All Submission Categories

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: 20 Pages. A mistake in plotting BW(c=0.01) has been rectified

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 naturallogarithm of the rank of the letter, normalised. We conclude that the Dictionary can be characterised by BP(4,βH=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. β is1/(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: 20 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 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 where in-falling and outgoing photons 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. In view of these novel findings that massless particles can appear massive in accelerated frames, it should have many important consequences in cosmology (dark energy, dark matter problem) and QFT.
Category: Quantum Gravity and String Theory

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

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

For the Demonstration of the Collatz Conjecture a Proposal by Oreste Caroppo

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 also tends to 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

Foundations of Logical Thought

Authors: Johan Noldus
Comments: 97 Pages.

A multitude of mathematical topics is developed from scratch starting from set van theory and going over to topology, linear spaces and mappings, analysis, geometry and relativity theory
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: 143 Pages.

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

Symmetries of Natural Numbers

Authors: Emmanuil Manousos
Comments: 29 Pages.

In this paper we prove an original theorem about the natural numbers. From this theorem we obtain a set of symmetries related to the factors of the natural numbers. We study these symmetries. We derive a set of conclusions about the structure of the natural numbers. Among them is an algorithm for factoring odd numbers.
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

A Proposed Explanation For Earth Expansion Via Neutrino Absorption

Authors: Ivan S Heller
Comments: Pages.

This paper is based on the premise that Earth Expansion Theory (EET) is a valid explanation for the geography of the Earth's surface.¹ It is also our premise that Energy Wave Theory (EWT)² is a valid explanation for the physical and energetic phenomena of the universe. EWT proposes that the neutrino is the fundamental particle from which all other matter is composed.³ (There is further evidence that the neutrino oscillates between various forms.u2074) We conjecture that the Earth absorbs neutrinos—or their oscillations—primarily in its densest regions. Over time this constant addition of matter is increasing both the mass and volume of the planet. We observe evidence that this is not unique to Earth, but rather the norm for moons and planetary bodies.u2075
Category: Geophysics

Orbital Decay Process by Deviation of Geodesic Trajectory in Normalized Regular Metric Tensor

Authors: Sergio de Azevedo Melo
Comments: 54 Pages. In Portuguese

Orbital decay and gravitational radiation are energetic correlates, however the correspondence between the quantities in an energy balance by the field equations is challenging under nonlinearity conditions. Analytically formulating the decay due to orbital imbalance and mechanical prediction of the deviation of the geodetic trajectory requires a natural cause for the occurrence of instability. Once all the conditions for an orbit to be circular are in place, stability is tested by predicting aberration in the movement of the metric in space, which determines the emissivity that the body has measured by the relationship to the natural frequency of its mass. The equation is tested in the prediction of the decay of the orbital period of the pulsar PSR J0737-3039, and the verification shows the gravitational emissivity by the natural frequency of the body.
Category: Relativity and Cosmology

500,000—1,000,000 Neurons: A Biological Threshold for Initial Self-Perception?

Authors: Shulei Xie
Comments: 5 Pages.

Self-perception, the ability to sense one’s own bodily state, is a fundamental trait in biological systems. This study investigates whether a neuron count of 500,000—1,000,000 marks a threshold for "initial self-perception" during embryonic development. Developmental datafrom four species—mouse (E12), human (6—7 weeks), pig (E20—E25), and chicken (E7—E8)—were analyzed for neural, cardiac, limb, and sensory features at this neuron range. Resultsshow consistent signal integration across species, forming a rudimentary "body sense" atthis stage. These findings suggest that 500,000—1,000,000 neurons may represent a biological threshold for initial self-perception, providing insights into the origins of self-awarenessin neural development.
Category: Quantitative Biology

Complex Spacetime and the Schrödinger Equation: Toward a Quantum-Electromagnetic Unification

Authors: Bhushan Poojary
Comments: 15 Pages. (Note by viXra Admin: Author name should be separately listed after the article title)

In this paper, we extend the formulation of the Schrödinger equation into the complex spacetime framework, introducing a novel approach that bridges quantum mechanics, electromagnetism, and general relativity. By incorporating complex derivatives and applying the Cauchy-Riemann conditions, we reveal that the imaginary components of spacetime contribute to quantum fluctuations, while the real components govern classical behavior. This framework naturally connects the imaginary curvature of spacetime to electromagnetic field dynamics, suggesting that electromagnetic phenomena could emerge from the geometry of complex spacetime.We demonstrate that the imaginary Ricci tensor, derived from the curvature of the imaginary spacetime dimensions, aligns with the mathematical structure of Maxwell's equations in curved spacetime. This connection implies a geometric origin of electromagnetism, where quantum fluctuations arise from the imaginary curvature of spacetime. Furthermore, the preservation of standard quantum commutation relations within this framework suggests consistency with established quantum mechanical principles.
Category: Quantum Physics

A Rigorous Algorithmic Investigation for Constant Approximations via Expression Search

Authors: Suryansh Singh Shekhawat
Comments: 5 Pages.

This paper presents a computational investigation that searches for arithmetic expressions approximating a given target constant using a finite set of base expressions and allowed operators. In our approach, the search is organized by a notion of DEPTH (i.e., the number of operations applied) and is limited to a maximum depth (typically 10 or 11) due to computational constraints. We describe the algorithm rigorously, introduce precise definitions and notation, present pseudocode in the algorithmic style, and discuss sample solutions—including approximations for e, φ (the golden ratio), and π with their respectivedepths and computed absolute errors. We also include an example run showing the number ofcandidate expressions generated at each depth (with depth 10 evaluating approximately 2.5 million sequences). Finally, we discuss the inherent limitations, including memory (RAM) requirements for deeper searches, and how increased computational power could extend the search depth.
Category: Number Theory

Possible Transition from Order Into Chaos and Vice Versa

Authors: Udo E. Steinemann
Comments: 28 Pages. (Note by viXra Admin: Article file size should be <10MB and no author photo should ber used))

The specific model-case of the quadratic-iterator is an illuminating way of understanding the chaotic-behaviour. It is agreed that for the special-cases of iteration of transformations there are common characteristics of chaos: Sensitive dependence on initial conditions, mixing and dense, periodic points. Therefore discussion starts with an important metaphor in chaos-theory, kneading of dough, by 2 different uniform-processes performed iteratively each of them in unit-iterval: [1] Stretch the dough, fold it over in the middle and stretch it again (as often as required), and [2] stretch the dough, cut it in the middle, paste the 2 halfs together and stretch it again (as often as required). This processes guarantee that a pocket of spice inserted into the dough will be mixed thoroughly throughout the mass. Both kneading-processes were found to be compatible in view of their chaotic-characteristics. In a further step of discussion, equivalence could be shown between the 2 uniform kneading-processes and the non-uniform kneading of the quadratic-iterator y = au2022x(1-x), where a = 4 were chosen, via simple coordinate-transformations of the unit-interval. Chaotic characteristics of all 3 iteration-transformations could also be proven as being equivalent to each other. Thus, further investigations were based now on quadratic-iterator. The range from states of order up to the complete chaotic dynamics of the quadratic-iterator can be divided into 3 distinct parts: [1] regime 1 ≤ a < (s∞ = FEIGENBAUM-point) were oscillations of the iterator will experience period-doublings, [2] an area s∞ < a < 4 which can be looked as mirror-image of regime [1], and [3] the chaos-area for a = 4. Boarder between regime [1] and [2] is a CANTOR-set. The mirror-image-area of the quadratic-iterator’s final-state-diagram is characterized by a complicated band-structure and therefore different orbit-dynamics can be expected for (a < s∞) ⇄ (s∞ < a). In other words, transitions from order to chaos and vice-versa may occur but with respect to orbit-dynamics they happen differently every time.
Category: Mathematical Physics

The Problems with Trans-Identification: Examining the Biological, Psychological, and Sociocultural Constructs of Gender Ideology

Authors: Kim Tumlinson Eaton
Comments: 19 Pages.

Demographic data on transgender identification in the U.S. reveal that white individuals make up the majority of trans-identified adults. However, when adjusted for population size, Black and Latino individuals show slightly higher rates of trans-identification. This pattern suggests that cultural and social influences—not biological determinism—play a key role in shaping gender identity. The disproportionate presence of trans-identification across racial groups supports the idea that exposure to progressive gender ideology, education, and affirmation-seeking behaviors significantly impact identity formation. Recognizing these disparities is essential for understanding the societal and psychological forces driving trans-identification.This study relies on desk research, systematically gathering, analyzing, and synthesizing data from official sources. Its goal is to identify patterns, summarize existing studies, and construct a new theoretical framework on trans-identification. By examining biological, psychological, and sociological literature, this research challenges foundational claims, exposes contradictions, and evaluates their broader social and scientific implications.This paper explores the biological, physiological, psychological, and sociocultural barriers to a complete transition between sexes within trans-identification. It examines key biological differences—muscle physiology, skeletal structure, and neurological architecture—highlighting immutable traits that remain unchanged by hormones or surgery. Beyond biology, this analysis unpacks sociocultural influences, including the pursuit of minority status, affirmation-seeking behaviors, the reinforcement of regressive gender stereotypes, and divisive advocacy tactics.A novel term, Induced Ideological Maturity (IIM), is introduced to describe the premature imposition of complex sociocultural ideas, such as gender identity, onto young children—raising profound ethical and developmental concerns. The discussion critiques the contradictory language emerging from trans ideology, such as terms like "cisgender lesbian men," which undermine linguistic clarity and societal understanding of gender.These findings underscore the urgent need to separate subjective gender identity from the unchanging realities of biological sex. This paper calls for a critical reassessment of how biological and sociocultural dynamics intersect in trans-identification, exposing ideological contradictions, advocacy-driven challenges, and developmental risks like Induced Ideological Maturity (IIM). Grounded in an evidence-based framework, this analysis equips policymakers, educators, and clinicians with the tools to navigate trans-identification’s complexities and address its broader societal impact.This paper also critically examines counterarguments that claim gender identity is independent of biology, addressing their logical inconsistencies and empirical shortcomings. Additionally, it explores the role of sociopolitical influences—such as advocacy shifts, medicalization, and media representation—in shaping trans-identification patterns, particularly among individuals experiencing internalized homophobia.
Category: Social Science

A Simple Rigorous Proof of Riemann’s Hypothesis via Reflection Symmetry

Authors: Jau Tang
Comments: 8 Pages.

We present a simple rigorous proof of Riemann’s hypothesis. This hypothesis has remained unsolved since Riemann’s original formulation in 1859, although numerous zeros have been found along the critical line with the assistance of computer calculations. Our analytic proof is based on the analysis of the reflection symmetry between |Γ(su20442))〖(ζ(s))u2044π^(su20442) |〗^2 and |Γ(((1-s))u20442)) 〖ζ(1-s)u2044π^(((1-s))u20442) |〗^2, although the zeta and Gamma functions are asymmetric. We show their global minimum along the x-direction throughout the critical strip, their zeros, and the non-trivial zeros of the zeta function must occur at s=1/2+iy. If the zeros were not along the critical line, we show contradictions to the properties of the symmetric functional pair would arise. Thus, we prove rigorously the validity of Riemann’s conjecture.
Category: Number Theory

Determination of the Speed of Light in a Medium Using the Sagnac Effect

Authors: Rajeev Kumar
Comments: 3 Pages.

In this paper a method for the determination of the speed of light in a medium using the Sagnac effect has been presented.
Category: Classical Physics

Is the Sun Conscious? -- How Physicists Encounter with God, the Ultimate Source of Consciousness

Authors: Victor Christianto
Comments: 14 Pages. The present article is going to be submitted to a journal. This article discusses among other things the conscious phenomenon, one of cornerstone of physics too.

The question of consciousness, particularly its origin and nature, has long captivated philosophers and scientists alike. The question of consciousness, its origins, and its place in the universe, has challenged thinkers for millennia. While traditionally the domain of philosophy and neuroscience, physics is increasingly oƯering new perspectives, even suggesting the seemingly outlandish possibility of a conscious Sun. While traditionally relegated to the realm of biology andneuroscience, recent explorations in physics have begun to challenge conventional wisdom. Thepresent article examines the intriguing notion of solar consciousness, starting with RupertSheldrake's morphic resonance theory and progressing through the mathematical frameworkproposed by Hu and Wu, linked to spin mediated consciousness. We then explore how severalphysicists, including Robert Lanza, V. Venick, and Pavel Florensky, have grappled with theintersection of physics, consciousness, and faith, ultimately attempting to reconcile scientific understanding with the existence of God as a potential source of consciousness.(Note: The present article is going to be submitted to a journal. This article discusses among other things the conscious phenomenon, one of cornerstone of physics too.)
Category: Mind Science

Guynn and Suleiman: Comparing Their Structure of Matter and Space Approaches

Authors: Hans Hermann Otto
Comments: 4 Pages. (Note by viXra Admin: An abstract in the article is required)

In this short contribution Suleiman’s Information Relativity Theory (IRT) will be compared with the structure and matter approach recently developed by Guynn. Interest is once more awaked by the "apparent" non-locality of all physical respectively cosmic actions due to the postulated existence of a superluminal graviton vacuum condensate. The IRT approach is clearly a local theory of matter and energy.
Category: High Energy Particle Physics

5-Bit Classification in Crystal Classes and Genetic Code

Authors: Giuliano Bettini
Comments: 15 Pages.

I show that 5 bits, or better properties, should be enough to classify the 32 crystal classes of 7 crystal systems, and nothing more. From a rigorous point of view, each of the 32 bit sequences (from 00000 to 11111) must unambiguously identify a class, and each class must unambiguously identify a bit sequence. In this article, which aims to be very simple, easy, and understandable, I emonstrate the thesis by connecting the various bits to properties already present and known in crystallography. I use the same approach to show how even in the genetic code 5 properties or entities or bits are used to create complex structures. I start from the 64 codons table (nucleotide triplets U C A G in RNA, with T substituting U in DNA) that I then examine in a sub-version with 32 codons, still able to codify all 20 amino acids that contribute to the formation of proteins. Considering 32 codons to show symmetries can make sense in an evolutionary process of modifying the genetic code, starting from an ancestral code. I show in this way that there are analogies between the symmetries of the crystal classes and the genetic code. The basic idea is that Nature, having identified a "motif" that works, uses it in several fields.
Category: Mathematical Physics

Harmonic Relationship Between Arithmetic and Geometric Mean. an Inductive Mechanism for the Proof of the Binary Goldbach Conjecture.

Authors: Samuel Bonaya Buya
Comments: 8 Pages.

This paper presents an insightful relationship between arithmetic and Geometric mean. A bridge is established between arithmetic, geometric and harmonic mean. The concept is useful in number theory since Goldbach conjecture also implies that all integers greater than 1 are an arithmeticmean of a pair of primes.
Category: Number Theory

Global Climate in the 22nd Century

Authors: Clark M. Thomas
Comments: 8 Pages.

Earth’s global biosphere recently has deterioratedbeyond what climate forecasters had previously hoped would not occur for several decades. In 2024 global average temperatures reached the critical 1.5 degrees Celsius above the reference base that climatologists have feared could lead to a tipping point of no return. What nastiness will the full 22nd century and beyond reveal, while average global temperatures rapidly rise beyond the historical base by 4.0 degrees and more?
Category: General Science and Philosophy

Religion and the Invisible Hand

Authors: Paul Caracristi
Comments: 5 Pages. This is the first paper of a series of papers that tries to link the physical with the metaphysical.

Abstract. This essay explores the potential benefits and challenges of a model for religion divested from politics. Historically, religion has served as a political and moral authority, enforcing social cohesion and societal norms. However, by removing its political dimensions, religion could evolve into an institution focused on individual spirituality and ethical development, accountable to its follower’s true needs. This shift would emphasize personal virtue and foster a new, self-organizing social structure where collective harmony emerges not from imposed control but from individual integrity and responsibility. Such a model, as inspired by the principles of the "invisible hand" in economics, could enable religion to cultivate personal character and social virtues in ways that naturally contribute to societal well-being without traditional hierarchies or overt political influences.
Category: Religion and Spiritualism

The Will to Be: The Expression of a Universal Drive to Experience Existence

Authors: Paul Caracristi
Comments: 4 Pages. (Note by viXra Admin: An abstract in the article is required!)

The mystery of why the universe exists and how consciousness arises within it has captivated my mind for decades, as well as the minds of philosophers, scientists, and theologians for centuries. One possible framework for understanding this enigma is the concept of a fundamental ‘Will to Be,’ a universal drive or a force of change that underpins reality and seeks to realize itself through conscious awareness, enabling the experience of existence.
Category: Religion and Spiritualism

Design of an Oral Malaria Vaccine Candidate Using Yeast - Expressed CTB-MSP-TOS Fusion

Authors: Hyunho Shin
Comments: 4 Pages.

