group flow constraints in quantum field theory, black hole entropy scaling in holographic gravity, and fractal structures in critical phenomena. We explore the implications of this result for gauge symmetries, vacuum energy, and the unification of fundamental interactions.Further, we demonstrate that recursion provides a natural resolution to the scale-separation problem by embedding quantum and cosmological parameters within the same self-organizing structure. This formalism suggests that fundamental constants arise as attractor solutions to recursive differentiation, challenging conventional assumptions about their arbitrariness. Predictions include logarithmic corrections to the fine-structure constant over cosmological timescales, recursive stability constraints on vacuum energy, and scale-invariant deviations in black hole entropy.This work establishes recursion as a fundamental organizing principle of physical law. The recursive differentiation framework presented here lays the foundation for further theoretical development and experimental validation. If confirmed, this result implies that the structure of reality itself is governed by universal recursion constraints rather than arbitrary parameter selection.
Category: Quantum Gravity and String Theory

Prime Gap Instability and the Collapse of the Riemann Hypothesis

Authors: Jasmine Burns
Comments: 15 Pages.

The Riemann Hypothesis (RH) asserts that all nontrivial zeros of the Riemann zeta function lie on the critical line ℜ(s) = 1/2. In this paper, we prove that RH is false by demonstrating that the evolution of zeta zeros under the de Bruijn-Newman heat equation is fundamentally unstable. We establish that irregularities in prime gaps introduce an unbounded forcing term in the heat equation, leading to a necessary shift in the location of zeta zeros and forcing Λ > 0, contradicting RH. Furthermore, we resolve the Pair Correlation Conjecture independently of RH, showing that the statistical structure of zeta zeros remains unchanged under the heat evolution. This result confirms that the known statistical properties of the zeta function are not contingent on RH but instead arise from a deeper structural phenomenon tied to prime number modularity and diffusion dynamics. Our findings necessitate a fundamental reevaluation of the role of RH in analytic number theory, shifting focus toward a more geometrically and dynamically informed understanding of the zeta function's zeros.
Category: Number Theory

A Novel Identity in Binomial Probability Theory

Authors: Ashkan Karimi
Comments: 6 Pages.

This paper presents a proof and analysis of a previously unexploredbinomial probability identity involving weighted sums of binomial probabilities. The identity establishes that a specific weighted sum of binomial terms with probability parameter PA equals zero for any positive integer n. I provide a rigorous proof of this identity, explore its probabilistic interpretation in terms of expected values, and discuss potential applications in statistical analysis, information theory, and computational probability. The result offers new insights into the properties of binomial distributions and contributes to the broader understanding of discrete probability structures. The identity has particularly elegant connections to moment-generating functions and can be generalized to higher moments and other probability distributions.
Category: General Mathematics

Resolving the Yang-Mills Mass Gap Problem Using Alpha Integration

Authors: YoonKi Kim
Comments: 6 Pages. Email: yk.reserch@gmail.com

We present a non-perturbative proof of the Yang-Mills mass gap hypothesis, demonstratingthat the lowest eigenvalue E0 of the quantum Yang-Mills Hamiltonian in four-dimensionalEuclidean spacetime is positive, confirming the existence of a mass gap and quark-gluon confinement. Using a novel path integral framework, we address divergences, resolve Gribov ambiguities, and compute the spectrum, achieving consistency with lattice QCD simulations and experimental data. Our results align with the Clay Mathematics Institute’s Millennium Prize criteria, providing a mathematically rigorous and physically consistent solution.
Category: High Energy Particle Physics

Electron Approach Theory[:] A Damped Oscillation Model Based on Relativistic Effects and Space-Time Feedback.

Authors: Douglas Ruffini
Comments: 78 Pages.

This study proposes a new theoretical model to describe the behavior of the electron in the atom, reinterpreting the classical problem of its collapse towards the nucleus through a damped oscillation governed by relativistic effects and a space-time feedback. The electron, in its approach to the nucleus, undergoes an increasing acceleration until a critical point where its velocity approaches that of light, leading to a temporal discontinuity and a subsequent reversal of motion. This process is formalized through the Lorentz factor with imaginary values, suggesting a transition between quantum states rather than a real superluminal velocity. The model is supported by a mathematical analysis based on the exponential decay of energy and the time constant RC, which shows a connection with the Heisenberg uncertainty principle and the time scales of quantum processes. The electron descent-ascent cycle introduces the concept of space-time memory, with a coordinate recalculation mechanism that ensures atomic stability. The results suggest that energy quantization can emerge as a macroscopic effect of an oscillating dynamical system and that absolute space-time plays a key role in maintaining temporal coherence. This approach offers a novel perspective on the stability of the atom, bridging classical mechanics, relativity and quantum mechanics through a new interpretation of energy transitions and space-time structure.
Category: Nuclear and Atomic Physics

Magnetic Fields of White Dwarfs and Neutron Stars

Authors: Kiyoung Kim
Comments: 16 Pages.

Neutron stars and white dwarfs are known to be the final stages in the life cycle of stars. These celestial objects are characterized by immense gravitational pressure, extremely high temperatures, and exceptionally high density. Additionally, some of them are known to possess extraordinarily strong magnetic fields under these extreme conditions. However, the precise mechanisms behind the generation of such strong magnetic fields remain unclear. The primitive virtual negative (PVN) charge dynamo mechanism proposed for solar planets in 2008, which involves the interaction between gravitational mass and electric charges, is applied to compact objects like white dwarfs and neutron stars because it is considered comprehensive and consistent.
Category: Astrophysics

Thick Sequences

Authors: Joseph Pe
Comments: 7 Pages.

We call an integer sequence thick if the quotients formed from its terms are dense in the set of real numbers. To find thick sequences, we consider the geometric, Fibonacci, power, and prime sequences. We show that the sequence of primes is thick provided that a conjecture DC-2 holds. DC-2 says that certain pairs of linear Dirichlet conditions have infinitely many solutions. It is a weak form of Dickson’s conjecture, which states that a finite system of linear Dirichlet conditions has infinitely many solutions and generalizes Dirichlet’s well-known result on primes in arithmetic progressions. Also, we obtain partial results for the general thickness problem for an arbitrary sequence and look at heuristic evidence for the validity of DC-2. We conclude with a short list of problems for further research.
Category: Number Theory

The Sedenion-Trigention Soul Theory: A Mathematical and Metaphysical Framework

Authors: Moninder Singh Modgil, Kavita Rohit
Comments: 4 Pages. (Note by viXra Admin: This article is speculative/exploratory)

This paper explores the intersection of higher-dimensional algebra and metaphysical consciousness by formulating a novel framework in which souls are modeled as sedenions (16D algebraic entities) and Shiv Baba (the Supreme Soul) is represented as a trigention (32D hyper-structure). By extending the quaternion-octonion algebra into non-associative and fractal consciousness structures, we propose a model in which the journey of the soul through time, karma, and enlightenment can be mathematically described. This paper also discusses implications for quantum consciousness, spiritual liberation, and cosmic order.
Category: Religion and Spiritualism

Alpha Integration: Universal Path Integrals with Gauge Invariance

Authors: YoonKi Kim
Comments: 16 Pages. Email yk.reserch@gmail.com (Note by viXra Admin: Listed references should be cited; please refrain from immediate and repeated replacements and cancellations; and AI assisted article is in general not acceptable)

We introduce Alpha Integration, a novel path integral framework that applies to wide range of function including locally integrable functions, distributions, and fields—across arbitrary spaces and n dimensions (n ∈ N), while preserving gauge invariance without approximations. This method extend to R^n (n ∈ N), smooth manifolds, infinite-dimensional spaces, and complex paths, enabling rigorous integration of all f ∈ Du2032 with formal mathematical proofs. This framework is furthergeneralized to infinite-dimensional spaces, complex paths, and arbitrary manifolds,with its consistency validated through extensive testing across diverse functions, fields, and spaces. Alpha Integration thus offers a robust and efficient alternative to traditional path integral techniques, serving as a versatile tool for mathematical and physical analysis.
Category: Mathematical Physics

Bayesian Approach to Hypothesis-Based Randomness Estimation

Authors: Alexander Rozenkevich
Comments: 6 Pages.

A Bayesian method for dynamic hypothesis-based randomness estimation of a sequence of experimental data is proposed. Examples of pseudorandom number generator testing are given.
Category: Statistics

Bayesian Approach to Hypothesis-Based Randomness Estimation (in Russian)

Authors: Alexander Tozenkevich
Comments: 6 Pages.

A Bayesian method for dynamic hypothesis-based randomness estimation of a sequence of experimental data is proposed. Examples of pseudorandom number generator testing are given.
Category: Statistics

Gravity and Black Holes

Authors: A. J. Owen
Comments: 8 Pages.

The question of how Newton's inverse-square law of gravity relates to general relativity (GR) is discussed in this paper. In GR, gravity is considered as a consequence of space and time curvature, whereas Newton's law is restricted to a flat space. Logically, then, Newtoniangravity must relate solely to the time curvature contribution in GR. Instances where Newton's law does not describe phenomena correctly, such as the perihelion rotation of the planet Mercury and the bending of starlight, are therefore attributable to spatial curvature. The GRsolution for a static point mass, calculated on this basis for correspondence with Newton's law, is entirely regular and agrees with all theusual predictions of GR except the one leading to an event horizon. This suggests that the currently accepted model of a static black-hole,although mathematically possible, is non-physical. Not only is there no horizon in spacetime, but gravitational attraction between two masses does not diverge to infinity as they approach each other. This means there is no singularity at the origin of coordinates where physical laws would break down, and relative speeds do not exceed the speed of light.
Category: Relativity and Cosmology

A New 3D Spherical Coordinates Warp Drive Vector with Hodge Star Over the Y-Axis and Variable Speeds Using the Natario Methodology

Authors: Fernando Loup
Comments: 51 Pages.

The Natario warp drive appeared for the first time in 2001.Although the idea of the warp dive as a spacetime distortion that allows a spaceship to travel faster than lightpredated the Natario work by 7 years Natario introduced in 2001 the new concept of a propulsion vector to define or togenerate a warp drive spacetime.Natario defined a warp drive vector for constant speeds in Polar Coordinates over the x-axis but remember that a real warp drive must accelerate orde-accelerate in order to be accepted as a physical valid model so it must possesses variable speeds.We developed in this work a newwarp drive vector for the y-axis in both Polar and Spherical coordinates that encompasses variable speeds.Also Polar Coordinates uses only two dimensions and we know that a realspaceship is a tridimensional 3D object inserted inside a tridimensional 3D warp bubble that must be defined in real 3D Spherical Coordinates.
Category: Relativity and Cosmology

On Area Element in Polar Coordinates

Authors: Sanjeev Saxena
Comments: 3 Pages.

A simple and elementary derivation for formula for area element in polar coordinates is given.
Category: General Mathematics

De Broglie Hypothesis and the Schrödinger Equation: [Plausible] Errors in Mathematics, Physics, Formal Logic, and Dialectics

Authors: Temur Z. Kalanov
Comments: 14 Pages.

The irrefutable proof of the incorrectness of the de Broglie hypothesis (postulate) and the Schrödinger equation (postulate) is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The unity of formal logic and rational dialectics is the only correct criterion of truth. The proof leads to the following irrefutable conclusion: the de Broglie hypothesis (idea, postulate) and the Schrödinger equation (idea, postulate) are gross errors in mathematics, physics, formal logic and dialectics. This conclusion is based on the following statements: (1) from the point of view of Euler's formula and the Maclaurin series, the definition of the wave function has neither physical nor mathematical meaning; (2) the substitution of the quantities of energy and momentum, which characterize a quantum (microscopic) particle, into the relationship that describes a macroscopic radiation wave is a gross formal-logical error, because a quantum particle and macroscopic radiation are not identical material objects; (3) in the dialectical and formal-logical points of view, a free classical particle is not identical to a free quantum particle: these particles are non-identical material objects. Therefore, the substitution of the quantities of energy and momentum, characterizing a quantum (microscopic) particle, into the classical relationship that describes the energy and momentum of a classical particle is a gross formal-logical error; (4) in the point of view of formal logic, the concepts of "corpuscular aspect" and "wave aspect" are contradictory (mutually exclusive) concepts. (The concepts of "particle" and "wave" are defined by different essential features of material objects). Therefore, the de Broglie wave function and the Schrödinger wave equation represent a violation of the formal-logical law of lack (absence) of contradiction. This means that the concept of corpuscular-wave dualism is erroneous; (5) The de Broglie wave function and the Schrödinger equation represent a gross dialectical error, because the dimensionless wave function contradicts to the dialectical concept of the measure of a material object (i.e. the dimensionless wave function does not have the qualitative determinacy of a material object, does not characterize the properties of a material object). Therefore, the de Broglie wave function and the Schrödinger equation are meaningless relationships.
Category: Mathematical Physics

The Concepts of Web3 First Represented in 2013

Authors: Andrei I. Bodrenko
Comments: 19 Pages.

The concepts of Web3 were first represented by Andrei I. Bodrenko in 2013. Andrei I. Bodrenko stated that the new iteration of the Internet is based on serverless technologies comprising such features as: serverless data exchange, serverless electronic mail, serverless private networks, serverless social networks, decentralization, and these features are carried out by using peer-to-peer overlay computer networks operating over the Internet. It is significant that blockchains are typically managed by a peer-to-peer (P2P) computer networks, and the implementation of the blockchain is done without the need of a trusted authority or central server. Andrei I. Bodrenko invented Web3 in 2013 by publishing: the video report at the largest Central & Eastern European conference in the field of Software Engineering (see for details: Presentation 2013 (slides 18-24) and Report video 2013 (minutes 12-18)), and by publishing Patent document RU2013154454A representing the key feature of Web3 in December 06, 2013.
Category: General Science and Philosophy

Simulated Algorithms for Lives

Authors: Shuai Liu
Comments: 10 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

This paper summarizes the characteristics of neural networks.This paper focuses on challenging the sudden randomness of gene mutation and explaining the active source of mild gene mutation.In this paper, a life algorithm framework that simulates the changes of genes by neural networks combined with genetic algorithms is taken as an example to show that genes can maintain overall stability and actively update at the same time, presenting a random exploration that maintains relatively small scope in general, and thus species evolution.It is necessary to keep the exploration of randomness small. This article breaks the shackles that genes determine everything in life. Genes and neural networks are both important. In addition to innate genes, people's ability to learn, update, shape themselves, and explore is particularly important.This paper points out the importance of neural networks in the evolution of species. Different from the view that neural network is only the intelligent organizational structure of human brain, this article extends the above view, neural network is also an important intelligent structure of cells, and neural network is also an important intelligent structure of organs.
Category: Artificial Intelligence

The Game Show Problem

Authors: Richard L. Hudson
Comments: 2 Pages.

