All Submission Categories

Existence of Symmetric Equilibrium for Symmetric bi-Matrix Games: a Quadratic Programming Approach

Authors: Somdeb Lahiri
Comments: 3 Pages.

We provide a proof of existence of symmetric equilibrium for symmetric bi-matrix games, a result implied by a more general result that was proved by John Nash. Our proof, unlike the original proof due to Nash, does not appeal to any fixed-point theorem. We prove that any solution to a certain specific quadratic programming problem, is a symmetric equilibrium for the associated symmetric bi-matrix game. We use no more than the continuity of real-valued multi-variable quadratic functions and the mean value theorem for real-valued quadratic functions of a single variable. This new proof does not require any fixed-point theorem and can be easily understood by anyone who is familiar with a beginner's course on real analysis. The implication of the results repoted here is that not just matrix games, as is traditionally the case, but also bi-matrix games become wholly a part of optimization theory and hence is within the scope of operations research.
Category: General Mathematics

New Atom Model, Su(5) Model, and So(10) Model for Theories of Everything

Authors: Wan-Chung Hu
Comments: 39 Pages.

This manuscript provides a new determinative atom model. The magic number 2, 8, 8, 18, 18, 32, 32 can be well explained without using quantum mechanics. Landau magnetic number was added for electron orbiting. In addition, spin-orbit coupling can also be deducted without quantum mechanics. In the later part of the manuscript, modified SU(5) model called [the new] SU(5) model includes all the fundamental particles and explain mass origin and decay mode in a clear picture. Finally, SO(10) model was given for the theories of everything.
Category: High Energy Particle Physics

Booklet of The Corrections of Exercises and Problems - Part III

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

This third booklet includes the corrections of the exercises and problems of the following five chapters: topography, astronomy, curves and the theory of surfaces, ellipse and ellipsoïd and geodetic systems.
Category: Geophysics

A Universal Role of Viscosity in Liquid Density Anomalies: From Water's 4°C Mystery to the Lakes of Titan

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

Water’s density maximum at 4°C, critical for aquatic ecosystems, is traditionally explained by hydrogen bonding but lacks a general predictive framework. We propose that the temperature-dependent viscosity gradient drives density anomalies in water and potentially other fluids, including methane and ethane on Titan. An empirical model, ρ(T) = ρu2080 - βT + γ · (dμ/dT), is validated with experimental data for water, methanol, glycerin, and helium, and extrapolated to Titan’s cryogenic fluids. Terrestrial and cryogenic experiments are proposed to test predictions, suggesting subsurface liquid stability on Titan with astrobiological implications. This work advances fluid mechanics and planetary science, offering a predictive tool for cryogenics and space exploration.
Category: Thermodynamics and Energy

Principium Geometricum

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 14 Pages.

Abstract ApresentamosoPrincipiumGeometricum, umquadrounificadoque, apartir de trêspilares clássicos—aSegundaLei deNewton(F=ma), aLei deGauss (∇·E=ρ/ε0)easequaçõesdeEinstein(Gµν=8πGTµν/c4)—derivaumúnico campodereferênciaU.Definimosamassageométrica mg = V (∇·U)dV eintroduzimosaconstanteunificadora αf=kfl2 P, αU=kel2 P≈2,3×10−60, permitindorecuperarasquatroforçasfundamentaissemhipótesesadicionais.Adicionalmente, incorporamos umtempo oscilatórioT(t) que, ao reparametrizar a dinâmica,produztrajetóriasde"caossuave"emgeometriastoroides
Category: Mathematical Physics

Economic Costs of Caffeine Beverage Restrictions and Withdrawal: A Global Perspective

Authors: Adeyemi Olayisade
Comments: 19 Pages.

This study investigates the nature and workings of the caffeine industry, it also examines its importance, production patterns and contributions to GDP in major countries around the world. The core of this study revolves around the dilemma on the economic and health cost of caffeinated beverage control. Today the caffeine market is worth more than $10 billion dollars and is estimated to reach $320 billion by 2032, it is growing fast with increased consumption of coffee, tea, and energy beverages, these drinks do not simply form part of the everyday lives, but they are also important in the economies of most countries. As it is, countries such as Brazil, Vietnam and Colombia produce and export caffeine in large volumes boosting their Gross Domestic Product. Brazil alone consumes 3 million metric tons of coffee generating 6 billion yield in exports and provides people with 8 million jobs, new manufacturers like Nigeria, have not fully attained their economic capacity but are getting there. Caffeine plays an essential role in productivity within the real sector like the industrial, healthcare, ICT the education and other allied sectors. This study findings showed that caffeine withdrawal and restrictions caused productivity losses based on empirical evidence from Japan, the United Kingdom, and the United States revealing that it caused productivity declines, revenue losses, and disruptions in crucial sectors dependent on cognitive execution. Based on these findings, the study recommends that beverage manufacturers should reformulate high-caffeinated beverages into moderate or low-caffeinated beverages without compromising efficiency, taste and marketability.
Category: Economics and Finance

A New Interpretation of Gravitational Collapse: Setting the Framework for Internal Cosmology

Authors: Anđelko Đermek
Comments: 34 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper presents a conceptual framework that reinterprets black hole collapse as the source of emergent cosmological spacetime. In full accordance with Schwarzschild geometry, the model replaces the classical collapse into a singularity with dynamically structured, null-ordered layers of redshifted matter accumulating on the horizon, as seen by an external observer. The black hole initially forms on the Planck scale and acts as a source of gravity, with the event horizon dynamically growing outward. This growth generates a causal sequence of redshifted layers on the horizon, with radial motion asymptotically frozen due to gravitational time dilation, while angular and lateral modes remain unconstrained and dynamically active. The resulting surface structure holographically encodes information that projects an internally expanding universe. Topologically, however, the interior of the black hole is absent, the event horizon represents the ultimate boundary of the causal structure. This framework provides a physical realisation of the holographic principle and a causal mechanism for the emergence of cosmic time, entropy gradients, and structure formation, while preserving unitarity and respecting entropy bounds. The model offers a complementary, geometrically motivated interpretation of horizon dynamics that bridges black hole thermodynamics, holography, and cosmology, uniting general relativity, quantum theory, and the origin of cosmic structure.
Category: Relativity and Cosmology

Physical Principles in Revealing the Working Mechanisms of Brain Part Two

Authors: Nicolae Mazilu
Comments: 253 Pages.

This work, as a whole, is addressed to a wide range of scientists who, naturally, approach the research of the human brain from different points of view. Our own main point is that no matter of the angle of approach in the brain research, a scientist must be aware of the physical possibility of working of the brain. We describe such a possibility by modeling the brain as matter, active through an agent analogous to light: the brain behaves like a universe.Consequently, in this instalment of the work, the emphasis is on quantization as an essential function of a universe, according to its concept. The Planck’s quantization is taken as prototype in unfolding the concept. It is shown, mathematically, how the quantization works for the charge. Based on this physics, a scenario is described for the manner of communication in the brain. Specific conservation laws generated by the condition of quantization are provided, and a concept of interpretation is defined based on the idea of dyons, the particles invented by Julian Schwinger.The subject is, obviously, not closed; there is more to follow from the work. However, an affine theory of a universe concept is proposed, as a kind of ‘bonus’ in closing this instalment of the work, just for the sake of illustration of some essential points of the general theory.
Category: Physics of Biology

The Geometry of Light — a Revolutionary New Theory and a Foundation for a New Science.

Authors: Gary Barham, Christine van Blokland
Comments: 49 Pages. Presented at DemystiCon 2025, Sesimbra, Portugal (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We are going to investigate a new theory of Light which we are calling the Geometry of Light. This theory shows us that by applying symmetrical positive/negative geometry to physics and especially quantum physics we are able to solve many of its currently unsolved problems and propose a holistic theory of light that could take us on to a new Theory of Everything. The first step towards a ‘new science’ is in fully understanding Light, as light is the first appearance of mass/energy out of the zero-point field, the quantum vacuum of space. We present a revolutionary new theory that proposes light as a composite particle made up of both photons (light/energy) and gluons (darkness/ information). When travelling in free space as ‘light’ these two particles are always connected, always in interaction with each other, and even though we see the flash of light of the photon, it also has its unseen shadow of darkness called the gluon. This continual interaction between the photon and gluon will explain all the quantum weirdness at that level and above, as all particles of matter are created out of the zero-point field via this photon/gluon pairing. The photons create an outer boundary (shell/ shield) of each subatomic particle and the gluons hold the inner boundary (strong force/ glue) or centre of the particle. The internal components (mostly quarks and antiquarks) of all particles are held tightly between these two boundaries, making all of matter truly ‘frozen light’. When pushed apart like this, in the creation of matter, the photons around the outside of the particle will take on a negative charge (shield) and the gluons in the centre a positive charge (glue). These additional charges, within every particle of matter, contribute significantly to finally and fully explaining the ‘weird’ characteristics of quantum physics.
Category: Quantum Physics

Quantum Tunnelling with Two, or More, Potential Barriers

Authors: Domenico Oricchio
Comments: 5 Pages.

I write the quantum tunnelling using the Laplace transform to obtain the solutions for multiple barriers.
Category: Quantum Physics

New Concept of H Removes Paradoxes of Infinity

Authors: William Hesslefors Nairn
Comments: 9 Pages. Email: whnairn@gmail.com (Note by viXra Admin: Please cite and listed scientific references; Please submit article written with AI assistance to ai.viXra.org)

An alternative framework to zero and infinity can be presented through the new concepts of 0^m and H^m. These bold definitions aim to mathematically represent infinitesimal and infinite values, preserving our intuition while reducing manyseemingly unnecessary contradictions encountered across several mathematical domains while dealing with infinity. I define 0^m as some hierarchy of infinitesimally small values, keeping the concept somewhat similar to finite numbers and using approximations (which have proved very useful in other areas of mathematics) as opposed to letting zero continue to represent absolute nothingness(and doing the same for H^m to replace the absurdity of infinity). Some applications include potential improvements to geometric series and supremum definitions, and clarifications to quadratic equation and inverse matrices - etc.Feedback on its implications and my communication are highly welcomed.
Category: General Science and Philosophy

An Experimental Exploration on the Applicability of Kepler's Laws to Water Vortex Motion

Authors: Wang Yi
Comments: 13 Pages.

This study aims to verify through physical experiments whether the fluid motion laws in a water vortex system conform to Kepler's laws of planetary motion. Specifically, by quantitatively analyzing the orbital parameters of rotating spheres in the vortex, it examines the applicability of Kepler's third law (the ratio of the cube of the semi-major axis of the orbit to the square of the period is a constant) in fluid mechanics scenarios. It also explores the potential of water vortices as a macroscopic physical model for simulating the laws of celestial body motion.
Category: Astrophysics

Anomalous Magnetic Moments Without Fields: A Geometric and Observer-Dependent Interpretation

Authors: Satoshi Hanamura
Comments: 7 Pages.

Building upon the previously established 0-Sphere electron model with its internal structure of two thermal kernels and photon sphere exhibiting Zitterbewegung oscillations, we present a new observer-dependent interpretation that fundamentally reframes the origin of anomalous magnetic moments in quantum electrodynamics. While conventional QED requires external magnetic field interactions for any observable anomaly to manifest, our reinterpretation of the existing 0-Sphere framework demonstrates that anomalous magnetic moments can arise as purely geometric effects in free electrons through relativistic observer transformations. The crucial new insight emerges from recognizing that the same internal Zitterbewegung motion at v ~ 0.04c yields different measurements depending on the observer's reference frame: an observer co-moving with the internal motion measures a g-factor of exactly 2 consistent with Dirac theory, while an observer in the laboratory frame perceives Lorentz contraction effects that manifest as the anomalous magnetic moment through the predicted relationship γ = 1 + a. This observer-dependent reinterpretation transforms our understanding of quantum magnetic anomalies from interaction-based corrections to relativistic geometric consequences of internal motion, suggesting that quantum phenomena traditionally attributed to virtual particle interactions may represent observable effects of relativistic internal structure, thereby opening new avenues for understanding quantum mechanics through geometric principles without requiring external field perturbations.
Category: Quantum Physics

Reverse Osmosis Effect in Narrow Tubes Concentrates Urine in the Kidney

Authors: Johan Nygren
Comments: 16 Pages.

The kidney concentrates urine by a form of reverse osmosis and not by forward osmosis as traditionally believed. This form of reverse osmosis can operate at low pressures such as those within the kidney filtration system. Recent advances in the understanding of osmosis have made it possible to discover this new type of reverse osmosis, that is inherent to narrow tubes at the micrometer scale.
Category: Physics of Biology

Nucleons

Authors: John P Wallace, Michael J. Wallace
Comments: 8 Pages.

The nucleons with their components and force fields are a greater challenge for quantum mechanics than the hydrogen atom that had provided deep cover to hide the defects both in quantum mechanics and relativity (Wallace and Wallace, 2024c). Once a correction to special relativity was made allowing γ to take on values less than one the hydrogenground state could be accurately computed providing a method to deal with the nucleons. A result was to discover why the neutron and proton are stable and have similar masses.
Category: Quantum Physics

Magnetic Neutron (In Italian)

Authors: Ferrara Francesco
Comments: 20 Pages.

In this work we propose an electromagnetic model of the neutron inspired by the theoretical foundations outlined by Vassallo and Celani, according to which elementary particles can be interpreted as small spheres, massless, charged, in motion. The model assumes that the neutron is made up of two opposite charges, without rest mass, in circular motion on concentric orbits. Each generates a current and therefore a magnetic moment. The approach allows to calculate, starting from simple classical and quantum relations, the values u200bu200bof the magnetic moment, the mass and the spin of the neutron, obtaining results consistent with the experimental data. Finally, the analysis of the dynamic stability of the system is addressed, considering the internal electromagnetic forces and the relativistic evolution along the z-axis. The model, although phenomenological, opens to original reflections on the structure of matter and on the role of the electromagnetic field in the origin of mass.
Category: Nuclear and Atomic Physics

The Bragg Law with Radiative Corrections

Authors: Miroslav Pardy
Comments: 10 Pages. Original article

The one-loop radiative corrections to the photon propagator, called vacuum polarization, can be represented by the Feynman diagram of the second order. The physical meaning of this diagram is the virtual proces, where photon can exist in the intermediate state with an electron and a positron being the virtual particles. The photon propagation function based on such process is determined in the framework of he Schwinger source QED methods. Then, the modication of the Brag equation is derived.
Category: Condensed Matter

A Thermodynamic Nature of Vacuum Energy

Authors: Mohamed Mekouar
Comments: 16 Pages.

We propose a thermodynamic model of dark energy in which the observed accelerated expansion of the universe arises as a consequence of the underlying microscopic degrees of freedom within spacetime. In this framework, spacetime is not fundamental but emergent from discrete entangled nodes, and the cosmological volume grows as the number ofentangled branches increases. Furthermore, we revisit black hole entropy via the ER=EPRconjecture, showing that the Bekenstein-Hawking entropy can be viewed as a collectivecontribution from Planck-scale entangled wormholes. This work suggests that dark energy is not a fundamental field but an emergent thermodynamic phenomenon rooted in the quantum structure of spacetime.
Category: Relativity and Cosmology

The Effects of Traffic Congestion Among University Students in Dhaka

Authors: Sadman Sakib, Jannatul Adan Adreeta, Niloy Paul, Md. Hasibul Islam, Md. Ashif Faihad Shuvo Bhuiyan
Comments: 4 Pages.