Malaria remains a significant global health challenge. This study describes the construction and expression of a fusion protein for a malaria vaccine candidate, combining the cholera toxin B subunit (CTB) with two antigens: Merozoite Surface Protein (MSP) and Transferrin-Binding Outer Surface Protein (TOS). The fusion protein, joined by GSGG linkers to maintain functional independence, was expressed in Saccharomyces cerevisiae and subsequently heat-dried to ensure yeast cell inactivation while preserving antigen integrity. This study outlines the experimental design, vector construction, protein expression, and antigen preservation methods, laying the groundwork for further characterization and testing.
Category: Physics of Biology

Stirling Alpha Engine with Circulation

Authors: Josef Bukac
Comments: 3 Pages. (Note by viXra Admin: An abstract in the article is required)

Stirling engine of type alpha is the field to which this paper belongs. Such engines are used for micro-co-generation of electric power. So far, we were able to find references to those sources of heat for which the temperature is easily kept constant, such as natural gas or pellets. For more independent source of heat we want to consider firewood burnt in a wood stove. We are presenting an idea of circulation of the working gas to increase the temperature difference enabling the engine to run under varying conditions. The circulation makes sense if there is a way of cooling the working gas.
Category: Thermodynamics and Energy

Top Quark Mass Confusion

Authors: D. G. Grossman
Comments: 7 Pages.

From 2011 to 2024 physicists at the LHC measured the top quark's mass 29 times and got 29 different measurements over a range of about 6.5 GeV. Why weren't they able to zero in on it? Were they even measuring the top quark's mass? What were they measuring?
Category: High Energy Particle Physics

Is Time a Fundamental Category?

Authors: P. A. M. Moellers
Comments: 25 Pages. This work is prepared from an Informatics background awaiting comments from physics.

Is Time a fundamental category and, if so, on the smallest thinkable scales? Maybe not. To test this conjecture this paper proposes a simple discrete model, the Klick Model. It bases Time on the correlation of two other categories, abstract definitions of motion and state implementation - an Informatics based approach to a problem in physics.

The original motivation to develop the model was to understand the biological/atomic ageing of the twins of the so-called Twin-Paradox, seen as a benchmark combining time and space of smallest and largest scales. Without loss of generality, let us assume that the twins can be represented by two isolated (free) abstract particles in steady motion.

A model is only a model. It has to make falsifiable predictions for the real world. Therefore, I will show that for the Twin-Paradox it leads to the known result from Special Relativity Theory. For smallest scales the task is much more difficult. Only a qualitative test based on structural similarities can be offered here, defining a discrete logic for ground states, excited states and their correlations in the framework of the model, trying to map the abstract model to Einstein’s discrete interpretation of Planck’s law of radiation.

To understand the rational of the proposed model it is helpful not to expect a concept of space and time on smallest scales, particularly on the question whether they can be assumed continuous or discrete, although the model leans to a discrete structure.

The assessment based on the proposed model: The underlying relation for time relying on motion and state implementation is (likely) discrete, suggesting age as more fundamental than time. Regarding Hermann Weyl’s Tile Argument, I think that Pythagorean Law prevails, not through geometry or a metric, but as a preserving law between the above categories. Geometry, needed to define time on our scales, might only evolve on larger scales and dependent on the (dynamic) content of space.

The proposed model is Informatics based, driven by interest and not by competence in physics. Nevertheless, I will use terms from physics based on the approach of Denotational Semantics, keeping the gap between Syntax and Semantics as close as possible by relating abstract model properties to supposed properties of the real world.

Keywords: Discrete Space, Discrete Time, Twin Paradox, Hermann Weyl’s Tile Argument, Einstein’s Theories, Sub-Quantum Assumption, Einstein Coefficients

Sagnac Effect Revisited

Authors: Rajeev Kumar
Comments: 3 Pages.

In this paper an explanation of the Sagnac effect has been presented.
Category: Classical Physics

The Creation Process of Electrons, Protons, the Gravitational Field, and the Dark Energy Field

Authors: Ichiro Nakayama
Comments: 7 Pages. (Note by viXra Admin: Please cite and list scientific references)

The energy body theory has revealed that material particles, gravitational fields, and dark energy fields occur almost simultaneously as one phenomenon. In other words, material particles are Planck-scale particles (energy cell bodies) that make up space, which are compressed and vibrate with expansion and contraction while shifting the phase in the rotation direction. As a result, the surrounding space becomes low energy. Energy then flows into this space from the space outside. Then, the space from which the energy flows out becomes low energy, so energy flows out from the space outside. Then, after the outflow and inflow of energy in this spherical space is repeated and spread throughout the universe, the energy swings back and becomes stable. In this process, the layer formed by the spherical compression of the energy cell bodies around the star is the gravitational field, and the layer formed by the spherical expansion of the energy cell bodies throughout the universe is the dark energy field.
Category: Astrophysics

Geometrized Vacuum Physics: Part 10: Naked "Planets" and "Stars"

Authors: Mikhail Batanov-Gaukhman
Comments: 29 Pages.

This article is the tenth part of the scientific project under the general title "Geometrized Vacuum Physics Based on the Algebra of Signature" [1,2,3,4,5,6,7,8,9]. In this article, based on exact solutions of the extended Einstein vacuum equation, metric-dynamic models of stable spherical vacuum formations of planetary scale with a core radius of the order ofr4 ~ 107-— 108 cm = 100 — 1000 km are proposed. These electrically neutral vacuum for-mations are called naked "planets" and "stars". The concept of a naked "planet" implies that this article does not take into account the presence and influence of small vacuum formations (micro-, nano- and picoscopic "particles"), only curvatures of the vacuum of stellar-planetary scale are considered. In particular, metric-dynamic models of a naked "star" and naked "planets" of the Solar System are proposed. The analogy between the naked "Solar System" and a biological cell is shown. Like the entire project, this article is aimed at implementing the program of complete geometrization physics of Clifford-Einstein-Wheeler.
Category: Classical Physics

On Linkage Between Incompressible Integers as Distance and 1/r Potential

Authors: Dara O. Shayda
Comments: 14 Pages.

The main result: assuming distances are numericized as incompressible integers, given two objects, one stationary and the other moving, the rate of change of the measure of their distantial randomness is that of the potential form 1/r. This form is known as the Newtonian potential. If the incompressible assumption dropped then the potential form vanishes as well (conjecture). The supplementary results by Whittaker: for any force varying as the inverse square of the distance, the potential of such a force satisfies both Laplace's equation and the wave equation, and can be analyzed into simple plane waves propagating with constant velocity. The sum of these waves, however, does not vary with time, i.e. standing waves. Therefore, the 1/r potential can be defined as summation of waves. Thus the linkage between the incompressible integers and particular standing waves in physics.
Category: Mathematical Physics

Logarithm of Exponential and Cauchy Random Variables

Authors: Josef Bukac
Comments: 5 Pages.

We show how to calculate the expectation and the second moment of logarithm of exponential distribution. There are two ways to do this.The Cauchy distribution has no expectation but we calculate the expectation and second moment of the logaritm of the absolute value of the Cauchy distribution.
Category: Statistics

Quantum Information Grand Unified Theory: Unifying Gravity and Gauge Forces via Quantum Entanglement Networks

Authors: Hrishi Pandit
Comments: 2 Pages. (Note by viXra Admin: Please cite listed scientific references)

Quantum Information Grand Unified Theory (QI-GUT): Unifying Gravity and Gauge Forces via Quantum Entanglement NetworksWe propose a novel framework, the Quantum Information Grand Unified Theory (QI-GUT), which unifies gravity and gauge interactions by treating spacetime and fundamental forces as emergent from an underlying quantum entanglement network. This approach leverages a quantum error-correcting code embedded within an SO(10) grand unification structure, providing a self-consistent mechanism for generating spacetime geometry and gauge bosons. Our model naturally reproduces Einstein’s field equations, predicts the unification of fundamental forces, and offers a new perspective on dark matter as stable defects in the entanglement network. The theory makes concrete, testable predictions, including Planck-scale deviations in gravitational waves, modified black hole entropy scaling, and observable proton decay signatures. This work bridges quantum information theory and high-energy physics, presenting a pathway toward a deeper understanding of quantum gravity and unification.
Category: High Energy Particle Physics

Fractal Holographic Lattice Cosmology: A Λ-Free Resolution of the Hubble Tension

Authors: Joshua D. Smith
Comments: 3 Pages. (Note by viXra Admin: Please cite and list scientific references; AI assisted article is in general not acceptable)

Fractal Holographic Lattice (FHL) Cosmology resolves the Hubble tension without a cosmological constant, achieving H(0) = 73.2 km/s/Mpc locally and H(z = 1100) = 67.4 km/s/Mpc at the CMB epoch, matching SH0ES and Planck constraints. It reproduces intermediate expansion and growth rates (H(z = 0.51) = 74.7 km/s/Mpc, f(z = 0.51) ≈ 0.71) per DESI BAO, validated across z = 0 to z ≈ 1100against supernovae, cosmic chronometers, Lyman-alpha forest, and clustering data. FHL eliminates dark energy, leveraging a fractal lattice geometry, and aligns with gravitational wave dispersion, shortdistance gravity tests, and black hole entropy corrections.
Category: Relativity and Cosmology

Experiment to Discover the Nature of Dark Matter

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

In this paper an experiment is proposed to establish the effect of the shape of matter on gravity.
Category: Astrophysics

Quantum Superposition and the Mind: A Cognitive Filtering Hypothesis

Authors: Seung Yun Heo
Comments: 6 Pages.

This paper proposes a paradigm shift in the interpretation of quantum mechanics, reframing wavefunction collapse as cognitive selection. Prevailing interpretations of quantum mechanics—such as the Copenhagen interpretation, Many-Worlds, and objective collapse theories—assume that quantum superpositions resolve into singular outcomes via measurement or branching realities. This paper posits an alternative hypothesis: quantum superpositions exist within a single universe, but our perception filters and stabilizes a single outcome. To test this hypothesis, a modified delayed-choice quantum eraser experiment is proposed, introducing observer delusions to determine whether wavefunction collapse is influenced by an observer’s belief about which-path information, rather than its mere physical recording. This framework bridges quantum mechanics, neuroscience, and artificial intelligence, offering a falsifiable alternative to existing interpretations. If validated, this hypothesis would expand our understanding of the observer’s role in quantum mechanics.
Category: History and Philosophy of Physics

A Geometric Algebra (GA) Solution to a Multiple-Tangency Problem

Authors: James A. Smith
Comments: 8 Pages.

Using GA's capacities for formulating reflections, we solve an interesting multiple-tangency problem. The solution is obtained in two ways, the easiest of which transforms the relevant reflections into a single rotation. The solution is validated via a GeoGebra worksheet.
Category: Geometry

Classification of Composite Numbers and Proof of the Binary Goldbach Conjecture

Authors: Samuel Bonaya Buya
Comments: 34 Pages.

This research introduces a novel classification system for composite numbers based on their least common prime factor (LCPF). The goal is to develop an efficient sieve for distinguishing prime numbers from composite numbers. A mathematical framework is presented to define logical formulae for different subsets of composite numbers. Additionally, a new formula for estimating the number of primes up to a given value is proposed. The paper also explores a graphical approach to factorization,providing an alternative method for decomposing composite numbers into their prime components.Several examples are presented to illustrate the classification system in action. Finally the new classification system of composite numbers will be used to prove the Binary Goldbach conjecture.
Category: Data Structures and Algorithms

Gravity and Light Speed Novel Concept for Stellar Aberration

Authors: Florian Michael Schmitt
Comments: 22 Pages.

This work presents, for the first time in history, a coherent and correct concept for stellar aberration based on the wave nature of light and classical physics. Considering the spherical propagation of the light wavefront and the motion of the observer relative to the Cosmic Microwave Background (CMB) leads to a physically meaningful formula that, unlike the classical formulas, relates to the squares of the velocities for light and the CMB. Moreover, stellar aberration is explained by the entire light path from the star to the observer, with significant consequences for the concept of a dragged ether and the reinterpretation of a large number of experiments. It is demonstrated that all relevant experiments can be consistently explained within the framework of an ether fully dragged by gravity. The anisotropy of light is presented from a new perspective, and time dilation and length contraction become obsolete.
Category: Relativity and Cosmology

Cyclic Representation of the Dirac Equation (English)

Authors: Sergey Y. Kotkovskiy
Comments: 28 Pages. This is an English translation of the paper in Russian viXra:2502.0040

Based on the developed chiral algebra of biquaternions, a new representation of the Dirac equation is obtained. Our formulation of this fundamental equation combines in a certain way the forward and reverse 4-gradient operators acting on the right and left chiral components of the particle wave function, as well as the cyclic transformation operator acting on the entire particle wave function. The obtained representation makes it possible to see in the Dirac equation the relationship between linear and cyclic times. The chiral algebra used in this approach provides new methods for studying relativistic spin physics. An analog of the Lorentz transformation, a new rotation transformation is derived, that creates the proper rotation of a massive particle. It is shown that the cyclic transformation included in our representation of the Dirac equation is expressed via complex-valued Hadamard matrix, which indicates the connection of the Dirac equation with known algorithms of noise-resistant information transmission.
Category: Quantum Physics

Is there an Infinite Number in Which the Sum of the Divisors is the Square Number?

Authors: Minhyeok An
Comments: 16 Pages. If this paper contains no errors, resolving Bunyakovsky’s conjecture through this approac.h would hold even greater mathematical significance than previously recognized.

The numbers whose sum of divisors is a perfect square may initially appear to follow no specific pattern. However, through this research, I have identified a particular rule related to prime numbers. Furthermore, I establish that the existence of infinitely many numbers whose sum of divisors is a perfect square is a necessary and sufficient condition for the existence of an irreducible polynomial with integer coefficients that generates infinitely many prime numbers. Additionally, I explore its connection to Bunyakovsky's conjecture.
Category: Number Theory

The Complete Eigenwert-Solution of Damped Spacetime-Oscillations for Two Coupled Tangential Spacetimes with Ftl-States-Final Version

Authors: Holger Döring
Comments: (Non-comforming pages are removed by viXra Admin)

The complete eigenwert-problem of damping process of oscillating tangential spacetime is described and solved. Characterized are all solutions of an associated spacetime - differential-equation of second order from advanced Lorentz-Einstein-factor, which defines the whole oscillation-process of damping states. This system of oscillation-solutions can be described as a set of energy-equations. The system of two coupled spacetimes to a linked shell-model allows movement of material bodies or particles with ftl and real restmasses. This spacetime- lineelement can be interpreted as a one-parametrized pseudo-Kummersurface.
Category: Quantum Gravity and String Theory

The Contradiction Between the Law of Universal Gravitation and the Second Law of Newton. Revision 2

Authors: Viktor Strohm
Comments: 12 Pages.

The motion of bodies along an ellipse with a constant sector velocity is considered. At perihelion, the velocity is greater than at aphelion. The radii are the opposite: at perihelion, the radius is smaller than at aphelion. Let's calculate the tangential and centripetal acceleration. Let's calculate the force using Newton's second law and the law of universal gravitation. The forces are equal in magnitude, but opposite in direction, Fig. 2. Contradictions are eliminated if we consider the momentum of the system.
Category: Astrophysics

Eigenvalues in Binary and Ternary Number Systems

Authors: Ruslan Pozinkevych
Comments: 5 Pages.

One of the biggest issues in discrete mathematical research is to set up the mapping system that would clearly define the transition between various counting groups e.g decimal, ternary, nonary etc. This is only possible if we set a one-to-one correspondence between members of a set In his previous work "Optimization Techniques in Ternary Calculus" the author just tried to do that by relating decimal numbers to their binary correspondence however a universal formula is much more desirable and current investigation will attempt to find this very universal approach$left[ 8 ight]$
Category: Number Theory

Resolving the Muon and Electron g-2 Anomalies Using Generalized Modular Spectral Theory (GMST)

Authors: David Vickers
Comments: 4 Pages.