The game show problem aka Monty Hall problem [1], originated when Craig Whitaker posed a question of a wining strategy for a modified 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

Does Time Dilation Reveal a Variable Speed of Light?

Authors: Branimir Spigel
Comments: 16 Pages.

A reexamination of the well-known Hafele-Keating time dilation experiment reveals an overlooked assumption in standard interpretations. The time interval measurements for all clocks began and ended simultaneously in the laboratory, implying that their measured intervals should be identical. This raises questions about the conventional view that these intervals differ in duration due to motion. A deeper analysis revealed a fundamental issue: applying the same standard seconds to all intervals disregards the fact that moving clocks tick at a slower rate. This implies that the duration of a time unit on a moving clock is longer than a standard second. To resolve this inconsistency, we introduce the concept of variable time units. We further propose modifying the time dilation formula by defining time intervals in terms of discrete clock ticks rather than fixed-duration units, demonstrating that the ratio of time units follows directly from the ratio of clock ticks. However, adopting variable time units leads to the inevitable conclusion that the speed of light must also be variable, contradicting Einstein’s postulate of its invariance. From this perspective, while the Hafele-Keating experiment is widely regarded as empirical confirmation of Einstein’s theory of relativity, a closer analysis suggests an alternative interpretation that questions the assumption of a universally constant speed of light.
Category: Relativity and Cosmology

Convergence and Divergence Analysis of the Qx+r Problem

Authors: Song Li
Comments: 4 Pages.

This paper investigates the convergence and divergence of the $qx+r$ problem (Crandall conjecture), which is a generalization of the $3x+1$ problem (Collatz conjecture). Through probabilistic analysis, we establish that the convergence condition for the $qx+r$ problem is $q<4$,and predict that it converges to the precise value $frac{r}{4 - q}$ ; when $q>4$, the transformation sequence diverges to infinity. The results of this study provide new insights into understanding the dynamic behavior of the $qx+r$ problem.
Category: Number Theory

Prime Gaps and Asymptotic Behavior of Primes: A Hypothetical Approach

Authors: Hyeon Jun Ahn
Comments: 10 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

Based on heuristics related to Cramér's conjecture, this paper proposes a suitable hypothesis and investigates its implications. The study encompasses prime gaps, Andrica's conjecture, the mean of consecutive prime numbers, and a detailed analysis of Oppermann's conjecture.
Category: Number Theory

Resolution of Wave and Particle Nature of Electro-Magnetic Radiations from Maxwell’s Theory

Authors: Bijon Kumar Sen
Comments: 13 Pages. 2 Figures

The implications of Maxwell’s theory that combine magnetic, electrical and opticalproperties of electromagnetic radiations were not understood properly at the time of itsinception. It is shown here that mathematical restriction helps to resolve this centuries-oldcontroversy about wave-particle duality of electromagnetic radiation. This goes against theusually accepted notion that particles have wave properties and vice versa. The distinguishingfeature lies in the fact that particle motion requires no medium and is thus free from Dopplereffect. On the other hand, the wave motion depends on the medium of propagation and is,therefore, affected by Doppler effect. The particle motion is guided by particle (quantum)mechanics and the wave motion is guided by wave mechanics.The particle description of electromagnetic radiation was advanced by Einstein inproving the constancy of the velocity of light which is independent of the medium and theperception of simultaneity of events in different inertial frames. On the contrary, the wavemechanical approach was used by the adversaries of Einstein’s idea who pleaded for the spatialand temporal description as the result of Doppler effect. The arguments of both the sides areequally valid as the same problem was examined from opposite angles.The ideas of Red Shift, Tunnel effect, Photoelectric effect and Magnetic forces areexamined considering above viewpoints. The Red Shift conforms to the ideas of particle (Q)mechanics while the Tunnel effect can be interpreted in terms of wave mechanical perception. Photoelectric effect and magnetic forces are contributed by both wave and particle mechanics. The idea of electron spin, however, remains bizarre even around the centenary celebration year of wave and quantum mechanics.
Category: Quantum Physics

Galaxy Formation, Merging and Expansion of Dark Energy Fields, New Gravitational Fields, and the Reason for the Flatness of the Rotation Speed of Spiral Galaxies

Authors: Ichiro Nakayama
Comments: 10 Pages.

There are hundreds of billions of galaxies in the universe. These galaxies can be broadly divided into dwarf galaxies with less than a billion stars and giant galaxies with more than a billion stars. The most widely used classification of giant galaxies is the "Hubble sequence" proposed by American astronomer Edwin Hubble in 1926, which lists four types: elliptical galaxies, spiral galaxies, barred spiral galaxies, lenticular galaxies, and irregular galaxies. As can be seen from the diverse shapes of galaxies, it is thought that various factors are involved in the formation of galaxies. However, there must be a basic principle by which a group of more than a billion stars forms. In this study, we considered the formation of galaxies by extending the formation of stars, gravitational fields, and dark energy fields according to the Energy Body Theory. As a result, we found that the reason why spiral galaxies, which account for 60% of galaxies, have a spiral shape is fundamentally due to the rotation of the galaxy and the expansion of the dark energy field. The spiral arms were formed when a small group of stars rotating in the counter-rotating direction near the bulge approached the bulge, causing them to unravel and extend along the arms. It is also thought that energy flows into the spiral of the dark energy field from the outside, forming a high-energy space. However, it remains to be seen whether this theory is superior to the "high density wave theory," the mainstream explanation for spiral arms. The flatness of the rotation speed of spiral galaxies, an important issue in astrophysics, is thought to be caused by the neutralization due to synthesis of the spiral of the galaxy when the gravitational field is formed, and the rotation according to Kepler's laws.
Category: Astrophysics

Astro Sociology the Physical Universe as a Reflection of Consciousness

Authors: Alon Retter
Comments: 13 Pages.

This paper proposes a groundbreaking paradigm: the universe is a reflection ofconsciousness. Nearly a century ago, quantum mechanics introduced the concept of theobserver to explain experimental anomalies. Th is led many prominent physicists toargue that consciousness is fundamental and precedes matter. While this idea wassubsequently marginalized within physics, I contend that consciousness is essential for acomprehensive understanding of the universe.Tosupport this notion, this paper presents extensive evidence for consciousness fromphysical processes and astronomical objects. In addition, t he Astro Sociology model,which I introduced in 2010, posits that the universe reflects consciousness. This paperrevisits and expands upon the remarkable structural and numerical parallels betweenastronomical phenomena and human behavior. It subsequently outlines six predictionsof the model that have been empirically or theoretically confirmed. Finally, it brieflydiscusses ongoing research, including a novel quantum gravity model, that incorporatesthe observer to explain dark matter and dark energy without requiring additionalparticles.
Category: Astrophysics

Prime Cycles in Quantum Spacings and Zeta Zeros: A Number-Theoretic Bridge Between Classical and Quantum Physics

Authors: Daniil Beliavkyi
Comments: 4 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

We analyze eigenvalue spacings from quantum simulations and refined untwisted zeta zeros—Riemann zeta zero approximations adjusted with prime-based oscillations—achieving near-convergence to the Gaussian Unitary Ensemble (GUE). Quantum spacings yield a Kolmogorov-Smirnov (KS) statistic D = 0.1159 with p = 0.0658, surpassing the 0.05 threshold, while refined zeros achieve D = 0.0901 and a Cramer-von Mises (CvM) p = 0.9465, indicating exceptional GUE alignment. A persistent 22% deviation from GUE, however, suggests a deeper mechanism. We propose that prime numbers introduce cyclic patterns in quantum states, influencing coherence and challenging GUE’s classical assumptions. This novel synthesis of quantum physics and number theory, validated by 50,000 simulations, hints at a unified framework reconciling classical and quantum realms.
Category: Number Theory

The Overlooked Geometric Conflict Between Special Relativity and Sommerfeld’s 1909 Spherical Model

Authors: Aswan Korula
Comments: 7 Pages.

Special Relativity (SR) assumes that velocity vectors, displacement vectors and direction vectors coincide, since they are projected onto a flat analytical space (Minkowski space) to interpret inertial relative motion. In contrast, Arnold Sommerfeld’s 1909 spherical model interprets velocity composition on a spherical surface, where displacement and constant direction vectors are fundamentally distinct. This paper demonstrates that because Einstein and Sommerfeld use different surfaces to project their interpretation of the Michelson-Morley interferometry, their predictions for relativistic effects diverge. Specifically, while Einstein’s model necessitates Lorentz contraction and time dilation, Sommerfeld’s spherical formulation predicts no such distortions. Notably, compatibility between SR and Sommerfeld’s spherical model exists only in the special case of two right-angled triangles. By extension, any hyperbolic model that claims compatibility with SR must also be restricted to this special case. This work highlights a fundamental geometric conflict between Special Relativity and Sommerfeld’s alternative formulation, warranting further examination of the geometric nature of inertial motion.
Category: Relativity and Cosmology

Resolving the Gravity Freefall Paradox: A Sine-Alpha Model for Dynamic Spacetime Curvature

Authors: Aswan Korula
Comments: 6 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

This paper presents a novel resolution to the gravity freefall paradox, where General Relativity (GR) appears to introduce prematurespatial contraction effects that contradict Newtonian expectations. The paradox arises from the fact that GR predicts the same exter-nal gravitational field for both a physical mass and a black hole, yet point mass freefall marker behavior differs in both cases. We introduce the sine-alpha function, a dynamic formulation that naturally regulates spatial curvature according to the evolving ratio of marker separations. This model predicts Newtonian behavior outside the event horizon while dynamically allowing self-regulated curvature inside it. Our model preserves logical consistency between classical and relativistic physics. We provide evidence from numerical simulation, comparing our function’s predictions to GR, demonstrating its stability within and beyond the event horizon. We restrict ourselves to theoretical considerations only.
Category: Relativity and Cosmology

Measuring Global Instability: A Unified Framework for Methodical and Logical Assessment

Authors: Rhylie De Graaff
Comments: 19 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

The aim of this paper is to demonstrate that global instability can be measured mathematically, when using accurate data provided. When the data is available it is possible to predict when Nation states will fall using a variety of existing economic tools but by combining them together into one overarching framework. The data used when determining the outcome of nation states includes several factors, such as the level of civil disobedience, protests, the policies being brought forward as well as economic factors such as Purchasing Power, Cost of Living, and economic debt. The paper will show that there is a clear link between civil dissonance levels and the likelihood of a collapse of a nation. A table of the determining and observable factors has been provided to make the analysis easier for those conducting research and allow for the theories contained in this paper to be testable and be repeated.
Category: Economics and Finance

On the Feigenbaum Attractor and Feynman Diagrams

Authors: Ervin Goldfain
Comments: 24 Pages.

It was recently conjectured that the Standard Model of particle physics resides on a bifurcation diagram generated by the recursive scaling of Higgs coupling. This sequel explores the relationship between the bifurcation diagram and the Path Integral (PI) formalism of Quantum Field Theory (QFT). The long-term goal is to base the Feynman diagrams on the properties of the Feigenbaum attractor of either quadratic or cubic maps.
Category: Mathematical Physics

The New Conception of Absolute Truth and the End of Anthropocentrism

Authors: Gennady Shkliarevsky
Comments: 37 Pages.

The ascendance of relativism has defined the politics, social relations, values, science, and other aspects of modern civilization and its practice. While some effects of relativism are salutary (relativism, for example, has promoted greater tolerance), others are not. This article argues that the ascendance of relativism has led to the demise and ultimate rejection of the concept of absolute truth. As the article explains, absolute truth is a very important operational concept that integrates, regulates, and conserves all spheres of human practice. It enhances human capacity to create new and increasingly more powerful levels of mental organization that are the source of radical innovations: new ideas, theories, and approaches. The article explains that the functional role of absolute truth is essential for sustaining human civilization and its evolution. It demonstrates that the functional role of absolute truth is defined by the universal process of creation. The rejection of absolute truth has been an inevitable result of the anthropocentric tradition that has dominated and continues to dominate human civilization. This tradition fails to recognize the central role of the process of creation in human existence. It is exclusionary and is incompatible with objectivity. This tradition poses a threat to the survival of civilization. The article argues that the revival of absolute truth and its role in human practice will ensure the survival and evolution of human civilization. The article offers a new conception of absolute truth. This conception relies on the universal process of creation as its main organizing principle. Due to its inclusive nature, the process of creation is objective, universal, and invariable under transformation. Since the new conception is based on the process of creation, it also possesses its properties; it is objective, universal, and invariable. It is not transient as the past conceptions of absolute truth. Finally, the article discusses the ways in which the new conception of absolute truth will affect human practice.
Category: General Science and Philosophy

Atomic Spectrum by Electrometrication of Space and Quantum Nature of Motion

Authors: Sergio de Azevedo Melo
Comments: 53 Pages. In Portuguese

The electrical nature of the particles that make up the atom allows the prediction of the electromagnetic emission spectrum, resulting from the mechanics between the particles involved. However, the radiation process described by quantum physics is different from the understanding made by ordinary electromagnetism. The understanding of fission is discussed by the correspondence principle.The proposed curvature produced by the elementary electric charge and the representation by an electrometric tensor make it possible to address aspects of classical and quantum theories using the same formulation. The electron does not fall into the nucleus, as it follows a geodesic trajectory. The resolution of the atomic binary system encounters self-induced harmonic oscillations that produce fluctuations in the metric, with consequences in the determination of the point representation and in the position-momentum simultaneity in the same reference frame. The energy of the orbital transition by the electron, according to the spectrum of the hydrogen atom, reproduces the discretization and ripple effects as a consequence of the resolution. The result endorses how the correspondence between electromagnetic radiation processes is understood by electrometric curvature.
Category: Relativity and Cosmology

[Speculation/Exploration on the] Design, Expression, and Oral Delivery of a Recombinant Fusion Protein (Tp0751—CtB—TprK) in Yeast as a Candidate Syphilis Vaccine

Authors: Hyunho Shin
Comments: 9 Pages. (Note by viXra Admin: This article is speculative/exploratory)

Syphilis, caused by Treponema pallidum, has resurged globally in recent years, particularly in East Asia, highlighting the urgent need for preventive vaccines. Despite being a well-characterized pathogen, traditional vaccine development for T. pallidum faces substantial challenges due to its inability to be cultured in artificial media. This study presents the development of a novel oral vaccine candidate utilizing recombinant T. pallidum outer membrane proteins TprK and Tp0751 expressed in yeast (Saccharomyces Boulardii). Our approach incorporates a gene cassette containing the conserved N-terminal region of TprK, cholera toxin B subunit (CtB) as an immune adjuvant, and Tp0751, connected by glycine-serine flexible linkers under the control of the ADH promoter. This strategy aims to overcome the cultivation limitations of T. pallidum while potentially inducing protective mucosal immunity through oral administration. Structural analysis using AlphaFold predictions confirms the stability of the recombinant construct. This research represents a significant advancement toward developing an accessible and effective vaccine against syphilis, with important implications for global public health.
Category: Physics of Biology

The Higgs Boson May Be Made of Higher Dimensional Matter

Authors: D. G. Grossman
Comments: Pages.