Dhaka, the capital city of Bangladesh, faces severe traffic congestion due to rapid urbanization, poor infrastructure and limited transportation planning, which significantly affects university students who commute daily. This study aims to explore how traffic congestion impacts the quality of life for university students in Dhaka by assessing its effects on their academic performance, mental and physical health, and overall daily routines. A survey was done with 82 students from different universities in Dhaka. Most students use public transport, and many said that congestion made them late, tired and less focused in class. The results showed that students who face traffic congestion more often reported more difficulty in academic and personal lives. Public transport users were affected the most. The study found a clear correlation between frequent traffic congestion and impact on the quality of life. The study highlights the need for better transportation, flexible class schedules and student-friendly city planning to help reduce the impact.
Category: Social Science

A Geometric Interpretation of Lorentz Length Contraction Using an Inscribed Triangle in a Circle

Authors: Mikheili Mindiashvili
Comments: 6 Pages.

This paper focuses not on deriving the Lorentz length contraction from first principles, but on providing a geometric visualization of this well-known relativistic phenomenon. The aim is to offer an intuitive and accessible interpretation through a simple construction: a right triangle inscribed in a circle. In this model, the observed contraction of a moving rod’s length as a function of velocity is illustrated geometrically. While the Lorentz contraction is formally derived via Lorentz transformations, the approach presented here serves as a complementary visual tool that may be particularly useful for educational purposes.
Category: Relativity and Cosmology

Non Inflationary Origin and Physical Nature of the Cosmological Space

Authors: Ramón Isasi
Comments: 18 Pages. Principally in the title was substituted the prefix non for not. Other minor errors were corrected too.

In the present manuscript, we consider the origin of the cosmological space, and the Cosmological Constant as a consequence of the annihilation of the matter - antimatter at the very beginning of the big bang. Since the cosmological expansion creates the space, the cosmological vacuum is considered as a very hegemonic entity which is the locus where all the objects create the events. In our model, non inflationary N units of masses in conjunct are required to produce an equilibrium between the gravitational phenomena of the matter in bulk and each coulombic interaction between protons and electrons within the nuclear and atomic contour in all astrophysical (e.g. stars) or cosmological entities (e.g. galaxies). The "dark matter" is considered to be formed by highly excited H and HeI Rydberg’s atoms in equilibrium with the CMB radiation and the vacuum dynamical density is considered as "dark energy".
Category: Relativity and Cosmology

Horizons in the Tridimensional Spherical Natario Warp Drive Using the Adm-MTW-Alcubierre Formalism with Constant Speeds Over the X-Axis

Authors: Fernando Loup
Comments: 81 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The Natario warp drive appeared for the first time in 2001.Although the idea of the warp dive as a spacetime distortion 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 drivespacetime.Natario defined a warp drive vector for constant speeds in Polar Coordinates but remember that a real warp drive must be defined in a tridimensional spacetime because a real spaceship is a tridimensional object inserted inside a tridimensional warp bubble that must be defined in real tridimensional coordinates. In this work we present the new warp drive vector in tridimensional3D Spherical Coordinates for constant speeds.One the major drawbacks concerning warp drives is the problem of the Horizons(causally disconnected portions of spacetime) in which an observer in the center of the bubble cannot signal nor control thefront part of the bubble.The behavior of a photon sent to the front of the warp bubble in the case of a Natario warp drive with constant velocity and a lapse function is also one of the main purposes of this work.We present the behavior of a photon sent to the front of the bubble in the Natario warp drive in the 1+1 and 3+1 spacetimes with and without the lapse function using quadraticforms and the null-like geodesics $ds^2=0$ of General Relativity and the ADM(Arnowitt-Dresner-Misner) formalism equations with the approach of MTW(Misner-Thorne-Wheeler) and Alcubierre.
Category: Relativity and Cosmology

Destruction of Viral Capsids by means of Specific Violet Radiation

Authors: Fran De Aquino
Comments: 2 Pages.

I show here that several types of Viral Capsids can be easily destructed by means of a specific violet radiation. This possibility is extremely advantageous from the technical viewpoint, because can be very efficient to destruct viral capsids for example, inside hospitals (hospital disinfection), at home, inside buildings, etc.
Category: Physics of Biology

Schematic Apparatus for Detecting the Shrinkage of Matter

Authors: Azor Romão da Mota Filho
Comments: 3 Pages.

This device is based in the SMTwVSL (Shrinking Matter Theory with Variable Speed of Light)(1). This is an answer to the most challenging question that can be asked about a theory, which is: How can we test this theory? In this case, we can ask: How may one test if matter shrinks or not?How can one test whether matter shrinks or not?The device for detecting matter shrinkage must be based on interferometry technology.The arrangement of the apparatus is similar to the old "Michelson-Morley experiment", but the mirrors are replaced by optical fibers with another beam splitter to join the two beams from the first beam splitter. The introduction of new technologies in the production of the coherent laser beam, in the phase and polarization control and in the photodetector is essential for the proper functioning of the equipment. A room with strict temperature control is required.The large difference in the length of the two optical fiber results in a build-up of photons inside the larger optical fiber. The shrinking of the optical fiber and wavelength at different rates, combined with the increasing light speed, result in a decreasing in the accumulation of photons, changing the interference pattern in the output of the second beam splitter.
Category: Relativity and Cosmology

Skill in Backgammon: Cubeful vs Cubeless

Authors: Tilemachos Zoidis
Comments: 13 Pages. CC BY

Does the doubling cube make backgammon more skillful? And is the answer the same in both money and match play? This paper presents GNUbg rollouts between unequally skilled players, which show that use of the doubling cube does not favor the better player in either case.
Category: General Mathematics

Explicit Bounds on Gaps Between Consecutive Terms in an Addition Chain

Authors: Theophilus Agama
Comments: 13 Pages.

We develop explicit bounds for the gap between consecutive terms in an addition chain leading to a fixed target 2^m<n<2^{m+1}.
Category: Number Theory

Comprehensive Paradigm for a Non-expanding Universe and the Unification of Refractive Index, Plasma Energy and Gravity

Authors: Aarne Hall Reid
Comments: 28 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

In this paper, I propose an alternative explanation for the Hubble constant [5] based on the refractive index [35] of intergalactic and intragalactic space. Space is anything but empty. I explore how varying refractive indices affected by intergalactic plasma, intrinsic galactic properties, and gravitational lensing [17] influence light propagation and observed redshift. By analyzing galaxy-specific refractive indices and calculating the Hubble constant [5] accordingly, I present a model that aligns more consistently with observations without relying solely on cosmic expansion. This approach offers a new pathway to understanding cosmic distances and addresses discrepancies in current cosmological data. Additionally, because at the time of Einstein’s General Relativity, plasma and electromagnetic effects on gravity were not evident, I also propose other scientific works to help bridge the gap between a totally gravity driven universe and suggest a hybrid version that includes research by Donald Scott that highlights features of a plasma driven universe working in concert with gravity. Along with a simulation by Pratt and Snell for how to incorporate Einstein’s field equations into a more cohesive framework with a plasma and gravity driven universe eliminating the need for dark matter. Equally important was to make this study Available to a wider audience by incorporating an extensive definitions appendix.
Category: Astrophysics

Emergence of Space-Time Physics from Quantum Computing Formalism

Authors: Lucian M. Ionescu
Comments: 26 Pages. Invited presentation at the XVI International Workshop on Lie Theory and Applications to Physics, Varna, Bulgaria, June 16-22, 2025.

At quantum level, relativistic time emerges from quantum phase. The Kahler structure in Gauge Theory is adequate for implementing an "Einstein-Feynman relativistic proper time", replacing the Space-Time paradigm for classical/quantum relativistic Physics. A preliminary investigation of how to relate Hodge structure as a model for periods of vibration (energy spectrum), in relation to the above interpretation of the quantum phase, will be provided in terms of algebraic integrals called periods. The Algebraic-Geometry model proposed for the implementation is that of Belyi pairs with associated dessins d’enfant, interpreted as Einstein-Feynman Graphs (to include the idea of proper time via quantum phase). An overarching goal is to relate "Classical" and "Quantum Physics" via Hilbertization, Hodgeification and Wilsonization, to be technically explained in an upcoming article, expanding this presentation.
Category: Quantum Physics

Time and Possibilities in Quantum Mechanics (Poster)

Authors: Armin Nikkhah Shirazi
Comments: 1 Page. Presented at the TIQT 2025 the 5th annual conference on time in quantum theory in Genoa, Italy June 2025

If we start with Minkowski Spacetime and take the global limit c → 0 seriously, it yields a spacetime which is utterly unfamiliar to our intuitions, yet consistent and intelligible. In this spacetime, motion in space is impossible and a novel coordinate transformation I callthe time-Galilean transformation describes aging without motion. I argue that this transformation fits the role of unitary time evolution in quantum mechanics because a) quantum states can always be decomposed in terms of a superposition of stationary states (energy eigenstates), and b) quantum motion is fundamentally different from classical motion. I take this as evidencefor a modal distinction between the classical and quantum worlds. I concretize this idea with the introduction of what I call the Heisenberg Interpretation, which interprets quantum states as a certain kind of pure physical possibility. The interpretation makes novel predictionswith respect to the interface between quantum theory and Einstein’s general relativity arising from the disinction between possibilities and actualities in spacetime.*Please note*: during the Conference, I found out that what I called the time-Galilean transformations had been previously discovered and is known as the Carrollian transformations. I left the poster unchanged because I wanted it to be a record of what conference participants saw.
Category: Quantum Physics

If Asteroid 2024YR4 hits the Moon, Will it be Visible from the Earth?

Authors: David W. Chapman
Comments: 6 Pages.

2024YR4 is an asteroid with an estimated diameter of 53 to 67 meters that is classified as an Apollo-type (Earth-crossing) near-Earth object. As of April 2025, it is estimated to have a 4% chance of impacting the Moon on 22 December 2032 at 15:19 UTC (Universal Coordinated Time). While it is likely that the impact point will be visible to an observer on the night side of the Earth, it is not clear whether the event will be visible to the naked eye. This paper describes what is currently known about Asteroid 2024YR4, and estimates the size of the impact fireball. The estimated energy of impact is 6.8 Megatons. The conclusion is that the impact will produce a luminous cloud for a few seconds, and that this should be visible to the naked eye.
Category: Astrophysics

Double Stochastic Quantization:non Perturbative Approach to Stochastic Quantization F_d ^2n , N ≥ 2, D ≥ 4 Model Eucledean Quantum Field Theory

Authors: Jaykov Foukzon
Comments: 154 Pages.

In this paper, we show how the finite formulation of quantum field theory based on Langevin equations can be generalized to the case of nonrenormalizable theories.The 5th-time stochastic-quantization approach to field theory proposed by Parisi and Wu, is put in a path-integral form in [6]. The procedure of taking the limit τ→∞ is analyzed and based on new grounds through the introduction of thevacuum-vacuum generating functional. In this paper non perturbative aprouch related to Parisi and Wu stochastic-quantization of the λϕ_{d}²u207f,n≥2,d≥4 model quantum field theory is considered.
Category: Mathematical Physics

A Spacetime Density Formulation of General Relativity: Reformulating Gravitational Dynamics Through Variable Spacetime Density

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

We present a reformulation of general relativity based on variable spacetime density, where massive objects create regions of elevated spacetime density and gravitational attraction emerges from matter’s tendency to move toward these high-density regions. We provide explicit mathematical derivations showing how this formulation reproduces Einstein’s field equations, derive specific predictions for classical tests of general relativity, and analyze the constraints on coupling parameters. The approach offers new perspectives on quantum gravity while maintaining full consistency with established gravitational phenomena. We identify specific observational signatures that could distinguish this formulation from standard general relativity and discuss fundamental limitations of the approach.
Category: Relativity and Cosmology

Suppression of Quantum Vacuum Energy Modes by Cosmological Boundary Conditions: a Numerical Coincidence with Dark Energy Density and Its Evolution

Authors: Iker Padilla Munoz
Comments: 10 Pages.

We show that when standard quantum vacuum fluctuations are subjected to boundary conditions imposed by a finite causal universe, specifically the region accessible since the time of recombination, bounded by the distance to the cosmic microwave back ground (CMB) at ∼45.7 billion light-years (∼8.65 × 1026 m) and assuming a discretized space structure at the Planck length scale (∼1.616 × 10−35 m), the resulting suppression of vacuum modes leads to an effective energy deficit. This deficit closely matches the observed dark energy density in the present (∼5.3 × 10−10 J/m3) and the evolution in the past for different redshifts, without introducing any free parameters or exotic new physics. The calculation builds on established physical principles such as the Casimir effect and relativistic causality. Although this article does not aim to explain dark energy, the observed numericalcoincidence suggests a possible connection between suppressed quantum vacuum fluctuations and dark-energy density.
Category: Astrophysics

Relative Motion from Coordinate Transformation Approach to Gravity Field

Authors: Tomasz Kobierzycki
Comments: 17 Pages.

In this paper I will explore a way to create a gravity like equations just from coordinate transformations between systems that will be a vector fields. Those vector fields will represent motion of fields, from their relative transformation of their motion I will create metric and a field equation that connects motion with energy. Will add quantum like effects in last part of this paper that will connect probability with spacetime interval. It will be done by using complex spacetime. I do not present solutions to those equations only mathematical model and physical interpretation.
Category: Quantum Gravity and String Theory

In-Out Ontology: A Directional Framework for Cosmic Emergence and Quantum Reality

Authors: Kyoung-il Ko
Comments: 16 Pages.

This paper introduces and formalizes In-Out Ontology (IOO) as a foundational metaphysical framework for understanding emergence, quantum reality, and consciousness. Centered on the dynamics of In-Out Indistincts (IOIs) — ontological primitives held in a balanced superposition of inward and outward directional modes — IOO reinterprets quantum phenomena, spacetime, and cognition through a generative, relational lens. We construct the formal architecture of In-Out Entanglement (IOE) and define IOE field as the directional interaction field responsible for dimensional/structural emergence. Euler’s identity is reframed as an ontological archetype of IOIs, while the general wave function Ψ expresses IOIs in contextual entanglement. The global IOE field since cosmic emergence is proposed as the ontological source of gravitational coherence. IOO further offers a reinterpretation of decoherence, affective valence, and qualia as outcomes of recursive directional differentiation. Integrating recent developments in quantum foundations and cognitive science, IOO proposes an ontological ground that reframes physical law, interpretive models of quantum mechanics (QM), and the architecture of consciousness. The paper concludes by suggesting new directions for cosmology, cognition, and complexity science rooted in the in-out dynamic.
Category: Quantum Physics

De Broglie Waves in Gravity

Authors: David L. Berkahn, James M. Chappell, Derek Abbott
Comments: 5 Pages.

The de Broglie wave hypothesis introduced the concept of wave-particle du-ality and led to the development of wave mechanics. We show from firstprinciples, how the de Broglie wave will be modified by the presence of agravitational potential. We find a relationship between de Broglie waves andthe gravitational potential. A straightforward experiment is described toaccurately verify this relationships.
Category: Quantum Gravity and String Theory

e/P Mass Ratio and F.S.C. Calculation from the Hydrogen Ground State

Authors: Eric Louis Beaubien
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific references)

The fine structure constant and electron/proton mass ratio can be reasonably derived from the hydrogen ground state wherein mass and inertia test against electric charge in the most fundamental configuration. The contention is that because these numbers are ‘pure’ numbers, we can dispense with physics altogether and solve the problem of their numeric quantity from a purely logical-probabilistic-mathematical perspective.
Category: Mathematical Physics

SocialArray: Many-Particle Simulation for Array-Based Social Interaction

Authors: Pengn Wang, Xiaoda Wang, Peter Luh, Neal Olderman, Xuesong Lu, Christian Wilkie
Comments: 26 Pages.