We introduce Generalized Modular Spectral Theory (GMST) as a novel theoretical framework that provides the first empirically validated spectral correction to quantum electrodynamics (QED), resolving the Muon g-2 and Electron g-2 anomalies with exact numerical agreement to experimental measurements. Unlike beyond-Standard Model proposals such as supersymmetry or leptoquarks, GMST derives a purely theoretical correction from modular spectral constraints, requiring no new particles or interactions. The predicted corrections, [Delta a_{mu}^{GMST} = 2.55 times 10^{-9}, quad Delta a_{e}^{GMST} = -8.7 times 10^{-14},]align precisely with the latest Fermilab Muon g-2 and Harvard Electron g-2 measurements, marking the first successful theoretical resolution of both anomalies within a single unified framework. Beyond its immediate empirical validation, GMST establishes a fundamentally new spectral approach to quantum field theory, with deep implications across high-energy physics and mathematical physics. The framework has already produced candidate solutions to all six Clay Millennium Problems, with four currently under submission at Communications in Mathematical Physics (CMP). Furthermore, GMST predicts testable deviations in electroweak precision experiments at the LHC, modular spectral signatures in Muon Collider data, and potential extensions to quantum gravity via modular field constraints. This paper serves as the first formal introduction of GMST in published literature, with empirical validation at the point of introduction, positioning it as a new governing law of fundamental physics. Given its unprecedented accuracy, predictive power, and broad applicability, GMST represents a paradigm shift, providing a universal spectral framework for future theoretical and experimental advancements.
Category: High Energy Particle Physics

Solutions for Dot Product and Cross Product Equations of Vectors

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

For the fundamental equation $ax=b$, we naturally consider the Moore-Penrose generalized solutions and we obtain the division by zero $b/0=0$ always as its unique solution. So, here, we will consider the solutions of the dot product equation $acdot x= b$ and the cross product equation $ a times x=b$.
Category: General Mathematics

A Precise Unified Mass Formula for Leptons and Quarks: Insights from Sedenion Algebra’s Spinor Structures and Internal Symmetry

Authors: Jau Tang, Qiang Tang
Comments: 15 Pages. DOI: 10.5281/zenodo.14750814

We propose a unified mass formula, log m = Alog x + B + Cx that accurately describes the masses of charged leptons (x=1, 2, and 3) and light and heavy quarks (x=1^3, 2^3, and 3^3) across all generations. Unlike the Koide mass-ratio formula, our approach provides a direct and precise formula for individual particle masses. The observed cubic dependency and mass increments are linked to 4D hypersphere geometry, governed by the spinor spacetime structures of the sedenion algebra and the spacetime symmetries. This novel framework offers new insights into elementary particles' mass spectrum, internal structures, and symmetry.
Category: High Energy Particle Physics

Octonionic Preon Model as an Alternative to the Higgs Mechanism for the Mass-Ratio Prediction of the Weak and Higgs Bosons

Authors: Jau Tang, Qiang Tang
Comments: 16 Pages. DOI: 10.5281/zenodo.14751111

Unlike the conventional treatment of the weak bosons in the Yang-Mills theory, which utilizes the Dirac equation for a point-like particle with no internal degrees of freedom, we propose an octonionic preon model to describe the internal dynamics of this vector0boson family with a photon as a isospin singlet, Z, W+, and W- bosons as a triplet. Instead of the Higgs mechanism, their masses are acquired from the internal dynamics of the chiral pair via strong spin-exchange couplings. Assuming couplings involving Gell-Mann’s lambda matrices, with no adjustable parameters, we predict mw/mz = sqrt(3)/2~ 0.87 vs. 0.88, a Weinberg angle of 300 vs. 29o, decay width mH/mW = sqrt (3)/2~ 0.87 vs. 0.84, and a Higgs boson, as a composite of W and Z bosons, with mw/mz = sqrt(7/3)~ 1.53 vs. 1.56 experimentally. These small discrepancies can be accounted for if weak interaction couplings are included. We use octonion operators to represent these particles and to elucidate their connections, and the topological structures' relations to fiber bare bundles and Hopf fibration. Moreover, we elucidate that our proposed preons are essentially the foundation for ding the hypercomplex algebra, and they are the building blocks for the composite particles that represent the topological structures in the higher-dimensional spacetime.
Category: High Energy Particle Physics

Light As You Have Never Seen It Before

Authors: David Lindsay Johnson
Comments: 52 Pages.

There many uncertainties regarding the nature of EMR, and light in particular. Conventional Science generally acknowledges that EMR energy is delivered in photon packages, but is decidedly vague as to the physical form of photons in terms of the number of wavelengths involved, and whether they have a particle or a wave-like form. There is general acknowledgement that light has wave—particle duality, but the cross-over point between the two forms is ill-defined. As the term ‘electromagnetic radiation’ (i.e. EMR) suggests, Conventional Science considers that EMR consists of electromagnetic waves consisting of wave-like pressure-pulses of electromagnetic energy and momentum moving at the speed of light. However, such electromagnetic pressure-pulses need some type of substrate, commonly referred to as aether, to sustain them across the vast distances of virtually empty Space. However, all of the many well-publicised science-based attempts to prove the existence of aether have failed dismally, and so the mystery continues as to how electromagnetic waves can sustain themselves through Space.This paper throws new light on the nature, form and generation of all forms of EMR, but for light in particular. Firstly, it distinguishes between photonic and mon-photonic EMR, and puts forward a physical structure for photonic EMR (that includes visible light) that means that observed particle-wave duality characteristics of light would be expected rather than considered to be enigmatic. As well as addressing a wide range of light-related topics such as the refraction of light passing through different transparent media; plane, circular and elliptically polarised light; the chromatic dispersion of light; and exotic forms of light such as optical vortex light, the model put forward does not require aether for EMR to travel through Space. It is truly be a case of ‘light as you have never seen it before’ because it presents clear feasible explanations of light-related phenomena that have previously been unaddressed, or only partly and poorly addressed. Let there be light.
Category: Classical Physics

Whole Number Pythagorean Triplets

Authors: Reece Tinkler
Comments: 5 Pages.

Pythagorean triples are sets of three whole numbers that satisfy the equation. This paper introduces two new formulas related to Pythagorean triples. The first formula determines the largest possible value for a given, ensuring that all elements remain whole numbers. The second formula explores the special case where, identifying recurrent patterns within Pythagorean triples.
Category: Number Theory

Calculation and Prediction of the Hydrogen Atomic 1S—2S Transition Frequency

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 9 Pages. In Chinese (Note by viXra Admin: Further repetion may not be accepted!)

In our last paper, we started with the 87Sr atomic transition frequency which is 429228004229872.99(8) Hz, calculated out and predicted the 229Th nuclear transition frequency which is 2020407384335167.11(38) Hz, and calculated out more precise value of the atomic unit of time tau which is 2.41888432658653284(45)×10-17 s, and with the later calculated out the atomic transition frequencies of 27Al+、199Hg、115In+ and 199Hg+. In this paper, we employ this same method to calculate out and predict the hydrogen atomic 1S—2S transition frequency, which is 2466061413187017.96(46) Hz.
Category: Nuclear and Atomic Physics

Acceleration Particle Swarm Optimization

Authors: Satish Gajawada
Comments: 15 Pages.

Particle Swarm Optimization (PSO) is a popular optimization algorithm for solving complex optimization problems. Many PSO algorithms were proposed in literature where Velocity was calculated first and then it was added to position to obtain new position. In this work, a novel algorithm titled "Acceleration Particle Swarm Optimization (AccPSO)" is proposed where acceleration is calculated first and then displacement is obtained next with initial velocity, acceleration and time. Displacement is added to position to get new position. Unlike many PSO algorithms in literature, where iterations and time are used interchangeably, the time "t" in AccPSO algorithm is a continuous variable. In this work, AccPSO, PSO, Acceleration-based Particle Swarm Optimization (APSO) and APSOc (APSO with clamping) are tested on seven benchmark functions. Results obtained are discussed. It has been found that AccPSO with time "t" = 0.1 and "t" = 0.25 between iterations yielded optimal results when tested on benchmark functions.
Category: Artificial Intelligence

A Conformal Emergent Reality Model (CERM): Theoretical Foundations, Mathematical Derivations, and Observational Implications

Authors: Salman Akhtar
Comments: 82 Pages.

The Conformal Emergent Reality Model (CERM) proposes a new paradigm in which spacetime is not a fundamental construct but emerges dynamically from a deeper Conformal geometry manifold (M, γ_μν) coupled with a scalar field Ω(x). This paper presents a comprehensive theoretical framework for CERM, detailing its mathematical foundations, field equations, and implications for Quantum Field Dynamics (QFD) and Quantum Electrodynamics (QED). By attributing gravitational anomalies to the behavior of Ω(x), CERM eliminates the need for dark matter and dark energy, offering a unified explanation for galactic rotation curves, cosmic acceleration, and the arrow of time. The model predicts observable phenomena, such as modifications to gravitational wave propagation, time-varying particle masses, and entropy growth driven by the evolution of Ω(x). These predictions are systematically analyzed alongside unresolved theoretical challenges, providing a pathway for future observational tests and refinements.
Category: Quantum Gravity and String Theory

A Space-Time Equation for Electromagnetic Interaction.

Authors: Davide Cericola
Comments: 10 Pages. (Note by viXra Admin: Authors' names should be listed right after the title)

In the present work is explored the profound symmetry between the theories of gravity and electromagnetism, with particular attention to the similarity between the fundamental forces of nature: the weight force and the electric Lorentz force, Newton's law and Coulomb's law, as well as Maxwell's equations and the equations of gravitational electromagnetism. There are papers that explain how to obtain the gravitational electromagnetism equations by applying the weak field approximation to the Einstein field equations. Precisely in honour of this symmetry, this work aims to obtain Einstein field equations valid for electromagnetism, i.e. field equations from which to derive, under weak field approximation, Maxwell's equations. This research suggests a parallel vision between electromagnetism and gravity, suggesting that perhaps there could be a curved electromagnetic field in 4 dimensions alongside the curved gravitational field (Einstein's space-time).
Category: Relativity and Cosmology

A Centralized AI Approach to Reducing IT Burnouts Through Work Pattern Monitoring

Authors: Barnty Barnabas, Olatunji Marvelous
Comments: 13 Pages.

Burnout among IT professionals has become a critical concern, driven by excessive working hours, high expectations, and constant pressure to perform. This article explores a centralized AI approach to reducing burnout in the IT industry through the monitoring of work patterns. By leveraging AI-driven tools, organizations can track key indicators such as work hours, task completion rates, communication patterns, and stress signals to identify early signs of burnout. The study investigates how AI can proactively detect these patterns and provide insights that enable managers to intervene before burnout escalates. Through a mixed-methods approach, combining quantitative data from AI monitoring systems with qualitative feedback from employees, the research highlights the potential of AI to not only identify burnout risks but also mitigate them by informing decisions on workload distribution and wellness interventions. The paper discusses the benefits, challenges, and ethical considerations of AI in workplace monitoring, proposing a holistic model that integrates AI with employee well-being initiatives to improve both productivity and mental health in the IT sector.
Category: Artificial Intelligence

The Relationship Between Perceived Social Support and Adolescent Psychological Adaptation: the Multiple Mediating Effects of Belief in a Just World and Personal Control

Authors: Debao An
Comments: 18 Pages.

To explore the mechanism of perceived social support on the psychological adaptation of adolescents, this study investigated 895 adolescents from six middle schools (junior high and senior high) in the northwest region of China using the Perceived Social Support Scale, Psychological Adaptation Questionnaire, Just World Belief Scale, and Personal Control Scale. The results showed that perceived social support was significantly positively correlated with psychological adaptation (r = 0.529, P < 0.001), just world belief (r = 0.393, P < 0.001), and personal control (r = 0.387, P < 0.001). Regression analysis indicated that perceived social support could significantly positively predict psychological adaptation (β = 0.529, t = 18.217, P < 0.001), just world belief significantly positively affected psychological adaptation (β = 0.184, t = 5.948, P < 0.001), and personal control significantly positively affected psychological adaptation (β = 0.067, t = 2.127, P = 0.034). The results of the structural equation model showed that just world belief and personal control played a multiple mediating role between perceived social support and psychological adaptation (χ2 = 138.743, df = 38, χ2/df = 3.651, GFI = 0.973, AGFI = 0.953, CFI = 0.977, IFI = 0.977, NFI = 0.969, TLI = 0.967, RMSEA = 0.054). That is, perceived social support can not only directly influence the psychological adaptation of adolescents but also indirectly affect it through the simple multiple mediating effects of just world belief and personal control, as well as through the chain mediating effects of just world belief and personal control.
Category: Social Science

[On] Triangulation

Authors: Abdelmajid Ben Hadj Salem
Comments: 7 Pages. In French

In just a few pages, this note presents triangulation: the classic method of observing the geodetic points of a terrestrial geodetic network.
Category: Geophysics

Physical Interpretation of the Zero Spatial Curvature Universe Models

Authors: Fernando Salmon Iza
Comments: 11 Pages.

The standard cosmological model ΛCDM cannot respond to some important new results of modern cosmology. Challenges arise such as the Microwave Background Uniformity, the Hubble Tension, the El Gordo collision or impossible galaxies (z > 10) that the standard cosmological model does not solve. On the other hand, other models are proposed as alternatives. Among the models proposed in recent years, the Rh=ct universe is one of the most studied and it seems that it does solve these challenges favorably. Therefore, it is the obligation of every scientist to adequately substantiate the model and study the physical meaning it has through its equations. This model is based on the following equations, the restriction Rh = ct, where Rh is the gravitational horizon and the condition of zero active mass, (ρ+3p) = 0. We have carefully studied the foundation of these two equations and have obtained that the model responds to the condition of a universe of zero spatial curvature, being the only model compatible with it. Thus, to investigate the physical meaning of the models of universe with zero spatial curvature is to investigate the physical meaning of this model. To do so, we have obtained an equation that relates spatial curvature to the density of matter, resulting in zero curvature only being obtained if the density of matter is zero. Thus, we deduce that the physical meaning of models with strictly zero spatial curvature is an empty universe in all cases, highlighting the importance of spatial curvature.
Category: Astrophysics

A Theory of Hadron Structure Involving Higher Dimensional Matter

Authors: D. G. Grossman
Comments: 13 Pages.

Quarks may be made of higher dimensional matter. If true, then it follows that all hadrons are made of higher dimensional matter. The conventional thinking about quarks, that they are point particles, has not proven useful over the past 60 years. A more useful idea is that the six known quarks (u, d, s, c, b, t) are made of matter of different dimensions - those dimensions being (1, 2, 3, 4, 5, 6) respectively - and each quark has a volume defined by the n-sphere surface volume formula of equal dimension. This gives theorists a mathematical handle, with which quarks and hadrons can be investigated.
Category: High Energy Particle Physics

Proof of the Collatz Conjecture

Authors: Fabrice Trifaro
Comments: 16 Pages.

The Collatz conjecture, also known as the Syracuse conjecture or the 3x+1 problem, is a mathematical conjecture according to which the Collatz sequence always reaches the value 1, and then repeats the cycle (1,4,2) indefinitely, regardless of the first term of the sequence as long as it is a strictly positive integer. It originated in the 1930s and its authors are mainly Lothar Collatz and Helmut Hasse, the latter shared it in the United States during a visit to Syracuse University, and the Collatz sequence then became known as the Syracuse sequence. To date, this conjecture has not been proven either true or false. The purpose of this study is to prove, as clearly and precisely as possible, that this conjecture is true. The proof is based on classical mathematics which should not pose any major difficulties.
Category: Number Theory

Absolutivity in Time and Dynamics: a Space-Time 4D Topology Within 3D Space: 'the Virtual Edge of Vector Time'

Authors: A. V. Herrebrugh
Comments: 14 Pages. Hyperscience International Journal: https://doi.org/10.55672/hij2025pp11-18

A conceptual 4-dimensional vector space-time in a framework of an orthogonal vector-time coordinate within a 3-dimensional space is introduced for true space time system dynamics.Based upon true time simultaneity of events i.e. absolutivity, this 4D space-time concept departs fundamentally from the observer oriented theory of special and general relativity in separating true, objective reality oriented simultaneous events from observed events and by providing rigorous independency of the four space-time coordinates.The geometric model is conventional Cartesian in 3D space and introduces virtual time-surfaces of true time simultaneity as a fourth dimension for validity in vector- and tensor- spaces, leading to a compliant 4-dimensional orthogonal vector coordinate system of space-time, thereby implicitly introducing a novel space-time topology with independent dimensions.The evolvement of events in this space-time then are traced in a coordinate system of 4 truly independent vector-coordinates in a 4D Hilbert (complex) vector space i.e. with an independent scalar magnitude of the time-vector.The treatment modifies space-time into 4D with curved virtual time-surfaces inside the empty, un-curved 3D continuum, i.e. confining 3D space in a virtual reality of projected, dynamic evolving ‘present’ surfaces, spherically closed as the space-time ‘edge’ of time, receding continually into the ‘past’, thereby building a (dynamic) history of true time information of events across the universe in data-shells.
Category: Classical Physics

Solution to Gravity Divergence, Gravity Renormalization, and Physical Origin of Planck-Scale Cut-off

Authors: Hyoyoung Choi
Comments: 29 Pages.