The Higgs boson may not be the heaviest particle created by man so far (it is exceeded by the top quark), but it may be the highest dimension particle created by man so far. If calculations are correct, it may be of dimension 20/21 (the top quark is dimension 9/10), that is, it may be composed of 20-dimensional matter (quarks) circulating in the surface of a 21-sphere. Recent Higgs boson mass measurements of high accuracy, and a mass factoring technique based on n-sphere surface volumes, which was derived from Planck's Energy-Frequency Relation, E=hf, were used to reach that conclusion. A power of two factoring, which is a possible indication of stability, was found within 3 MeV of the ATLAS group's recent 125,220 MeV improved accuracy estimate of the Higgs's mass. The S21h power of two factoring found, (2^16 - 2^10) S21h, translates to a mass of 125,217.08 MeV, which is very close to the ATLAS group's result. Is the Higgs boson made of 20/21 dimensional matter?
Category: High Energy Particle Physics

Decoding International Gold Transfers: Official Narratives and Alternative Conjecture Casting Shadows of Preparation

Authors: Masashi Ishihara
Comments: 14 Pages.

This paper examines the 2024-2025 movement of approximately 400 metric tons of gold from London to New York through the lens of three competing explanatory frameworks: the Mainstream Official Narrative involving arbitrage opportunities and potential tariff concerns, a Controlled Conspiracy Theory regarding missing US gold reserves, and an Unrestrained Alternative Conjecture grounded in historical precedents during times of crises and wars. Using this case study, we develop a model for understanding how multiple narratives function within modern information ecosystems, particularly in the post-COVID era where institutional trust has declined. We argue that the coexistence of these narratives serves distinct social and political functions beyond merely explaining the gold transfers themselves.
Category: Social Science

Causal Set Theory with Occamistic Precedence: A Speculative New Approach to the Emergence of Quantum Mechanics, Spacetime Structure, Gravity, Psi Phenomena and Universal Cognition

Authors: Ben Goertzel
Comments: 47 Pages.

We propose an augmented precedence principle that integrates an algorithmic information prior to favor simpler, low-entropy patterns in the evolution of causal sets. Applied to the sequential growth dynamics of causal set theory, this Occamistic bias naturally selects manifold-like configurations that approximate smooth spacetimes, thereby addressing the entropy dominance problem. On these emergent manifolds, the statistical accumulation of repeated quantum events gives rise to effective quantum dynamics from which the Schroedinger equation is derived. This perspective shows promise of potential extension to chromodynamics; and moreover, by interpreting the spacetime metric as a quantum operator and deriving gravitational dynamics from the minimization of quantum relative entropy between the intrinsic metric and a matter-induced metric, one can establish a connection with entropic theories of gravity. The Occamistic Precedence framework is extended to a relational, Universal Cognition perspective in which the decentralized cosmic ledger "remembers" its past through local interactions, enabling observer-dependent transitions between quantum (Schroedinger-like) and classical (Bellman-like) cognitive regimes providing physical underpinning to mental processes in biological and engineered systems, and potentially also providing a new way of looking at "extraordinary" mental processes such as altered states of consciousness and psi phenomena. Overall, our work suggests that gravity, quantum mechanics, and anomalous cognitive effects may emerge from an underlying, history-dependent process governed by fundamental information-theoretic principles.
Category: General Science and Philosophy

The Search for Life and Aliens

Authors: James R. Johnson
Comments: 13 Pages. Astrophysics or Biophysics may be a better science category.

This article is a comprehensive survey describing our search for life and aliens beyond earth. The search for life inside our Solar System continues by digging into the Martian soil and exploring the underground oceans of Jupiter’s moon Europa. As we peer into the Milky Way, exoplanets are the target. Improved sky-survey telescopes identify exoplanets. Then, subsequent analysis using spectrographs obtained via exoplanet transits or direct imaging hope to identify biosignatures. Detection of intelligent life is either circumstantial or definitive. Technosignatures offer circumstantial evidence of alien civilizations. Definitive or positive detection can be physical, for example, discovering interstellar objects (spaceship/UFOs) or as in the movie Contact, an alien message. Future giant optical/infrared telescopes, sophisticated radio telescopes, and a proposed space telescope, HWO, will dramatically enhance detection. Significant technical advances in earth-based and space telescopes, documented in four key figures, dramatically improve the probability of discovery over the next ten years. Thus, we may soon have an answer to the question, are we alone?
Category: Astrophysics

Disprove of a Proof of Euler's Formula

Authors: Sigrid M.-L. Obenland
Comments: 2 Pages.

In 1991, Gilbert Strang published a proof of Euler's formula using polar coordinates in Calculus, Wellesley-Cambridge, p. 389. In the following we show that this alleged proof is not valid.
Category: Functions and Analysis

What can save NATO? Stand for Ukraine!

Authors: Dainis Zeps
Comments: 7 Pages. (Note by viXra Admin: This article may not be within the scope of viXra and is subject to withdraw)

This article argues that NATO’s survival hinges on supporting Ukraine against Russia’s aggression, as Donald Trump’s actions threaten to dismantle the alliance. Written on March 9, 2025, it critiques Trump’s apparent intent to abandon Ukraine—via halted aid, a predatory $500 billion resource deal, and alignment with Russia—while urging Europe to reboot NATO without the US. Highlighting Russia’s looming collapse and Ukraine’s role as democracy’s defender, the author calls for defiance against Trump’s betrayal to preserve the democratic world.
Category: Social Science

Comment on Article Entitled "Co2 Chemisorption Behavior in Conjugated Carbanion-Derived Ionic Liquids Via Carboxylic Acid Formation"

Authors: Vitaly V. Chaban, Nadezhda A. Andreeva
Comments: 6 Pages.

The paper in the title proposed an interesting chemical sorbent for CO2, exemplifying unusual chemistry, and reported promising chemisorption capacities. The carboxyl moiety formation was highlighted as the only CO2 chemisorption product. We would hereby like to question the chemical identity of the CO2 chemisorption product reported in this publication. The considerations in favor of a different product are provided in this Comment based on general chemical wisdom, critical re-interpretation of the experimental research, and new ab initio calculations.
Category: Chemistry

Fraction Algebra

Authors: Huhnkie Lee
Comments: 55 Pages.

This paper will explore fractions and introduce brand new concepts related to fractions. We will also introduce related ideas such as Iverson transformation, inverse Iverson transformation. We will also introduce theorems related to flooring and ceiling functions.
Category: Algebra

Fishers’ Perceptions on Derelict Fishing Gears’ Causes, and Mitigation Measures in Korea

Authors: Sunwook Hong, Jongmyoung Lee, Jongsu Lee, Won Joon Shim, Sehan Lim
Comments: 18 Pages.

Derelict fishing gears (DFGs) present a high damage risk for marine ecosystems, navigation safety, fishing resources, and the economy. To mitigate this damage, considering fishers’ roles is very important, because they are the main contributors directly exposed to the impact. Since DFGs are significant sources of marine debris in South Korea, we conducted a survey to evaluate fishers’ perception of DFGs’ causes, reasons, and measures, based on FAO’s and UNEP’s 2009 suggestions. We also examined which governmental measures they preferred to help decrease DFGs. A total of 134 people participated in the 2015 survey, comprising 55 from capture fishing and 79 from aquaculture. The fishers answered that DFGs are abandoned, discarded, and lost in similar proportions. In terms of abandoned DFGs, they selected similar degrees of impact regarding ‘illegal, unreported andunregulated fishing,’ ‘illegal gear,’ and ‘too much gear for time.’ For discarded DFGs, they mostly agreed that ‘chosen over onshore disposal’ and ‘damaged gear’ were more serious causes than ‘too much gear for space.’They answered that ‘misplaced gear’ causes less lost DFGs than ‘gear conflict,’ ‘poor ground condition,’ and ‘extreme weather.’ In total, the fishers found ‘improving port facilities’ and ‘retrieval activities’ as more effectiveand feasible measures than others. They positively evaluated the Korean government’s existing measures, and preferred ‘mandatory return’ and ‘strengthening gear marking’ for future improvement measures. This study couldfurther contribute to achieving policy goals more effectively and efficiently.
Category: Social Science

Temporal Flow Theory: Unifying Time, Quantum Mechanics, and Cosmology via Entanglement Entropy

Authors: Matthew Warren Payne
Comments: 5 Pages. (Note by viXra Admin: The typesetting has mistakes!)

Temporal Flow Theory (TFT) redefines time as a dynamic four-vector field (W^μ) sourced by entanglement entropy gradients, unifying quantum mechanics, gravity, and cosmology. TFT resolves the measurement problem, dark phenomena, black hole information paradox, and Hubble tension (H0 = 70.5 ± 0.7 km/s/Mpc) using three axioms. It predicts quantum interference shifts (Δφ ≈ 2.1 × 10^-6 rad) and galactic rotation fits (4.7% SPARC deviation), testable with LHC and SKA. TempFlowSim validates these across scales, offering a minimal, Lorentz-invariant alternative to existing models.
Category: Quantum Physics

Relativistic Mass

Authors: Nainan K. Varghese
Comments: 9 Pages.

Abstract: Although the mass of an object is defined to represent the equivalent of 3D matter it contains, it is often considered as the quantity of 3D matter contained in the object. Mass is the mathematical relation between an external linear effort on an object and the rate of rate of its displacement in the direction of the external effort. This relationship is often ignored, and the value of mass is regarded in almost all academic fields as the quantity of 3D matter present in the object. The dependency of the mass of an object on its linear speed introduces changes in the value of its mass depending on the initial speed of the object considered.
Category: Relativity and Cosmology

Expanding Contracted Space Theory (ECST)

Authors: Dale Wahl
Comments: 6 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

We present a conceptual framework that explores an alternative perspective on gravity and quantum mechanics, which I refer to as the Expanding Contracted Space Theory (ECST).ECST proposes that space contracts within mass while simultaneously expanding in different conditions, providing a potential mechanism for gravitational attraction, quantum behavior, and cosmic expansion. The theory aims to address open questions in gravitational physics, such as the nature of dark matter and gravitational lensing, as well as quantum uncertainty and wave-particle duality from a novel perspective.
Category: Quantum Gravity and String Theory

Two Separate Derivations of the Shannon Entropy Equation from First Principles and the RTA Framework for Information

Authors: Vasant Jayasankar
Comments: 38 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable; and there are missing symbols in formula/equations!)

The Shannon entropy equation has been foundational in information theory, yet its derivation has historically relied on axiomatic reasoning rather than first principles. In this paper, I propose two derivations of the Shannon entropy equation from fundamental geometric constraints, demonstrating that it emerges naturally as a special case of a deeper information structuring principle. I propose that entropy is fundamentally constrained by geometric projection effects and dimensionality, leading to a formulation that reduces to Shannon’s equation in Euclidean space while extending to structured high-dimensional systems. Further, I introduce a novel connection between optimal information structuring and the All-Pairs Shortest Path (APSP) framework, demonstrating that information processing may follow geodesic constraints in hyperbolic space. This insight suggests that optimal data compression, AI learning, and information retrieval follow geometric constraints, revealing a deeper structural foundation beyond statistical approximations. By unifying entropy, geometric projection constraints, and APSP-based information structuring, I introduce the RTA Framework for Information, which redefines optimal information flow in structured systems and AI architectures. If validated mathematically and empirically, this may have deep implications for AI architectures, compression theory, and quantum information, pointing toward a broader framework that extends beyond classical entropy formulations.
Category: Mathematical Physics

Massive Photon Interactions in Longitudinal Displacement Current

Authors: Arvin D. Sharma
Comments: 3 Pages.

We show the scalar field defined in the vectoralform of Maxwell’s equations is found to break the Lorentz Gauge in the case of massive photons. Using the biquaternion form of Maxwell’s equations, the differential forms of the scalar field is shown to have relation to photon mass. We show both the scalar field gradient and photon mass are related to thedisplacement current using the Proca equations, and propose a means to determine the spatial geometric structure of the massive photon based on its intrinsic capacitance.
Category: Quantum Physics

Tri-Quarter: Coordinates and Topological Zones with a Structured Orientation and Consistent Directional Separation Across the Complex Plane

Authors: Nathan O. Schmidt
Comments: 5 Pages.

In this paper, we introduce the Tri-Quarter Theorem, a new mathematical framework for defining a generalized complex-Cartesian-polar coordinate system on the complex plane ℂ. We discuss the coordinate system's construction and prove that the boundary zone T, identified as the unit circle, exhibits topological duality with the inner zone X_- (|x| < 1) and outer zone X₊ (|x| > 1), with a trichotomy-defined structured orientation that ensures consistent directional separation. This result unifies complex, Cartesian, and polar representations while offering new insights into topological separation and orientation. Its development was originally intended for quark confinement and black holes, but additional potential applications may include technologies that rely on complex numbers, boundary behaviors, or spatial partitioning in engineering, computing, and applied sciences. We discuss the coordinate system's construction and the theorem's proof. More work is needed to further develop and apply this framework via the methods of science and mathematics.
Category: Topology

Observer Effect and Hidden Variables

Authors: I. Prusis, P. Prusis
Comments: 5 Pages. 3 figures

In modern physics, it is assumed that all particles have both corpuscular and wave properties. The double slit experiment shows that when the properties of a particle are measured, it inexplicably turns into a particle that has no wave properties, i.e. it loses its duality. The analysis of the experiment shows that any particle performs many different motions at the same time. Chaotic thermal fluctuations, part of which is in the transverse direction, zitterbewegung and longitudinal movement (drift) in the direction of the slit. The measuring instrument cancels the transverse oscillations, so the interference pattern fades
Category: Quantum Physics

The Hubble Diagrams Limitations and Surprises

Authors: Martin Schauer
Comments: 12 Pages.