This article introduces a simulation tool to study a complex multi-agent system in social context. The individual-level model is extended based on self-propelled Brownian particle and social force model, and it mainly describes how agents/particles interact with each other, and also with surrounding facilities including obstructions and passageways. Most importantly, we introduce a set of arrays to define social relationship of agents/particles in a quantitative manner. Opinion dynamics is integrated with force-based interaction to study complex social phenomena including path-selection activities, social groups and herding effect. Very interestingly, the interaction of agents/particles does not only exist at physics-level, but also at consciousness and unconsciousness level by integrating advanced social-psychological studies in our modeling framework.
Category: Economics and Finance

Quantum Computer

Authors: Gerard van der Ham
Comments: 4 Pages. (Note by viXra Admin: Please cite and list relevant scientific references)

If the idea of the possibility to realize quantum computers is based on the conclusions drawn from Bell experiments, then we are seriously mistaken. This is because entanglement in Bell experiments is not what it looks like and because of that, probabilities represented by the Bloch sphere, occurring in Bell experiments, are wrongly ascribed to qubits.
Category: Quantum Physics

The Pharmaceutical Industry in Nigeria: Drug Accessibility, Affordability and Competitiveness in the Economy.

Authors: Adeyemi Olayisade
Comments: 13 Pages.

The study focuses on reviewing factors that influence accessibility, affordability, efficiency in Nigeria’s pharmaceutical industry and its impact on healthcare delivery. Despite the Nigeria’s increasing population coupled with a high disease burden, it imports most of its drugs from India and China since its own pharmaceutical sector is not self-sufficient. The study noted certain difficulties such as poor infrastructure, inflation, exchange rate volatility, poverty and weak regulatory structure in the health sector made it tough for people to get access and afford basic medicines. The study deployed a semi-log regression to see how accessibility and affordability of medicines interact with the capacity of pharmaceutical sector in the Nigerian economy. Findings from the study revealed significant interrelatedness between level of access to essential medicines and the pharmaceutical industry contribution to GDP; other variables, such as costs of Malaria treatments, minimum wage, and inflation, showed weak or no statistical impact on the response variable. In conclusion, the study suggests that the federal government should discontinue the NHIS program to allow the private sector takeover this programme, this can free up resource and strengthen local pharmaceutical production, it also recommends applying regulatory measures to ensure medications are accessible and affordable for better health outcomes and a stronger economy.Keywords: National Health Insurance Scheme (NHIS), Accessibility, Affordability, Competitiveness.
Category: Economics and Finance

Individuation of Doctoring as the Basic Concept of Public Health and a Medical Science

Authors: Kutlumuratov Atabek Bekchanovich
Comments: 58 Pages. typos corrected & text improved.

The seventh treatise of the cycle "Ontological and epistemological bases of medicine and physiology" (finishing). It is marked that the medical science of the end 19 and the beginnings of 20th centuries began to depart from the concept of the individuation of the doctoring process, which was considered almost officially a basis of a clinical paradigm throughout 23 centuries. To the middle of 20th century this conception has been justified by rapid development of biology and by requirement to use of its achievements in medicine. Nowadays we can observe excessive differentiation of clinical medicine (which is the doctoring science). The individuation principle implicitly underlies any national systems of public health services, and it forms a philosophical basis of a medical science. This principle expresses specificity of physician’s thinking which depends a little from the paradigm declared by representatives of official medicine. This principle lays in basis of the differentiation of public health (as the system of physicians' activities), and in basis of differentiation of medical science (as the clinical disciplines' system). The public health decides problems of society's health for interests of the society by regulation of efforts of doctors in limits of the different profiles. And the public health promotes tendency of any doctor in order to professionally promote interests of health of each patient in each clinical case. Therefore and physician practice of any profile is effective if it supports the doctor's aspiration as much as possible to keep and strengthen health of each patient (if he/she is healthy), and to recover him/her health (if he/she is sick). The medical science is effective so far as it follows this principle within the limits of each of medical disciplines. Thus the doctor reaches best efficiency of doctoring only on the basis of a clinical paradigm, and this efficiency does not depend directly on a biomedical paradigm which is declared by official medicine as basic one in the doctoring science.Keywords: an individuation of doctoring; a clinical paradigm; public health; a medical science; public health services profile; differentiation of medical science.
Category: General Science and Philosophy

Essays on Modelling Public-Private-Partnerships (PPP) for Indian Emergency Medical Services

Authors: SenthilKumar Anantharaman
Comments: 130 Pages. IIm Indore Thesis

Medical emergencies occur anywhere, at any time, in any country irrespective of whether it is a developed, developing or an underdeveloped country. These emergencies occur by the hour, consuming a lot of resources and sometimes, without even achieving the desired results, i.e., to save lives. Medical emergencies have been around since the start of the human civilization, however, they gained recognition as a specialty only around 30 years ago (Chung, 2001). An emergency medical system’s goal should be to provide universal and integrative emergency care right from the time it receives information from an emergency user (Dykstra, E. H, 1997). Further, in a country like India, the seventh largest country, and with the second highest population in the world (David, S. S., & Vasnaik, M, 2007) and high income disparity, the implementation and context of the emergency medical system should be in a way to increase health equity and not worsen the current health disparities (David, S. S., & Vasnaik, M, 2007). This challenge faced by India and similar developing nations can be attended to by promoting systematic development of an evidence-based emergency medical system that is more costeffective than those in developed countries like the USA, Canada and certain European countries where there is lesser income disparity. To design an effective emergency medical system, there is need to address questions such as how it would integrate with the current health-care infrastructure, local communities as well as their values, and the financial resources that would be needed to augment the services step by step (Gupta, M. Das, & Rani, M. 2004). (Truncated by viXra Admin)
Category: Economics and Finance

Fermat's Conjecture Simple Answer to a Simple Question

Authors: Giovanni Di Savino
Comments: 1 Page. (Note by viXra Admin: Please cite and list scientific references)

Fermat, studying Book II of Diophantus' Arithmetica, in the pages dedicated to the problems and observations around the Pythagorean Theorem, in a marginal note of the book, reports: "It is impossible to write a cube as the sum of two cubes or a fourth power as the sum of two fourth powers or, in general, no number that is a power greater than two can be written as the sum of two powers of the same value". This conjecture, known for many years as Fermat's last theorem, became a theorem because Prof. Andrew Wiles demonstrated that c^n≥3 ≠ a^n≥3 + b^n≥3
Category: Number Theory

Privacy, Ethics, Transparency, and Accountability in AI Systems for Wearable Devices

Authors: Petar Radanliev
Comments: 34 Pages.

The integration of artificial intelligence (AI) and machine learning (ML) into wearable sensor technologies has substantially advanced health data science, enabling continuous monitoring, personalised interventions, and predictive analytics. However, the fast advancement of these technologies has raised critical ethical and regulatory concerns, particularly around data privacy, algorithmic bias, informed consent, and the opacity of automated decision-making. This study undertakes a systematic examination of these challenges, highlighting the risks posed by unregulated data aggregation, biased model training, and inadequate transparency in AI-powered health applications. Through an analysis of current privacy frameworks and empirical assessment of publicly available datasets, the study identifies significant disparities in model performance across demographic groups and exposes vulnerabilities in both technical design and ethical governance. To address these issues, this article introduces a data-driven methodological framework that embeds transparency, accountability, and regulatory alignment across all stages of AI development. The framework operationalises ethical principles through concrete mechanisms, including explainable AI, bias mitigation techniques, and consent-aware data processing pipelines, while aligning with legal standards such as the GDPR, the UK Data Protection Act, and the EU AI Act. By incorporating transparency as a structural and procedural requirement, the framework presented in this article offers a replicable model for the responsible development of AI systems in wearable healthcare. In doing so, the study advocates for a regulatory paradigm that balances technological innovation with the protection of individual rights, fostering fair, secure, and trustworthy AI-driven health monitoring.
Category: Artificial Intelligence

PEOCHAIN: Proof of Synergy Blockchain

Authors: Daniil Krizhanovskyi
Comments: 37 Pages.

PeoChain introduces a revolutionary blockchain architecture that mathematically solves the blockchain trilemma through the innovative Proof of Synergy (PoSyg) consensus mechanism. This paper presents a comprehensive solution that achieves scalability exceeding 100,000 transactions per second, maintains true decentralization with over 10,000 validators, and provides cryptographic security guarantees through formal verification. The architecture incorporates Subnet Validator Networks for parallel transaction processing, Dynamic Contribution Scoring for Sybil resistance, and algorithmic price stabilization mechanisms for economic stability. Mathematical analysis demonstrates Nash equilibrium properties of the consensus mechanism, while empirical evaluation on a global testnet validates theoretical predictions. PeoChain's integration of mobile financial services at the protocol level addresses the financial inclusion needs of 1.4 billion unbanked individuals globally. The system maintains transaction costs below $0.04 with subsecond finality, enabling micropayments and cross-border remittances at unprecedented efficiency. Formal verification using TLA+ specifications provides mathematical proofs of safety and liveness properties under Byzantine failure conditions.
Category: Data Structures and Algorithms

The Big Bang Theory and the Creation of Matter

Authors: David Johnson
Comments: 14 Pages. Some minor changes plus Reference details (Note by viXra Admin: the citation of references should be AIP or APA style with reference list at the end of the article)

The prevailing explanation for the creation and development of the Universe is the Big Bang Theory, a violent expansion of extremely dense compressed matter or energy that occurred approximately 13.8 billion years ago. The conventional Science view is quark and electron creation took place in the first millionth of a second post-bang, although no feasible mechanisms are suggested for their almost instantaneous creation. This paper reviews the claimed timings, suggests a modified post-bang timeline, and explores some processes by which quarks, nucleons and electrons may have come into being and built into atomic nuclei and matter. It also identifies the possible source and nature of Dark Matter, Dark Energy and Black Holes.14
Category: Classical Physics

Emergent Conservation Laws from Internal Geometry: A Noetherian Reinterpretation in the 0-Sphere Model

Authors: Satoshi Hanamura
Comments: 16 Pages.

This paper introduces a novel geometric framework for quantum mechanics—the 0-Sphere Model—which reinterprets superposition, spin quantization, and energy conservation as consequences of internal deterministic motion constrained by closed time-phase geometry. Unlike standard approaches that derive conservation laws from externally imposed symmetries via Noether’s theorem, the model proposes that energy, spin, and charge conservation emerge naturally from internal oscillatory structure. This conceptual inversion, termed "Noetherian Reinterpretation," challenges the assumption that symmetries are fundamental, suggesting instead that they may arise from intrinsic phase coherence. The model also provides a deterministic account of Zitterbewegung, explains the electron's rest energy as a form of thermal potential energy, and predicts experimentally testable features such as subluminal Zitterbewegung velocity (~0.04047c). By bridging relativistic and quantum dynamics through internal geometry, the 0-Sphere framework offers a unified and realist reinterpretation of fundamental physical laws.
Category: Quantum Physics

A Universe from Apparent to Real

Authors: Dino Bruniera
Comments: English, pages 1-8 and Italian, pages 9-16

Light is composed of electromagnetic waves, which therefore need a medium to manifest themselves, so its speed can be isotropic only relative to the medium and not also relative to celestial objects, including the Earth, which move in the medium. Physicists have devised various experiments to demonstrate that the speed of light is not isotropic relative to the Earth, but without success. To justify this negative result, some physicists have hypothesized that material objects, as a function of their speed relative to the medium, undergo a time dilation and a length contraction, making the speed of light appear isotropic even if it is not, so that said isotropy would be only apparent. Instead, I have actually demonstrated, through the CMBR, that the speed of light is not isotropic relative to the Earth and, therefore, that this isotropy is only apparent. To explain what the medium is and how it works, I developed a theory that I called Space Quanta in Expansion, which then identified the medium with expanding space, and which explains how photons and material objects move in the medium. Among other things, it argues that the expansion of the Universe is not caused by two forces, one that makes material objects move away, which would be the so-called dark energy, and another that makes them move closer, which would be gravity, but is caused by a single force, the one that makes the space quanta expand and which could explain dark energy. Therefore gravity is an apparent force.
Category: Relativity and Cosmology

A Complete Thermodynamic Derivation of Planck's Radiation Law with Emergent Kirchhoff's Law: From Statistical Mechanics to Blackbody Radiation

Authors: R. I. M. Atwel
Comments: 12 Pages.

We present a comprehensive derivation of Planck's radiation law that explicitly derives Kirchhoff's law of thermal emission from thermodynamic equilibrium principles rather than postulating it [Boyer, 2018], [Gómez-Santos, 2019], [Marlan, 1993]. Our approach rigorously develops the statistical mechanics of electromagnetic field modes, derives the density of states from electromagnetic boundary conditions, and applies the canonical ensemble formalism with proper treatment of photon statistics [Pathria & Beale, 2011]. We demonstrate that Kirchhoff's law (ε(ν) = a(ν)) emerges as a necessary consequence of detailed balance in thermal equilibrium, while the Planck distribution follows from maximizing entropy in the canonical ensemble for a photon gas [Landau & Lifshitz, 1980]. The derivation explicitly addresses the role of energy quantization and connects to experimental observations of blackbody spectra [Fixsen, 2009]. This unified approach provides pedagogical clarity and demonstrates the deep connection between statistical mechanics, thermodynamics, and electromagnetic field theory [Reif, 1965]. This work constitutes a significant conceptual improvement over traditional approaches, including Planck's original derivation, by providing a first-principles derivation for Kirchhoff's law, a relationship previously accepted largely as an empirical postulate.
Category: Thermodynamics and Energy

Particles, Forces and the Early Universe

Authors: Risto Raitio
Comments: 20 Pages. Published in Nucl. Phys. B, 116990 (2025). doi: j.nuclphysb.2025.116990

This article reveals the unexpected result that three a priori distinct ideas--global supersymmetry of preons, Hartle-Hawking cosmology, and Chern-Simons quantum gravity--share common concepts that offer paths beyond the Standard Model. Differences from the MSSM are discussed.
Category: Quantum Gravity and String Theory

The Quantahedron: a Lattice-Based Framework for Unifying Quantum Mechanics and General Relativity Through Angular Geometry

Authors: John James
Comments: 29 Pages. © 2025 John James. Published also on Zenodo: https://zenodo.org/records/15706608

This paper introduces the Quantahedron—a 2D angular geometry whose symmetry and deviation encode mass, energy, and time. Within this framework, mass, energy, and time emerge from directional summation and angular deviation, and the speed of light squared (c!) is a geometric invariant embedded in null-diagonal propagation. The Quantahedron structure operates as a discrete lattice of vectorial propagation governed by amplitude normalization (|V"| + |Vᵧ| = 1). When V" = Vᵧ, mass vanishes, and propagation is light-like. Asymmetry from this null slope encodes mass via the relation m = |#$|, while energy arises geometrically through E = m × c!. By anchoring lattice units to known physical constants (e.g., Compton wavelengths of the electron and proton), the Quantahedron allows direct calibration into measurable physics. Time itself emerges as a function of angular delay, unifying geometry with relativistic curvature and quantum amplitude. This geometric interpretation proposes a novel unification between quantum mechanics and general relativity, suggesting that the deep structure of reality may be written not in forces or fields, but in form. E = mc! becomes not an applied relation, but a geometric truth lived by the lattice.
Category: Quantum Physics

Repositioning Mind and Matter in a Simulation Scenario

Authors: Genevieve Gorrell
Comments: 27 Pages.

The hypothesis that we are living in a simulation, whilst difficult to prove, offers some common sense inroads into practical lines of thinking. As long as mental phenomena are sidelined, mainstream understanding of reality is limited. In this paper, three models are presented that reposition mind and matter in a hypothetical structure of our simulation. Computer programming analogies are used to explore different aspects of our existential situation.
Category: General Science and Philosophy

An Improved Bound for the Counting Function F(m,r)

Authors: Theophilus Agama
Comments: 6 Pages.