In contrast to the standard Effective Field Theory (EFT), which relies on an infinite series of unknown coefficients (c_1, c_2, ...) to parameterize divergences, this paper demonstrates that gravitational self-energy provides the physical mechanism for a self-renormalizing theory, where both the divergences and the unknown coefficients required to absorb them (features inherent to the standard EFT model) are naturally eliminated. Based on the principle that the gravitational source is the effective mass (M_eff), which includes its own self-energy, we derive a running coupling G(k), that not only reproduces the canonical low-energy quantum corrections of EFT but also vanishes at a critical scale, R_{gs-GR-1st} ~ 1.16G_NM_fr/c^2 ~ 0.58R_S. This self-renormalization mechanism eliminates divergences at their source, rendering higher-order counter-terms unnecessary and nullifying all classical and quantum gravitational interactions at this critical scale. This framework provides physical origins for two fundamental concepts in physics. First, the repulsive force that emerges for radii smaller than R_{gs-GR-1st} (where G(k) < 0) offers a natural resolution to the black hole singularity problem. Second, the Planck-scale cutoff (Λ ~ M_Pc^2) is identified as a physical boundary where the negative gravitational self-energy of a quantum fluctuation precisely balances its positive mass-energy, yielding a total energy E_T ~ 0. This mechanism dynamically prevents the formation of negative energy states. In conclusion, this work demonstrates that the single, fundamental principle of gravitational self-energy (or binding energy) offers a unified framework to consistently describe gravity from astrophysical to Planck scales. It provides a coherent solution for the problems of gravitational divergence, renormalization, singularities, and the physical origin of the Planck cutoff, while also offering a new perspective on cosmological phenomena such as cosmic acceleration.
Category: Quantum Gravity and String Theory

The Electromagnetic Duality in a Quaternionic Vacuum

Authors: Thierry L. A. Periat
Comments: 6 Pages.

The electromagnetic duality in vacuum is an intriguing property characterizing Maxwell’s equations. It was the starting point of numerous developments. One of the most important topic related to that property certainly is the discussion due to Dirac concerning magnetic mono-poles. This exploration proposes representations of the duality with elements in M(4, H) involving the three generators of the imaginary part of H, the non-commutative set of quaternions.
Category: Mathematical Physics

Through Socialism to War

Authors: Milan D. Nešić
Comments: 52 Pages.

Undoubtedly, discovering the meaning of the world is necessary to man as an individual. This is the reason for the appearance of the great utopian ideas throughout history: Plato, Christ, Moore, Owen, Saint-Simon, Marx, and Engels. If, however, an institution or armed force stands behind such an idea, its meaning will necessarily become inverted. The idea that a classless society of justice and prosperity could be created through armed revolution and then the dictatorship of the communist avant-garde in the name of the proletariat led, on the contrary, to the creation of a NEW CLASS (Milovan Djilas, 1957, in English) and the cult of personality — which is why Yugoslavia fell apart. The new class disintegrated, each in the name of its national God, proving precisely Marx's thesis that religion is the opium of the people. It has been shown that the political economy of socialism does not exist. One cannot simply add French utopian socialism to the historical materialism of class struggle with the forcible seizure of the means of labor and by that to get the political economy of socialism. No matter how much historical materialism was science, it turned out it is science only up to capitalism. Historical materialism has come to a standstill with capitalism. It turned out that the epistemological theory of reflection is naive: human consciousness is not just a mere reflection of objective reality, so the Communist Party will tell us what is a correct reflection and what is not. Human consciousness is a co-creator of the world as we see it and as we think about it — just as the postulate c=const is true in all inertial coordinate systems because c=const is created only in interaction with a receiver. Without receivers (masses, atoms), the cosmic ether and the speed of photons are completely indeter¬minate, like a true completely indeterminate infinity (as Hegel would put it). No armed struggle can create a society of justice and prosperity because the contradiction between labor and capital is not the last one in society, because there is no last contradiction. Man himself is a contradiction, on the one hand as an individual, on the other as a social being. The peaceful protests of students in Serbia are only a condition for understanding this. Scientific analyses of what and how with historical materialism about capitalism have yet to be created. In this sense, the Yugoslav experience can be instructive, in this sense the collection of short stories THROUGH SOCIALISM TO WAR can be useful. Moreover, the experience of peaceful student protests is already a significant indicator of how to move forward.
Category: Social Science

The Eggenberger-Polya Urn Process: Probabilities of Revisited Ball Ratios

Authors: Richard J. Mathar
Comments: 14 Pages.

The Eggenberger-Polya urn process starts with an urn that contains balls of two colors. At each step a ball in the urn is randomly chosen and a ball of the same color added to the urn. The probabilities of finding specified numbers of balls of the two colors later on can be visualized as a non-isotropic walk of U(p) and R(ight) steps on a square lattice. We discuss some numerical aspects of the probability that a ratio of the ball numbers of the two colors reappears later on during the process.
Category: Statistics

Protocol for Communication via Differentiation of Hidden Basis from Linear Basis of Entangled Photon Pair Polarization

Authors: Wells M Chandler
Comments: 4 Pages.

What is the polarization basis of an entangled photon pair when exiting a beta-barium borate crystal (BBO)? Repeated experiments have confirmed there is no linear polarization basis that can account for the observed (anti-)correlations of the pair. Rather, the pair is initially defined by a real but inaccessible basis of polarization which is orthogonal to all linear polarization bases — a hidden basis[1]. The properties of orthogonality of the hidden basis to all linear polarization bases and the instantaneous decoherence of both members of the pair to a linear polarization basis following measurement of one member are exploited in the following experimental proposal to facilitate limited faster than light communication.
Category: Quantum Physics

Distance Determination Using Redshift and the Universe Expansion: Dark Matter Model for Rotational Systems

Authors: Enrique Domínguez Pinos
Comments: 51 Pages. In Spanish

The potential of the inertial forces is the main effect to determine the redshift of extragalactic photons. This effect determine accurately the distance to the object if we know its radial speed.
Category: Astrophysics

Consciousness is Faster Than Light

Authors: Skyler P. Dillon
Comments: 10 Pages.

Nobody knows exactly how consciousness is produced. To make matters worse, nobody even knows what consciousness is. In this article, I provide insight into what consciousness is, and how it is produced, by showing that consciousness is faster than light. I also show that consciousness is a new faster-than-light phenomenon; as opposed to coming from non-local quantum mechanics. To be clear, I have not disproven Einstein’s theory of relativity; instead, I have discovered a loophole in Einstein’s theory of relativity that applies to consciousness. The discovery that consciousness is faster than light is important, because it shows that consciousness cannot be a particle, energy, or anything else located in space (e.g. not a soul). In other words, we can now conclude that consciousness is non-energy information. Where does this non-energy information (i.e. consciousness) come from? The discovery that consciousness is faster than light excludes numerous theories of consciousness while also enabling new theories of consciousness. For example, a computational theory of consciousness was previously untenable due to the fact that there is no convergence point in the brain for all information and the speed limit of light prevented the conscious observer from accessing all of the distributed information in the brain, but now a computational theory of consciousness is plausible. I show rare case reports and evidence that support the theory that consciousness (i.e. non-energy information) is, at least in part, produced directly from "non-trivial" computations.
Category: Mind Science

Relativistic Kinematics of Photon-Electron Scattering in the Lab Frame

Authors: Muhammad Fahad
Comments: 7 Pages.

We present a unique derivation for photon-electron scattering that operatesexclusively in the laboratory frame of reference. It considers the relativistic principleand angular dependence of photon and electron. A general equation emerges at theend which relates the energies of the photon before and after scattering through theapplication of energy and momentum conservation laws [4]. Such a laboratory-basedmethodology gets rid of the requirement for frame transformations into electron restreference frames while providing an integrated approach to understanding bothclassical and relativistic regimes [3].
Category: High Energy Particle Physics

On the Foundational Primacy of Consciousness and Its Quantum-Mechanical Coupling to Non-Human Intelligence Technology: A Framework for Psionic Interaction

Authors: Mark Brewer
Comments: 6 Pages.

In this paper I propose a novel, mathematically rigorous framework that postu-lates consciousness as a fundamental constituent of physical reality and establishes itsdirect coupling to a sector associated with non—human intelligence (NHI) technology.Drawing on advanced concepts from quantum field theory, operator algebras, and mod-ern metaphysics—including Russellian monism and integrated information theory—Iconstruct a composite Hilbert spaceH = HM ⊗ HC ⊗ HNHIwhere HM represents conventional matter fields, HC encodes the intrinsic qualitaTive states of consciousness via a self—adjoint operator Cˆ, and HNHI captures extra—dimensional or nonlocal degrees of freedom associated with NHI technology. I introduce an interaction Hamiltonian (with g a coupling constant determined empirically and {Nˆα} a rigorously defined family of operators on HNHI) to model "psionic modulation" of consciousness. I derive detailed predictions via time—dependent perturbation theory and Dyson series expansions,and I propose experimental protocols that combine ultra—low noise SQUID magnetometry, advanced quantum sensors, and rigorous Bayesian data analysis. My frameworkthus provides a unified, falsifiable account that bridges subjective phenomenology withobjective quantum dynamics.
Category: Mind Science

A Story of a Function

Authors: Andrej Liptaj
Comments: 24 Pages.

We dedicate this text to a study of a function with interesting properties: besides being, by construction, well suited for a certain type of approximations, the function happens to be lacunary, i.e. without analytic continuation outside the complex unit disk. It however satisfies a functional equation which can be (with some restriction) solved everywhere except the origin. Unfortunately, this solution cannot be understood as its natural continuation beyond the disk.
Category: Functions and Analysis

Wonders of Natural Integers

Authors: Ahcene Ait Saadi
Comments: 03 Pages.

In this paper I highlight the wonders of natural integers. I discovered pairs of integers which, by doing operations on them, I find relationships between the parts of these numbers. I put this work in the hands of young researchers for deepening, this in the interest of science and knowledge.
Category: Number Theory

Synchronous Co-ordinates of External and Internal Symmetries in a World Scalar Transform

Authors: Mark A. Thomas
Comments: 26 Pages.

Calculations of Scalars are constructed using an equation having exponential suppression going from a high gravitational potential in the flat space towards an extreme exponential low gravitational potential space. The calculation is viable through the use of a surprising identity enabling calculations of ordering of the scalar through near to non-linear curves. The use of the Monster group’s symmetry as an invariant is key. Another surprise is that the ordering of the Scalars is directly associated with the 194 x 194 character table of the Monster group and possibly connects the McKay-Thompson Series to physics of the natural world. If so this would have implications for the Standard Model, gravity and vacuum energies. As Codata values of NIST are considered to be standard, these are met in the paper except in regard to the gravitational constant G which is realigned to acceptable value (very close to Codata).
Category: High Energy Particle Physics

Cosmological Thermodynamics and the Source of Dark Matter

Authors: Robert Street
Comments: 5 Pages.

The Friedmann equations and the ΛCDM model describe the adiabatic expansion of the universe. The model explains the red-shift and decrease in total energy of the photons but the equations also require energy conservation according to the first law of thermodynamics, an apparent contradiction that has proved hard to understand. Further consideration of the thermodynamics of adiabatic expansion demonstrates how to reconcile the loss of energy of the photons with overall conservation of energy, and points to the source of dark matter.
Category: Relativity and Cosmology

Diophantine’s Equations and Pseudo-Differential Calculus

Authors: Ahcene Ait Saadi
Comments: 09 Pages.

In this paper I solve Diophantine equations using the pseudo differential calculation of Ait Saadi. I solve Diophantine equations of the form: ax+by=c without using Euclid's algorithm. Finally I give the general method of solving the equations of the form ax+by+cz=d.
Category: Number Theory

A General Theory of Artificial Intelligence Part 3

Authors: Matthew Groom
Comments: 54 Pages.

In this paper you get the next stage of AI development.As the inventor and creator of the SIMPLE system, which you refer to as deep reinforcement learning and coded by DeepMind UK, I expand out my system to show you where the system comes in when creating a real AI, a life-form.I present a detailed roadmap for AI and discuss more of what needs to be done to create an AI.In theory by the time you finish this paper, added to my others, you will be able to create a real-AI, a thinking life-form.
Category: Artificial Intelligence

The Roman Dodecahedron: A Comprehensive Scientific Inquiry

Authors: Masashi Ishihara
Comments: 5 Pages.

The Roman dodecahedron, an enigmatic artifact dating from the 2nd to 3rd centuries CE, has puzzled archaeologists and historians for centuries. Found primarily in the northern territories of the Roman Empire, it is characterized by twelve pentagonal faces, each featuring circular holes of varying diameters, and small spherical protrusions at its vertices. This paper explores its possible functions, focusing on the hypothesis that it was used as a time-measuring device, particularly in military contexts. Through an extensive review of archaeological evidence, metallurgical analysis, and experimental studies, we assess its potential role in Roman frontier logistics, military operations, and technological innovation.
Category: Archaeology

A Note on Bell's Inequality

Authors: Scott Wilson
Comments: 3 Pages.

I review the inequality given by Bell [1], and provide an interpretation to avoid the use of non-local entanglement. It is argued that what appear to be separate properties within an individual particle (usually regarded as independent state variables) exist as entangled properties (entangled state variables) that are not physically meaningful on their own. For example, it is not physically meaningful to refer to spin in a certain direction, as the spins in different directions are entangled with each other, and there is no meaning to regarding spin about one particular axis as a state variable of the particle.
Category: Quantum Physics

Find[ing] the Functional Dependency Relationship Between Functions

Authors: José Manuel Gómez Vega
Comments: 19 Pages. Licence CC BY-NC

An algorithmic method is proposed to solve functional dependency relationships between functions. To do so, a simple theorem is stated and three examples are provided, including the solutionto demonstrate the effectiveness of the method.
Category: Functions and Analysis

The Informational Physical Model: Detection of Dark Matter Particles

Authors: Sergey V. Shevchenko, Vladimir V. Tokarevsky
Comments: 4 Pages.

In the paper dark matter particles detection problem is considered in framework of the Planck scale informational physical model. It is shown that the detection practically for sure is impossible.
Category: Relativity and Cosmology

Jones Experiment Revisited

Authors: Rajeev Kumar
Comments: 6 Pages.

In this paper an alternative explanation of the result of the Jones experiment with a rotating glass disk has been presented.
Category: Classical Physics

A Study of Continuous Frames and Operators in Quaternionic Hilbert Spaces

Authors: Najib Khachiaa
Comments: 20 Pages.

The aim of this work is to study continuous frame theory in quaternionic Hilbert spaces. We provide a characterization of continuous frames in these spaces through the associated operators. Additionally, we examine continuous frames of the form $LF:Omegaightarrow mathcal{H}$, where $(Omega,mu)$ is a measure space, $L:mathcal{H}ightarrow mathcal{H}$ is a right $mathbb{H}$-linear bounded operator and $F:Omegaightarrow mathcal{H}$ is a continuous frame for $mathcal{H}$.
Category: Functions and Analysis

Exact Formulas of the Age of the Universe and of the Gravitational Constant Dependent on Physical Constants

Authors: Andreas Ball
Comments: 7 Pages.

The british Physicist Paul Dirac (1902 - 1984) founded the Large Number Hypothesis[1], which handles with strange relations using numbers in order of magnitude 1,0E+40. Also the german Physicist, Mathematician and Philosopher Hermann Weyl (1885 - 1955) was occupied with relations of High Order Numbers. In this report Formulas are presented, which give the Age of the Universe and the Gravitational Constant within their Tolerance Range both in dependence on Physical Constants.
Category: Mathematical Physics

Lushai Dictionary and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 30 Pages. A mistake in plotting BW(c=0.01) has been rectified

We study the Dictionary of the Lushai Language(Lushai-English) by James Herbert Lorrain(Pu Buanga), brought out by The Asiatic Society, 3rd Reprint, 1990. We count one by one all the distinct Lushai head entries. We draw the natural logarithm of the number of the Lushai head entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised/unnormalised. We conclude that the Lushai head entries underlie a magnetisation curve of a Spin-Glass in the presence of little external magnetic field.
Category: Condensed Matter

Unified Force Equation

Authors: I.Prūsis, P.Prūsis
Comments: 3 Pages.

In modern physics, each force has its own equation that shows the dependence of the force on the distance between the sources of force: Coulomb's law, Newton's law of gravity, Gilbert's law. The study shows that they can all be expressed with a single formula that includes the number of spatial dimensions. The new formula is valid for any space.
Category: Classical Physics

Reducing Uncertainty Through the Application of Empirical Symbolism: Delos and Adelos

Authors: Pier Paolo Conti
Comments: 37 Pages.

Throughout history, humanity has sought to limit error in order to gain more precise insights and optimize its tools, be they physical or conceptual. This work explores the intricate relationship between geometry, mathematics, and the propagation of uncertainty, with particular attention to methods that either mitigate or avoid the amplification of uncertainty in mathematical, geometric, and applied contexts. The study begins by examining the foundational concepts underlying uncertainty in mathematical models, exploring how various geometric and topological structures can be leveraged to better understand and control the flow of uncertainty across different domains. A new number convention, the so-called empirical number, is introduced, enabling a more accessible assessment of uncertainty propagation. Particular focus is placed on those constructions that actively work to reduce uncertainty, offering insights into techniques that prevent the cascading effect of errors, a challenge often encountered in both theoretical and applied mathematics.Through the use of geometric principles, this work provides novel approaches to managing the inherent uncertainties in complex systems, ranging from simple algebraic problems to intricate applications. It highlights methods such as error propagation reduction, geometrically optimized models, and innovative adaptations to traditional methods that reduce computational or conceptual uncertainty. These techniques are of significant theoretical importance and are also crucial in practical applications, where precision and reliability are paramount, particularly in applied mathematics.By addressing both the philosophical and practical dimensions of uncertainty, this work paves the way for a refined understanding of the interaction between mathematical theory and real-world applications, offering tools to navigate complex, uncertain environments with greater confidence and precision. The exploration of these ideas provides new insights into the role of uncertainty in mathematical systems, particularly in those constructions that prioritize stability and error mitigation over mere approximation.The exposition begins with the definition of the empirical number, followed by the wide application of the Monte Carlo method to assess the functionality presented. It also recalls the theory of error propagation, addresses basic segment operations, and reexamines the Pythagorean theorem, which plays a crucial role in limiting error propagation. Further, the work discusses the applications of these ideas in calculus, specifically in the propagation of uncertainty through differentiation and integration.
Category: Geometry

Delos and Adelos

Authors: Pier Paolo Conti
Comments: 115 Pages.