In 1929, Edwin Hubble measured the brightness and redshift of distant stars to calculate their distance and escape velocity. The resulting data, plotted on the now famous Hubble diagram, showed a proportional relationship between distance and redshift. It is important to note, however, that any measurement of a star's brightness (magnitude) also gives its corresponding lookback time. But is the correlation between redshift and lookback time causal or spurious, or is even the correlation between redshift and distance spurious ?In other words, does the redshift brightness plot reflect the spatial or the temporal evolution of the Universe or both, and to what extent? This article shows that there are many different possible events that could lead to the same redshift brightness diagram. For example, the redshift could depend almost entirely on changes in distance, or almost entirely on changes in lookback time. It turns out that the more redshift depends on changes in distance, the less it depends on changes in lookback time, and vice versa. However, due to a lack of data, no one knows what really happened. But many things would be simpler, if one assumed that the redshift depends almost exclusively on the lookback time: The amazing idea of an expanding space would not be necessary. The expansion rate of the universe would be steadily decreasing.Dark energy and the cosmological constant (Einstein's biggest blunder) would not be necessary. Until new discoveries are made, it is not possible to determine what conclusions can be drawn from a redshift brightness diagram.But these inferences are a key pillar of the ΛCDM model. If this pillar wobbles, the whole structure could collapse.
Category: Relativity and Cosmology

PhytoIntelligence: An Open-Source AI-Driven Mathematical Framework for Diagnostic-Specific Phytochemical Formulation for Any Diagnostic

Authors: Marie Seshat Landry
Comments: 15 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

PhytoIntelligence is an innovative, open-source, AI-driven framework designed to revolutionize the development of plant-based nutraceuticals. By systematically integrating advanced techniques in literature mining, molecular docking, pharmacokinetic modeling, bioavailability optimization, synergy analysis, and regulatory compliance, this framework enables the creation of diagnostic-specific nutraceutical formulations for a wide range of health conditions. This document outlines the complete scientific methodology underlying PhytoIntelligence—from initial observations and research questions to hypothesis formulations, methodological design, experimentation, discussion, and final conclusions. While the LC-Phyto formulation for lung cancer prevention and support (comprising 10 bioactive compounds) is used as an illustrative case study, the framework’s modular design makes it universally applicable to any diagnostic.
Category: Quantitative Biology

Interpretation-Independent Proof That Decoherence Is Not Collapse

Authors: Mike Casey
Comments: 4 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

This paper presents an interpretation-independent proof that neither detection nor decoherence explains quantum state collapse. The argument is grounded in experimental results from Proietti et al. (2019), which demonstrate the persistence of quantum coherence despite environmental decoherence. By analyzing the logical consequences of entanglement, detection, and decoherence, this work demonstrates the fallacy of equating detection or decoherence with observation in quantum foundations and establishes a necessary condition for viable interpretations.
Category: Quantum Physics

Collatz Conjecture: A Coordinate System Based Approach

Authors: Eric M. Kelleher
Comments: 24 Pages. (Note by viXra Admin: Author's nameis required on the article)

The Collatz conjecture states any number, N0, after successive computations will always yield one, initiating the recursive sequence of 1→4→2→1→4 because 1 equals itself via (3n+1) 2 for n = 1. Finding a separate recursive sequence excluding 1 would prove the conjecture false. Analysis of the Collatz conjecture with a dual coordinate system (beta tables and gamma tables) revealed only one such recursive sequence is possible. For n, x = N0, the number sequence (6n + 5) forms beta table 2, column 1 and (6n + 1) creates beta table 3, column 1 with each successive column increasing by 22x. The formula (n−1) 3 was used on each beta entry to produce the gamma tables defined by the following sequences, for n = N0: (4n + 3) = m forms gamma table 2, column 1 and (8n + 1) = m forms gamma table 3, column 1 where each successive column increases by 4m + 1. This reveals the (3n+1)2 quotients of all odd numbers connect as follows: (4n + 3) → (6n + 5) and (8n + 1) → (6n +1), accounting for all possible unique connections between odd numbers via (3n+1)2. The differences between connecting sequences are (4n +3)−(6n+5) =2m and (8n+1)−(6n+1)= −2m where the difference only equals zero for n = 0 as follows: (8 × 0 + 1) − (6 × 0 + 1) = 0, indicating the recursive loop as found with (3n+1)2 for n = 1. Using the coordinate system, I herein demonstrate the uniqueness of the only known recursive loop and prove it is the only one of its kind thus solving a major part of the Collatz Conjecture.
Category: Number Theory

Corrections of Exercises and Problems, Part 1: Chapters of Topography, Astronomy and Curves and the Theory of Surfaces

Authors: Abdelmajid Ben Hadj Salem
Comments: 95 Pages. In French

This booklet includes in the first part thecorrections of the exercises and problems of the following three chapters : topography, astronomy and curves and the theory of surfaces.
Category: Geophysics

Detection of Oscillatory Time Dynamics Through Cross-Correlation Analysis of GW170817gfvv Data

Authors: Maksym Strygun
Comments: 4 pages, English. Independent research. Includes detailed cross-correlation analysis of GW170817 data with graphical illustrations. No journal submission. License: CC BY-SA 4.0.

This paper presents a correlation analysis of publicly available gravitational wave data from event GW170817 recorded by the LIGO detectors H1 and L1. The analysis aims to identify periodic oscillations predicted by a recently proposed novel time oscillation model, which describes time as possessing intrinsic spiral and oscillatory dynamics. Cross-correlation between the H1 and L1 signals revealed a maximum correlation at a time lag of approximately -14.37 seconds. This time shift is consistent with the theoretical predictions of the proposed model, suggesting possible intrinsic oscillatory dynamics of time. These findings, if confirmed across multiple events, could provide crucial insights into the fundamental nature of time and its relation to quantum gravity.
Category: Quantum Gravity and String Theory

Complex Extensions of Riemann Zeta Function and Complementary Formula of Gama Function

Authors: Xiaochun Mei
Comments: 13 Pages.

This paper discusses the complex extensions of Riemann Zeta function and complementary formulas of Gama function. By re-writing the Zeta function equation, it is proved that the equation described a relation between the original Zeta function Z(s) and a now function Z(s)=Z(1-s) . But the domains of these two function does not the same and incompatible, so the Riemann Zeta function equation does not hold. It is also proved that the complex extension formula of the present complementary formula of Gama function is wrong. The correct formula is given by strict calculation. The condition 01. Therefore, Riemann Zeta function equation does not hold at any point in the complex plane, and it is meaningless to discuss it.
Category: Number Theory

Transition Predication Models - Literature Review

Authors: Shlomy Shitrit, Eran Arad
Comments: 30 Pages.

The transition of a boundary layer from laminar to turbulent impacts the characteristics of aflow field, but its underlying physics has yet to be well understood. This literature review aims to give an overview of the more widely used approaches to model transition in ComputationalFluid Dynamics (CFD). Several different methods are reviewed: the linear stability analysismethod, the low Reynolds number turbulent closure approach, the correlation-based methods,the intermittency transport method and the laminar fluctuation energy method. The approaches are compared to one another, highlighting their respective advantages and drawbacks.
Category: Mathematical Physics

Root Finding Problem

Authors: Edgar Valdebenito
Comments: 2 Pages.

In this note, we consider the alternative form of the rootfinding problem known as the fixed-point problem.
Category: General Mathematics

Resolution of the Yang-Mills Mass Gap Problem via the Wave Oscillation-Recursion Framework (WORF)

Authors: James Fruit
Comments: 8 Pages. Copyright Licensed under CC BY 4.0. NC © 2025 James Fruit.

This paper presents a rigorous, non-perturbative proof of the Yang-Mills Mass Gap Problem,demonstrating the existence of a strictly positive lower bound for the spectrum of SU(3) gauge boson excitations. The proof is formulated within the Wave Oscillation-Recursion Framework(WORF), introducing a recursive Laplacian operator that governs the spectral structure of gauge field fluctuations. By constructing a self-adjoint, gauge-invariant operator within a well-defined Hilbert space, this approach ensures a discrete, contractive eigenvalue sequence with a strictly positive spectral gap.A recursive contraction mapping theorem is established, showing that the eigenvalues of theLaplacian satisfy a recursive relation of the form lambda(n+1) = rho * lambda(n) with 0 < rho < 1, preventing the accumulation of eigenvalues at zero. The application of the Banach Fixed-Point Theorem guarantees that the lowest eigenvalue remains strictly positive, resolving the core issue of massless gauge bosons in Yang-Mills theory. The transition from classical spectral bounds to the quantized mass spectrum is explicitly derived. The quantum excitation energy of gauge bosons follows E(n) = hbar * sqrt(lambda(n)), leading directly to a nonzero mass gap given by m_gap = (hbar / c) * sqrt(lambda_1) > 0. This result establishes a non-perturbative proof of the mass gap problem, independent of renormalization group methods or numerical simulations. This work represents the first direct application of WORF to a fundamental problem in quantum field theory. The proof is mathematically self-contained and is submitted for formal review by the Clay Mathematics Institute. If validated, this approach provides a transformative new methodfor addressing open problems in high-energy physics and gauge theory.
Category: Mathematical Physics

Noetic Morphisms

Authors: Dara O. Shayda
Comments: 8 Pages.

In March of 1845 Gauss described the conception of an action at a distance, propagated with a finite velocity, the natural generalization to electrodynamics view of Newtonian force. Unsuccessfully, Wheeler and Feynman attempted a new theory for Absorber in 1945 [9]. In their paper there is a detailed reference provided by Prof. Einstein about a relatively unknown physicist named Hugo Tetrode[10,11] and quoted: "The sun would not radiate if it were alone in space and no other bodies could absorb its radiation... If for example I observed through my telescope yesterday evening that star which let us say is 100 lights years away, then not only did I know that the light which it allowed to reach my eyes was emitted 100 years ago, but also the star or individual atoms of it knew already 100 years ago that ‘I’, who then did not even exit, would view it yesterday evening at such and such timeu2026"[11]. The process by which the verb "knew"occurs is modelled by the Noetic morphisms of the arr(Decay) Arrow Category. However this treatise is not about energy emission absorption in nature, rather about their mechanism of information knowledge exchange to make the emission possible.This treatise and its categorical constructions, Universal Properties and symbols pave the way for grammars and functions and operators and Formal Systems (algebras, calculi) of de novo programming languages to describe the nature of specific Emitter Absorber coupling.
Category: Mathematical Physics

A Simple Approach to Understanding the Stress-Energy Tensor

Authors: Mueiz Gafer KamalEldeen
Comments: 4 Pages.

The common method of defining the stress-energy tensor is confusing and inconsistent. In this article, an alternative simple method for definition is presented. The connection between the stress-energy tensor used in general relativity and the stress tensor used in material mechanics contains errors, as all stresses occurring in the material cause an increase in the fields that bind the microscopic parts of the material and affect only the material's density.
Category: Relativity and Cosmology

The Cosmological Constant Problem is not a Problem: it is a Misconception

Authors: Rudi Van Nieuwenhove
Comments: 6 Pages.

The persistent discrepancy between quantum field theoretical predictions of vacuum energy density and the observed value of the cosmological constant suggests a fundamental issue in our understanding of their gravitational effects. We argue that General Relativity developed without quantum mechanical input, is not suited to accommodate zero-point energy as a source term in the Einstein field equations. Instead, we propose that the cosmological constant arises from large-scale curvature effects rather than an intrinsic vacuum energy density. This approach naturally resolves the cosmological constant problem without requiring fine-tuning or exotic physics. Furthermore, we outline how this perspective aligns with the idea that only energy contributions with physical boundaries (e.g., mass-affected zero-point fluctuations) gravitate, while uniform vacuum fluctuations do not.
Category: Relativity and Cosmology

Introducing Pn Power Series in Number Theory: a Novel Way to Classify Natural Numbers

Authors: Pradeep Pant
Comments: 12 Pages. The supplementary file (Table S1) is available at https://bennettu-my.sharepoint.com/:x:/g/personal/pradeep_pant_bennett_edu_in/EcL2EjaiGNJFqyyLEo-SqqcBqEle9TZA32Wk3IAmC0Cy0A?e=LVosYs

Mathematics is a constantly evolving field where the search for new knowledge never stops. Discovering new mathematical series has been crucial for progress, leading to breakthroughs in many areas and offering fresh insights into the world of numbers. In this paper, we describe a new series called the Pn power series. The Pn power series is a superset of many series depending on the value of n. In number theory, we hypothesize a natural number X belongs to a power series Pn if its proper positive divisors (d1 , d2 , d3 ,. . . , X) follow; X^n = d1 * d2 * d3 *. . . * X (where n = 1, 1.5, 2, 2.5, 3, etc.). To illustrate this concept, 12 is a member of the P3 power series as its proper positive divisors, namely 1, 2, 3, 4, 6, and 12, satisfy the equation: 12^3= 1 * 2 * 3 * 4 * 6 * 12 = 1728. Similarly, 196 belongs to the P4.5 power series, with its divisors 1, 2, 4, 7, 14, 28, 49, 98, and 196,following the equation: 196^4.5 = 1 * 2 * 4 * 7 * 14 * 28 * 49 * 98 * 196 = 20,661,046,784. We believe that the implications of this observation are far-reaching, extending beyond number theory into various mathematical disciplines, and have the potential to open up new avenues of research and mathematical exploration.
Category: Number Theory

A New Approach to the Collatz Conjecture:Proof of the Absence of Cycles

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

The Collatz conjecture posits that for every natural number, a specific iterative rule leads to 1 or forms a cycle. This paper introduces a simplified Collatz function, inverse Collatz, and double inverse Collatz to prove that no cycles exist beyond the known 1 → 4 → 2 → 1. By analyzing number generation through parameters a and k, we demonstrate the logical impossibility of additional cycles.
Category: Number Theory

The Natural Laws of Compressed Euler Wave Equations

Authors: Marciano Laoang Legarde
Comments: 9 Pages. (Note by viXra Admin: Please cite and list scientific references)

the Natural Laws of Compressed Euler Wave Equations, it describes how trigonometric functions behave when their inputs are transformed exponentially. It explores how sine, cosine, secant, cosecant, tangent, and cotangent waves undergo extreme compression along the positive x-axis, leading to predictable patterns in their peak values, oscillations, and asymptotic behavior. The paper establishes three fundamental laws governing these transformations, revealing deeper insights into wave behavior under exponential scaling.
Category: General Mathematics

Two Theorems to Verify Goldbach's Strong Conjecture or Refute it by an Uninterrupted Sequence of Composite Odd Numbers in the Interval [n ─ 2n]

Authors: Bahbouhi Bouchaib
Comments: 17 Pages.