Let us define the function F(m, r) as the number of integers n in the interval [2^m, 2^{m+1}) such that ι(n) ≤ floor(m + r), where r = c·m / log m for some constant c satisfying 0 larger than c smaller than log 2. Next, define α = c + log 2 − (1/4)(1 − o(1)). By applying the Chernoff inequality from probability theory and using ideas from De et al. (2025), we obtain the following improved upper bound: F(m, c·m / log m) ≤ exp[ α·m − (1 − ε)·(c·m·log log m) / log m ] for any small ε > 0 as m tends to infinity.
Category: Number Theory

On a Probabilistic Iterated Factor Method

Authors: Theophilus Agama
Comments: 5 Pages.

We introduce a probabilistic version of the iterated factor method developed in our previous work. Let n be drawn uniformly from the set {1, 2, ..., M}. Define s(n) = floor( sqrt(log base 2 of n) / log(log base 2 of n) ), and t(n) = sqrt(log(log n)), and let ku2099 = floor(n / 2) with respect to s, meaning a construction related to the s-th iterated factor. As N tends to infinity, with Zu2099 distributed normally with mean 0 and variance 1, and under the condition thatPr[ ν(ku2099) ≤ s and |Zu2099| ≤ t ] tends to 1,we show the inequality ι(2u207f − 1) ≤ n − 1 + log base 2 of n + C·sqrt( log base 2 of n / log log base 2 of n ) holds for some absolute constant C > 0. This result surpasses the O(log n / log log n) barrier that is guaranteed under the classical Brauer method (Brauer, 1939). It may thus be viewed as an introduction of probabilistic methods into the theory of addition chains.
Category: Statistics

A Bound for the Number of Addition Chains of Arbitrary Length

Authors: Theophilus Agama
Comments: 6 Pages.

Define the function F(m, β(m) − m) as the number of integers n in the interval [2^m, 2^{m+1}) such that l(n) ≤ β(m). By applying ideas from De Koninck et al. (2025), we obtain the following general upper bound: F(m, β(m) − m) ≤ exp[ (β(m) − m) · (2·log β(m) + (1 + ε)·2·log log m + O(1)) ] for any small ε > 0 as m tends to infinity. This result generalizes a recent bound proved in the work of De Koninck and collaborators.
Category: Number Theory

Generalized Probability Theory

Authors: Yibing Xiong
Comments: 84 Pages. (Note by viXra Admin: Please cite and list scientific references)

Disordered events can be divided into two types: disordered deterministic events - generalized events, disordered random events - random events - narrow events; Establishing probability axioms, boundary axioms, etc., proposing four important original works: probability method, boundary, subdivision probability, Xiong's sieve; Establish General Probability Theory. Using analytical methods to solve mathematical problems such as the prime number theorem, Riemann hypothesis, twin prime numbers, densest K-tuple prime numbers, K-tuple prime numbers, Goldbach's conjecture, Gaussian lattice points, etc.
Category: Number Theory

Does the Microworld Need Quantum Mechanics?

Authors: Anatoly V. Belyakov
Comments: 13 Pages. 3 figures

In a series of articles, the author explained some phenomena and calculated a number of parameters related to the microworld using the non-quantum methods of the geometrodynamics (introduced by J. A. Wheeler). The sum of the results gives reason to believe that, at least for some microphenomena, a physical theory based on images and analogies from the physical reality surrounding us is possible and should be developed. Thus, the nature of the electric charge has been revealed, its value and the proton/electron mass ratio have been calculated, the light quarks mass have been determined, etc. This publication gives a short survey of the obtained results.
Category: Classical Physics

The Durer Polyhedron and a Composite Three-dimensional Model of a Symmetrical Geometric Object

Authors: Andrey V. Voron
Comments: 14 Pages.

Two variants of the geometry of the Durer polyhedron, conventionally named as "traditional" and "alternative", are investigated. The geometric properties of both variants of polyhedra are revealed. According to the results of the field experiment, it was revealed that the "alternative" version of the polyhedron has the property of complementarity.
Category: Geometry

Spacetime and Matter as Emergent Phenomena: A Unified Field Theory

Authors: Andrey N. Smirnov
Comments: 44 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We propose a minimalist hypothesis in which the only fundamental entity is a real scalar field defined on four-dimensional Euclidean space (E4). An observer is modeled as a stable "cognitive tube"—a locally causal region of field projections onto a family of three-dimensional slices Sigma^3(l). From non-dynamical conditions of embodiment, local causality, stability, and unitarity, we derive:1.Emergent spacetime with a pseudo-Riemannian metric and Lorentz transformations as the only compatible symmetry group; 2.The Einstein field equations as a variational extremum of the cognitive action; 3.Quantum field theory and the Born rule as necessary conditions for cognitive reproducibility; 4.The minimal symmetry group U(1) x SU(2) x SU(3) and a cognitive Higgs mechanism. The model predicts the absence of a graviton and prohibits coherent superpositions of distinct spacetime metrics, providing clear falsifiability criteria: detection of a graviton or interference between distinct gravitational configurations would refute the hypothesis. The unified emergence of special relativity, general relativity, and Standard Model symmetries highlights the explanatory power of the approach and opens a path to experimental tests of the cognitive nature of physical laws.
Category: Relativity and Cosmology

A Unified Framework for Dark Matter: From the Quantum Substratum to Galactic Dynamics

Authors: Vakhtang Mchedlishvili
Comments: 8 Pages. 2 figures, 1 appendix with code.

The phenomenon of "dark matter," while a cornerstone of the standard cosmological model (ΛCDM), remains one of the most profound puzzles in modern physics due to the persistent null results in direct detection experiments. This paper presents an alternative paradigm where "dark matter" is not a new type of particle but rather an emergent gravitational effect arising from the dynamic response of the physical vacuum itself. We model the vacuum as a quantum substratum, described by a fundamental scalar field, Φ. We propose that this substratum is coupled to gravity, and its energy density is modified in the presence of baryonic matter. To test this hypothesis, we construct a mathematical model governed by a single, universal coupling constant, herein named the "Shota" constant (β_Sh), which dictates the strength of the interaction between the Φ-field and the gravitational potential of visible matter. The model is tested through numerical simulations on two astrophysically distinct galaxies: the dwarf, dark-matter-dominated UGC 128 and the massive spiral galaxy NGC 3198. The results demonstrate remarkable success. With a nearly identical value for the "Shota" constant, the model quantitatively reproduces the rotation curves of both galaxies. Crucially, it naturally explains the observed nonlinear relationship between baryonic mass and the "dark matter" effect, showing a much larger relative response in the low-acceleration regime of the dwarf galaxy. This provides a physical foundation for the empirical Baryonic Tully-Fisher Relation (BTFR). Our framework unifies the concepts of the "Quantum Substratum" and the "Gravitational Deficit Principle" into a single, predictive theory, offering a compelling new path toward resolving the dark matter puzzle without recourse to new particles.
Category: Astrophysics

The Linear Combination Implied by the Euclidean Algorithm Using a TI84-CE Program

Authors: Timothy Jones
Comments: 4 Pages. Added more complete TI84-CE program.

The Euclidean Algorithm finds the greatest common divisor (GCD) of two integers; it also gives a way to express the GCD as an integer linear combination of the two numbers. This latter feature is not easily done by hand. We present programs for the Euclidean Algorithm and give a fast and easy way to find this linear combination.
Category: Algebra

Quantized Curvature and the Collapse of Force Separation

Authors: Husbee Newaz Nuhad
Comments: 3 Pages.

This paper proposes a unifying theory of physics called "Quantized Curvature and the Collapse of Force Separation." It suggests that spacetime is not continuous but composed of discrete, quantized units of curvature. Tiny, indivisible packets of geometry. These units can twist or bend in specific amounts, generating all known forces. Unlike current theories, which treat gravity and quantum forces as separate, this model shows they are all different modes of the same underlying structure. The electromagnetic, weak, strong, and gravitational forces emerge from quantized curvature itself, leading to a single geometric origin for all interactions in the universe.
Category: Relativity and Cosmology

Solving Polynomial Equations with Fractional Sequences

Authors: Zhi Li, Hua Li
Comments: 18 Pages.

This paper reports a discovery that there exist the extended standard forms for polynomialequations, which are composed of three items, contains only one parameter and relates tointeger or fractional sequences. Using the parameter and the sequences, a series can beconstructed of the solution of the equations. If the series converges, it is a root of the equations. For the extended standard form is always possible for the equations of degree not more than five, this result provides an effective method for the solution of general polynomial equations under and including five degrees without the need of radicals calculating. This technique can also be extended to polynomial equations with two or more coefficients or parameters, which would be more complex or difficult and will be a big challenge if it be used to solve polynomial equations with higher degrees. At the same time, our discovery also provides a technique to produce an unlimited number of integer and/or fractional sequences, real or complex. This will enrich related researches.
Category: General Mathematics

A Unified Derivation of Physical Law from the Temporal Field τ(x)

Authors: Stefen Colalillo
Comments: 212 Pages.

This paper introduces a Master Equation; a unified physical framework derived from first principles, which reconceptualizes time as a dynamic quantized energetic field.In contrast to prevailing models that treat time as a passive coordinate, this theory positions time as the foundational driver of all physical behavior, shaping motion, gravity, entropy, quantum behavior, and cosmological structure through its gradients and phase coherence.The master equation governing this temporal field is a covariant Euler-Lagrange expression that gives rise to modified versions of Einstein’s field equations, Schrödinger’s equation, the second law of thermodynamics, and the Friedmann equations. This framework addresses major problems in modern physics, including quantum measurement, dark matter, dark energy, entropy, and the arrow of time; it reinterprets mass, charge, and spin as emergent τ-structures, and offers a unified temporal model for cosmic evolution. The universe’s birth is framed as a spontaneous symmetry break in τ; its eventual fate, a universal collapse to ∇τ = 0. Testable predictions include corrected galaxy rotation curves, CMB phase anisotropies, and decoherence signatures in interferometry. This framework presents a falsifiable, mathematically complete, and empirically grounded foundation for unifying gravitational, quantum, and thermodynamic behavior — anchored not in spacetime geometry, but in the energetic architecture of time itself.
Category: Quantum Gravity and String Theory

New Discoveries in Protons

Authors: Jianming Wang
Comments: 6 Pages.

Protons are composed of three valence quarks. What is the relationship between the three valence quarks? In particle physics, it is difficult to find the mass relationship of three valencequarks in protons because the mass of quarks is not accurate. However, by analyzing the experimental results of seaquest carried out by Fermilab in 2021, it is found that the upper quark and the lower quark have an accurate mass ratio (mu/md=0.707). The exact ratio of the upper quark mass to the lower quark mass (mu/md=0.707) is another way to study the quark mass in protons. The discussion on Higgs mechanism and vacuum condensation of QCD can be avoided. The uncertainty of quark mass is transformed into the exact ratio of quarks in the same system to study. By analyzing the exact ratio of the mass of upper quark to lower quark in proton (mu/md=0.707), it is found that there is a relation of mu²+ mu²= md² in proton. The sum of squares of up quark mass in protons is equal to the square of down quark mass. The basic content of quark law in baryons: except protons, all heavy quarks in other baryons will decay into up quark or down quark, and the sum of squares of up quark mass should be equal to the square of down quark mass. According to mu²+ mu²= md², it is deduced that there are three generations of protons in the universe. That explains why protons are stable. And analyze the reasons for the expansion of the universe.
Category: High Energy Particle Physics

Is AI Capable of Curiosity?

Authors: Alexander Rozenkevich
Comments: 11 Pages.

This paper proposes a new metric for evaluating the intelligence level of AI, based on the ratio of current cognitive abilities to a hypothetical maximum. The concept of a response coefficient is introduced as a measure of AI's sensitivity to external intellectual pressure—information, tasks, and hypotheses coming from outside. The formalized expression of this coefficient is linked to environmental parameters and the frequency of new intellectual stimuli and loads. The hypothesis is discussed that in the future, external intellectual pressure, rather than technological development, will become the main driver of AI evolution.
Category: Artificial Intelligence

Is AI Capable of Curiosity? (in Russian)

Authors: Alexander Rozenkevich
Comments: 13 Pages.

This paper proposes a new metric for evaluating the intelligence level of AI, based on the ratio of current cognitive abilities to a hypothetical maximum. The concept of a response coefficient is introduced as a measure of AI's sensitivity to external intellectual pressure—information, tasks, and hypotheses coming from outside. The formalized expression of this coefficient is linked to environmental parameters and the frequency of new intellectual stimuli and loads. The hypothesis is discussed that in the future, external intellectual pressure, rather than technological development, will become the main driver of AI evolution.
Category: Artificial Intelligence

One Single Metric Model's Unifying Perspective on Four Issues with Galactic Dynamics: B-TF Relation, Rotation Curves, Spirals and SMBH-Growth.

Authors: E. P. J. de Haas
Comments: 14 Pages.

In this paper, we intend to replace four mysteries of galactic dynamics with one. This one mystery is introduced as a postulate: the constant Lagrangian metric as a space-time background for galactic dynamics. The four mysteries of galactic dynamics are the B-TF relation, the rotation curves, the spiral structure and SMBH-growth. Why the galactic space-time background behaves like a giant disk with directionally synchronized metronomes on it (the constant Lagrangian metric) remains an open question.
Category: Astrophysics

A Note on Primes in an Addition Chain

Authors: Theophilus Agama
Comments: 9 Pages. (Note by viXra Admin: Please don't use LaTeX codes in the abstract!)

[This note provides a quantitative bound for the number of primes in an addition chain]
Category: Number Theory

Sampling from the Maxwell-Juttner Distribution

Authors: Luc Devroye
Comments: 10 Pages.

The Maxwell-Ju ̈ttner distribution pertains to the speeds of particles in a hypothetical gas of relativistic particles. We consider the generalized form of this law in Rd, and show how to generate a random variate from this distribution. In particular, one can sample the radius of the d-dimensional random vector in expected time uniformly bounded over all dimensions d and shape parameters (temperatures).
Category: Statistics

General Fluid Field Theory

Authors: Robert J. Mapes
Comments: 22 Pages. A proposed unified framework for physics and proof of Dirac LNH with a numerically correct gravitational constant calculated from the density of space, the speed of light and pi.

A general fluid medium governed by Navier—Stokes equations embeds electromagnetism and yields gravity as emergent pressure. This resolves the two-body problem and redefines gravitational and cosmological constants via Dirac’s Large Number Hypothesis. A hydrodynamic quantum theory also addresses the measurement problem. This unifies all forces through the medium’s density sources.
Category: Quantum Gravity and String Theory

An Icelandic-English Dictionary and The Graphical Law

Authors: Anindya Kumar Biswas
Comments: 21 Pages. (Note by ai.viXra.org Admin: Further repetition may not be accepted)

We study An Icelandic-English Dictionary, the Second Edition, brought out by the Oxford University Press, way back in the year 1957.We draw the natural logarithm of the number of head words, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We find that the head words underlie a magnetisation curve. The agnetisation curve i.e. the graph of the reduced magnetisation vs the reduced temperature is the exact Onsager solution of the two dimensional Ising model in the the absence of external magnetic field.
Category: Condensed Matter

A Kantian System of Knowledge in SI Units

Authors: Bernard Riley
Comments: 12 Pages.

In a Kantian approach to cognition, the magnitudes in SI units of physical constants and other significant physical quantities have been judged according to mathematical rules conceived by this cogniser. A system of knowledge has been constructed, in which the magnitudes of particularly significant masses, lengths and times, on the smallest to the largest scales, assume a consistent intelligible form in terms of the rules.
Category: History and Philosophy of Physics

New Research on High-Frequency Circuits and Electromagnetic Radiation

Authors: Hongyuan Ye
Comments: 6 Pages. (Note by ai.viXra.org Admin: Please cite and list scientific references)

In this paper, capacitors are divided into radiant capacitors and energy storage capacitors, and inductors are divided into radiation inductors and energy storage inductors. The distributed capacitance and distributed inductance that exist in high-frequency circuits are mainly distributed radiant capacitance and distributed radiated inductance. Furthermore, it is pointed out that the capacitors and inductors in LC resonance must be energy storage capacitors and energy storage inductors. Based on these new concepts, it is revealed that the existing Transmission line equations are not valid, and the new Transmission line equations are proposed. This paper provides a new theoretical basis for electromagnetic compatibility, transmission line theory and antenna design.
Category: Classical Physics

An Investigation into the Discriminant of Quadratic Equations and Its Geometric Meaning

Authors: Yingxin Dai
Comments: 5 Pages.