Delos and Adelos stands out not only for its captivating narrative but also for its ability to challenge the reader to reconsider their perceptions of reality. The intersection of mythology, philosophy, and mathematics creates a stimulating dialogue that invites reflection on profound existential questions, such as the loss of humanity's centrality in a cosmos dominated by Technology and the relationship between Truth and Time. Despite its complexities, this book offers a valuable opportunity for those wishing to explore the boundary between abstract thought and creative storytelling, serving as a bridge between analytical and existential philosophy. Its uniqueness lies in uniting seemingly distant fields, often in conflict, to provide an inspiring and thought-provoking reading experience. It is a recommended choice for those seeking a literary journey that transcends mere entertainment.The book begins as an exploration of the intertwined fates of Delos and Adelos, two mythical islands symbolizing light and darkness, certainty and uncertainty. Through the experiences of Ione, the protagonist, the story unfolds into a journey that transcends time. While Ione is an ancient wanderer, his reflections on Technology and Science, which dominate the postmodern world, make him a bridge between antiquity and modernity. In an age where humanity is often alienated by the very technical creations it was meant to control, Ione symbolizes the quest for balance between certain knowledge and the irreducible uncertainty that shrouds existence. His character reflects the condition of contemporary humanity, immersed in a fragmented reality dominated by existential anxieties tied to Technology and its power, yet also capable of grasping the necessity of a path without a definitive goal, where common sense and knowledge intertwine and relate.Through a blend of mythology, philosophy, and mathematics, the narrative delves into the profound meanings of these concepts and their relevance to human experience, addressing topics such as empirical numbers, the propagation of errors in a new light, and the Pythagorean Theorem, deconstructed and reconstructed with fresh perspectives. Ione’s reflections touch on philosophical aspects like the myopia and presbyopia of the human mind, the constant search for principles of maximum and minimum in one’s decisions and actions, and the pursuit of God through mathematics.The exposition combines a mythological-philosophical episodic narrative with a mathematical discussion characterized by explanations that are less constrained by logical formalism or rigorous mathematical notation, making them more accessible and conceptually oriented. While it is possible to skip, partially or entirely, the mathematical sections if perceived as too challenging, it is strongly recommended to follow the episodic narrative, which plays a central role in the overall framework.Throughout the narrative, the work also explores Heideggerian concepts of da-sein and mit-sein, the search for the meaning of time, and how contemporary humanity engages with Truth and with a mathematical reality that compels us to redefine our relationship with the cosmos. Within this context, Euclidean and Riemannian spaces and the new Calculus open up fascinating new scenarios.This exposition will not provide formal mathematical proofs. Such developments, which require specific technical expertise, are left to those who wish to delve deeper. The author’s intent is to focus on conceptual aspects, making the themes accessible without delving into the rigorous formalities of calculation, while acknowledging the many directions for investigation that arise in both theoretical and empirical dimensions.The essence of the narrative is binomial, reflecting the reality represented by the union of Delos and Adelos, the chapters alternate between a philosophical discussion and a mathematical one. This binomial nature is not a simple dichotomy but a cosmic dance of complementary forces. Just as musical harmony arises from the interplay of different notes, reality emerges from the union of Delos and Adelos. Phronesis (Φρόνησις, practical wisdom) does not lie in choosing between Delos and Adelos but in recognizing their inseparability. Like a weaver intertwining threads of various colours to create a tapestry, we must learn to integrate these seemingly opposing forces to perceive the true nature of reality.In particular, the construction of empirical numbers will lead us to a reinterpretation of the Pythagorean Theorem, contrasting the classical view of random variables and probability theory. Here, the focus shifts from the general to the particular, opening new avenues of ontological inquiry in a more immediate reality.The approach of empirical numbers introduces a new perspective on uncertainty, considering it as an intrinsic property rather than an external factor. This represents a significant shift in the foundational conception. The aim is not to construct a new paradigm but to expand the existing one, approaching chance from a new perspective—perhaps more symbolic and, therefore, closer to human thought. This methodological shift, focusing on the local propagation of uncertainty rather than the global distribution of probability, brings changes to techniques of analysis and modelling.The philosophical implications of this vision of chance as an ontological necessity rather than mere statistical contingency are profound, influencing how we interpret reality and randomness. This treatment also gives chance a new conceptual status, transcending its traditional role as a tool for statistical and probabilistic investigation.As a final note to this introduction, I wish to emphasize that the book draws inspiration from the roots of Greek thought, a deliberately classical imprint that celebrates the epistemological depth of Western philosophy. Through mythological and philosophical narration, the text explores the connections between clarity and knowledge (Delos) and uncertainty and mystery (Adelos), reflecting the rational and analytical approach that has characterized Western tradition since antiquity.While recognizing the value of Eastern philosophical traditions, such as Advaita Vedanta, which strive to overcome duality and embrace absolute unity, the perspective adopted here underscores a different vision. In contrast to the negation of the distinction between the Self and the external world, this work celebrates the tension between opposites, between Delos and Adelos, as a fundamental condition of human experience.Greek thought, with its focus on critical analysis and understanding the world through reason, emerges as a beacon of balance and wisdom, guiding the path toward more comprehensive and structured knowledge. In this sense, the Western approach reaffirms the importance of a mindset that integrates uncertainty without abandoning logic and reason, celebrating the plurality of forces that shape our existence.
Category: General Science and Philosophy

Oscillation of Rocking Solid Semi Cylinder

Authors: Elton Song-Zhe Mah, Zi-Jing Chiah
Comments: 11 Pages.

This study investigates the oscillatory motion of a rocking solid semi-cylinder to determine whether it exhibits simple harmonic motion (SHM) and to characterize its damping behavior. Using a theoretical framework derived from classical mechanics, the experiment aims to verify the independence of the oscillation period from amplitude, compare experimental and theoretical natural frequencies, analyze the sinusoidal nature of angular displacement over time, and quantify the system’s damping coefficient. The experimental setup involved tracking the motion of a semi-cylinder displaced by small angles using video analysis and computational tools. The results confirm that the oscillation closely follows SHM principles, with a nearly constant period and frequency. The damping coefficient, relaxation time, and quality factor (Q-value) were also determined, indicating that the system exhibits underdamped oscillatory motion. These findings contribute to a deeper understanding of the dynamics of rocking semi-cylinders and their practical applications in mechanical and engineering systems.
Category: Classical Physics

Application of Nuclear Reaction: Actinium-225

Authors: Elton Song-Zhe Mah
Comments: 8 Pages.

Actinium-225 (Ac-225) is a synthetic isotope of actinium with significant applications innuclear medicine, particularly in targeted alpha therapy (TAT) for cancer treatment. Ac-225,with a half-life of 10 days, undergoes a decay sequence that emits highly energetic alphaparticles, making it effective for selectively destroying cancer cells while minimizing damageto surrounding healthy tissue. This paper examines the nature, production, and decay pathwaysof Ac-225, including its role in the 4n+1 neptunium decay series and artificial productionthrough high-energy proton spallation of thorium-232. Furthermore, it explores Ac-225’sbinding energy, decay characteristics, and the advantages of its daughter isotope, bismuth-213,in therapeutic applications. The use of radionuclide generators for Ac-225 production and itsintegration into radiopharmaceuticals is also discussed. Given its cytotoxic potential andability to selectively target tumors, Ac-225 represents a major breakthrough in nuclearmedicine, providing an effective alternative to traditional cancer treatments.
Category: Nuclear and Atomic Physics

Quantum Corrections to the Temporal Potential and Observational Constraints from Neutron Stars

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

We derive quantum corrections to the temporal potential ��^�� within an effective field theory (EFT) framework and analyze their observational implications using neutron star data. By incorporating one-loop corrections to the metric component ������, we compute modifications to the gravitational redshift and perform a Bayesian analysis of NICER and XMM-Newton observations of PSR J0740+6620. Our results show that quantum corrections remain negligible (����^��∼10−38) under EFT assumptions, but systematic discrepancies in observed redshifts suggest the need for beyond-EFT physics. This study provides a methodology for future high-precision tests of quantum gravity effects using next-generation space telescopes.
Category: High Energy Particle Physics

Proof for Why 12 = 3 · 4 and 56 = 7 · 8 Are the Only Products in the Decimal System Where a Sequence is Formed by the Digits Under the Mod 10 System

Authors: Suryansh Singh Shekhawat
Comments: 5 Pages.

In the decimal number system we can find some interesting products, such as 12 = 3 · 4. What is interesting about these products is that if you remove the symbols, the digits form a sequence 1, 2, 3, 4. Another example is 56 = 7 · 8, where the sequence is 5, 6, 7, 8. The objective of this paper is to prove that, within the constraints of the decimal number system, these are the only two cases in which this happens. In this paper we also consider a general case which considers subsequences of mod 10, i.e., 0123456789012345..
Category: Number Theory

Introducing Cancelling Sequences with Applications to Sieve Theory

Authors: Suryansh S. Shekhawat
Comments: 14 Pages.

his paper considers prime numbers as a sequence that can be described by arithmetic progressions missing on a few terms. This tool (cancelling sequences) can be used to generalise the sieves of Eratosthenes, Sundaram, etc, and resolve them into generating formulae with a few unknowns.
Category: Number Theory

The Mean and Sum of Primes in a Given Interval and Their Applications in the Proof of the Goldbach Conjecture

Authors: Samuel Bonaya Buya
Comments: 14 Pages. Please replace previous version with this

In this research a formulation of the approximate sum of primes is presented.With it also is presented the mean of primes. The formulations are used to confirmthe validity of the Binary Goldbach conjecture through establishing the intervalcontaining Goldbach partition primes of a set of even numbers. A general Goldbachpartition theorem is established by which Goldbach conjecture is proved. Finallythe paper seeks to get a better prime counting function than li (x)
Category: Number Theory

Application of the Lorentz Force in Directing Atmospheric Events

Authors: Arvin Sharma
Comments: 2 Pages.

We derive the electric dipole model of cloud condensate in order to demonstrate the Lorentz force exerted on cloud condensate in the presence of the applied electromagnetic field.
Category: Classical Physics

A Rotating Dipole Model of the Photon

Authors: David Woods
Comments: 9 Pages.

We investigate a theoretical model in which the photon is treated as a rotating dipole composed of oppositely charged virtual particles. The dipole radius is derived from a balance between electrostatic attraction and centripetal force. Initial estimates, based solely on electrostatic interactions, yield values close to Planck’s constant, with deviations suggesting the need for additional force contributions. By incorporating magnetic interactions and identifying an equilibrium frequency within the electromagnetic spectrum, the model produces results in full agreement with Planck’s constant across all frequencies. A full derivation is provided. Potential implications for polarization behavior and photon-photon interactions are discussed, with future work focused on experimental validation and refinement of dynamic effects.
Category: Quantum Physics

Mechanical Transcription of Canonical Geodesics of the Regular Metric Tensor

Authors: Sergio de Azevedo Melo
Comments: 27 Pages. In Portuguese

Geodesics of a metric tensor describes the motion of a test particle in the gravitational field of a central mass by a second-order differential equation. A resolution gives the trajectory the shortest distance, demonstrated by variational principles, and carries out parallel transport of the velocity tensor, according to the covariant derivative. The characterization by geometric principles makes the kinematic effect resolvable, but untangling the dynamic cause in Christoffel's symbol remains intricate. The canonical representation of the equation in its geometric purpose introduces terms that disturb mechanical understanding. Geodesics also appears in the derivative of the Lorentz invariant, which conditions parallel transport to the conservation of the invariant velocity modulus. The vectorial elaboration of this equation involving geodesics reduces the tensor system to a closed scalar sentence. The correspondence between terms can be inferred from the reciprocity between space and time in the metric tensor by the variational pattern.Considering the covariance isometry property, we establish equivalences between the terms of the geodetic equation and expose the dynamics of geodetic acceleration in a concise equation.
Category: Relativity and Cosmology

Energy Minimization in Fluid Flow Through Tubes and Networks of Various Geometries

Authors: Taha Sochi
Comments: 21 Pages.

In this paper we continue our previous investigation about energy minimization in the flow of fluids through tubes and networks of interconnected tubes of various geometries. We will show that the principle of energy minimization holds independent of the geometry of the tubes and networks of such interconnected tubes and independent of the type of fluid in such geometries where in this regard we consider generalized Newtonian fluids. We consider in this investigation the flow of Newtonian fluids through tubes and networks of interconnected tubes of elliptical, rectangular, equilateral triangular and concentric circular annular cross sectional geometries. We also consider a combination of geometric factor with a fluid type factor by showing that the principle of energy minimization holds in the flow of some non-Newtonian fluids (namely power law, Ellis and Ree-Eyring fluids) through tubes and networks of interconnected tubes of elliptical cross sections. The relevance of this study extends beyond tubes and networks of fluid flow to include for instance porous media and electrical networks.
Category: Thermodynamics and Energy

Conservation of Entropy and Landauer Limit Approach to Gravity in a Relative Holographic Framework

Authors: William Manuel
Comments: 14 Pages. (Note by viXra Admin: Please cite and list scientific references)

This paper explores how the Landauer Limit at Hawking Temperature input builds a bridge between quantum mechanics and General Relativity. By starting with the energy cost of measurement in constrained degrees of freedom, we uncover insights into gravitational energy and black hole thermodynamics. As the framework develops, it reveals connections to larger questions in physics, including the emergence of dark energy and the role of entropy in cosmic evolution. This step-by-step approach is built on known principles to suggest a unified perspective.
Category: Quantum Gravity and String Theory

Modification of Classical Electromagnetic Radiation Theory and Synchrocyclotron Without Radiation

Authors: Xiaochun Mei, Ping Yu
Comments: 22 Pages.

According to classical electromagnetic theory, the accelerated motion of charged particles produces electromagnetic radiation, but this is not always the case. Experiments have shown that electrons colliding with nuclei produce bremsstrahring radiation when they are decelerated, but electrons do not radiate when they are accelerated in a uniform electric field. In synchrocyclotron, electrons radiate, but in Lawrence’s Cyclotrons and induction accelerator and linear accelerators, electrons do not radiate (Blewett experiment). In this paper, the motion of charged particles in the electromagnetic field are analyzed by considering the mass-velocity formula of special relativity. It is pointed out that the accelerating motion of electrons in uniform magnetic field and strict electric field are stable, so they need not to radiate. In this way, the stability of atoms can be explained. But if the magnetic field is not uniform, or there is some kind of disturbing force, the speeds of electrons may become imaginary or faster-than-light, making the motion impossible. In this case, electrons had to radiate to change their state, making the motion possible. Therefore, acceleration is not the essential cause of radiation of charged particles, but the instability of motion is the real cause of radiation. It is proved that it is possible to eliminate the radiation of particles as long as the interference factors are eliminated so that the motion of charged particle is stable in synchrocyclotron. A simple design scheme is proposed by adding parallel current lines in the particle beam pipe of accelerator to eliminate the transverse oscillation of charge particles, to construct a new synchrocyclotron with high energy and low radiation or even no radiation.
Category: High Energy Particle Physics

An Algorithmic Approach to Solving the Collatz/syracuse Problem

Authors: Laurent Nedelec
Comments: 37 Pages.