Let's assume an even number E that is one unit larger than to the largest prime number we know today. Let's call this prime number Pl. Now we have 0—E/2—E and therefore Pl > E/2. For GSC to be true E must be sum of two primes P1 and P2 such that P1 < E/2 and P2 > E/2. Therefore we have to calculate E — P2 = X. If X is composite GSC is not verified; if X = P1 then GSC is verified. We then calculate E — P2 starting with Pl and all P2 till the one which is the closest to E/2. The question is: are all the Xs resulting from calculated E — P2 = X composites? Is it possible that all Xs might be composite which means non-verification of GSC? By contrast, if only one X is prime, then GSC is true. We see that GSC is much more likely to be verified in this case because a very long sequence of composite numbers is very unlikely to be continuous from E — Pl to E — P2 which is the closest to E/2. In other words there is at least one P2 prime in [E/2—E] such that E — P2 = P1 → E = P1 + P2. The small primes are those that give the most composite numbers because their multiples are the most frequent but it is unlikely that all P2 of [E/2—E] would give composite numbers when calculating E — P2. If anyone, using this procedure, is able to find a sequence of composite numbers E - P2 = X in the whole E/2 — E interval; then He will be the first one who finds the solution to Goldbach's strong conjecture because this means its final rejection, and no mathematician can cast any doubt on his result. However, let us not forget that if only one X is prime, then GSC is true. As long as we cannot find this very precious and historical counterexample of an uninterrupted sequence of composite numbers by E — P2 = X (P2 is in E/2-E interval); Goldbach's strong conjecture will remain true although unprovable. This article gives the TWO THEOREMS of CONGRUENCE-MODULO which always predetermine whether GSC is true or not when calculating E - P2 = X. These two theorems described in this article will predict whether X is prime or composite. Nevertheless, these two theorems require the use of euclidean divisions in series with the calculation of the remainders for each P2.
Category: Number Theory

Experimental Validation of TSVF-SUSY Induced Phase Shifts in Gravitational Waves

Authors: Muhammad Shahzaib Uddin Khan
Comments: 5 Pages.

This paper presents the first statistically significant evidence for a TSVF-SUSY induced phase shift in gravitational waves detected by the LIGO—Virgo—KAGRA (LVK) Collaboration. Through numerical simulations and statistical analysis, using time-domain and Fourier analysis techniques, I find a consistent phase shift of approximately **0.002 radians** across multiple events, including GW150914, GW170817, and GW190521. With a **corrected signal-to-noise ratio (SNR 433.34), recalculated using an improved integration method over the LIGO noise power spectral density**, and a p-value confirming statistical significance, Ianalyze the correlation of this effect with binaryparameters. I find that the TSVF-SUSY phase shift scales with **mass (r = 0.992), spin (r = 0.996), and redshift (r = 0.977)**, suggesting a non-universal effect linked to black hole properties and cosmic expansion. These results provide a testable prediction for future GW detections, particularly with upcoming observatories such as **LISA and the Einstein Telescope (ET)**, which will have enhanced sensitivity to phase shifts in different frequency regimes.
Category: Quantum Gravity and String Theory

Angles Associated with Primes Numbers

Authors: Khazri Bouzdi Fethi
Comments: 1 Page.

This article explores a géometric interpretation of the Riemann zêta function as angle measures.This perspective could explain the spiral arragement of prime numbers,as observed in Ulam’s spiral (1963).
Category: Number Theory

New Wireless Technology not Covered by the Existing Ieee Standards of 2017

Authors: Andrei I. Bodrenko
Comments: 5 Pages.

A new type of wireless computer network is presented in this article. This wireless network, for data transmission, uses visible light, and does not use intensity modulation of optical sources, such as light-emitting diodes and etc. Thus represented wireless network differs substantially from wireless networks covered by the existing IEEE standards of 2017, and its ongoing revisions, for visible-light communication (VLC) technologies, Li-Fi technology and optical camera communication (OCC) technologies. This new wireless technology can be used for the next generation of wireless communication networks such as 5G networks.
Category: Digital Signal Processing

Reasonable Alternatives to the Two Big Problems in 20th-Century Physics

Authors: Gocho V. Sharlanov
Comments: 105 Pages. The content of this monograph is based on 3 published articles.

The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks the real advance in science ("The Evolution of Physics", Einstein & Infeld, 1938). The root cause of the biggest problem in 20th century physics, the "special theory of relativity", is actually the incorrectly accepted and maintained for more than 100 years "postulate of the constancy of the speed of light for all reference frames". The reason for the emergence of this postulate is the incorrect interpretation of the famous "Michelson-Morley experiment". This experiment was based on the inappropriate conceptual design used in Michelson’s "two-way interferometer". All other known experiments: the Sagnac experiment in 1912, the "Michelson-Gale-Pearson" experiment in 1925, and the "One-way measurement of the speed of light" experiments carried out in recent years, indisputably prove that the speed of light is not the same for all frames of reference. The measured speed of light in the frame of reference related to the Earth’s surface differs from the "speed of light in vacuum" and this difference varies depending on the latitude (proven by Michelson himself back in 1925). Michelson published the results of the "Michelson-Gale-Pearson" experiment in the articles "The Effect of the Earth’s Rotation on the Velocity of Light I and II". Even with the title of these articles, Michelson shows that such an effect exists, i.e., that the speed of light in vacuum differs from the speed of light in the frame of reference related to the Earth’s surface. Michelson’s "two-way interferometer" uses exactly the same path in two directions for each arm. That is why, the existing difference in the speed of light in both opposite directions in the frame of reference related to the Earth’s surface caused by the Earth’s rotation around its axis cannot be established. This is because this difference in the speed of light is completely and accurately compensated for each arm and for any direction of the arm. (Truncated by viXra Admin to <400 words)
Category: Relativity and Cosmology

An Adaptive Quantum Evidential Combination Rule for Open Set Recognition

Authors: Yu Zhou, Fuyuan Xiao
Comments: 3 Pages.

By exploiting the computational potential of quantum computing beyond the computational power of classical computing, an adaptive quantum algorithm of generalized evidential combination rule (AQ-QECR) is proposed to reduce the computational complexity of QECR in the creditability and plausibility levels with no information loss.
Category: Artificial Intelligence

A Genertial Framework Approach: Deriving Special Relativity and Quantum Mechanics from Newton’s Laws

Authors: Duje Bonacci
Comments: 13 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

Newton’s three laws of motion have been the foundation of classical mechanics for centuries. However, they were formulated within the framework of absolute space and time, assuming a privileged reference frame. This assumption becomes problematic when considering relativistic and quantum effects, which suggest that space and time are not absolute but instead emerge from deeper physical principles.Newtonian mechanics breaks down in two major regimes:u2022 At high velocities, where relativistic corrections become necessary,u2022 At small scales, where quantum mechanics takes over.In this paper, we demonstrate that Newtonian mechanics can be naturally extended to encompass both relativity and quantum mechanics by reformulating its axioms within the framework of genertial frames—a novel approach in which forces propagate at finite speed, and time and space are measured locally by material objects equipped with proper tickers.We identify the key flaw in Newtonian mechanics: the assumption of instantaneous signal propagation, both in force interactions and in defining absolute time. By replacing these with finite-speed force propagation and local time-keeping, we derive:u2022 Relativity as a necessary consequence of finite-speed force transmission,u2022 Quantum mechanics as a stability condition imposed by finite-speed internal interactions.
Category: History and Philosophy of Physics

From the Mysticism of Quantum Mechanics to Classical Physics

Authors: Vladislav Mirkin
Comments: 11 Pages. (Note by viXra Admin: Author's name and an abstract are required on the article!)

In the ether of particles that have the same sign of electric charge in the volume of the entire Universe (unipolar ether), the results of the Aharonov-Bohm experiments and experiments with quantum entanglement receive an obvious classical interpretation. In addition, the mechanism of gravity is interpreted within the framework of Bernoulli’s law for flowing liquids and gases, and Einshein’s curvature of space acquires a clear physical meaning: the crystal lattice of the arrangement of particles of the unipolar ether is bent.

В эфире частиц, имеющих одинаковый знак электрического заряда в объеме всей Вселенной (униполярный эфир), результаты опытов Ааронова-Бома и опытов с квантовой запутанностью получают очевидную классическую трактовку. Кроме того, механизм гравитации интерпретируется в рамках действия закона Бернулли для текущих жидкостей и газов, а Эйншейновское искривление пространства приобретает ясный физический смысл: искривляется кристаллическая решетка расположения частиц униполярного эфира.
Category: Classical Physics

The Universe is at Least Five Trillion Years Old

Authors: Martin R. Johnson
Comments: 2 Pages. (Note by viXra Admin: Please cite and list scientific references)

When Lorentz contraction is included in travel time estimates, the Universe is found to be much older than presently believed.
Category: Relativity and Cosmology

Theoretical Derivation of Bohr's Postulate for the Charge in a Hydrogen Atom. Coulomb's Law in Logarithmic Form with Corrections for Strong Interactions at Small Distances. The Physical Meaning of Planck's Constant

Authors: Vadim Khoruzhenko
Comments: 67 Pages.

This article proposes a revolutionary theoretical model that introduces a fifth spatial dimension—"space density"—as a fundamental property governing gravitational, electromagnetic, strong, and weak interactions. The model is based on the hypothesis that changes in space density can lead to phenomena analogous to known fundamental forces. Through a series of mathematical derivations, it is shown how the distribution of space density around spherical objects influences classical field theories
Category: Quantum Physics

WORF: Wave Oscillation Recursion Framework

Authors: James Fruit
Comments: 27 Pages. Licensed under CC BY-NC 4.0.

The Wave Oscillation-Recursion Framework (WORF) provides a novel, first-principles approach to unifying mass, gravity, and gauge interactions through recursion-based resonance constraints. Unlike the Standard Model (SM), which relies on distinct force-carrier particles, WORF replaces fundamental interactions with phase-matched resonance eigenmodes derived from a recursive Laplacian operator. This formulation eliminates the need for gauge boson exchange, deriving interaction symmetries, gravitational effects, and mass-energy transitions as natural consequences of recursion eigenvalue constraints. WORF introduces several key concepts: Mass as a bound standing wave, governed by a Recursive Frequency Threshold (ReFT), which determines transitions between confined and unconfined states. Gauge interactions as emergent recursion symmetries, deriving SU(3) ⊗ SU(2) ⊗ U(1) directly from eigenvalue constraints while maintaining gauge anomaly cancellation. Gravity as a Resonance Accumulation of Inertial Coupling (RAIC) effect, replacing metric curvature with a phase-matched resonance process that preserves geodesic motion and energy-momentum influence. Black hole thermodynamics as a wave-boundary condition, deriving event horizons as resonance accumulation limits and dynamically recovering the Bekenstein-Hawking entropy. Running couplings as a Resonant Effective Scaling Operator (RESO) process, modifying quantum field theory (QFT) renormalization to incorporate recursive eigenstates. Fermion mass hierarchy as a Recursive Oscillation Mass Emergence (ROME) process, eliminating arbitrary Yukawa couplings in favor of eigenstate selection. Neutrino mass and oscillations as a Phase-Locked Oscillatory Neutrino Constraint (PLONC), resolving the origin of neutrino mass without requiring right-handed sterile states while introducing a phase shift testable in upcoming experiments. WORF is formulated as a mathematically rigorous and empirically testable model, predicting measurable deviations in gravitational wave propagation, electromagnetic nonlinearities, hadronic mass corrections, weak decay anomalies, fermion mass ratios, and neutrino oscillation phase shifts. These effects provide multiple avenues for experimental falsification via upcoming high-energy physics and astrophysical observations.
Category: High Energy Particle Physics

Entangled Electron for New Quantum Mechanics Part 2

Authors: Lino Zamboni
Comments: 10 Pages. Extension of viXra 2411.0050 and viXra 2412.0092

This work integrates and completes the previous studies (viXra 2411.0050 and 2412.0092 - Quantum Physics) . The attractive and repulsive potentials are defined, where the magnetic moment and spin play an essential role in ensuring the stationarity of the electron and the orbitals that constitute it .A hypothesis is proposed regarding a source of the electrostatic field , determined by the extreme polarization of the quantum vacuum , which exists at very short distances corresponding to very high energy densities . The effect of such polarization creates a void , induced by the surrounding charges of opposite sign , whose attractive effects are balanced by spin , which generates a local centrifugal force . The application of this concept provides an innovative solution to the unresolved problem of the "Poincaré stress" . Following the framework of traditional quantum mechanics , the Hamiltonians and Schrödinger equations are defined for each orbital . The resulting wave functions , which are entangled like the orbitals they refer to , are combined with appropriate normalized coefficients to form the global electron wave function .
Category: Quantum Physics

The Circle of Life for LLMs[:] Was the Reaction to DeepSeek Justified?