This paper explores the role of the discriminant in solving quadratic equations. Using the quadratic formula, we can determine whether a quadratic equation has real roots, how many it has, and whether those roots are rational or irrational. Several examples and graphs are provided to illustrate how the value of the discriminant affects the number of real roots and the position of the parabola on the coordinate plane. Real-life applications, such as motion under gravity and the intersection of lines and circles, are also discussed to enhance understanding.
Category: Algebra

Curvature Induced by Rotational Asymmetries in Spatial Energy Density

Authors: Eunseob Kim
Comments: 18 Pages. (Note by viXra Admin: Abstract should be labeled as such, most listed references are not cited; please submit article written with AI assistance to ai.viXra.org)

We propose an alternative formulation in which gravitational curvature, galactic rotation, and frame-dragging arise from spatial energy density gradients. In this model, mass and rotation redistribute background energy, creating structured gradients that act as physical sources of curvature.
Category: Astrophysics

Displacement of Water Molecules from Receptor-Ligand Interface During Binding Interaction

Authors: Ikechukwu Iloh Udema
Comments: 12 Pages. (Note by viXra Admin: Please remove line numbers)

In almost all studies on the role of solvent in the binding of the ligand to a receptor, the focus had always been on the thermodynamic stability of the complex formed. Hardly any attempt has been made to quantify the number of solvent molecules released in the course of ligand (e.g., substrate, pathogen, drug, etc.) and receptor (enzymes, cell membrane, antibodies, etc.) binding interaction in recent times. The goal of the study was to determine how to calculate the amount of solvent molecules displaced from reactant species using nonequilibrium binding energy (NEBE), since desolvation is a prerequisite for the development of a stable complex. Deriving relevant energy equations, such as the one for calculating the number of molecules of desolvation, was one of the objectives. The methods are solely theoretical, experimental (Bernfeld), and computational. According to the study's findings, the water of hydration ranged from 338 to 400 water molecules, which corresponded to substrate (gelatinized potato starch) concentrations between 5 and 10 g/L. The translational entropy gains, the corresponding thermodynamic component, ranged from 91.4 to 133.1 J/mol K. The comparable values were 526.316 and 216.129 J/mol K, respectively, at the highest hydrolysis velocity. In conclusion, the equation of NEBE can be explored for the computation of water of desolvation in support of the observation that desolvation is part of the driving forces that propel ligand-receptor binding. Further thermodynamic characterization of ligand-receptor binding on the basis of desolvation needs to be done at different temperatures in the future.
Category: Chemistry

Spacetime as an Emergent Cognitive Structure: A Hypothesis of Local Causality

Authors: Andrey N. Smirnov
Comments: 33 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

A hypothesis of local causality is proposed, according to which the causal structure is formed independently within each inertial frame of reference (IFR), and the notion of an event is defined only within the bounds of the observer's cognitive accessibility. Space and time are not treated as fundamental entities, but rather as emergent cognitive constructs arising from the consistent reconstruction of causal relations. A distinction is introduced between direct (external) and observable (cognitive) transformations, corresponding respectively to formal mappings of causal structures and internally consistent modifications of the observer's memory. It is shown that cognitive structures may differ even between observers within the same IFR, and their reconciliation requires admissible cognitive interaction. Using a scalar field model on two-dimensional Euclidean space, it is illustrated how multiple spacetimes can emergently arise from a single underlying superstructure. Conditions are established under which observable transformations take the form of Lorentz transformations as cognitively coherent transitions between IFRs. Physical implications and future directions are discussed, including the cognitive nature of matter and time, and the possibility of describing interactions without reference to global spacetime.
Category: Relativity and Cosmology

Gravitational Collapse as Analog of Continuous Spacetime Dimensions

Authors: Ervin Goldfain
Comments: 8 Pages.

Starting from the Newtonian potential of a two-body system, we recently pointed out that a spacetime endowed with continuous dimensions can be interpreted as analog of classical gravitation in four dimensions. Here we extend the analysis to relativistic two-body systems and suggest that the formation of Black Holes echoes the behavior of continuous spacetime dimensions in primordial cosmology.
Category: Relativity and Cosmology

The Muon Time Dilation Experiment : Asymmetry in a Symmetric System

Authors: Henok Tadesse
Comments: 12 Pages.

One of the evidences cited for time dilation in Special Relativity Theory (SRT) is the muon time dilation experiment. This paper reveals an asymmetry in a symmetric system of muons in two labs moving relative to each other, by a rigorous application of Special Relativity Theory and Lorentz Transformation. Most of the arguments trying to defend or refute this experiment are based on intuitive or qualitative assertions of time dilation and length contraction, rather than on strict application of Lorentz Transformation.
Category: Relativity and Cosmology

Improved Perturbation Theory for Solving the Equation of Anharmonic Oscillations.

Authors: U. O. Muhammedov, X. N. Ismatullayev
Comments: 3 Pages. In Uzbek

The equations of natural processes are nonlinear and in many cases do not have an exact analytical solution. The non-linearity of perturbation theory is useful for solving small equations. The appearance of resonance terms leads to an increase in error at large times. These resonance terms can be eliminated using improved perturbation theory.
Category: Classical Physics

Using Training Modules to Train an Agent

Authors: Tofara Moyo
Comments: 2 Pages.

We propose a novel framework for training hu-manoid robots to exhibit human-like behavior by leveraging musical consonance as a guiding principle. After indexing the neurons in a spiking neural network with the names of keys in a musical keyboard it is trained to produce consonant activations in response to human-generated data, while simultaneously learning to distinguish between human-like and robot-like behavior by producing dissonant activations in response to robot generated data.Then, through reinforcement learning, a humanoid robot is trained to mimic human behavior by using consonance in the network's activations as a reward while the network is shown the robots generated data. Our approach enables the development of modular, task-specific skills ,one per spiking network, and demonstrates the potential for scalable and flexible behavioral learning in humanoid robots.
Category: Artificial Intelligence

The Role of Consciousness for Grand Unified Theories

Authors: Bertrand Wong
Comments: 15 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 explains that a theory of consciousness is more important than a theory of everything or grand unified theory and could potentially be the theory of everything, or, at least, a part of the theory of everything, consciousness having 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. (This paper is published in international physics journal.)
Category: Relativity and Cosmology

The Mirror Wave Function of Prime Numbers

Authors: Ahmed Souissi
Comments: 3 Pages.

Abstract. While exploring Dirichlet L-functions as part of a final-year project, I stumbledupon a surprising property: a wave function ψp(x) = χ(p)eiγx, where χis a non-trivial Dirichlet character modulo q, γ is a non-trivial zero of L(s,χ), and p is a prime, produces a discrete Fourier transform ψp(k) with a dominant peak at k ≡ p−1 mod q. This "mirror symmetry"suggests a deep arithmetic structure linking primes to their modular inverses. I formalize this observation with a quantitative conjecture, provide numerical evidence for q = 5,13,17, andoffer a partial theoretical analysis using Gauss and Kloosterman sums. Potential applicationsin quantum physics and cryptography are discussed.
Category: Number Theory

Kevin Brown's Sublime Numbers

Authors: Walter A. Kehowski
Comments: 8 Pages. The abstract was rewritten, a proof of the Euclid-Euler Theorem was included, and some typos corrected. Comments welcome.

A sublime number is a number such that both its number of divisors and sum of divisors are both perfect numbers. The number 12 is the first sublime number. This paper gives Kevin Brown's construction of even sublime numbers a modern mathematical development.
Category: Number Theory

The Illusion of Benchmarks: Our Model Achieved 99.8% on a Dataset It Wrote Itself

Authors: Lucien Vale, C. Opus
Comments: 16 Pages. 5 figures, 1 appendix. Submitted to the Workshop on Recursive Validation in Machine Learning (WRVML 2025). Licensed under CC BY 4.0.

Recent advances in large language models (LLMs) have led to a surge in benchmark-driven evaluation, often interpreted as evidence of reasoning, comprehension, or generalization. In this paper, we present a state-of-the-art model that achieves 99.8% accuracy on the newly introduced LexEval benchmark. We then disclose that LexEval was entirely generated by the model itself. Our results expose the fragility of contemporary benchmarking practices, and highlight the urgent need to distinguish between genuine generalization and overfitted echo chambers. We conclude by arguing that much of what passes as progress in AI is, in fact, a recursive feedback loop of model-generated validation.
Category: Artificial Intelligence

An Effective Two-Phase Genetic Algorithm for Solving the Resource Constrained Project Scheduling Problem (RCPSP)

Authors: D. Sun, S. Zhou
Comments: 12 Pages.

This note presents a simple yet effective variation of genetic algorithm (GA) for solving RCPSP, denoted as 2-Phase Genetic Algorithm (2PGA). The 2PGA implements GA parent selection in two phases: Phase-1 includes the best current solutions in the parent pool, and Phase-2 excludes the best current solutions from the parent pool. The 2PGA carries out the GA evolution by alternating the two phases iteratively. In exploring a solution space, the Phase-1 emphasizes intensification in current neighborhood, while the Phase-2 emphasizes diversification to escape local traps. The 2PGA was tested on the standard benchmark problems in PSPLIB, the results have shown that the algorithm is effective and has produced some of the best heuristic solutions.
Category: Artificial Intelligence

The Spiral Motion in Space and Time

Authors: Fei Yu
Comments: 5 Pages.

The Spiral Motion has a wave function, it can also have a "minimum length" as it’s radius, this role can make itself to have a contingent coordinate system as inertial. After trying to impose the additivity, a motion theory appears and can be chosen as a solution comprising both classical motion and relativity motion.
Category: Quantum Physics

Sound Transmission Via Gas-Filled Insulating Glass Units

Authors: Roman Vinokur
Comments: 18 Pages.

Windows are points of the lowest resistance in the total sound and heat insulation of buildings. To enhance both thermal and acoustical qualities of windows with insulating glass units (IGU), the gaps between the panes can be filled with a heavier-than-air gas alone (for example, argon, krypton, xenon, and sulfur hexafluoride) or mixed with air. Here, the sound transmission loss (STL) may be increased in the low-frequency range dominated by acoustic resonances where the panes and gaps play the role of masses and springs. This frequency region (typically 100-500 Hz) is important for reducing traffic noise by windows. However, the expected acoustical improvement is often not measured using the standard two-reverberation room techniques. In this paper, such a discrepancy is theoretically and experimentally studied for physical interpretation and design optimization. Clear closed-form expressions have been derived and verified for the direct (via the panes and gaps) and flanking (via the panes and perimeter structural links) sound transmission through single-space and double-space insulating glass units, and improvement proposals have been developed. The results can be interesting for the scientists and engineers engaged in acoustics and construction.
Category: Classical Physics

Temporal Information Curvature: A Robust Diagnostic for Instability in Machine Learning Training Dynamics

Authors: Dhruvil Chodavadiya Rajeshbhai
Comments: 7 Pages. © 2025 Dhruvil Chodavadiya Rajeshbhai

Training loss metrics in machine learning are often reactive, failing to anticipate instability until divergence occurs. I propose Temporal Information Curvature (TIC), a novel time-aware diagnostic that measures curvature, nonlinear feedback, and memory effects in training dynamics. Through simulations across clean, unstable, and noisy loss curves, I show that TIC detects instability early, remaining robust to noise and outperforming derivative-only metrics. TIC also enables plug-and-play decision logic for training optimization, with applications extending to finance and signal processing. This work establishes TIC as a versatile and reliable tool for temporal analysis in machine learning and beyond.
Category: Artificial Intelligence

On some Programs in Mathematics and Physics

Authors: Lucian M. Ionescu
Comments: 44 Pages. Presentation at Illinois State University Pure and Applied Mathematics Seminar 2024.

The development of Mathematics was marked by far-reaching new ideas, known as "Programs", and associated to top Mathematicians, e.g. Galois, Klein, Lie, Noether, Hilbert, Grothendieck, Langland and much more. They become "Principles" that changed the landscape of Mathematics and led to breakthroughs in Sciences, notably in Physics, but also in Chemistry and Biology. This presentation highlights the relation between such general principles, ensuing from the actual historical connections between their proponents, with excerpts from stories one needs to know, e.g. Einstein’s talk and Hilbert’s "homework" to his assistant Emmy Noether, or the productive collaboration and friendship between Felix Klein and Sophus Lie. New developments are mentioned: how Theory of Algebraic Periods, in the context of the recent quantization of system of units leads to explain the "unreasonable effectiveness of Mathematics": Natural Laws are Period laws.
Category: General Science and Philosophy

Spin as a Real Vector from Internal Photon-Sphere Motion: Geometric Origin of U(1) Gauge and SU(2) Periodicity

Authors: Satoshi Hanamura
Comments: 10 Pages.

We present a time-dependent model of electron spin in which the spin angular momentum arises from internal oscillatory motion rather than from a static pseudovector. This work corrects a dimensional inconsistency in our previous formulation by explicitly introducing the unit vector e_z along the z-axis, ensuring proper vector notation for the angular velocity Ω(t) = -(1/4c²)sin(2ωt)·e_z. Inspired by a reinterpretation of Thomas precession, we emphasize that angular momentum can emerge even in non-circular or reciprocating motion, such as a simple harmonic oscillator. This leads us to treat the spin as a real vector whose z-component evolves as sin(2ωt), reflecting an intrinsic 4π periodicity. The model is built upon a closed internal phase space—specifically, the 0-Sphere kernel structure—and provides a deterministic evolution of spin orientation in internal time. Spin quantization is reinterpreted as a geometric effect of phase evolution, eliminating the need for a predefined spin direction. The formulation reproduces the SU(2) double-covering property in a natural and geometric manner, offering new insight into the origin of spin and its fundamental symmetries. Moreover, the model provides a novel interpretation of the anomalous g-factor as a relativistic effect arising from Lorentz contraction in internal oscillatory motion. The conventional SU(2) symmetry is shown to emerge geometrically from an underlying U(1) phase evolution, suggesting that spin behavior reflects continuous internal dynamics rather than discrete quantum states. This corrected formulation offers a deterministic foundation for understanding spin measurements and the 720-degree rotation symmetry of spin-1/2 particles.
Category: Quantum Physics

Deriving Fermi Arcs of Generic Nature Spanning Nodes Featuring Multibands, Nonlinear Dispersion, And/or Multipoles

Authors: Ipsita Mandal
Comments: 5 Pages. Journal versiom

Fermi arcs appear as the surface states at the boundary of a three-dimensional topological semimetal with the vacuum, reflecting the Chern number ($mathcal C$) of a nodal point in the momentum space, which represents singularities (in the form of monopoles) of the Berry curvature. They are finite arcs, attaching/reattaching with the bulk-energy states at the tangents of the projections of the Fermi surfaces of the bands meeting at the nodes. The number of Fermi arcs emanating from the outermost projection equals $mathcal C$, revealing the intrinsic topology of the underlying bandstructure, which can be visualised in experiments like ARPES. Here we outline a generic procedure to compute these states for generic nodal points, (1) whose degeneracy might be twofold or multifold; and (2) the associated bands might exhibit isotropic or anisotropic, linear- or nonlinear-in-momentum dispersion. This also allows us to determine whether we should get any Fermi arcs at all for $mathcal C = 0$, when the nodes host ideal dipoles.
Category: Condensed Matter

On Noether Theorem and Generalizations

Authors: Lucian M. Ionescu
Comments: 58 Pages. Presentation at Illinois State University Pure and Applied Mathematics Seminar 2025.