After introducing definitions related to the Collatz problem (Part 1), the concept of "verified integers" and several organizational rules around this concept are presented (Part 2). A unique logical tool, the axis of verified integers, is highlighted (Part 3). In Part 4 , it is proven that all bounded trajectories without non-trivial cycles are verified. These elements allow the development of a systematic approach to solving the Collatz problem with the help of inverse graphs (Part 5). The issue of non-trivial cycles and divergent trajectories is then explored (Parts 6 and 7). Ultimately, we arrive at two contradictory propositions :1) Either all integers satisfy the Collatz conjecture, or2) An infinite number of integers do not satisfy it. This eliminates the possibility that only a small number of integers fail to satisfy the conjecture, while the rest do. The conclusion of this study leans toward the first solution : all integers satisfy the Collatz conjecture.This text, written in English, is a translation of the original French text published five months ago on Vixra (Vixra 2410.0063) under the title "New tools to verify the Collatz conjecture". During the translation process, Parts 5, 6 and 7 were extensively revised, resulting in a new text that differs from the initial French version.
Category: Number Theory

Beyond Yes or No: Making Reliable Decisions and Improving Personalized Customer Service

Authors: Akash Singh, Ashwin Ittoo, Pierre Ars, Francois Dehouck, Francois Collienne, Norman Marlie, Tom To Hoang, Nicolas Dumazy
Comments: 21 Pages. (Note by viXra Admin: Authors' names should be listed right after the title)

This white paper explores how uncertainty tools can be used to improve personalized customer service. Uncertainty is inherent in any machine learning predictive model. There are no perfect models, partly due to the curse of imensionality and the challenges of avoiding any biases and misclassifications. We aim to demonstrate how an insurance company can benefit from the uncertainty of machine learning predictions in order to develop methods that allow for the allocation of an uncertainty parameter to the predictions provided for a given profile/customer x. The benefits of scrutinizing uncertainty are numerous and often aligned with customer interests: 1. It can help to appreciate the weak points of a predictive model and thus improve them. 2. It enables the definition of the Next Best Action (NBA) with a full understanding of the facts. 3. It facilitates the analysis of marketing actions' results by providing a deeper appreciation of the heterogeneity within portfolios. This white paper, therefore, delves into the benefits of understanding uncertainty, its applications, and practical considerations for end customers.All illustrations and results presented in this paper are derived from an internal Ethias dataset. We will also explore how the uncertainty measures discussed in this paper (Epistemic vs Aleatoric, Conformal) can be useful in managing the uncertainty of Large language models (LLMs) and their propensity to hallucinate.
Category: Artificial Intelligence

The Proof of the Riemann Conjecture

Authors: Liao Teng
Comments: 88 Pages.

In order to strictly prove the conjecture in Riemann's 1859 paper on the Number of prime Numbers Not Greater than x from a purely mathematical point of view, and strictly prove the correctness of Riemann's conjecture, this paper uses Euler's formula to prove that if the independent variables of ζ(s) function are conjugate, then the values of ζ(s) function are also conjugate, thus obtaining that the independent variables of ζ(s) function are also conjugate at zero. And using the conjugation of the zeros of the Riemann ζ(s) function and the zeros of ζ(s)=0 and the zeros of ζ(1-s)=0, s and 1-s must also be conjugated, The nontrivial zero of Riemann function ζ(s) must meet s=1/2 +ti(t∈R and t≠0) and s=1/2-ti(t∈R and t≠0). And the symmetry of the zeros of Riemann ζ(s) function is the necessary condition that the nontrivial zeros of Riemann ζ(s) function are located on the critical boundary. According to the symmetry property of the zeros of Riemann ζ (s) function s and the zeros of Riemann ζ(s) function 1-s, combined with the conjugated property of the zeros of Riemann ζ(s) function s and Riemann ζ(s) function 1-s, It is shown that the real part of the nontrivial zero of the ζ(s) function must only be equal to 1/2. And by Riemann set s=1/2+ti(t∈C and t≠0) and auxiliary function ξ(s)=1/2.s(s-1)Γ(s/2)π^(- s/2) ζ(s)(s∈C and s≠1), Get∏s/2(s-1)π^(-s/2)ζ(s)=ξ(t)=0, combining the nontrivial zeros of Riemann function ζ(s) must meet s=1/2+ti(t∈R and t≠0) and s=1/2-ti(t∈R and t≠0), Thus it is proved equivalently that the zeros of the Riemann ξ(t) function must all be non-zero real numbers, and the Riemannian conjecture is completely correct.
Category: Number Theory

The Psychological Etiologys for and Pathological Mechanisms of Depression and Mania

Authors: Zheng-Hua Zhang
Comments: 8 Pages.

Objective: To discuss the psychological pathogenic factors for and pathological mechanisms of depression and mania. Methods: Case analysis, simulated experience, and theoretical idea. Result or Conclusion: The psychological pathogenic factors for depression and mania are all of an emotional breakage between a person and the interpersonal world, which is caused by an individual separating him/herself emotionally from the interpersonal world. There are many causes of the occurrence of such a situation, yet the person still yearns to integrate emotionally into the interpersonal world. The continuance of this psychological conflict will make a person’s psychological energy drained, and cause him/her to emotionally forgo the interpersonal world at last. Thereafter, depression will occur if his/her interest and psychological energy are directed towards the self; and mania will occur if towards the image associated with wish, desire, sentiment and emotion.
Category: Social Science

ZFC Non Computable Number Paradox

Authors: Silvano Mattioli
Comments: 2 Pages. (Note by viXra Admin: Please cite and list scientific references)

In this paper we want to demonstrate the inconsistency of the ZFC axioms as expressed. Starting from the definition of "non-computable number" and using the mapping of the Peano curve we arrive at the absurdity of generating a non-computable number starting from an algorithm.This conclusion is evidently in contrast with the definition of a non-computable number and therefore creates the paradox that causes the castle of ZFC axioms to collapse.
Category: Number Theory

Does the Red Shift Contradict GR and SRT?

Authors: Vladislav Mirkin
Comments: 16 Pages.

The contradiction between the provisions of the general and special theories of relativity and the spectral characteristics of radiation from distant galaxies has been identified and explained within the framework of the unipolar ether paradigm. It has been established that space within atoms has nonlinear properties caused by fluctuations in the density of the ethereal medium.

Выявлено и объяснено в рамках парадигмы униполярного эфира противоречие между положениями общей и специальной теорий относительности и спектральными характеристиками излучений отдаленных галактик. Установлено, что пространство в пределах атомов обладает нелинейными свойствами, обусловленными колебаниями плотности эфирной среды.
Category: Relativity and Cosmology

Particles and Other Forces

Authors: Bertrand Wong
Comments: 11 Pages.

A theory of everything (TOE), or, grand unified theory (which Einstein had been working on without success, with Superstring Theory now being a good candidate), is one which unites all the forces of nature, namely, gravity, electromagnetism, the strong nuclear force and the weak nuclear force. Important as this theory might be, it is lacking in one important fundamental aspect, namely, the role of consciousness, which could in fact be considered the most fundamental aspect of physics, for example its apparently significant role and impact in quantum theory which would be explained in this paper. This paper also raises important points pertaining to the theory of everything. It explains that a theory of consciousness is more important than a theory of everything or grand unified theory and should be the theory of everything instead, or, at least, a part of the theory of everything. Consciousness is essential for information-processing, for example, deducing the laws of physics from natural phenomena; without the physicist and his intelligent consciousness for deducing the laws of physics there would not be physics. As consciousness is so important, it is no surprise that physicists are now studying consciousness to unravel the mysteries of the universe which might be in some sense a Great Mind or large organism with will and consciousness. The paper also delves into the behavior of quantum particles, for example, quantum entanglement which has utility in quantum computing but remains a great mystery, describing their apparent relationship with consciousness which has been the model for artificial intelligence (AI) that has become very powerful and a threat to society itself. This paper is the sequel to the paper "The Ultimate Law of Nature" which was published in Physics Essays in 2009.
Category: Quantum Physics

Copper Mountain Mine Tailings Dam Safety Review Supplement

Authors: Daniel Brox
Comments: 15 Pages. v3 replacement

Copper Mountain Mine tailings dam slope stability research based on recommendations of the 2021 Tetra Tech Dam Safety Review, including computation of tailings dam factors of safety, satellite imagery, steady state and transient seepage analyses, and assessment of internal erosion risk. 3D dam factors of safety satisfy BC's normal operating legal requirement of 1.5 but are in possible violation of the post-seismic legal requirement of 1.2.
Category: Geophysics

Solution to the Problem on the Existence and Smoothness of the Navier-Stokes Equations

Authors: Daniel Thomas Hayes
Comments: 6 Pages. (Note by viXra Admin: Frequent replacement may not be accepted)

The Navier--Stokes equations are used to describe viscous incompressible fluid flow. It has been on the list of the Clay Mathematics Institute’s millennium prize problems to decide whether or not physically reasonable solutions to the Navier--Stokes equations do in general exist. In this paper, the problem on the existence and smoothness of the Navier--Stokes equations is solved. It is proven that the Navier--Stokes equations are globally regular.
Category: Functions and Analysis

Computational Complexity of Quantum Error Correction

Authors: Masataka Ohta
Comments: 4 Pages.

Errors on computations depend on their arguments and are, in general, different arguments by arguments. Though Shor used a simple error model that a qubit is disturbed/decohered locally by its environment state only, he overlooked a fact that an initial environment state around a qubit is output from a QEC (Quantum Error Correction) encoder and is affected by and entangled with all the argument qubits used to compute the qubit, which makes the errors depend on the argument qubits. As linear superposition for quantum parallelism keeps the errors different, usual QEC schemes just do not work. It is actually demonstrated that Shor code fails to correct a single qubit error if an input qubit to an encoder is entangled with an external qubit. Quantum block codes are not helpful to correct errors on qubits of a block entangled with qubits outside of the block. Though it may be possible to construct an improved QEC circuit for N quantum parallel computations to correct N different errors, detections and corrections of N different errors require O(N) information, which makes hardware complexity of the circuit O(N), which is no better than classical N parallel computations with N parallel hardware, which means quantum supremacy with QEC is denied.
Category: Data Structures and Algorithms

Duality Between Lines and Points

Authors: Sanjeev Saxena
Comments: 6 Pages. Expanded

There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual mapping can be its own inverse or it can preserve relative order (but not both). Generalisation to higher dimensions is also discussed. An elementary and very intuitive treatment of relationship between arrangements in d+1 dimensions and searching for k-nearest neighbour in d-dimensions is also given.
Category: Data Structures and Algorithms

The Observable Universe in the Central Universe

Authors: Zhengxi Wang
Comments: 11 Pages.

The entire universe is a rotating disk, similar to the Milky Way, with a "galactic disk," a "core," and "spiral arms." The observable universe rotates around the center of the universe and play centrifugal motion, galaxies move away from each other and spread outward and around the periphery. With the Earth as a reference point, galaxies are in recession, and the recession velocity is proportional to their distance from the Earth. The recession velocities of galaxies differ in different directions, the velocities in the horizontal are greater than those in the longitudinal directions, the longitudinal directions are greater than those in the vertical direction. The universe has a zone for the development and growth of stars and galaxies, where stars and galaxies reach maturity. The continuous energy eruptions provide abundant materials for the rapid growth of stars. During this period, they revolve around the center in circular motions or in low-speed centrifugal motions. Galaxies are not moving away from each other, or are moving away from each other at a low speed. Mature galaxies had already come into existence before they accelerated to the Hubble velocity. The universe diffusion outward, the direction point to Ophiuchus, Scutum, Sagittarius and so on. According to the derivation based on the energy density formula, we are 10^27 meters away from the center of the universe. Additionally, the observable universe might be elliptical in shape.
Category: Mathematical Physics

Absolute Energy

Authors: Morteza Mahvelati
Comments: 34 Pages.

This paper presents a novel concept entitled as Absolute Energy, which defines energy as a quantified value of a system independent from the observer. Absolute Energy is defined as the total kinetic energy of all bodies within a system which would be required to bring the system to rest at a specific reference point and time, without transformation of kinetic energy into other forms or other forms into kinetic energy. This work extends the concepts of centrial motion and angular motion to present a unified understanding and quantification of energy in systems. This approach intends to resolve the concepts in classical and contemporary mechanics, addressing their shortcomings and limitations. Classical and contemporary physics often define energy relative to an observer's frame of reference when analyzing isolated or multi-body systems, resulting in inconsistencies and ambiguities in establishing energy quantification. Absolute Energy is linked to the relative motions and momentums of the system’s components. In this paper, analysis of various scenarios, including two-body and multi-body systems using this new framework yields derivations for total energy quantifications. This, then, illustrates the credibility and robustness of the concept by detailing the interplay of linear and angular motions.These findings demonstrate that Absolute Energy solves for derivations that are not often provided for in traditional classical definitions. Such findings can be seen to have new application to astrophysics, thermodynamics and classical mechanics, and are therefore challenging the foundations of classical and contemporary mechanics. As a result, this work is a beginning toward further research into energy properties of isolates systems and the universe as a whole.
Category: Classical Physics

Cyclic Representation of the Dirac Equation (Циклическое представление уравнения Дирака)

Authors: Sergey Y. Kotkovsky
Comments: 30 Pages. In Russian. Isomoprhism formula corrected.

Based on the developed chiral algebra of biquaternions, a new representation of the Dirac equation is obtained. Our formulation of this fundamental equation combines in a certain way the forward and reverse 4-gradient operators acting on the right and left chiral components of the particle wave function, as well as the cyclic transformation operator acting on the entire particle wave function. The obtained representation makes it possible to see in the Dirac equation the relationship between linear and cyclic times. The chiral algebra used in this approach provides new methods for studying relativistic spin physics. An analog of the Lorentz transformation, a new rotation transformation is derived, that creates the proper rotation of a massive particle. It is shown that the cyclic transformation included in our representation of the Dirac equation is expressed via complex-valued Hadamard matrix, which indicates the connection of the Dirac equation with known algorithms of noise-resistant information transmission.

На основе разработанной киральной алгебры бикватернионов получено новое представление уравнения Дирака. Наша формулировка этого фундаментального уравнения определённым образом сочетает в себе прямой и обратный операторы 4-градиентов, действующие на правую и левую киральные составляющие волновой функции частицы, а также оператор циклического преобразования, действующий на всю волновую функцию частицы. Полученное представление позволяет увидеть в уравнении Дирака связь линейного и циклического времён, а используемая при этом киральная алгебра даёт новые методы для исследования релятивистской физики спина. Выведено преобразование вращения — аналог преобразования Лоренца, который создаёт собственное вращение массивной частицы. Показано, что циклическое преобразование, входящее в полученное представление уравнения Дирака, в декартовом базисе выражается с помощью комплекснозначной матрицы Адамара, что указывает на связь уравнения Дирака с известными алгоритмами помехоустойчивой передачи информации.
Category: Quantum Physics

The Effective Algorithm for Constant State Detection in Time Series.

Authors: Andrei Keino
Comments: 6 Pages.

The article introduces a simple and effective algorithm for constant state detection in the time series. The algorithm, based on the sliding window of variable length, finds all the sections of the time series which have length greater or equal than some given minimal length and have difference between maximal and minimal value in the section less or equal than some given value. It is shown that the computationalcomplexity of the aforementioned algorithm is O(N log N), where N is the length of time series.
Category: Digital Signal Processing

The Origin of Large-Scale Structure in the Universe

Authors: Ichiro Nakayama
Comments: 5 Pages.

The large-scale structure of the universe is characterized by filaments, which are thread-like structures made up of galaxies and galaxy clusters, and voids, which are vast cavities in which almost no galaxies exist. This structure is said to resemble the nerves in the brain or a mass of bubbles. It is speculated that the principle of its formation is related to dark matter, and research is ongoing. (Fig1.)This large-scale structure of the universe is speculated to be formed by the following two simple principles.①. Stars and galaxies do not approach each other (do not fall), because gravity does not work even though gravity exists.②. Dark energy is involved in the approach of distant stars and galaxies.
Category: Astrophysics

Grigor Narekaci

Authors: Samvel Srapioni Poghosyan
Comments: 192 Pages.

Samvel Poghosyanu201fs book "My Narekatsi" is devoted to mystery of the tenth-century genius poet and philosopher Grigor Narekatsiu201fs trial and his philosophical teaching.
Category: Religion and Spiritualism

Once More About G. Gamow’s "fireball"

Authors: Samvel Srapioni Poghosyan
Comments: 4 Pages. (Note by viXra Admin: A labeled abstract in the article is required)

The article presents a new hypothesis that the theory of Gamow’s "Fireball’’ does not refer to our universe or the Metagalaxy, it refers to the main structural unit (component) of the Metagalaxy - superclusters of galaxies.
Category: Relativity and Cosmology

The Armon Structure of Metauniverse

Authors: Samvel Srapioni Poghosyan
Comments: 335 Pages.