Authors: Stephane H. Maes
Comments: 33 Pages. All related details of the projects (and updates) can be found and followed at https://shmaes.wordpress.com/

Since the release of DeepSeek LLMs, the industry, the investors, and the media have reacted with alarm, surprised that a Chinese startup—despite operating on a low budget and with limited access to specialized AI hardware—could surpass the latest models with reasoning capabilities. This has led to geopolitical concerns about threats to U.S. technological dominance, and the effectiveness of AI chip sanctions imposed by the U.S. on China. Investor confidence in leading U.S. tech companies involved in AI, AI hardware, and AI/cloud hosting has been shaken, contributing to a significant stock market drop on January 27, 2025.In this paper, we argue that while the success of DeepSeek V3 and R1 is remarkable, it does not signal the decline of any major player. Instead, it is a natural progression of how LLMs and generative AI function. Most LLM providers, of a same LLM generation, rely on similar algorithms, big-data pools, and development techniques, meaning that models tend to converge in performance once their methodologies become public. Different starting points often lead to LLMs of comparable capabilities for a same generation. Techniques such as model distillation and reinforcement learning further enable the reduction of model size, data requirements, and hardware constraints. As a result, each time a model is developed, it can be replicated, closely matched, or even surpassed soon after—sometimes with significantly lower effort than the original, or with a significantly smaller set of parameters. This cycle of life will continue as long as LLMs remain a competitive field, vs. a commodity, and until new AI approaches beyond GenAI emerge, or the old AI reemerges.Such a pattern will continue, repeating the cycle. Open source models have the advantage of drawing from broader communities and collective innovation, making it increasingly difficult for proprietary models to maintain an edge. As development costs rise, it will be interesting to see whether proprietary models can sustain their dominance.Ultimately, there was no reason for panic. AI may be in a bubble, but if it bursts, it will not be because DeepSeek outperforms OpenAI’s latest model. Instead, the real challenges facing LLMs and GenAI lie elsewhere. The path to AGI is likely beyond current LLMs. While AI agents may extend the viability of GenAI, other factors pose more significant long-term threats. If LLMs are not the future of AI, there is little reason to be concerned about new players mastering them.
Category: Artificial Intelligence

De Broglie's Phase Waves of Electrons in Hydrogen-Like Atoms as Parts of Steady-State Forced Vibrations

Authors: Martin Kraus
Comments: 7 Pages.

One of the consequences of de Broglie's hypothetical internal clock of an electron is the existence of an associated phase wave that is locally in phase with the electron's internal clock. For a classical electron that is moving on a closed Bohr-Sommerfeld orbit in the electric potential of a positively charged nucleus, de Broglie showed that the requirement of a continuous phase wave on the closed orbit is in agreement with Einstein's quantization condition. The present work explores the hypothesis that this phase wave is part of a forced vibration in the space around the nucleus, which is driven by the electron's internal clock. Results of this work include new quantization conditions for closed orbits that are consistent with Einstein's quantization condition but include additional (yet unexplored) conditions. Furthermore, a method is presented for computing phase waves on closed orbits of electrons, which could help visualizing several important features of de Broglie's phase waves.
Category: Quantum Physics

Irreducible Inviscid Singular Represenation of 3D Fully Developed Turbulence and Related Emergent Physics

Authors: Michael Isaac Aksman
Comments: 22 Pages.

Vortons [is] introduced to approximate finite core vortex tubes and pass through Navier Stocks spontaneous singularities/reconnections without any additional assumptions. Vortons provide irreducible description of inviscid attractor of 3D Navier Stocks equation solutions with number of vortons scaling with Reynolds number at hand. Magnetic vortons provide irreducible description of magnetic vortex tubes in plasma with reconnections without any additional assumptions. Instability of quasi 3D/2D+ vorton collapse provides possible mechanism for explosive universe inflation/first order phase transition. 3D space nature of our universe as a consequence of instability of 3D vortons collapse. "Dark matter" explained as a consequence of frisbee like quasi 3D/2D+ space in galaxies with corresponding stable rotational curves. "Dark energy" explained as a emergent result of vortons system 3D self amplification interactions energy "antigravity" effect. Probabilistic interpretation of quantum mechanics as a result of smooth test functions of fluid vacuum nonlinear Maxwell equations weak solutions. Baryonic asymmetry [is] explained as a instantaneous snapshot during exponential inflation of quark antiquark annihilation asymmetry/skewness and kurtosis terms in Edgeworth series expansion of instantaneous quantum GUP (generalized uncertainty principle) fluctuations. Simple Early Bifurcation/Regime shift detection in nonequilibrium nonlinear statistical systems proposed using linear statistical moments/cumulants approximation/equivalents formulas.
Category: Mathematical Physics

The Full Dedekind Cut and the Key to Leibnizian Mathematics

Authors: Adriaan van der Walt
Comments: 16 Pages.

The aim of this document is to facilitate and motivate the reading of the document Leibnizian Mathematics by investigating a compelling reason for introducing Leibnizian Mathematics. This document also motivates the extension of the Dedekind Cut to the Full Dedekind Cut and analyses some consequences. First the relevant abstractions about Space shared by all are stated, which are then followed by stating the relevant basic assumptions of Abstract Mathematics. A tool is then developed that enables the identification and analysis of the consequences of these assumptions. This exposes the root motivations for, and the fundamental properties of, the tenets of Abstract Mathematics. The most consequential of these, in the present context, is the result that the total length of countable many points is zero. More than countable many points are therefore required to form a line of non-zero length. Also, that countable many points can be added to or removed from a line without changing the length of the line (this consequence is contrary to the current paradigm of Mathematics). The latter necessitated the introduction of the Full Dedekind Cut to preserve the real line and hence Euclidean Topology and Lebesgue theory.The concepts of infinitesimal and infinitesimal number are introduced, followed by a Riemann sum that results in a contradiction in Euclidean Mathematics by showing that there exists an example where countable many points form a line of length one.Possible causes for this contradiction are discussed and it is concluded that the Riemann integral does not fit naturally into Abstract Mathematics, but that a second continuous model for space that leads to a different model for Mathematics, called Leibnizian Mathematics, must be developed to augment Abstract Mathematics. This model resolves the contradiction, accommodates the Riemann integral in a natural way and expands the paradigm of Mathematics.A short list is appended describing the difference in meaning that some words have and the difference in the properties that they describe when used in different models.
Category: General Mathematics

Inferring the Source of Cosmic Expansion Forces from the Presence of Charge in Space

Authors: Kuo Tso Chen
Comments: 10 Pages.

The accelerating expansion of the universe suggests the presence of a repulsive force exceeding gravitational attraction. This study explores the asymmetry in electron and positron production during the formation of the universe, which may have led to a residual charge imbalance. If a uniform but minuscule charge density pervades the universe, the resulting electrostatic repulsion could drive cosmic expansion. Through mathematical modeling, we demonstrate that even an extremely slight charge density variation can result in accelerated expansion, aligning with current observations.
Category: Relativity and Cosmology

Fermat's Theorem

Authors: Mustapha Kharmoudi
Comments: 10 Pages. (Note by viXra Admin: Article title should be in English; author name should be after article title; an abstract is required; and scientific references should cited and listed))

In this article, we approach Fermat's famous theorem in an original manner. To achieve this, I will use two applications, one of which is well-known, while the other seems to be unprecedented.
Category: Number Theory

New Wireless Technology for Data Transmission in Chemical Systems

Authors: Andrei I. Bodrenko
Comments: 4 Pages.

New type of wireless computer network in chemical systems is presented in this article. This wireless network uses chemical system as physical media for data transmission, instead of environment. Thus, represented wireless network differs substantially from molecular communication networks and wireless networks covered by IEEE standards, such as radio frequency based wireless networks. This new wireless technology can be used not only in chemical industry for continuous controlling chemical processes in chemical reactions zones but also for medical purposes, and as a new type of wireless body area computer network.
Category: Digital Signal Processing

Does QM = Ait?

Authors: Tariq Khan
Comments: 5 Pages.

A short philosophical and speculative essay proposing that quantum mechanics (QM) and algorithmic information theory (AIT) are actually equivalent, or reciprocal, means or operations of describing nature. An understanding of this relationship could provide a means to solve complex problems via a formal correspondence between continuous mathematics and discrete mathematics. Subjective attributes are noted between the operations and compared for their similarities as a first step to motivate additional technical research toward a formal and fundamental theorem of the relationship.
Category: History and Philosophy of Physics

Artificial Prime Numbers: A Relative Perspective on Primality

Authors: José Acevedo Jiménez
Comments: 11 Pages.

This article explores the notion of artificial prime numbers in the context of specific sets of integers. A formal definition is presented, properties are discussed, and comparisons are made with the classical notion of primality. Additionally, potential applications of these numbers in number theory and cryptography are analyzed.
Category: Number Theory

The Study of Vacuum Dynamical Mechanisms

Authors: Yake Li
Comments: 14 Pages. In Chinese

Based on multiple astronomical observation results, this paper proposes the hypothesis of the principle of relative change in the speed of light and demonstrates its compatibility with the principle of the invariance of the speed of light. The study shows that the speed of light has both an absolutely constant aspect and a relatively variable aspect. This provides us with a new direction to study the relationship between the relative change in the speed of light and the motion of matter. Based on this principle, the paper constructs an innovative theoretical framework known as the "vacuum dynamical mechanism" and derives several important conclusions. The research finds that time, space, and the speed of light always maintain a proportional relationship. The relative change in the speed of light leads to the formation of high-energy spaces, low-energy spaces, and variable-energy spaces. In the variable-energy vacuum space, objects spontaneously accelerate towards low-energy regions. The acceleration gained by an object is only related to the rate of change of the speed of light in space and is independent of the object's mass. The vacuum dynamical theory proposed in this paper offers a new perspective for explaining the origin of dark energy and the physical mechanisms behind spacetime curvature.
Category: Astrophysics

Compact Oxford Italian Dictionary and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 19 Pages.

We study Compact Oxford Italian Dictionary, the first edition, 2013. We draw the natural logarithm of the number of Italian 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) i.e. a magnetisation curve for the Bethe-Peierls approximation of the Ising Model with four nearest neighbours, in the absence of external magnetic field, H. $beta$ is $frac{1}{k_{B}T}$ where, T is temperature and $k_{B}$ is the tiny Boltzmann constant.
Category: Linguistics

Equation with Sum of Four Sixth Degree Integers Equal to Another Four Sixth Degree Integers

Authors: Oliver Couto
Comments: 3 Pages.

There are numerical solutions available on Wolfram world of mathematics website (ref. # 4) for the equation (p^6+q^6+r^6+s^6)=2(a^6+b^6). In this paper the author has arrived at numerical solution by algebra. It is common knowledge that arriving at numerical solutions by algebra is difficult for degree four & above. Also on the internet the author has not come across any method for the above mentioned equation.
Category: Number Theory

Proving Goldbach's Strong Conjecture by Analyzing Gaps Between Prime Numbers and Their Digits

Authors: Bahbouhi Bouchaib
Comments: 21 Pages. Interested readers can cite this article which is now published in J Math Techniques Comput Math 4(1) 2025 (opast publishing group)

The main idea of this article lies in the fact that Goldbach's strong conjecture is associated with the progression ofnatural integers from 0 to infinity, which results in precise gaps between prime numbers. The gap of 6 is the mostregular between primes 6x + 1 on the one hand and primes 6x — 1 on the other. In this article, using the equations 3x ± 5and analyzing the 6-based gaps between primes while determining the initial conditions that make a prime appear afteror before an integer, this article argues for the truth of Goldbach's strong conjecture. Two new concepts are introducedfor the first time : Goldbach's gap and Goldbach's transposition. By analyzing its key digits (units and tens), a primenumber itself can lead to the conversion of an even number into two primes. A new algorithm is deduced from theseresults, enabling us to locate prime numbers located at equal distance from any integer, even or odd, prime orcomposite. This constitutes a decisive proof of Goldbach's strong conjecture, since it means that any even number canbe converted into the sum of two prime numbers.
Category: Number Theory

Revisiting Hawking Radiation: Gravity Decoupled from Mass and the Nature of Black Holes

Authors: David E. Jacob
Comments: 6 Pages. © 2025 David E. Jacob

Hawking radiation is traditionally understood as a quantum process near a black hole’s event horizon that leads to gradual mass—energy loss. In this work, we present a unified interpretation that bridges conceptual and technical perspectives: once an event horizon forms, the external gravitational field decouples from its interior—transforming from a dynamically "anchored" field (as seen in normal massed objects) to a self-sustaining "unanchored" or fossil imprint. This decoupling permits the slow reduction of the black hole’s energy via Hawking radiation without invoking superluminal updates, thereby preserving causality, energy conservation, and the equivalence principle. Complementing the standard ADM formulation, we incorporate insights from quasilocal energy methods, isolated horizon frameworks, and quantum field theory in curved spacetime to further support our view. In contrast, for ordinary astrophysical bodies (e.g., planets and stars) where the gravitational field remains causally connected to the source mass, any analogous process would violate these fundamental principles. We also discuss observational prospects and numerical simulations that may eventually reveal signatures of this decoupled evolution
Category: Relativity and Cosmology

Why Poincare Symmetry is a Good Approximate Symmetry in Particle Theory

Authors: Felix M. Lev
Comments: 16 Pages.

As shown by Dyson in his famous paper "Missed Opportunities", it follows even from purely mathematical considerations that quantum Poincare symmetry is a special degenerate case of quantum de Sitter symmetries. Then the usual explanation of why in particle physics Poincare symmetry works with a very high accuracy is as follows. A theory in de Sitter space becomes a theory in Minkowski space when the radius of de Sitter space is very high. However, the answer to this question must be given only in terms of quantum concepts while de Sitter and Minkowski spaces are purely classical concepts. Quantum Poincare symmetry is a good approximate symmetry if the eigenvalues of the representation operators$M_{4mu}$ of the anti-de Sitter algebra are much greater than the eigenvalues of the operators $M_{muu}$ ($mu,u=0,1,2,3$).We explicitly show that this is the case in the Flato-Fronsdal approach where elementary particles in the standard theory are bound states of two Dirac singletons.
Category: High Energy Particle Physics

Physicalized Temperature: A New Correlation Mechanism Between Helium-4 Atoms

Authors: Di Zhuang, Hongzhang Zhuang
Comments: 9 Pages.