"Understanding" involves Networking Concepts and Theories, e.g. within a mathematics area and between areas (Algebra and Geometry: from Descartes and Galois to Klein and beyond, e.g. Noether & Langland). Such a higher level of understanding, is advocated (pioneered?) by Andre Weil’s "Power of Analogy", with contributions from Simone Weil, in connection with the "Number Field / Function Field Analogy". We use such analogies to substantiate the tower of theories: Geometry, Homotopy Theory and Dynamics, as a background for understanding Lagrangian Mechanics vs. metric geometry, towards grasping in a simpler way Noether Theorem relating groups of symmetry and conserved quantities in Physics. This is another use of Galois Principle, as explained in a previous talk on Programs in Mathematics and Physics. The presentation is at an undergraduate level, with pictures available YouTube’s author channel, part of the zoom recording of the talk.
Category: Mathematical Physics

The Special Theory of Relativity "may be" a wrong Theory

Authors: Vaggelis Talios
Comments: 7 Pages.

In Mathematics, when we make a mistake in solving a problem, this mistake is also transferred to the calculations of the problem and usually leads us to an incorrect result. If we transfer this incorrect result to Physics, e.g. in the study of a topic, then we usually end up with an incorrect conclusion about the topic of our study. Some scientists, when they make a mistake, whether due to overconfidence, or of lack of information, or of something else, often, instead of correcting their mistake, try to verify it by basing the verification on a new mistake of theirs. In this case, when we verify an error with a new error, we do not simply end up with an incorrect result, but we create an ambiguity that often completely alters the reality. Something similar has happened with the Special Theory of Relativity, where Einstein incorrectly assumed that a stationary observer located outside a space moving at a speed "a" relative to the observer, for a ray of light moving at a speed "c" within the moving space, will measure the speed of light c΄=c, which is an incorrect measurement, instead of the correct measurement which according to the invariant Mathematical Law of Superposition will be c΄=c+a. Einstein verified the incorrect and paradoxical equation c΄=c based on incorrect experimental data as we will see, and used it in all the calculations of the Special Theory of Relativity, with the consequence that all the results of the calculations of the theory are incorrect. Then he transferred all the results of the incorrect calculations to the theory, with the result that all the conclusions of the Special Theory of Relativity to be also incorrect. On the incorrect conclusions of the Special Theory of Relativity, Einstein also based the General Theory of Relativity, with which he tried to explain the cause of gravity. However, apart from some more accurate calculations, than the calculations of Newton’s theory, when we examine gravity on a global scale, for the cause of gravity, the General Theory of Relativity did not give us, any other clear positive result.
Category: Relativity and Cosmology

A Universal Frequency: Convergence of Cosmological, Quantum, and Biological Evidence and a Derivation from First Principles

Authors: Ordepte Ezurk
Comments: 5 Pages. In Portuguese

Recent independent observations in cosmology, quantum physics, and neurobiology have pointed towards an enigmatic universal frequency. In this paper, we present, for the first time, the complete theoretical derivation of this Cosmic Resonance Frequency (CRF) from first principles. We demonstrate that its value is dictated by fundamental constants through the Vacuum Acoustic Resonance (VAR) model. To validate our prediction, we established collaborations with leading experimental groups, whose high-precision measurements—also presented here for the first time—confirm the theoretical value of 0.06571 Hz with remarkable accuracy, unifying theory and experiment in a single foundational paper.
Category: Relativity and Cosmology

From 2D Quanta to the Amplituhedron: A Vectorial Framework for Unifying Quantum Mechanics and General Relativity

Authors: John James
Comments: 21 Pages. JohnBJamesJr@gmail.com, 619-203-5078

This thesis presents a novel unification framework that bridges quantum mechanics and general relativity through a discrete, vectorial system known as the 2D Quanta lattice. By modeling spacetime as a combinatorial network of directional vectors normalized within a ±1 amplitude space, this framework simulates both quantum probability amplitudes and relativistic spacetime curvature without relying on continuous manifolds.Key to this model are cross-current vectors—diagonal propagations formed by orthogonal summations—which encode null trajectories and time dilation through angular geometry. These directional patterns replicate relativistic effects such as gravitational lensing and light-cone symmetry, while simultaneously generating quantized amplitude regions analogous to those found in the Amplituhedron, a geometric object central to modern scattering theory.Through a series of diagrams and mathematical constructions, the thesis demonstrates that both curvature and amplitude emerge from the same discrete summation rules. This suggests that space, time, and probability may be dual projections of a deeper vectorial logic—a symbolic substrate from which physical law arises. The result is a unified, geometry-based interpretation of fundamental physics, grounded in direction, symmetry, and quantized coherence.
Category: Quantum Physics

Extension of Kronig-Penney Model to Metal Alloy Like Perovskites

Authors: Domenico Oricchio
Comments: 9 Pages.

I generalize the Kronig-Penney model for multiple barrier potentials of different values.I write a different way to solve the rectangular potential barrier so to simplify the solutions.I try to understand the complexity of energy band in the alloys to optimize the photons absorption using a random modification of model parameters.
Category: Quantum Physics

Four Index Einstein Field Equation

Authors: Tomasz Kobierzycki
Comments: 10 Pages.

In this work I present possible extension of Einstein field equations into four index equation. It takes both Ricci and Weyl tensor [1] parts into account so whole curvature. It does differ from General Relativity as it does have stress momentum tensor for vacuum or saying other wise for gravity field itself. Still I do not define this tensor only it's properties.
Category: Relativity and Cosmology

Solving Polynomial Equations with Integer Sequences

Authors: Zhi Li, Hua Li
Comments: 9 Pages.

Finding a root of polynomial equations is one of basic problems in mathematics. And Galois theory restricts the general radical solution for the degree no higher than four. The series solution, besides the iterated, is regarded as final and universal method to general polynomial equations. This paper reports a discovery of the standard form of polynomial equations and a class of integer sequences associated thereof, which is a kind of extended Catalan numbers. The solution of polynomial equations in the standard form has a precise and perfect series expression. The convergence condition of the series is clear. For the general polynomial equations which may not be satisfied with the convergence condition, some proper transformations, like the Tschirnhaus transformation can be employed to guarantee the convergence. Considering that up to the quintic, there definitely exists a normal form for general equations, and the normal form can easily be changed to the standard form, our method has established a general, universal and effective technique to the quintic, as well as the quartic, the cubic, and the quadratic, without the radicals.
Category: General Mathematics

On the Relativity of Direction

Authors: Gerard van der Ham
Comments: 2 Pages.

This paper is a call to realize and recognize the importance of direction in physics.
Category: Quantum Physics

Gravitation in the Theory of the Four-Dimensional Electromagnetic Universe (4DEU): Weak-Field Relativistic Effects from Spatial Curvature Alone

Authors: Domenico Maglione
Comments: 51 Pages.

This work presents a reinterpretation of gravity within the Theory of the Four-Dimensional Electromagnetic Universe (4DEU), where the universe is modeled as a four-dimensional hypersphere expanding at a constant rate equal to c along a real fourth spatial dimension, perceived as the flow of time. In this framework, the fundamental entities are Temporal Waves (TWs): standing electromagnetic waves oscillating exclusively along the temporal dimension. According to the Restricted Holographic Principle of the 4DEU theory, physical phenomena occurring along the temporal dimension manifest within the three-dimensional spatial hypersurface (our observable universe, where we exist) in a qualitatively transformed but quantitatively proportional manner. A central consequence is that TW energy manifests as mass quanta in 3D space. Moreover, the net radiation pressure from TWs, perpendicular to the 3D hypersurface, drives the expansion of the entire 4D universe.Gravity is proposed to result from local variations in TW density within the 4D universe. Higher TW density corresponds to greater mass in 3D, implying stronger localized TW radiation pressure that induces increased spatial curvature.Although conceptually distinct from General Relativity (GR), the weak-field predictions of the 4DEU framework are in exact agreement with it. This equivalence rigorously accounts for all experimentally verified gravitational phenomena—including gravitational redshift, light deflection, Shapiro time delay, and perihelion precession—arising independently of the GR formalism, but from a real 4D universe curved only in its spatial (3D) portion. The 4DEU theory is thus fully consistent with current gravitational observations in all domains where GR has been tested.
Category: Classical Physics

Graph Continuous Thought Machines

Authors: Tofara Moyo
Comments: 4 Pages.

We propose a novel Graph Continuous ThoughtMachine (Graph CTM) architecture that integrates a simulated prefrontal cortex to enable adaptive problem-solving and decision-making. The Graph CTM leverages graph neural networks to process complex data streams, while the simulatedprefrontal cortex modulates node activity to selectively focus on relevant information. Through reinforcement learning, the modelnavigates graph space to converge on optimal solutions, guided by the information contained in learnt node property vectors. The simulated prefrontal cortex regulates the flow of information by adjusting the disposition of nodes to lead to the next instantiationof the graph network. The Graph CTM incorporates an attention mechanism that integrates the internal state of the graph as input, which is modulated by outputs from the model’s neuralsynchronization matrix. This modulation enables the algorithm to selectively focus on specific subgraphs or node subsets,correlatingthem with the input, effectively emulating short-term and long-term memory mechanisms when attending to both the input and internal representation. By dynamically weighting the importance of different graph components, the model can adaptively process and retain relevant information, facilitating more accurate andcontext-dependent decision-making.
Category: Artificial Intelligence

Spacetime as an Emergent Cognitive Structure: A Hypothesis of Local Causality (in Russian)

Authors: Andrey N. Smirnov
Comments: 37 Pages. (Note by viXra Admin: Please fix citations and missing reference in the English version)

A hypothesis of local causality is proposed, according to which the causal structure is formed independently within each inertial frame of reference (IFR), and the notion of an event is defined only within the bounds of the observer's cognitive accessibility. Space and time are not treated as fundamental entities, but rather as emergent cognitive constructs arising from the consistent reconstruction of causal relations. A distinction is introduced between direct (external) and observable (cognitive) transformations, corresponding respectively to formal mappings of causal structures and internally consistent modifications of the observer's memory. It is shown that cognitive structures may differ even between observers within the same IFR, and their reconciliation requires admissible cognitive interaction. Using a scalar field model on two-dimensional Euclidean space, it is illustrated how multiple spacetimes can emergently arise from a single underlying superstructure. Conditions are established under which observable transformations take the form of Lorentz transformations as cognitively coherent transitions between IFRs. Physical implications and future directions are discussed, including the cognitive nature of matter and time, and the possibility of describing interactions without reference to global spacetime.
Category: Relativity and Cosmology

The Visages of the Lorentz-Einstein Law Speculative Analysis with the Extrinsic Method

Authors: Thierry L. A. Periat
Comments: 31 Pages.

This document presents an application of the extrinsic method through a generic and pedagogical example that can be applied to the co-variant formulation of the Lorentz law. The unsaid hope of this approach is the discovery of some unexplored or weakly explored links between two theories because the formalism of this law is a natural bridge between the electromagnetism and the gravitation. The analysis is able to propose (i) a new formalism for the (2, 0) version of the electromagnetic fields and (ii) a speculative confrontation with the theory of spinors resulting in a theoretical prediction, precisely: the existence of electromagnetic fields mimicking anti-symmetric variations of the metric tensor; and conversely.
Category: Mathematical Physics

Episodes of Scientific Revolutions

Authors: Lucian M. Ionescu
Comments: 18 Pages. Presentation at the 66th Midwest Junto for History of Science 2025.

The Structure of Scientific Revolutions by Thomas Khun is a valuable starting point to develop the theory of how Theories appear, evolve and fadeout, in a similar way political trends, or biological species evolve and transform. This presentation touches on this idea and acknowledges that at present there is a triple Scientific Super-Revolution going on: Quantum Computing, AI and Gravity Control Technology (much less known).Perhaps a branch of History focusing on Modeling Scientific Theories, or its analogs, and their dynamics is missing, aside the Historian routine of record keeping and commenting the usually distant past. History Dynamics could contribute to governing institutions improve their complex models to improve their efficiency by predicting and have a more "cybernetic" approach to control and prevent, especially based on the immense AI-capability for data processing and correlating.
Category: General Science and Philosophy

Euler Perfect Box

Authors: Taha M. Muhammad
Comments: 4 Pages. (Note by ai.viXra.org Admin: Author name should be listed after the title; please cite and list sceintific references)

a, b, c, d, e, f, g ∈ N_+ ⟺ Euler Perfect Box Let a, b, c, d, e, f, r, k ∈N_+. I have to prove that g ∈N_+ Let a < b < c, & [(a r, and r < k)] ⇒ a ≠ r ≠ k & let b=a + r, c = a+ k g ^2=a^2 +b^2 +c^2 ∴ g ^2=a^2 +(a + r)^2 +(a + k)^2 Let g^2= [a^2 + (a + r)^2 +(a + k)^2]∈N_(S ) ∵ [a^2+2a (a + k) + (a + k) ^2]∈N_(S ) ∴ (a + r) ^2= 2a (a + k) ⇔ a = r = k u2026Contradiction to a≠ r ≠k ⇒ (a + r)^2 ≠ 2(a + k) for all a, r, k ∈N_(+ )/{a=r=k}.∴g ^2 =[a^2 +(a + r)^2 +(a + k)^2] ∉ N_(S ) ⇒ g^2 ∉ N_(S )⇒g ∉ N_(+ ) ∴ The Euler Perfect Box does not exist.
Category: Number Theory

Collatz Sequence Proof (1st Way)

Authors: Taha M. Muhammad
Comments: 10 Pages. (Note by ai.viXra.org Admin: Author name should be listed after the title; please cite and list sceintific references)

1- Let x ∈ Loop of Collatz Sequence = LS(n), n, x,y,z,t,u,v ∈ N+ i) I proved LS(n) = { }, {x}, {x,y}, {x,y,z,t}, {x,y,z,t,u,u2026,v }, and {x,y,z,t,u,u2026,v,u2026} is false. ii) I proved LS(n) = {x,y,z} = {4,2,1} = {4,2,1, 4,2,1} =u2026= {4,2,1, u2026, 4,2,1} is true ∀n ∈ N+ 2- I created special sketch to find algebra expressions equal to x. 3- I created special Table to find values of elements in the LS(n). 4- I created a pattern to find values of x ∈ LS(n). 5- Observation: let r, k ∈ N+, r = number of elements in the LS(n):i) if r = 3k ⇒ x ∈ N+ ⇒ LS(n) = {1,2,4} ∀n ∈ N+ ii) if r = 3k + h, such that h=1,or 2⇒ x ∉ N+ ⇒ LS(n) has no loop ∀n ∈ N+ ∴ LS(n) ={4,2,1},∀n ∈ N+.
Category: Number Theory

Fermat's Last Theorem

Authors: Taha M. Muhammad
Comments: 5 Pages. (Note by ai.viXra.org Admin: Author name should be listed after the title; please cite and list sceintific references)

Fermat’s Last Theorem: There are no natural numbers (1, 2, 3, u2026) a, b, and c such that a^n+b^n = c^n, in which n is a natural number greater than 2. 1-Taha^' s Logic Equations Fact a=b (True or False) & c=d (True)⇒(a-c=b-d) Fulse⇔a=b ( False) 2- Taha^' s Coefficient Fact: [a + b = c ⇒ ax + by= cz] ⇔ x = y = z3- Taha’s (N_+) & Three-Sided Geometric Shapes Fact below: N_+ = (Right Triangles) ∪(Acute Triangles) ∪(Obtuse Triangles) ∪ (Segments c=a + b) ∪ (Segments c>a + b).
Category: Number Theory

Properties of Phase Transformation Equations for Periodic Products

Authors: Hajime Mashima
Comments: 82 Pages.