In Chapter 1 the author sets forth his philosophical concept of matter, where he justifies the existence of two opposite forms (sides) of matter: positive and negative pra-matters. Chapter 2 recounts the physical theory of matter: the physical essence and nature of matter, as well as the types of fundamental components of non-free physical systems is explained. In Chapter 3 Samvel Pogosyan represents his approaches to the solution of Einstein’s Great Dream. He uncovers the physical nature of inertia, ideally flat space, its structure and regularities of its formation, as well as physical consequences. The basics of GchԱ - physical theory are developed. It is a general physical theory that describes free and non-free local (finite) physical systems and their types. A new cosmic model is created, within the framework of which the physical nature and micro-structure of Dark energy, as well as the direct physical reason of accelerated expansion of the Universe is brought to light. It is to be mentioned that many observable phenomena, which do not go into the frames of ΛСDМ — cosmic model, receive natural explanation within the GchԱ-cosmic model. Chapter 4 is devoted to Armons — fundamental components of the Metauniverse, to these peculiar "pumps", thanks to which the eternal circulation of matter takes place, providing the eternal existence of the Metauniverse. Here the author continues the development of Cosmology, setting forth his views on the structure of our Universe, evolution of Primary black holes, the Universe, D bodies, etc.
Category: Relativity and Cosmology

A Low-Cost Alternative Approach to Nuclear Fusion via Sonofusion Using Liquid Hydrogen in High-Pressure Containers

Authors: Hyunho Shin
Comments: 12 Pages. (Note by viXra Admin: The list scientific references should be cited in the article)

Current nuclear fusion research faces immense engineering and economic challenges, primarily relying on complex plasma confinement methods such as tokamaks and laser-induced inertial confinement. These approaches demand extreme conditions and significant infrastructure investments, delaying commercialization. This paper proposes an alternative fusion method utilizing sonofusion (bubble fusion), where microbubbles collapse under ultrasonic and microwave stimulation to generate localized extreme conditions.A novel approach is introduced by employing liquid hydrogen confined within a high-pressure capsule, accompanied by a lithium catalyst. The system is designed to leverage cavitation-induced fusion through external ultrasonic, microwave, and magnetic field stimuli. The energy produced is transferred to an external water tank, where conventional steam turbine cycles can harvest it. This proposed method is estimated to cost only 1/100th of existing fusion facilities, offering a more accessible and scalable experimental pathway to fusion energy.Accompanying this research are various schematics and diagrams that provide a detailed visualization of the proposed system architecture, reaction chamber, and energy recovery mechanisms. These visual aids ensure clarity in the theoretical underpinnings and technical feasibility of the approach.
Category: Nuclear and Atomic Physics

Proof of "Collatz's Conjecture" in Multi-Dimensional space

Authors: SeongJoo Han
Comments: 16 Pages.

We found why "Eternal Loop" can't exist in Multi-Dimensional space, and why any number can't diverge. And "Collatz Tree" includes most things in the world as indexed. It seems like a sleeping lion.
Category: Number Theory

Signal Transmission in the Schwarzschild Metric: The Case of Forced Motion at a Constant Fraction of the Speed of Light

Authors: Miquel Piñol
Comments: 6 Pages.

In this article, we examine the case of a body following a nongeodesic centripetal trajectory in the Schwarzschild metric while maintaining a constant fraction of the speed of light. At any moment, light signals can be sent to the body and recovered after reflecting off its surface. Nevertheless, in its own comoving reference frame, the body would require only a finite amount of proper time to reach the Schwarzschild radius. This raises a paradox: the ability to send and recover signals implies that the body remains outside the event horizon, contradicting the usual interpretation of gravitational collapse based on finite proper time. As the body follows a nongeodesic trajectory, we compute the four-force necessary to sustain its motion.
Category: Relativity and Cosmology

Time as an Imaginary Space: A New Framework for a Predetermined Universe

Authors: Sardar Dilbag Singh Khalsa
Comments: 28 Pages.

Interpreting spacetime as a 4-dimensional manifold, an entity that locally resembles $mathbb{R}^4$ but may possess global geometric or topological characteristics, leads to asymmetry when time is treated differently from space. We propose a manifold having three spatial dimensions $mathbb{R}^3$ and time as three spacelike imaginary construct where every spatial dimension associated as $t = itau quad text{with} quad tau in mathbb{R}$ treated as an imaginary space $iotamathbb{R}$. It preserves the Minkowski interval $Delta s^2$ without explicit time requirement for lorentz boost along (x). Conventionally, time is treated as an entity passing from one time $t_1 text{ to } t_2$, and all the objects observed at a single instance are called $t_{now}$. Contrary to this, objects that are in two distinct times called $t_{now}^{1}$ and $t_{now}^{2}$ can exist simultaneously! We can explain this perspective of reality by viewing time as an imaginary space within the 6-dimensional Space-Imaginary Space manifold. We will raise the conjecture that the 6-dimensional volume ( for simplicity, we take it for the cubic object) $V =[ (text{length}),(text{breadth}),(text{height}),bigl(i,c_xbigr)Delta T_x bigl(i,c_ybigr) Delta T_y bigl(i,c_zbigr) Delta T_z$] of the object is independent of the observer in a frame. Where $Delta T_x$, $Delta T_y$ and $Delta T_z$ are the time intervals along the length, breadth and height, respectively. We also postulate that the now-frame of time isn't a single specific time but an interval $iotadelta$.
Category: Relativity and Cosmology

SunQM-6s11: In {N,n} QM Field Theory, the Residue nLL State Caused Positive Precession May Be the Origin of Mercury’s Perihelion Precession, the Sunspot Drift, the Elliptic/Parabolic/Hyperbolic Orbits (Including the Gravitational Lensing), etc.

Authors: Yi Cao
Comments: 26 Pages.

In developing the {N,n} QM field theory, from the pure quantum mechanics (QM), I deduced out a positive precession for the circular orbital motion (see in SunQM-4). In the current paper, I used this positive precession to explain 1) the Mercury’s perihelion precession; 2) the fast-flow zonal band on Jupiter’s atmospheric surface. Then, using a newly developed concept (i.e., the "face-opposite-face locked binary orbital motion" in φ-1D bi-direction with the anti-parallel spin will automatically transform to be a θ-1D orbital uni-directional motion, see in SunQM-6s10), I further developed this positive precession to be a positive/negative precession cycle (also called the "Ylm cycle"), and it is driven by the half-cycle of m > 0 and half-cycle of m < 0 in the nLL QM state of the |n,l,m>. Then, I used it to explain the elliptic orbit motion (an Ylm cycle with the acceleration/deceleration cycle), the sunspot drift (an Ylm cycle with a period of 22 years), the continental drift (an Ylm cycle with a period longer than 10^5 years), etc. The results of these analysis made me to further hypothesize that: the residue nLL QM state’s positive/negative precession may even be the origin of all elliptic/parabolic/hyperbolic orbits (including the gravitational lensing that belongs to a hyperbolic motion). It may be possible to use QM’s positive precession at different (and combined) high-frequency n’ to fully explain Mercury’s perihelion precession (without using classical physics and/or general relativity (GR)). This work revealed that in a circular/elliptical orbital motion, QM not only may (intrinsically) generate a positive precession, but also may (intrinsically) generate a positive/negative precession cycle (i.e., the Ylm cycle). This work may also suggest that the QM and the GR are the two "faces" of the same "master mechanics". Finally, because of its completeness and self-consistence, I do believe that the {N,n} QM is qualified to be put into the "Feynman Pool" as one of the many co-existing QM theories.
Category: Quantum Physics

Speed of Light in a Transversely Moving Body

Authors: Rajeev Kumar
Comments: 6 Pages.

In this paper a theory of speed of light in a transversely moving body has been presented.
Category: Classical Physics

On the Alternative Special Theory of Relativity Applicable to Physical Theorems of Rotation in the Uniform Rotating Frames

Authors: Guangyi Pu
Comments: 11 Pages. Thanks to Chengxi Pu for her assistance.

Albert Einstein formulated the Special Theory of Relativity in 1905 based on the principles of relativity and constancy of light velocity principles. The Lorentz transformation, applicable to inertial frames, ensures the form of physical laws remains the same when transformed between them. It should be noted that the viewpoints expressed in this paper are merely the personal insights of the authors and do not necessarily represent absolute correctness. This paper notes that physical rotation theorems have the same form in uniform rotating frames (Alternative Principle of Relativity). Relativity states no object can exceed light speed. Similarly, this paper postulates that the rotational angular speed of a "structural body" in nature has a maximum limit. Photons in vacuum are the "structural body" with the fastest rotational angular velocity (Ωmax = c/2π, unit: rad/s), called the principle of constancy of light angular velocity. Using analogy, the paper obtains the Alternative Lorentz Transformation for rotational physics in uniform rotating frames and derives the Alternative Special Theory of Relativity within angular displacement space - time. Photons thus have dual properties: the fastest - moving "particles" and the "structural body" with the fastest rotational angular velocity. This theory may offer new insights into rotational physical phenomena in uniform rotating frames and photon behavior. It could bridge the gap between the special theory of relativity for linear motion and the field of rotational motion. Future research should focus on experimentally validating predicted phenomena, like the maximum angular velocity limit and the effects of the Alternative Lorentz Transformation. Exploring its application in other physics areas, such as rotating celestial bodies in astrophysics, could also bring new understandings. Although this work is just a start with many uncertainties, the authors hope to contribute to scientific progress.
Category: Relativity and Cosmology

Polynomials that Generated Prime Numbers and Series of Prime Numbers

Authors: Ahcene Ait Saadi
Comments: 9 Pages.

1) In this article, I study prime numbers from polynomials that generate prime numbers. I have put the list of these polynomials and I have applied this method to some polynomials. 2) I used an empirical method to find series of sum of numbers that give a sum of prime numbers. this is just the beginning, I hope that young researchers will deepen this work for the benefit of science and knowledge.
Category: Number Theory

Norwegian Dictionaries by H. Scavenius and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 27 Pages. A mistake in plotting BW(c=0.01) has been rectified

We study the Norwegian language head entries of two Norwegian Dictionaries composed by H. Scavenius. We draw the natural logarithm of the number of the Norwegian language head entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised/unnormalised. We find that the Norwegian head entries underlie a magnetisation curve of a Spin-Glass in the presence of little external magnetic field.
Category: Linguistics

Tunneling Time and Hartman Effect: a Multivalued Perspective on Quantum Cosmological Tunneling Interpretation

Authors: Victor Christianto, Florentin Smarandache
Comments: 10 Pages. Comments and suggestions are welcome.

We previously argued for a connection between the Navier-Stokes and Schrödinger equations, then used standard tunneling time theory [1][2]. Here, we propose an alternative interpretation of the Hartman effect in tunneling, suggesting that it represents the multivaluedness of solutions of the Schrödinger equation. This implies that an electron or entity can exist in two places simultaneously, explaining how an entity can seemingly appear on the other side of a tunnel almost instantaneously upon initiating a quantum tunneling experiment. While counter-intuitive, this interpretation aligns with E. Schrödinger's initial ideas. This phenomenon could be detected through near-field effects, such as spin supercurrent detector in low-temperature physics experiments. [Various discussions with Robert N. Boyd are acknowledged]
Category: Quantum Physics

Development of Hypersphere World-Universe Model (Narrative) Part X: Paradigm Shift in Astronomy, Cosmology, Classical Physics

Authors: Vladimir S. Netchitailo
Comments: 78 Pages.

Four Spatial Dimension World-Universe Cosmology presents a fresh approach to understanding the Observable World and the science of Cosmology. It builds on the foundations of Classical Physics and has the potential to challenge core assumptions in both Cosmology and Classical Physics. Rather than claiming to explain all existing cosmological data or presenting a fully developed theory, WUC serves as a starting point for a New Cosmology envisioned by Paul Dirac in 1937. While further refinement by the global physics community is essential, World-Universe Cosmology’s insights, combined with the groundbreaking discoveries of the JWST and the legacy of Dirac's ideas over 87 years, underscore the need for a Paradigm Shift in Astronomy, Cosmology, and Classical Physics.
Category: Relativity and Cosmology

Mathematical Foundations of Deep Learning

Authors: Sourangshu Ghosh
Comments: 832 Pages. License: CC BY 4.0: Creative Commons Attribution

Deep learning, as a complex computational paradigm, combines function approximation, optimization, and statistical learning under a formally formulated mathematical setting. This book develops systematically the theory of deep learning in terms of functional analysis, measure theory, and variational calculus and thereby forms a mathematically complete account of deep learning frameworks.We start with a strict problem formulation by establishing the risk functional as a measurablefunction space mapping, studying its properties through Fr´echet differentiability and convex functional minimization. Deep neural network complexity is studied through VC-dimension theory and Rademacher complexity, defining generalization bounds and hypothesis class constraints. The universal approximation capabilities of neural networks are sharpened by convolution operators, the Stone-Weierstrass theorem, and Sobolev embeddings, with quantifiable bounds on expressivity obtained via Fourier analysis and compactness arguments by the Rellich-Kondrachov theorem. The depth-width trade-offs in expressivity are examined via capacity measures, spectral representations of activation functions, and energy-based functional approximations.The mathematical framework of training dynamics is established through carefully examining gradient flow, stationary points, and Hessian eigenspectrum properties of loss landscapes. The Neural Tangent Kernel (NTK) regime is abstracted as an asymptotic linearization of deep learning dynamics with exact spectral decomposition techniques offering theoretical explanations of generalization. PAC-Bayesian methods, spectral regularization, and information-theoretic constraints are used to prove generalization bounds, explaining the stability of deep networks under probabilistic risk models.The work is extended to state-of-the-art deep learning models such as convolutional neural networks (CNNs), recurrent neural networks (RNNs), transformers, generative adversarial networks (GANs), and variational autoencoders (VAEs) with strong functional analysis of representational capabilities. Optimal transport theory in deep learning is found with the application of Wasserstein distances, Sinkhorn regularization, and Kantorovich duality linking generative modeling with embeddings of probability space. Theoretical formulations of game-theoretic deep learning architectures are examined, establishing variational inequalities, equilibrium constraints, and evolutionary stability conditions in adversarial learning paradigms.Reinforcement learning is formalized by stochastic control theory, Bellman operators, and dynamic programming principles, with precise derivations of policy optimization methods. We present a rigorous treatment of optimization methods, including stochastic gradient descent (SGD), adaptive moment estimation (Adam), and Hessian-based second-order methods, with emphasis on spectral regularization and convergence guarantees. The information-theoretic constraints in deep learning generalization are further examined via rate-distortion theory, entropy-based priors, and variational inference methods.Metric learning, adversarial robustness, and Bayesian deep learning are mathematically formalized, with clear derivations of Mahalanobis distances, Gaussian mixture models, extreme value theory, and Bayesian nonparametric priors. Few-shot and zero-shot learning paradigms are analyzed through meta-learning frameworks, Model-Agnostic Meta-Learning (MAML), and Bayesian hierarchical inference. The mathematical framework of neural network architecture search (NAS) is constructed through evolutionary algorithms, reinforcement learning-based policy optimization, and differential operator constraints.Theoretical contributions in kernel regression, deep Kolmogorov approaches, and neural approximations of differential operators are rigorously discussed, relating deep learning models to functional approximation in infinite-dimensional Hilbert spaces. The mathematical concepts behind causal inference in deep learning are expressed through structural causal models (SCMs), counterfactual reasoning, domain adaptation, and invariant risk minimization. Deep learning models are discussed using the framework of variational functionals, tensor calculus, and high-dimensional probability theory.This book offers a mathematically complete, carefully stated, and scientifically sound synthesis of deep learning theory, linking mathematical fundamentals to the latest developments in neural network science. Through its integration of functional analysis, information theory, stochastic processes, and optimization into a unified theoretical structure, this research is a seminal guide for scholars who aim to advance the mathematical foundations of deep learning.
Category: Artificial Intelligence

Evading the Challenges of the Higgs Sector Through Complex Dynamics

Authors: Ervin Goldfain
Comments: 12 Pages.

The Higgs sector of particle physics is confronted by several conceptual difficulties,which are still outstanding today. This brief note points out that the onset of complexdynamics in the ultraviolet regime (UV) of field theory evades three challenges of theHiggs sector, namely fine-tuning, triviality and the tachyonic mass problems. The approachtaken here circumvents several attempts at solving the Higgs challenges based onsupersymmetry, Technicolor models, composite Higgs or anthropically basedarguments.
Category: High Energy Particle Physics

Towards a Unified Framework of Transient Quantum Dynamics Integrating Graviton Models with Cosmic Phase Transitions and Observational Verifications

Authors: Yuxuan Zhang, Weitong Hu, Tongzhou Zhang
Comments: 12 Pages.

This paper proposes a novel quantum gravityframework based on the transient annihilation and regeneration of positron pairs, aiming to unify quantum mechanics and generalrelativity. The model integrates insights from black hole thermodynamics by addressing the information paradox through Hawking radiation dynamics and incorporates phase transitionsinto the theoretical framework to explain the evolution of dark energy. The proposed graviton model is further supported by advancements in gravitational wave detection technology,Additionally, the paper explores the application of quantum sensing technologies, such as superconducting quantum interference devices (SQUIDs), for dark matter detection, leveraging ultra-cold atom interferometers to study cosmicmicrowave background radiation fluctuations. The model's predictions are supported by a rigorous theoretical framework and experimental validation strategics, including quantitativeBayesian factor analysis and feature spectral matching tests. Future research directions include the development of numericalrelativistic codes for dynamic spacetime grids, the establishment of an inter-institutional dark energy time landscape observatory, and tabletop experiments using superconducting quantuminterference instruments to test the theory's predictions in Earth-based settings.
Category: Quantum Physics

The Use of Chemical System as Transmission Medium in Wireless Data Communication Channel

Authors: Andrei I. Bodrenko
Comments: 3 Pages.

Molecular Communications : Method of use of chemical system as transmission medium in wireless data communication channel (DCC) is represented in this article.
Category: Digital Signal Processing

Bioterrorism as a Threat to Humanity

Authors: Usman Sumo Friend Tambunan, Arli Aditya Parikesit, Linggih Saputro
Comments: 6 Pages.