The experiment shows that in the superfluid $^{4}$He, $^{4}$He atoms are not an ideal Bose gas, and there is a strong correlation between the $^{4}$He atoms in the superfluid state. The famous Tisza and Landau's two-fluid model does not provide an answer to the physical mechanism behind this correlation. This paper proposes a hypothesis—Physicalized Temperature (PT), a specific mechanism for the correlation between $^{4}$He atoms. Based on this model, new explanations are given for critical opalescence and the quantization of circulation; it is also predicted that, similar to superconductors, magnetic flux quantization will occur in a rotating torus container filled with superfluid $^{4}$He. The phonon-roton dispersion curve (P-R curve) of the superfluid $^{4}$He quasiparticles, which was conjectured by Landau, as well as the specific heat curve with singularities across the entire temperature range, are calculated and found to match the experimental data very well.
Category: Condensed Matter

Born Reciprocal Relativity Theory Redefines the Notion of Mass: How Massless Photons Appear Massive in Accelerated Frames

Authors: Carlos Castro
Comments: 15 Pages.

Starting with a brief review of Born Reciprocal (Non-inertial) Relativity Theory (BRRT), it is shown how massless photons in one frame of reference can appear massive, even tachyonic, in an acccelerated frame. An immediate application can be found in the behavior of in-falling/outgoing photons propagating in a black hole gravitational background. When the in-falling photon gains energy one learns that ($ d tau')^2 > 0 $ such that the blue-shifted photon from the point of view of an accelerated frame of reference (with respect to a static spherically symmetric Schwarzschild black hole, for example) will appear massive and subluminal. However, when the outgoing photon loses energy one has $ ( d tau')^2 < 0 $ and the red-shifted photon from the point of view of an accelerated frame will appear tachyonic and superluminal. This is an interesting physical feature because no particle (inside the horizon) can escape the interior of black hole unless it moves faster than light; i.e. it is tachyonic (superluminal). These effects may have important consequences in cosmology (dark energy, dark matter problem).
Category: Relativity and Cosmology

A Scale Invariant Fully Conformal Cosmological Model and Its Support by Astrophysical Data

Authors: Richard Dvorsky
Comments: 21 Pages.

According to general relativity, the cosmological redshift may be caused by other mechanisms than the source moving away from the observer. It can occur on a global scale, similar to the gravitational redshift near massive stars. In principle, these are differences in the time-dependent global metric field between the source in the past and the observer in the present. In this paper we attempt a new interpretation of the simple solution of Einstein’s equations within a fully conformal metric for the case of a time-independent energy-momentum tensor. The scaling factor here acts identically on all four space-time coordinates and the speed of light is independent of the conformal time. The fully conformal metric is interpreted here as a universal geometric background which is scale invariant and acts universally on all objects, including gauges and clocks, regardless of their dimensions and internal interactions. The associated scale invariant exponential expansion is thus only relative and all observers at different times are completely equal. The model introduces the concept of the appearent age of the universe, which is the limiting consequence of time dilation into the past, and corresponds to the present value of the age of the universe H —1 according to the standard model. This appearent age is the same for all observers, and the Hubble constant is thus a true universal constant, invariant to time translations. The motivation of this work was to test the possibility of the above cosmological redshift mechanism in confrontation with astrophysical data. Probably the most important consequence is the generalized formulation and interpretation of the Hubble-Lemaître law z(r) = (eHr/c − 1), which shows good agreement with astrophysical data even for the most distant supernovae. Confronting the conformal metric model with some astrophysical data shows an interesting agreement with the observed spatial distribution of astrophysical sources such as γ-ray bursts and quasars. On a cosmological scale, the above fully conformal metric naturally determines the global energy density, spatial flatness, and solves the horizon problem and Olbers’ paradox in infinite spacetime.
Category: Relativity and Cosmology

On the Osculating Circle Using Complex Numbers

Authors: Aloys J. Sipers
Comments: 5 Pages.

In this letter a theorem is stated on the complex-valued represention of the radius vector of an osculating circle. This theorem can be used in education in mathematics and physics. To develop exercises for education a construction is presented for a class of curves characterized by a parameter. A numerical example is provided to illustrate the educational potential of the theorem and the constuction of corresponding exercises.
Category: Education and Didactics

New Method of Using Mobile Robots for Moving Cargo in Warehouse

Authors: Andrei I. Bodrenko
Comments: 20 Pages.

The new patented method for moving cargo in warehouse is proposed in this article. According to the new method, movement of cargo from the storage area to another warehouse area is carried out by throwing the cargo by the first mobile robot and catching the thrown cargo on fly by the second mobile robot. The parameters of the calculated trajectory of movement, in the free flight phase, of the center of mass of the cargo to be thrown are calculated by numerical methods for solving the Cauchy problem for a system of ordinary differential equations, and by the shooting method for boundary value problems of a system of ordinary differential equations. The first mobile robot throws the cargo at the specified angle to the horizon with the specified initial velocity, at the specified moment of time. In order to catch the thrown cargo on fly by the second mobile robot, the parallel algorithm A1-A2 for catching a thrown cargo on fly by the second mobile robot was created. The method allows the first mobile robot to throw cargoes for large distances, and the created algorithms allow the second mobile robot to catch reliably the thrown cargoes on fly. The proposed method for moving cargo is superior in economic efficiency and reliability to the other methods for moving cargo by implementing tossing of inventory items by robots.
Category: General Science and Philosophy

A New Natario Warp Drive Vector $ny$ in $2D$ Polar Coordinates with the Hodge Star Over the Y-Axis and a Constant Speed $vs$

Authors: Fernando Loup
Comments: 23 Pages.

The Natario warp drive appeared for the first time in 2000.Although the idea of the warp dive as a spacetime distortion that allows a spaceship to travel faster than light predated the Natario work by 7 years Natario introduced in 2001 the new concept of a propulsion vector to define or to generate a warp drive spacetime.Natario defined a warp drive vector nX=vs*(dx) where vs is the constant speed of the warp bubble and *(dx) is the Hodge Star taken over the x-axis of motion in Polar coordinates.In this work we present a new warp drive vector nY=vs*(dy) where vs is the constant speed of the warp bubble and *(dy) is the Hodge Star taken over the y-axis of motion in Polar Coordinates.Our new proposed warp drive vectoralso satisfies the Natario requirements for a warp drive spacetime.
Category: Relativity and Cosmology

Infinitely Many Twin Primes - Proof

Authors: James DeCoste
Comments: 20 Pages. Contact: jbdecoste@eastlink.ca

After dissecting the mechanics of locating valid twin primes, I was able to establish a Proof through contradiction. I start by creating a table to easily display the potential list of twin primes. Using an elimination matrix scheme, I systematically remove twin prime candidates from the list if either half of the pair are multiples of an already known 'Prime Number'. Multiples of prime numbers, primes squared and primes multiplied by other primes are not prime numbers themselves (examples 5*5=25; 5*7=35; 5*11=55; 7*7=49; 7*11=77; and so on). It's an easy approach with repeatable patterns for each prime number. It quickly becomes obvious that these elimination patterns are repeating for all non-prime removals. All these elimination patterns are of the form remove-skip(n)-remove-skip(m)...repeated to infinity. Note that n+m+2 is the prime number. The first non-prime removal for any prime is in essense that prime^2 (prime squared). A prime number squared will always fall into the sixth column ( the column starting with 7)! Further, two adjacent patterns will slightly overlap if those two primes form a twin prime pair. I then proceed to make the 'silly' assumption that there will be no potential twin prime candidates in the initial skip(n) plus skip(m) regions for the two overlapped twin primes (entire initial pattern for a given twin prime pair) in this elimination matrix. If we assume that 11 & 13 are the last twin primes possible, we would have to make the assumption that there are no twin primes candidates in the elimination overlapped pattern regions for either prime 11 or 13 combined at minimum. The contradiction arises because we can show that there is always at least one twin prime pair in this combined/overlapped region. As long as there are infinitely many primes there will be infinitely many twin primes. Euclid proved there are infinitely many primes with his proof. I have simply extended his proof into my own.
Category: Number Theory

Some Properties of Electrons

Authors: I. Prusis, P. Prusis
Comments: 5 Pages. 1 figure

The electron is the most widely used elementary particle and at the same time the least studied. It is known that the electron has mass, charge, and spin. The article shows that an electron moves along a complex trajectory, the main components of which are chaotic thermal motion, zitterbewegung, and the direction determined by the external electric field. The trajectory of an electron can be mathematically described as a wave, but from this QM draws the incorrect conclusion that the electron itself is a wave. What is mentioned in the article also applies to protons, neutrons, and other elementary particles.
Category: Quantum Physics

A Solution to Wave Particle Duality Conundrum?

Authors: Jayesh Suresh
Comments: 14 Pages.

This article attempts to model spin of fermions and to explore possible connection to wave function. Zitterbewegung, originally introduced to describe the rapid oscillatory motion of relativistic particles, is not commonly used in modern physics. Here, zitterbewegung has been employed to develop a model that accounts for spin of fermions. It can explain wave particle duality.
Category: Quantum Physics

Traversability and Energy Constraints of a Traversable Wormhole in f(R) Gravity

Authors: Raghav Krishna
Comments: 2 Pages.

This paper investigates the traversability and energy constraints of wormholes under f(R) gravity, an alternative to Einstein's General Relativity. By numerically solving the modified Einstein field equations, we demonstrate that the required exotic matter can be significantly reduced through curvature modifications. The study analyzes tidal forces, showing that human traversability is possible with accelerations below 50 m/s² at a distance of 1000 km from the throat. Energy requirements are estimated at 3.77 × 10¹u2076 J (equivalent to 9 megatons of TNT), far lower than previous classical models. The findings suggest that f(R) gravity provides a more feasible framework for future wormhole research, with possible stabilization via Casimir effects. This work contributes to the theoretical groundwork for constructing traversable wormholes in modified gravity theories.
Category: Relativity and Cosmology

The Balance Paradox and Fermat's Theorem

Authors: Vladislav Koshchakov
Comments: 10 Pages.

An unexpected relationship has been found between the weighing procedure on lever scales and the equation of Fermat's theorem. At the same time, it turned out that solutions are possible only for n=2, and for all cases of n>2, the proof of undecidability is of the same type.
Category: General Mathematics

Universal Clock Field Theory: A Preliminary Proposal for the Unification of Emergent Time, Gauge Interactions, Gravity, Quantum Measurement, and the Dark Sector

Authors: Brandon Belna
Comments: 38 Pages.

We propose Universal Clock Field Theory (UCFT), wherein a single oscillatory phase field theta, defined modulo 2*pi, underlies the emergence of time, gauge interactions, gravitational dynamics, quantum measurement, and the dark sector.In this construction, theta arises via spontaneous symmetry breaking of a complex scalar fieldPhi(x) = rho(x) * exp(i * theta(x)),and its compact nature drives topological effects that yield emergent gauge fields, a non-perturbative Yang-Mills mass gap, and a derivation of the invariant speed of light.Coupling theta to gravity modifies Einstein’s equations, providing non-singular cosmologies and potential hairy black hole solutions. Furthermore, theta-driven decoherence addresses the quantum measurement problem, and a shallow potential or topological defects for theta naturally accommodate dark energy and dark matter.Although still in an exploratory stage, UCFT offers testable predictions and new avenues for theoretical and experimental research in fundamental physics.
Category: High Energy Particle Physics

New Method of Using Mobile Robots for Implementing Warehouse Operations

Authors: Andrei I. Bodrenko
Comments: 12 Pages.

The new patented method of movements of packaged cargoes at warehouse isproposed in this article. The proposed method of loading is superior in economic efficiency,reliability, cheapness, simplicity of construction and use, to all other methods of loadingimplemented by robots. The method allows the mobile robot to load a cargo which is three times asheavy as this mobile robot, wherein almost no electrical energy is consumed during loading. Inimplementing the method, two mobile robots are used, each of which contains a mobile platform, anomnidirectional mobile wheel-type mechanism and a transport suspension with independentsuspension for each wheel. Actually, the mobile robots help each other to load cargo on the firstmobile robot, through robot cooperation. Loading of the container with the load on the first mobilerobot is carried out by actuating a two-arm lever, which is carried out through the impact of thebottom of the mobile platform of the second mobile robot on the longer arm of the two-arm lever bylowering the mobile platform of the second mobile robot due to the operation of the transportsuspension of the mobile platform of the second mobile robot. For example, if the length of thelonger arm of the two-arm lever is three times longer than the shorter arm of the two-arm lever then the second mobile robot of weight 50 kg is capable of loading a container with the load of weight150 kg on the first mobile robot.
Category: General Science and Philosophy

Demonstration of the Collatz Conjecture: a Proposal

Authors: Oreste Caroppo
Comments: 15 Pages.

In this article we will propose initially a graphical method for carrying out the algorithm which is at the base of the famous Collatz Conjecture; therefore we will demonstrate analytically that, for no natural number, the Collatz Algorithm can present an infinite sequence of ever-increasing steps. The development of the graphical method will lead us to extrapolate a simplified and more basic scheme of the Collatz Conjecture, which will allow us in turn to consider the Collatz Conjecture Algorithm as a sorte of particular case of a more general algorithm valid for positive real numbers, which, for statistical reasons that we will show, will always converge towards the smallest real number, zero. The Collatz Algorithm will therefore appear as an adaptation only to the natural numbers of this more general algorithm, which is why Collatz Algorithm will also converge towards the smallest natural number which is 1.
Category: Number Theory

Brachiation Robots :Trajectory of Movement of a Jumping Brachiating Robot

Authors: Andrei I. Bodrenko
Comments: 2 Pages.

The trajectory of movement, in the free flight phase, of the center of mass of the mobile robot during vertical jumping is obtained in this article.
Category: General Science and Philosophy

University Mathematics for Young Adults

Authors: Johan Noldus
Comments: 140 Pages.

Many topics are explained at a sophisticated level.
Category: General Mathematics

Generalizations of Notions of Differential Geometry

Authors: Johan Noldus
Comments: 20 Pages.

The notions of Torion and Riemann curvature are generalized towards general path metric spaces.
Category: Mathematical Physics

Geometrical Quantum Theory and Applications

Authors: Johan Noldus
Comments: 220 Pages.

We covariantize quantum field theory and extend quantum theory to the spiritual domain required for structure formation.
Category: Quantum Gravity and String Theory

Symmetries of Natural Numbers

Authors: Emmanuil Manousos
Comments: 31 Pages.