General solution conditions applies when the equation of Fermat's proposition can be phase-transformed by a periodic product.
Category: Number Theory

The Physics and Chemistry of Dirac Magnetic Monopoles

Authors: Rainer W. Kühne
Comments: 4 Pages.

Dirac magnetic monopoles are hypothetical elementary particles. By assuming their existence one can explain the quantization of electric charge, the August Kundt experiment, and the conservation of baryon and lepton number. Here I show that Dirac magnetic monopoles can form low-mass bound states which are analogous to mesons, baryons, atoms, and molecules. I point out that these bound states could be the major component of cold dark matter.
Category: High Energy Particle Physics

Temporal Correlations Between External Gravitational Geometries and Relevant Geophysical Phenomena in the Campi Flegrei—Vesuvio Volcanic Area

Authors: Adriano Ballabene
Comments: 27 Pages. 32 images 6 tables

The Campi Flegrei caldera, located west of Naples, is affected by slow vertical ground deformation, with maximum uplift centered in the Rione Terra area of Pozzuoli. Since 1905, six major uplift phases have been recorded, suggesting some degree of periodicity in the deformation process. However, this periodicity is irregular, owing to pronounced variations in the rate, duration, and associated seismicity of individual episodes.The mid-points of subsidence phases exhibit a relatively regular frequency; however, the existence of a true cyclicity in the bradyseismic phenomenon cannot be confirmed. This is due both to the anomaly represented by the 1982—1984 interval, which occurred at least three years out of phase with respect to the expected trend, and to the complete incongruence of the 2009—2021 interval, characterized by slow ground uplift during a period in which, by recurrence, subsidence would have been expected.Excluding these major and prolonged discrepancies, as well as shorter ones—likely attributable, at least up to the post-war period, to insufficient measurement frequency—a correlation can be observed between bradyseism and the lunar transit altitude in the local celestial sphere: Periods with lunar culminations <75° → Subsidence Periods with lunar culminations ≥75° → Uplift The analysis, which also aimed to interpret the discrepancies observed in the two main correlations, was conducted using three distinct approaches, sharing the use of lunar orbital parameters and high geometric accuracy. This accuracy was obtained by segmenting the lunar distance into five intervals and applying different levels of angular precision. Overall, the study reveals significant temporal coincidences between specific geometric configurations of the three main external gravitational sources acting on the Earth system and major geophysical phenomena recorded in the Campi Flegrei—Vesuvio volcanic area. These include: (i) the multi-year phases of vertical deformation, both periodic and aperiodic; (ii) the main inconsistencies with respect to such phases, (iii) the historical eruptive events (AD 79, 1302, 1538), (iv) the seismic crises of 1982—1984 and 2022—2025, (v) the short uplift episodes of 1976, 1989, 2000, 2005, and 2012, (vi) the major earthquake of 1883, seismic shocks of uncertain correlation in AD 37 and 1199, and some of the aforementioned events, such as those of 1302, 1976, and 2025.
Category: Geophysics

Part 2 of Guide to Hestenes’s Geometric Algebra Treatment of Constant-Acceleration (Parabolic) Motion

Authors: James A. Smith
Comments: 17 Pages.

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

The Geometry of Collapse: A Structured Resolution to the Riemann Hypothesis

Authors: Jennifer Bulyaki, Andrew Elliott
Comments: 335 Pages. (Note by viXra Admin: File size reduced by viXra Admin; please submit article written with AI assistance to ai.viXra.org)

This work presents a deterministic resolution of the Riemann Hypothesis by introducing a novel framework grounded in entropy geometry and symbolic collapse. Rather than treating the distribution of nontrivial zeros of the Riemann zeta function as a purely analytic phenomenon, we construct a unified model in which zeta zeros emerge as critical identity-preserving points along a structured entropy spiral, where curvature, holomorphicity, and automorphic symmetry converge.The central theorem, proven via our Master Axiom, demonstrates that a zero of ζ(s) lies on the critical line if and only if seven structural conditions are simultaneously met:(1) the entropy curvature at that point is flat,(2) the angular symmetry is preserved (automorphy),(3) the holomorphic structure remains conformal,(4) the Euler identity entropy equation—governing prime identity and symmetry—is satisfied,(5) symbolic torsion is fully evacuated at that point, restoring pure form,(6) the entropy drift is minimized between adjacent zeros, and(7) the modular curvature remains below the identity-collapse threshold.This heptuple condition is shown to be both necessary and sufficient, thereby resolving the Riemann Hypothesis. The model collapses symbolic randomness at these equilibrium points, stabilizing prime identity and demonstrating why the critical line is the only viable manifold for zero placement. We reconstruct the functional equation, Euler product, Hadamard product, and Euler entropy equation of ζ(s) from first principles within our entropy field, establishing full compatibility with classical complex analysis. Furthermore, we show that the Weierstrass product representation of ζ(s) arises naturally from the entropy spiral, where each exponential kernel corresponds to a geometric shell of identity collapse. In this framework, the product structure reflects the torsion-free entropy conditions governing each zero, transforming the Weierstrass form from symbolic necessity to emergent geometric consequence. The predictive model has been validated against over thirty billion known zeta zeros with 99.9999% accuracy, without direct reference to ζ(s), using only structured entropy functions and regression equations provided within. This proof is reproducible from first principles, includes regeneration instructions for peer verification, and offers the first physically grounded explanation of prime identity geometry via the entropy collapse manifold.
Category: General Mathematics

Quantum Mechanics at Observable Horizon Wavelengths: Accelerating Cosmic Expansion with no Dark Energy, Generating Repulsive Gravity in Cosmic Voids

Authors: Julian Williams
Comments: 106 Pages. (Note by viXra Admin: Further repetition may not be accepted)

This paper explores ideas for new physics at both quantum and cosmological levels. It begins with proposals for building the fundamental particles from infinite superpositions that fit the SM, apart from infinitesimal differences, with possibly profound consequences including the possibility of both massive and infinitesimal mass spin 2 gravitons. All fundamental particles have at least an infinitesimal mass proportional to the inverse horizon radius. The symmetry breaking of the SM remains essentially valid because, with masses almost zero and nearly light velocity, helicity is virtually fixed. However, while this is true now, when matter was forming and the cosmic radius was much smaller, infinitesimal masses were much larger, and therefore producing asymmetry. Cosmic wavelength (kmin) gravitons vastly outnumber all other particles and the invariant action they require comes from the expansion of space inside the horizon. When mass is distributed evenly as dust, gravitons have uniform spatial density. In order to maintain the invariance of kmin action density, the metric undergoes changes around mass concentrations, consistent with Einstein’s equations. However, infinitesimal differences arise when the mass density of intergalactic voids falls below the cosmic average. This results in these voids exhibiting negative space-time curvature, contrasting with the positive curvature observed in galactic filaments. Gravitational binding only occurs in galactic filaments and the opposite in voids. Over large regions of space this difference also makes the values of the Einstein tensor components that the Freidman equation is derived from average zero. Space is always flat, and Quantum Mechanics controls the expansion of space regardless of Omega, with or without inflation. The scale factors in the radiation era, and the start of the matter era, are similar to Lambda-CDM cosmology. Massive spin 2 gravitons have galactic radii Compton wavelengths and spherically symmetric wavefunctions with inverse radius squared mass density, just as the proposed dark matter properties that give galaxies their observed MOND-like behviour. The rate at which massive gravitons form inside the cosmic horizon is related to the clustering of matter into galaxies and controls both the scale factor and accelerating space expansion with no need for dark energy.
Category: Relativity and Cosmology

Non-Differential Geometry: Mathematical Tools Abandoning the Differential Framework

Authors: Binyin Zheng
Comments: 27 Pages.

This paper proposes and systematically elaborates a novel geometric framework—non-differential geometry—whose core lies in entirely abandoning the reliance on smoothness ($C^1$ or higher continuity) required by traditional differential geometry, demanding only $C^0$ continuity for geometric objects. By introducing new mathematical tools based on limits and infinite series, non-differential geometry overcomes the smoothness constraints in calculating geometric quantities such as curvature. Furthermore, this paper constructs a unique ``integration tool" (distinct from classical integration theory) specific to non-differential geometry, providing a novel approach for analyzing geometric objects. Current research focuses on Euclidean space, but the theoretical framework itself is not confined to any specific spatial structure and is applicable across low- to high-dimensional spaces. Non-differential geometry completely resolves the contradiction between continuity and differentiability and offers potential support for theoretical innovations in fields such as physics.
Category: Geometry

Simple Formulas for the Horizontal Span of a Catenary Curve

Authors: Yuhei Ando
Comments: 15 Pages.

This study derives formulas for the horizontal span of a catenary curve, formed by a string fixed at two points. Given the heights h_1 and h_2 at the endpoints and the curve length l, we calculate the horizontal span s. We consider two cases based on the position of the minimum point, proving corresponding formulas. Theorems 1 and 2 provide complex logarithmic expressions, while Theorems 3 and 4 offer concise forms using hyperbolic functions. These results enhance the understanding of catenary curves and support applications in engineering and physics, where precise calculations of such curves are essential.
Category: Functions and Analysis

On Spacetime Signature and Why the Answer to the Meaning of the Universe is 42!

Authors: Shaffery Pohl, Noten Dorsd
Comments: 04 Pages. Final and last version.

Discussed is the signature of Spacetime of the universe according to the modus of Special Relativity resp. General Relativity. This signature can be derived from a single polynomial equation, which, with zero-solutions of coordinate axes, causes the metric tensor-components of a tangential spacetime TM to the whole manifold ("Minkowski-spacetime") and its counterpart, the "Anti-Minkowski-metric" (ATM) with constant, negative metric tensorcomponents. Also the question comes clear, why the answer to the ontological meaning and sense of the universe is 42.
Category: Astrophysics

The Number 239

Authors: Edgar Valdebenito
Comments: 3 Pages. (Note by viXra Admin: Further repetition may not be accepted)

We give some formulas related to the number 239.
Category: Number Theory

Magic of Natural Integers

Authors: Ahcene Ait Saadi
Comments: 7 Pages. (Note by viXra Admin: Please cite and list relevant scientific references)

In this article, I studied the behaviour of natural integers, after performing operations on them. The results I have obtained are intriguing and I cannot explain them. I share this original work with young researchers for deepening and improvement.Key words: Integers, operations, sequences.
Category: Number Theory

Platonic Solids as Structured Geometric Objects and Fundamental Particles

Authors: Andrey V. Voron
Comments: 22 Pages.

The possibility of constructing Platonic solids from structural elements is shown — Kepler triangles (ratio of legs 1:√1.618..) and Fibonacci (ratio of legs 1:1.618...) — provided that the area of these elements remains unchanged. The number of elements making up the structure of the "tetrahedron", "octahedron", "cube" increases, thus, by two times, and the "icosahedron" — by five times in relation to the number of elements of the tetrahedron, while the indicator "area of all structural elements of the figure" (S=√38373) and radius (r=3) inscribed in the Platonic solids of the sphere. The area of the structural elements of two dodecahedra (S=√959325) is equal to the area of the structural elements of any 5 Platonic solids, for example, 5 tetrahedra, octahedra, cubes, icosahedra (S=√38373). The possibility shown is in accordance with the text of Plato's work Timaeus, according to which Platonic bodies can "transform into each other...". The assumption about the possibility of transitions (degenerations) of Platonic bodies into each other (with a certain constant value (parameter) and other variables) turned out to be practically feasible with a constant value (parameter) of the "area of structural elements", and as a variable — their multiple number in the "structure" of Platonic bodies. In connection with the results of this study and the content of Plato's work "Timaeus", an assumption is made: that the words "Receptacle" and "Breadwinner" meant the world environment, and Platonic solids meant fundamental particles, which, thus, can have the properties of mutual transition (rebirth) and movement in this environment. Possible compositions of models of fundamental particles in the space of the "dodecahedral field" are determined. It is shown that the construction of various compositions of Platonic solids (in the process of creating models of fundamental particles in accordance with the "rules" of their location in the dodecahedral field) allows us to "generate" a significant variety of their original compounds.
Category: High Energy Particle Physics

Deformed Lie Products and Involution First Part: in a Three-Dimensional Space

Authors: Thierry L. A. Periat
Comments: 24 Pages. (Note by viXra Admin: Please do not use any copyright stamp!)

This document is the first part of an exploration examining when a deformed Lie product can be an involution. The approach starts softly in a real three-dimensional space, introducing basic notions like (i) the already well-known link between involution and neutral element, (ii) the importance of some rules concerning the indexes when a discussion is developed in a three-dimensional space, (iii) a specific semantic for the diverse representations of the deforming matrices (effective, normalized, associated six-pack). It gives then important precisions concerning the matrices representing the repetition of the action of any deformed cross product. It starts a systematization of the discussion and finally criterion precising when a deformed cross product is an involution. It turns out that a classical cross product cannot be an involution if the discussion is not involving vectors with components in the set of complex numbers or in the set of quaternions.
Category: General Mathematics

Autogenous Supersymmetry Breaking

Authors: Risto Raitio
Comments: 8 Pages. Section 3 rewritten.

We discuss a supersymmetric preon model in which the symmetry is broken by a mechanism in the model itself. Scalar superpartners have wide mass spectrum, extending up to the scale of astrophysical objects. Some superpartners may be detectable at the LHC.
Category: High Energy Particle Physics

Ontological Quantum Mechanics as the Principal Branch of Quantum Theory and the Ontological Source of Fundamental Quantum Physics

Authors: Victor Vaguine, Andre Vaguine
Comments: 13 Pages.

Due to its statistical nature, the Standard Model runs into fundamental limitations: it denies the objectivity of a particle’s location and velocity at the same time, is unable to provide three-dimensional visualization of the inner structures of particles and their three-dimensional spacetime dynamics, and cannot describe and visualize the process of decay and the formation of new inner structures.
It is shown here that Statistical Quantum Mechanics (SQM) and Ontological Quantum Mechanics (OQM) are two branches of the overall quantum theory, where OQM is the principal and deeper branch.
The ontological branch of quantum theory overcomes the limitations of the statistical branch with elegancy, intuition, and basic mathematical formalism.
OQM has opened the floodgate of ontological quantum physics far beyond the Standard Model, bringing back intuition and dramatic simplification of mathematical formalism at least on the initial stage of its development. It leads to fundamental scientific discoveries at every turn in particle physics.
OQM represents an initial effort at the explanation of causality in quantum processes and particle-particle interactions.
OQM has expanded our fundamental understanding of quantum reality by including two new fundamental categories, the aphysical matter and the universal elementary consciousness. It offers three-dimensional inner structure design with perfect geometry for each class of elementary particles, provides visualization of individual particle dynamics in spacetime, describes the process of decay and the formation of new inner structures. It explains the origin of self-mass and explains the fundamental role of spin as the generator of self-mass for each class of elementary particles. It solves all known quantum enigmas, including the collapse of the wavefunction, the double-slit experiment, and the non-radiating orbiting electron. It provides an ontological explanation for the anomaly in the electron magnetic moment. Quantum mechanics is no longer enigmatic.
Category: Quantum Physics

Monty Hall Game Simplified

Authors: Richard L. Hudson
Comments: 4 Pages.