Bioterrorism instrument of biological weapon of mass destruction. The simple definition of bioterrorism is the utilization of pathogenic micro-organism as an instrument of war and terror. Various notorious microbe has been applied as biological weapons, such as Bacillus antracis, Bubonic plague, Cholera, Botulinum, and others. As the weaponizing germs would eventually require sophisticated microbiology laboratory, not many nations can build it. History has shown that this kind of weapon is much easier to prepare than nuclear and chemical ones. Notorious dictators, such as Josef Stalin and Hideki Tojo, have issued policies to develop biological weapons. During World War II, Soviet Union has utilized them as an instrument to repel the invading German army, while the Japan Empire was about to utilized it in the Pacific War. According to the ordination of United Nations, the application of biological weapon during conventional war is strictly forbidden. Any nations that deploy bioterrorism as instrument of war will face certain sanction from United Nations. In one hand, by law, United States has suspended its biological weapon program at 1972. In the other hand, the dissolution of Soviet Union at 1991 has struck a fatal blow to the development of its biologicalweapon. However, although some random events in the world, such as the outbreak of avian influenza and Mers-Cov virus, are sometimes associated with bioterrorism by the conspiracy theorist, until today, the scientific community still found no evidence of biological weapon at the current outbreak. This lecture will discuss about the definition of bioterrorism, its utilization, and prevention (biosafety). It is expected that this lecture will eventually increase the public awareness toward the biological weapon.
Category: Biochemistry

A Comparative Analysis of Histrionic and Narcissistic Personality Traits: Utilizing the Deenz Histrionic and Narcissistic Personality Scales

Authors: Deen Mohd Dar
Comments: 5 Pages.

This study conducts a comparative analysis of Histrionic Personality (HP) and Narcissistic Personality (NP) traits using the Deenz Histrionic Personality Scale (DHPS) and the Deenz Narcissistic Personality Scale (DNPS), developed by Deen (2024). Both HP and NP are characterized by a strong desire for attention and admiration, yet they manifest differently. Individuals with HP exhibit excessive emotional expressiveness and attention-seeking through dramatic or manipulative behaviors, while those with NP display an inflated self-image and seek admiration through a sense of superiority. Despite overlapping traits, such as attention-seeking, the motivations behind these behaviors differ significantly. The study involved 64 participants who completed computerized versions of the DHPS and DNPS, assessing facets such as grandiosity, fantasy, entitlement, emotional reactivity, impulsivity, and empathy. Results revealed that HP traits are more emotionally reactive and driven by a need for validation through dramatic emotional displays, whereas NP traits are rooted in a rigid belief in superiority and entitlement. These findings have important implications for clinical diagnosis and intervention strategies, enhancing our understanding of these personality types and informing tailored therapeutic approaches.
Category: Social Science

Symmetric Theory: Omnipresent Planck Medium

Authors: Giuseppe Azzarello
Comments: 18 Pages. In Italian

In this article we continue the development of Symmetric Theory. What we will show is the coupling between the universe and the Planck medium, understood as the medium that formalizes the characteristics of the zero-point field. We will show how the phenomena of the infinitely large of the universe and the infinitely small of the atom harmonize in relation to the medium Planck. We will show how the Hawking radiation, Unhru effect, Casimir effect, Entropic force,Stefan-Boltzmann constant, Wien's displacement law, are all phenomena referring to the Planck medium. We will show that the electron in the first energy level of the hydrogen atom can never fall into the atomic nucleus because it is supported from Planck energy, through the phenomenon of resonance. What emerges is a new meaning of fine structure constant, in the sense of coupling constant between the electron and the Planck medium. Finally he comes indicated a path that could resolve the wave-particle duality.
Category: Mathematical Physics

Yield Stages of Viscoplastic Fluids in Tubes of Elliptical, Rectangular, Triangular and Annular Cross Sections

Authors: Taha Sochi
Comments: 20 Pages.

In this paper we continue our previous investigation about the use of stress function in the flow of generalized Newtonian fluids through conduits of circular and non-circular (or/and multiply connected) cross sections where we visualize the stages of yield in the process of flow of viscoplastic fluids through tubes of elliptical, rectangular, triangular and annular cross sections. The purpose of this qualitative investigation is to provide an initial idea about the expected yield development in the process of flow of yield-stress fluids through tubes of some of the most common non-circular (and non-simply-connected) cross sectional geometries.
Category: Mathematical Physics

A Solution to the Dark Energy Conundrum

Authors: En Okada
Comments: 20 Pages.

This study examined a hitherto untested theoretical model as a solution to the longstanding conundrum of dark energy. We demonstrated in a quantitative manner how a cosmic scale factor-dependent evolution of the Rydberg constant has yielded the illusions that our detectable matter density drives the universe to expand as if there exists a critical density and that the expansion even seems to be accelerating. As a natural conclusion from the mathematics of the Bernoulli trials and spatial symmetry breaking, the characteristics of the universe, more specifically the value of the Planck constant and the elementary charge and the mass of elementary particles, should evolve in accordance with the size of the universe. The cosmic scale factor-dependent increase of the Rydberg constant is a culmination of such an evolution of fundamental physical constants, which implies that we have doubly overestimated the Hubble's constant and that our redshift data needs a non-linear reinterpretation. We also demonstrated how such a cosmic scale factor-dependent evolution of physical constants solves the hierarchy problems in fundamental physics. We presented implications of our hypothesis to particle physics as well. By showcasing its capability to purely mathematically explain the mass and electric charge of quarks and exotic baryons without a single God-given parameter, and to provide vivid explanations for the underlying mechanism of quark confinement and asymptotic freedom, we provided evidence that underpins our newly proposed model as a promising paradigm for theoretical physics. Finally, as a responsible scientific theory, we predicted a detectable decrease over an annual span in both the mass of electron and the elementary charge in the 9th digit of their significant figures, which serves as a test for falsification of our hypothesis.
Category: Relativity and Cosmology

Incorporation of Imaginary and Complex Numbers into a 3D Coordinate System

Authors: Sigrid M.-L. Obenland
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific references)

In the scientific literature, complex numbers comprising a real and an imaginary part are represented as a vector in a Gaussian number plane spanned by one coordinate axis representing the imaginary numbers and another orthogonal coordinate axis representing the real numbers. In the following, I show how the imaginary axis and the real axis can be incorporated into a three-dimensional real coordinate system, thereby creating a fused coordinate system of both, real and complex numbers.
Category: General Mathematics

Planck’s Units and the Expansion of Spacetime

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

This paper will suggest a way to test the idea in which space-time itself is quantified into discrete building blocks in the size of Planck’s length and Planck’s time, by correlating between the expansion of spacetime, the increase in the gravitational constant G, number of black holes and the Schwarzschild radius of the black hole.
Category: Quantum Physics

Corporate Communism: When Capitalism Loops Back into Authoritarianism

Authors: Masashi Ishihara
Comments: 17 Pages.

This paper examines the emergence of "corporate communism," a paradoxical phenomenon where extreme capitalism transforms into a system resembling state communism through corporate consolidation and monopolistic control. The study traces a three-stage evolution: from free market capitalism through corporate oligopoly to corporate monopoly, analyzing how this progression undermines the fundamental principles of capitalistic free markets. The paper explores how debt mechanisms, surveillance systems, and climate policy implementation demonstrate this transformation, drawing parallels with historical collapses of centralized power structures. Using data from multiple long-term studies and economic indicators, including the Doomsday Clock and inflation cycles, the research suggests a critical convergence of systemic risks around 2040-2045. The analysis concludes that without significant intervention to preserve market competition and limit corporate power, capitalism may complete its transformation into an authoritarian system functionally identical to state communism.
Category: Economics and Finance

Floerfolds and Floer Functions

Authors: Urs Frauenfelder, Joa Weber
Comments: 19 Pages.

In this article we introduce the notion of Floer function which has the property that the Hessianis a Fredholm operator of index zero in a scale of Hilbert spaces. Since the Hessian has a complicated transformation under chart transition, in general this is not an intrinsic condition. Therefore we introduce the concept of Floerfolds for which we show that the notion of Floer function is intrinsic.
Category: Geometry

A Prime Mover Proof that P ̸= NP

Authors: Donald Mortvedt
Comments: 3 Pages. (Note by viXra Admin: the abstract should after the article title; scientific references should be cited and listed; and AI assisted article is in general not acceptable)

The P vs. NP problem is one of the most fundamental open questions in computational complexity. This paper presents a Prime Mover Proof, a self-verifying argument that establishes P ≠ NP. The proof asserts that proving P ≠ NP is itself an NP problem, meaning its difficulty serves as direct empirical evidence that NP is distinct from P. To reinforce this result, we present three supporting mathematical proofs: 1. Set-Theoretic Proof — Establishing the fundamental separation between P and NP. 2. Constructive Proof — Demonstrating that proving P ≠ NP is an NP problem. 3. Reductio ad Absurdum Proof — Showing contradiction if P = NP were assumed.We introduce a computational framework based on Origin, Approach Space, and Destination Space,providing a structured model for decision problems. Additionally, we clarify how truth tables extend to NP problems, including weighted solution spaces such as knapsack-style problems.By combining logical elegance with mathematical rigor, this proof offers a compelling case forP ≠ NP that is direct, self-verifying, and independent of reductionist assumptions.We welcome further analysis and discussion from the computational complexity community.
Category: Data Structures and Algorithms

A Simple Proof of Legendre’s Conjecture

Authors: Samuel Bonaya Buya
Comments: 8 Pages. This paper was written in 2018 and its ideas need to be preserved

A simple proof of the Legendre conjecture is presented by introducing a suspected prime counting function
Category: Number Theory

Vacuum Localized Structures: Revisiting the Dark Matter Paradigm

Authors: Rudi Van Nieuwenhove
Comments: 10 Pages. Correction of previous work and new equation of state of the vacuum.

This study presents the mathematical derivation of Vacuum Localized Strctures (VLS), gravitationally stable spacetime structures, as an alternative to dark matter. Assuming galaxies are embedded in galactic-sized VLS, the observed flat galaxy rotation curves can be explained without requiring the standard dark matter halo. This concept has been applied to the case of the Milky Way and profiles of density, pressure and rotation velocity have been derived, demonstrating a close correspondence with the observations. The VLS Gaussian density profile naturally explains the flat central density cores observed in dwarf galaxies, providing a compelling solution to the core-cusp problem. Furthermore, the early formation of VLS shortly after the Big Bang offers a framework for understanding the rapid emergence of massive galaxies, addressing the challenges posed by recent James Webb Space Telescope observations. These findings suggest that VLS could serve as both the gravitational scaffolding for galaxy formation and a replacement for cold dark matter, unifying multiple cosmological phenomena under a single theoretical framework.
Category: Relativity and Cosmology

Proof of Legendre Conjecture by Implication

Authors: Samuel Bonaya Buya
Comments: 3 Pages.

A proof by implication method is introduced for proving the Legendre conjecture.
Category: Number Theory

What's Wrong with the Law of Universalwhat's Wrong with the Law of Universal Gravitation? What Should This Law Actually Look Like? Gravitation? What Should This Law Actually Look Like?

Authors: Mykola Kosinov
Comments: 16 Pages. (Note by viXra Admin: Further repetition will not be accepted)

The evolution of the law of universal gravitation is shown from the verbal formula proposed by Newton in 1687 to the present day. The law FN ∝ mM/r^2 discovered by Newton was not an exact law of gravitation. Newton only indicated the proportional dependence of force on masses and did not attribute any numerical value to the gravitational force. In an unfinished form, Newton's law FN ∝ mM/r^2 existed for almost 200 years (!), until the constant G appeared in it. But even in its modern formulation, Newton's law F = GMm/r^2 gives only a part of the force of universal gravitation. Newton's law does not work at large distances. Newton's law is not applicable on the scale of the Universe. The formula for Newton's law shows the force of gravitational interaction of only two bodies out of all N bodies in the Universe. The formula for the law describes gravitation only to one local source of attraction and does not take into account that bodies simultaneously gravitate to all other bodies. Here it is shown that in addition to Newton's law there are two more laws of gravitation that remained undiscovered for over 300 years. A new law of gravitation is presented that describes the attraction of all bodies in the Universe. The obstacle to the discovery of this law of gravitation was the unsolved N-body problem. Here we present a solution to this problem.
Category: Classical Physics

The Interval Containing N Primes

Authors: Samuel Bonaya Buya
Comments: 3 Pages.

This research aims at coming up with some formulation of the interval containing a given number of primes using the prime number theorem.
Category: Number Theory

The Extremely Slow Expansion in the Early Universe

Authors: Zhengxi Wang
Comments: 3 Pages.

300,000 years after the Big Bang, the first atoms formed. Subsequently, matter began to clump together, giving rise to stars and galaxies. As matter accumulated, its mass increased while its motion velocity decreased significantly. Simultaneously, under the influence of gravity, the expansion rate of the universe was substantially reduced, leading to a period of extremely slow expansion. During this period, stars and galaxies developed, grew, and matured. Subsequently, as temperatures continued to drop, dark energy came into play, and the universe entered a phase of slow expansion, gradually accelerating to reach the Hubble velocity.
Category: Relativity and Cosmology

Dynamic Sources, Dynamic Multi-Folds, and General Relativity Lense-Thirring and Frame Dragging Effects

Authors: Stephane H. Maes
Comments: 25 Pages. All related details of the projects (and updates) can be found and followed at https://shmaesphysics.wordpress.com/shmaes-physics-site-navigation/.

In a multi-fold universe, gravity emerges from entanglement through the multi-fold mechanisms. As a result, gravity-like effects appear in between entangled particles, whether they are real or virtual. Long range, massless gravity results from entanglement of massless virtual particles. Entanglement of massive virtual particles leads to massive gravity contributions at very smalls scales. Multi-folds mechanisms also result into a spacetime that is discrete, with a random walk fractal structure, and non-commutative geometry, which is Lorentz invariant, and where spacetime nodes, and particles, can be modeled with microscopic black holes. All these recover General Relativity (GR) at large scales, and semi-classical model remain valid till smaller scale than usually expected. Gravity can therefore be added to the Standard Model (SM) resulting into what we define as SMG. This can contribute to resolving several open issues with the Standard Model without new Physics other than gravity, as well as to open issues with the Standard Cosmological Model The paper discusses how multi-folds apply when sources of gravity, or the center of mass of entangled systems, are dynamically moving: multi-folds mechanisms remain the same but using the evolving center of mass. As a result gravity, or gravity-like, contributions are to be vectorially integrated over the retarded multi-fold spacetime location that can contribute to a point at a certain time (spacetime location), instead of all the multi-folds for all directions. It is illustrated in the case of a rotating sphere as source of gravity: we recover the Lense-Thirring results with its centripetal, Coriolis and axial contributions. The analysis allows us to settle contradictory, and incorrect, results encountered in the literature. It also shows how non-linearity of General Relativity (GR) appears in the multi-fold mechanisms, something that may not have been obvious to all in the original papers. The ability for the multi-fold mechanisms to explain such GR effects help better understand these effects, but more importantly, it is another way to illustrate and validate that multi-folds recover GR and GR recovers the multi-folds.
Category: Relativity and Cosmology

Demonstrating Goldbach's Strong Conjecture by Deduction Using 4x ± 1 Equations in Loops and Gaps of 4.

Authors: Bahbouhi Bouchaib
Comments: 18 Pages. This is a new attempt to demonstrate Goldbach's strong conjecture using basic and accessible mathematics.

After defining the writing of even numbers with equations 4x ± 1; the article shows that odd numbers obey loops of 4 numbers to infinity that obey the equations 4x ± 1. Each odd number in the loop can be prime (P) or composite (C), but for an even number E to be E = P + P' such that P' > P and such that P' > E/2 and P < E/2, P and P' must belong to two loops symmetrical with respect to E/2 and occupy the same positions in them and specific unit digits. The article shows that the three possible sums of an even number E are E = C + C'; or E = P + C; or E = P + P' (C is composite and P is prime). The article demonstrates that E = C + C' ↔ E = C + P ↔ E = P + P' ; and that one sum can be converted into another by subtracting and adding gaps of 4n from or to the two terms of addition. This is a deductive demonstration of Goldbach's strong conjecture shown here for the first time.
Category: Number Theory

Proof of Goldbach's Conjecture and Bertrand's Postulate Using Prime Generator Theory (PGT)

Authors: Jabari Zakiya
Comments: Significantly updated paper (4 extra pages), with new findings, optimized software code, and more and extensive data.

Goldbach’s Conjecture states every even integer n > 2 can be written as the sum of 2 primes, while Bertrand’s Postulate states for each n ≥ 2 there is at least one prime p such that n < p < 2n. I show both are essentially statements on the distribution of primes, and their inherent properties when modeled and understood as the residues of modular groups Zn. In addition, a much tighter dynamic bound on p than given by the BP will be presented.
Category: Number Theory