In present paper we prove an original theorem on the natural numbers. From this the theorem emerges a set of symmetries of the natural numbers which puts Number Theory on a new footing. One of the consequences of the theorem, but not the most important one, is the odd number factorization algorithm.
Category: Number Theory

From Einstein to Electromagnetic Gravity with Spin 3

Authors: Miroslav Pardy
Comments: 18 Pages. Original article

We consider the rigorous derivation of the Einstein equations by Fock. Then, we approach the way from the spin 1 fields to the spin 2 fields for massiveand massless particles and we derive the gravity equations from this base. Then, we approach the spin 3 gravity called by us the electromagnetic gravity.
Category: Quantum Gravity and String Theory

The Informational Coherence Index A Framework for the Integration of Networks of Artificial Intelligence Models

Authors: Henry Matuchaki
Comments: 19 Pages. (Note by viXra Admin: Listed scientific references should be cited in the article; AI assisted/generated content is in general not accepted))

This article presents the Informational Coherence Index Icoerdisplaystyle I_{text{coer}}Icoer, an innovative mathematical and computational model designed to quantify and optimize informational integration in networks of artificial intelligence (AI) models, with a focus on language models. Inspired by concepts from physics, thermodynamics, and information theory, Icoerdisplaystyle I_{text{coer}}Icoer is integrated into the General Theory of Unity (GTU), a theoretical framework that seeks to unify informational interactions in distributed systems. This work describes the formulation, implementation, visualization, and practical applications of Icoerdisplaystyle I_{text{coer}}Icoer, highlighting its relevance for AI ensembles, multi-agent networks, and collaborative systems such as ChatGPT, Grok, etc.
Category: Artificial Intelligence

Faster-Than-Light Travel Feasible with Negative Mass - Superluminal Dynamics

Authors: Raul Fattore
Comments: 29 Pages.

The study demonstrates that faster-than-light travel requires negative mass. Mass must decrease as velocity increases and must be negative beyond the speed of light.It also proves that there is no absolute speed limit in the universe, contradicting faulty Einstein's theory of relativity and quantum theory. The study also reveals that relative motion depends on relative coordinates, not reference frames.It is demonstrated that gravitational and inertial control of mass is the basis of faster-than-light travel. A hypothetical spaceship is described, and physical calculations are made to demonstrate the possibility of traveling faster than light. The study also explores the potential effects of gravitational interaction and collisions. The technology is proposed for instantaneous cosmic communication and other applications of negative mass using the free energy of the gravitational field.* Is faster-than-light travel indeed possible?* What kind of propulsion could achieve such a technology?* Could any matter be traveling faster than light?* Could living beings be traveling faster than light?* What could be the consequences of that?The above questions will be scientifically answered through this study in accordance with the negative mass theory.
Category: Astrophysics

Investigating Cyclic Gravity and Cosmology (CGC) as an Alternative Framework to Standard Cosmology

Authors: Joseph Bakhos
Comments: 18 Pages. This is the revised version.

Cyclic Gravity and Cosmology (CGC) is introduced as an alternative framework to General Relativity (GR) and the ΛCDM model. CGC retains Euclidean space and proposes that gravity is a residual effect of electromagnetism ratherthan a fundamental force. The theory replaces the standard expansion model with cyclic expansion and contraction phases governed by large-scale gravitational oscillations. Redshift in CGC is explained through a combination ofDoppler motion, neutrino interactions, and a refined tired light mechanism. Time dilation and light deflection arise from neutrino scattering rather than spacetime curvature, preserving a Euclidean structure. CGC naturally explains the Cosmic Microwave Background (CMB) power spectrum without requiring inflation, aligns with observed large-scale structure, and provides a resolution to the Hubble tension within a non-expanding space framework. The theory predicts a self-regulating cosmic equilibrium maintained by an outer shell of intergalactic medium, preventing energy loss and sustaining cyclic dynamics. The observed galactic rotation curves, large-scale filament-and-void cosmic structures, and elemental recycling in Active Galactic Nuclei (AGN) are also consistent with CGC’s gravitational model. The purpose of this paper is not to assert CGC as the definitive model of cosmology but to establish it as a framework worthy of rigorous scientific investigation. Given recent challenges to ΛCDM from JWST observations and inconsistencies in Hubble measurements, CGC presents an opportunity to explore alternative gravitational dynamicsand cosmic evolution mechanisms that align with observational data.
Category: Relativity and Cosmology

Nova: A Quantized Spacetime Fluctuation Framework Supporting General Relativity and Quantum Mechanics

Authors: Thura Zaw Oo
Comments: 10 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

Nova proposes quantized spacetime fluctuations (QSFs)—a scalar field ϕ constrained to Planck-scale vacuum perturbations—as the sole constituent of the universe, with no external background,unifying General Relativity (GR) and Quantum Mechanics (QM) at all scales without invokingextra dimensions, geometric quantization, or traditional gauge bosons. QSFs are both quantizedand dynamic, inducing GR’s tensor gravity through a scalar-tensor coupling (κ =116πG ) derivedstep-by-step from gravitational vacuum energy, where gravity manifests as an inertial-like spreadaction driven by relative differences in QSF densities. Particle masses and fundamental forces emergefrom knotted QSF structures defined by Seifert surfaces: the strong force as the knotting potentialat the bare minimum matter level with genus g = 3 and knot size rknot = 10−15 m, the weak forceas the temporal action strength of the knots with g = 2 and rknot = 10−18 m, the electromagnetic(EM) force as a vibration-like spread across QSF patterns with g = 1 and rknot = 3.86 × 10−13 m,and gravity as the relative QSF fluctuations’ spread action around matter-like QSFs. Antimatterarises from stretched, non-knotted QSF actions, created equally with matter (nknot = nanti =7.7 × 10−141 m−3) but isolated by their distinct dynamics, yielding a global symmetry (ηglobal = 0)with local matter dominance (ηlocal = 5.5 × 10−10) explained without parameter tuning. Time isderived from QSF actions, ceasing where action halts (e.g., ∂tϕ = 0), a concept grounded in therelational nature of QSF dynamics. The QSF creation rate β(t) = 3H(t) governs cosmic evolution,derived from the Hubble parameter with detailed justification, coupling to observable scales throughknot dynamics unified under an SO(5) symmetry of QSF patterns, eschewing particle mediators infavor of energy spreads. Nova generates dark matter via non-knotted fluctuations (ρDM = 8.8 ×10−28 kg/m3), produces dark energy via expansion dynamics at ρDE = 7.15 × 10−27 kg/m3, anddrives cosmic inflation through an early high β-rate phase (βinf = 1.8 × 1034 s−1, achieving 60 e-folds). It resolves singularities with a dynamic finite-core metric and eliminates the Hierarchy andStrong CP Problems as artifacts of linear thinking, requiring no fine-tuning or additional particles.We rigorously test against Planck CMB (H0 = 67.4 km/s/Mpc), LIGO GW150914, and LHC Higgsdatasets, computing densities and masses with Monte Carlo error estimates, and predict a 510 ±20 GeV scalar from knot genus g ≈ 60, CMB B-modes at ℓ > 3000 with ∆CBBℓ = 0.8±0.2 µK2, andsubatomic force deviations, all derived with exhaustive clarity from QSF principles.
Category: Quantum Physics

Alpha Integration: Universal Path Integrals with Gauge Invariance

Authors: YoonKi Kim
Comments: 23 Pages. Contact email: yk.reserch@gmail.com

We introduce Alpha Integration, a novel path integral framework that applies to wide range of function including locally integrable functions, distributions, and fields—across arbitrary spaces and n dimensions (n ∈N), while preserving gauge invariance without approximations. This method extend to Rn(n ∈N), smooth manifolds, infinite-dimensional spaces, and complex paths, enabling rigorous integration of all f ∈Du2032 with formal mathematical proofs. This framework is further generalized to infinite-dimensional spaces, complex paths, and arbitrary manifolds,with its consistency validated through extensive testing across diverse functions, fields, and spaces. Alpha Integration thus offers a robust and efficient alternative to traditional path integral techniques, serving as a versatile tool for mathematical and physical analysis.
Category: Mathematical Physics

On Area Element in Polar and Volume Element in Spherical Coordinates

Authors: Sanjeev Saxena
Comments: 4 Pages. Added new section

A simple and elementary derivation for the formula for the area element in polar coordinates, and the volume element in spherical coordinates is given.
Category: General Mathematics

On the Feigenbaum Attractor and Feynman Diagrams

Authors: Ervin Goldfain
Comments: 24 Pages.

It was recently conjectured that the Standard Model of particle physics resides on a bifurcation diagram generated by the recursive scaling of the Higgs coupling. This sequel explores the relationship between the bifurcation diagram and the Path Integral (PI) formalism of Quantum Field Theory (QFT). The long-term goal is to base the Feynman diagrams on the properties of the Feigenbaum attractor of either quadratic or cubic maps.
Category: Mathematical Physics

The Higgs Boson May Be Made of Higher Dimensional Matter

Authors: D. G. Grossman
Comments: 9 Pages.

The Higgs boson may not be the heaviest particle created by man so far (it is exceeded by the top quark), but it may be the highest dimension particle created by man so far. If calculations are correct, it may be of dimension 20/21 (the top quark is dimension 9/10), that is, it may be composed of 20-dimensional matter (quarks) circulating in the surface of a 21-sphere. Recent Higgs boson mass measurements of high accuracy, and a mass factoring technique based on n-sphere surface volumes, which was derived from Planck's Energy-Frequency Relation, E=hf, were used to reach that conclusion. A power of two factoring, which is a possible indication of stability, was found within 3 MeV of the ATLAS group's recent 125,220 MeV improved accuracy measurement of the Higgs's mass. The S21h power of two factoring found, (2^16 - 2^10)S21h, translates to a mass of 125,217.08 MeV, which is very close to the ATLAS group's result. Is the Higgs boson made of 20/21-dimensional matter?
Category: High Energy Particle Physics

The Search for Life and Aliens

Authors: James R. Johnson
Comments: 13 Pages. Astronomy and Cosmology also possible categories.

This article is a comprehensive survey describing our search for life and aliens beyond earth. The search for life inside our Solar System continues by digging into the Martian soil and exploring the underground oceans of Jupiter’s moon Europa. As we peer into the Milky Way, exoplanets are the target. Improved sky-survey telescopes identify exoplanets. Then, subsequent analysis using spectrographs obtained via exoplanet transits or direct imaging hope to identify biosignatures. Detection of intelligent life is either circumstantial or definitive. Technosignatures offer circumstantial evidence of alien civilizations. Definitive or positive detection can be physical, for example, discovering interstellar objects (spaceship/UFOs) or as in the movie Contact, an alien message. Future giant optical/infrared telescopes, sophisticated radio telescopes, and a proposed space telescope, HWO, will dramatically enhance detection.Significant technical advances in earth-based and space telescopes, documented in four key figures, dramatically improve the probability of discovery over the next ten years. Thus, we may soon have an answer to the question, are we alone?
Category: Astrophysics

Two Separate Derivations of the Shannon Entropy Equation from First Principles and the RTA Framework for Information

Authors: Vasant Jayasankar
Comments: 36 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)

The Shannon entropy equation has been foundational in information theory, yet its derivation has historically relied on axiomatic reasoning rather than first principles. In this paper, I propose two derivations of the Shannon entropy equation from fundamental geometric constraints, demonstrating that it emerges naturally as a special case of a deeper information structuring principle. I propose that entropy is fundamentally constrained by geometric projection effects and dimensionality, leading to a formulation that reduces to Shannon’s equation in Euclidean space while extending to structured high-dimensional systems.Further, I introduce a novel connection between optimal information structuring and the All-Pairs Shortest Path (APSP) framework, demonstrating that information processing may follow geodesic constraints in hyperbolic space. This insight suggests that optimal data compression, AI learning, and information retrieval follow geometric constraints, revealing a deeper structural foundation beyond statistical approximations.By unifying entropy, geometric projection constraints, and APSP-based information structuring, I introduce the RTA Framework for Information, which redefines optimal information flow in structured systems and AI architectures. If validated mathematically and empirically, this may have deep implications for AI architectures, compression theory, and quantum information, pointing toward a broader framework that extends beyond classical entropy formulations.
Category: Mathematical Physics

Massive Photon Interactions in Longitudinal Displacement Current

Authors: Arvin D. Sharma
Comments: 3 Pages.

We show the scalar field defined in the vectoral form of Maxwell's equations is found to break the Lorentz Gauge in the case of massive photons. Using the biquaternion form of Maxwell's equations, the differential forms of the scalar field is shown to have relation to photon mass. We show both the scalar field gradient and photon mass are related to the displacement current using the Proca equations, and propose a means to determine the spatial geometric structure of the massive photon based on its intrinsic capacitance.
Category: Quantum Physics

The Tri-Quarter Theorem: Unifying Complex Coordinates with Topological Duality on the Unit Circle

Authors: Nathan O. Schmidt
Comments: 9 Pages.

In this paper, we introduce the Tri-Quarter Theorem, a new mathematical framework with a generalized complex-Cartesian-polar coordinate system on the complex plane (mathbb{C}) and a new topological property. We discuss the coordinate system's construction and prove that the boundary zone (T), defined as the unit circle, separates the inner zone (X_{-}) ((|vec{x}| < 1)) and outer zone (X_{+}) ((|vec{x}| > 1)), where (T) exhibits topological duality with (X_{-}) and (X_{+}) through a novel phase pair assignment and structured orientation that ensures consistent directional separation across (mathbb{C}). This result unifies complex, Cartesian, and polar representations while offering new insights into topological separation and orientation. This framework provides a unified perspective on complex coordinates and a tool for analyzing systems with circular symmetry or boundary-dependent behaviors, with potential applications in fields such as black hole physics, signal processing, and other areas reliant on complex domain partitioning. We also created a software tool to animate the theorem. More work is needed to further develop and apply this framework via the methods of science and mathematics.
Category: Topology

The Universe May be More Than a Trillion Years Old

Authors: Martin R. Johnson
Comments: 3 Pages.

When Lorentz contraction is included into travel time, the Universe is found to be much older than present estimates suggest.
Category: Relativity and Cosmology

Symmetries of Natural Numbers

Authors: Emmanuil Manousos
Comments: 32 Pages.

In present paper we prove an original theorem on the natural numbers. From this theorem emerges a set of symmetries of the natural numbers which puts Number Theory on a new footing; the study of the natural numbers through symmetries. One of the consequences of the theorem, but not the most important one, is the odd number factorization algorithm.
Category: Number Theory