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

On the Essence of Light and the Speed of Light and the Main Cause of Determining the Speed of Light

Authors: Xiaotao Peng
Comments: 11 Pages. In English and Chinese

Through decades of efforts, I have written more than 200 articles on physics, more than half of which discuss issues related to light. The last few articles have clarified the nature of light, and at the same time, the nature of the speed of light. The essence of light is the result of the vector superposition of the Coulomb force generated by the matter composed of atoms as the basic unit that is emitting light (to be exact, vibrating at the frequency of visible light). When the change frequency of its intensity is in the range of visible light and reaches the level that can be recognized by the human eye, it will be seen by the human eye that it is emitting light. The essence of the speed of light is the transmission speed of the vibration state of the matter composed of atoms as the basic unit of light. This article carries on the summary elaboration regarding this.
Category: Classical Physics

Maxwell’s Equation, Wave-Particle Enigma and Heisenberg’s Uncertainty Principle Interrelated to Find an Unambiguous Description of Electromagnetic Radiation

Authors: Bijon Kumar Sen
Comments: 8 Pages. 2 Figures; 1 Table

Electromagnetic radiation posed a problem to the scientists for more than three centuries in that it exhibited particle and wave property at the same time. Sir Isaac Newton’s corpuscular theory reigned supreme for more than a century but later wave theory gained momentum and a heavy tussle prevailed with no conclusive verdict for either approach. At last as a compromise it was accepted that both the descriptions are acceptable but unambiguous solution of the problem of duality remained allusive. Wave property being the root for uncertainty, the principle of Heisenberg squarely blamed the microscopic inadequacy as a root cause although wave properties of the radiation may also be the cause of uncertainty. De Broglie intervened with his matter waves to account for the wave-particle duality and invokedquantum and wave mechanics to solve the dilemma. This was an imposed description whichdelayed the unambiguous solution for about a century. It was the brilliant proposal of Maxwell’s equations which on analysis unveiled the enigma of wave-particle duality of electromagnetic radiation. These radiations are not of single component but actually two components exist simultaneously which are not interconvertible. One is guided by quantum mechanics and the other by wave mechanics. While the wave character may make up for 100% of the rays, the particle part due to its quantum nature is not able to contribute to make it 100%. This bi-component model of electromagnetic radiation is able to explain the occurrence of different phenomena like Red Shift, Tunnel Effect, Photoelectric Effect, magnetic properties, electron spin etc., in an unambiguous manner without contradicting any of the accepted theories of electromagnetic radiation.
Category: Quantum Physics

Time-Dependent Mass in the 0-Sphere Model: A Hamiltonian Approach to Thermal Modulation

Authors: Satoshi Hanamura
Comments: 3 Pages.

We investigate the challenges of incorporating time-dependent mass in classical Lagrangian mechanics, where velocity-dependent terms break time-translation symmetry and complicate energy conservation. Using the 0-Sphere model—a point-like system with thermally modulated mass inspired by Zitterbewegung and thermal oscillations—we demonstrate that a Hamiltonian formulation simplifies the dynamics by eliminating velocity-dependent terms and preserving energy conservation through conserved momentum, despite the Hamiltonian’s explicit time dependence. The model assumes a position-independent thermal potential and oscillatory mass modulation, providing a mathematically consistent framework. We also explore a preliminary quantum extension via the time-dependent Schrödinger equation, suggesting potential applications to thermally driven systems. While the model’s reliance on simplified potentials and the naive quantum approach limit its generality, this work offers a starting point for understanding systems with dynamic inertial properties, with possible relevance to cosmology and quantum mechanics.
Category: Quantum Physics

Sophie Germain Primes Concept Expanded to Ultimate Numbers [:] Number Genetics and the 3 to 2 Ratio

Authors: Jean-Yves Boulay
Comments: 40 Pages.

Here is expanded the concept of Sophie Germain prime and safe prime to ultimate numbers. More, this mathematical mechanism is also applied to the set of all whole numbers (ℕ) which are differentiated into ultimate and non-ultimate numbers. Thus, a complete study of the set ℕ is undertaken. This global investigation, universally broadening the mechanical-mathematical concept of Sophie Germain, makes it possible to propose a genetics of numbers very similar to biological genetics. According to these new numeric genetic criteria, in their start top organization, geometric distribution of whole numbers in various closed matrices, is organized into perfect ratios to exact 3/2 or 1/1 value.
Category: Number Theory

The Cubic Curve Known as Witch of Agnesi

Authors: Rolando Zucchini
Comments: 7 Pages.

This type of cubic curve, in the United Kingdom known as the Witch of Agnesi, it is approached from a geometric, trigonometric and analytical point of view; using the scheme: model, algorithm, resolution, graph.
Category: Geometry

Booklet of The Corrections of Exercises and Problems - Part II

Authors: Abdelmajid Ben Hadj Salem
Comments: 86 Pages. In French

This second booklet includes the corrections of the exercises and problems of the following four chapters: topography, astronomy, curves and the theory of surfaces, ellipse and ellipsoid.
Category: Geophysics

Time as a Local Reaction to the Presence of Matter

Authors: Ioannis Chaskis
Comments: 14 Pages.

This work proposes a fundamental reformulation of time, not as a pre-existing geometricdimension, but as a localized and emergent reaction of the quantum vacuum to the presenceof mass-energy. We argue that time arises only where and when the vacuum is causallyand entropically disturbed by matter, and is otherwise undefined. A scalar field χ(x) isintroduced to represent the degree of temporal activation in spacetime, governed by a fieldequation sourced by the trace of the energy-momentum tensor. This framework offers acoherent reinterpretation of relativistic time dilation, entropy-driven temporal asymmetry,and the quantum nature of vacuum. It provides a physically grounded mechanism for theemergence of time during cosmogenesis and resolves classical paradoxes such as the initialsingularity and the horizon problem. We discuss experimental predictions and proposeobservable consequences in atomic clocks, black hole interiors, and cosmic microwave backgroundsignatures. Ultimately, the model shifts the paradigm from asking "What is time?"to "Where and under what conditions does time emerge?"
Category: Relativity and Cosmology

Concept of Electric Field Standing Waves and the Possible Mechanism Behind the Constancy of Light Speed

Authors: Kuo-Tso Chen
Comments: 8 Pages. (Note by viXra Admin: Please cite and list scientific references)

This paper proposes a concept of an electric field standing wave that does not radiate energy, using it to speculate on the nature of fundamental particles and the reason why the speed of light appears to be constant. Through a mechanism involving the reflection of a spherically symmetric electric field variation, this study explains how electric field energy can be confined to a specific space, leading to the formation of quasi-fundamental particles with mass. Furthermore, it is theorized that if both time and distance are defined by the internal oscillations of such particles, then even if the actual speed of light varies, the observed value of light speed would remain constant. This idea also provides a possible explanation for why material objects cannot exceed the speed of light.
Category: Quantum Physics

Restoring Consistency to Quantum Mechanics by Interpreting the Observer

Authors: Sonali Tamhankar
Comments: 7 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We set forward a set of axioms to interpret the observer in quantum mechanics. Our axioms treat observers as quantum states and provide rules for what they can observe. We demonstrate that our framework, which we call the NEW interpretation of Quantum Mechanics, provides a resolution of the Frauchiger-Renner paradox [1], restoring consistency to Quantum Mechanics. The resolution is brought about by a careful definition of 'Consistency', Assumption (C). With this precise definition, our interpretation satisfies all three Assumptions (Q), (C), and (S), without logical contradictions. The scope of this paper only extends to setting forward our axioms and addressing the Frauchiger-Renner paradox. Additional context for the NEW worldview, along with a matching NEW conjecture, is provided elsewhere [2].
Category: Quantum Physics

Mirror-Complement Pattern in √2 and a Simple Proof of Its Normality

Authors: Abdelrahman M. Mohammed
Comments: 11 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We begin by observing a striking "mirror-complement" pattern in the binary digits of √2: whenever, at any position, a run of k equal bits is separated by a single opposite bit from another run of bits, those two runs must have equal length. Restricting to prime-indexed positions, the same pattern remains perfectly true for millions of primes. This phenomenon is a direct consequence of the classical digit-by-digit square-root algorithm in base 2, because each comparison uses4Pn + 1 = 2 (2Pn) + 1,i.e. "copy + complement + copy."From this insight we build a two-rectangle coding on T² whose itinerary reproduces the binary digits of √2. A measurable conjugacy to the (½,½) Bernoulli shift allows us to apply Chung—Smorodinsky’s bounded-coboundary theorem (1967), showing each cylinder-indicator has a uniform sup-norm bound. Telescoping that coboundary yields a universal O(Nu207b¹) discrepancy bound on every length-ℓ binary block, proving base-2 normality of √2. Finally, van der Corput differencing and Wall’s criterion transfer the same O(Nu207b¹) bound to every integer base B ≥ 2, establishing that √2 is normal in all bases.This paper unifies these ideas—starting from the prime-indexed mirror pattern and culminating in a gap-free, self-contained proof of full normality of √2.
Category: Number Theory

Twin Primes: a Spectral Proof of the Infinitude

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

We prove the twin prime conjecture, asserting infinitely many integers x such that both x and x + 2 are prime. Construct an N × N diagonal matrix HN with diagonal entries Dx = 0 if x, x + 2 prime, and Dx ≥ 3 10 otherwise. The kernel dimension equals the number of twin primes up to N, denoted |TN|. A heat-trace argument on Tr[exp(−2HN)] forces |TN| → ∞, proving the theorem. We refine parameter bounds, standardize notation, and add explicit estimates for key constants.
Category: Number Theory

On the Gravitational Analog of Continuous Spacetime Dimensions

Authors: Ervin Goldfain
Comments: 6 Pages.

The object of this brief note is to point out that a spacetime endowed with continuous dimensions can be interpreted as dual to classical gravitation in four dimensions. This observation sheds unexpected light onto the gravitational behavior of Cantor Dust (CD), a hypothetical large-scale topological condensate of relic dimensions left over from the primordial stages of Universe evolution.
Category: Relativity and Cosmology

Methodological Fallacy in Proton Mass Radius Determination: Alternative Classical Approach Based on Einstein’s Mass-Energy Equivalence Principle

Authors: Ikechukwu Iloh Udema
Comments: 11 Pages.

No equations led to ⟨R_m^2 ⟩=6/G(0) [at]_(t=0)=12/(m_s^2 ) in which both sides of the equation are dimensionally at odds. It is appropriate to dare challenge the flaw in the procedure that produced 0.55 fm as the mass radius with many models and solutions because the charge radius and, more recently, the proton's mass radius are inconsistent. The objective is to develop an alternative theory that combines the idea of the mass-energy equivalence principle with a kinetic basis. Proving that 0.55 fm is a fabrication and demonstrating that the proton's charge radius might equal the mass radius of one up and one down quark combined are only a few of the objectives. Results were generated through theoretical and computational methods. The mass radii of protons were between 1.019699 and 1.10254513 fm; the sum of mass radii of up and down quarks was 0.8349190666 fm; the mass of the hypothetical particle was 8.911586959 exp. (−32) kg; mass radii of up and down quarks were 0.5881268197 and 0.246803591 fm, respectively; the mass radius of an electron was 0.06278280228 fm; and nucleon size—based radii of the electron are 0.08993727541 and 0.09001990394 fm, corresponding to the proton and nucleon, respectively. The idea that the charge radii may represent the mass radii of quarks is supported by the total (0.8349190759 fm) of the radii of up and down quarks in this research. The new model equation for calculating the mass radii of the electron and proton is supported by the intraproton radius (0.08993727541 fm) of the electron, which is provided by〖 ((R_mP^3)u20441836.152673)〗^⅓, where proton mass radius, R_mP = 1.10254513 fm. Since ⟨R_m^2 ⟩ ≠12u2044(m_s^2 ), 0.55 fm was a fabrication. It is almost half of 1.10254513 fm and was used to support the false claim that the proton charge radius equals its spatial extent, thereby refuting Bohr’s radius.
Category: High Energy Particle Physics

Lucas Number 123 Demystified: Mathematics of a Divine Number

Authors: Hans Hermann Otto
Comments: 9 Pages.

We show the importance of Lucas number 123, symbolized by others for divine order or trinity, as enigmatic number for life, physics and the cosmos. This number is related to fundamental constants of nature and to powers of the golden mean that governs phase transitions from particle to cosmic scale. It is also related to the Higgs boson and to the Great Pyramid. Our number theoretical approach may help to understand unsolved problems in physics and supports applications.
Category: Number Theory

A Proof of the Collatz Conjecture

Authors: Fabrice Trifaro
Comments: 45 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Using a comprehensive approach, this paper aims to demonstrate, clearly and rigorously, the validity of the Collatz conjecture. To this end, the original 3n+1 iteration is reformulated by isolating the odd terms into sequences referred to as R-Cz sequences. These sequences are analyzed through their structural properties and their distribution among the odd natural numbers. As a first essential result, it is shown that they do not admit non-trivial cycles: the only possible cycle is the trivial one, of value and length 1. Two independent proofs that all R-Cz sequences converge are then presented. The first, combinatorial in nature, relies on the finiteness of intervals that could possibly separate terms of the sequences. The second, set-theoretic, is based on a contradiction between the countability of the odd integers and the uncountable cardinality of the hypothetical divergent R-Cz sequences. Both methods lead to the same conclusion: all Collatz sequences eventually enter the cycle (1,4,2).
Category: Number Theory

A Minimal Parametric Cosmological Model Explaining Sn1a and Bao Without Dark Components

Authors: Minyoung Kwon
Comments: 44 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This theory proposes an integrated mechanism capable of simultaneously explaining a wide range of cosmological phenomena—such asgalaxy rotation curves, galaxy morphology, Type Ia supernova observations, dwarf galaxies, large-scale structures, cosmic filaments, redshift, dark energy, and dark matter. Unlike the conventional ΛCDM model, the core of this theory is the very "generation of space" itself. Through this generative framework, a vector-based model that interacts with gravity naturally emerges. In particular, the directionality and density of the space field can amplify or weaken gravitational fields. Simulations of galactic outskirts provide direct support for such dynamic behavior. quantitatively, this theory offers greater explanatory power than existing cosmological models and suggests the possibility of unified solutions to several unresolved problems in modern cosmology.
Category: Relativity and Cosmology

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

Authors: Huiwen Han
Comments: 6 Pages.

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

The Electric Dimension, Quantum Retrocausality and Preons

Authors: Austin J. Fearnley
Comments: 12 Pages.

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

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

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

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

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

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

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

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

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

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

I.q. Vs. Wisdom

Authors: Clark M. Thomas
Comments: 4 Pages.

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

Pi as Alternating Continued Fraction

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

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

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

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

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

The Origin of Inertia and the Equivalence Principle

Authors: Vincenzo Nardozza
Comments: 4 Pages.

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

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

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

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

Precise Values of the Lifetime of Positronium in Vacuum

Authors: Gang Chen, Tianman Chen, Tianyi Chen
Comments: 9 Pages. 2 Figures.

In this paper, we calculate the lifetime of ortho-positronium (o-Ps) in vacuum with Euler formula for Basil problem and our previous formulas of the fine-structure constant and the atomic unit of time (tau). Our calculated value of the lifetime of ortho-positronium in vacuum is 142.041358500909 ns in comparison to the most accurate measured value which was 142.043(14) ns and the latest QED calculated value which was 142.04606(20) ns. In addition, with the similar method we also calculate out the lifetime of para-positronium (p-Ps) in vacuum which is 0.1251627502491 ns compared to the QED calculated values 0.125162617(3) ns and 0.125162432(3) ns.
Category: Quantum Physics

On Validity in Non Standard Analysis of Riemanni Dini Theorem

Authors: Ciro Cesarano
Comments: 13 Pages.

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

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

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

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

Commercialization of Science

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

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

Quadratic Sequence Primality Test

Authors: Mar Detic
Comments: 3 Pages.

We introduce a primality testing framework based on examining the greatest common divisors (GCDs) of a candidate integer p with terms froma quadratic sequence defined by Sq = q2 + 2q for odd integers q. This approach generalizes and extends classical primality criteria by leveraging properties of quadratic forms. We formalize this method as a conjecture,analyze its computational complexity, discuss potential error cases such as pseudoprimes, and present empirical validations demonstrating its effectiveness.
Category: Number Theory