All Submission Categories

On the Low Energy Addition Chain Equation

Authors: Theophilus Agama
Comments: 3 Pages.

We develop a criterion for an addition chain to have low energy and pose a related classification problem.
Category: Number Theory

A Method [for Mapping] Cell Lineage with Mutant Mitochondrial Transfer

Authors: Jaba Tkemaladze
Comments: 15 Pages. (Note by viXra Admin: Please don't name the method after the author's name - Please conform))

The comprehensive mapping of cellular lineages from the zygote to a fully formed organism remains a fundamental and unresolved challenge in developmental biology. While modern single-cell technologies offer snapshots of cellular heterogeneity, they lack the inherent, permanent markers required to trace progeny through the complex events of asymmetric division and migration over time. This work introduces the Tkemaladze Method, a novel lineage-tracing approach that utilizes mutant mitochondrial DNA (mtDNA) as a stable, inheritable genetic label. The method involves the isolation of mitochondria from cytoplasts harboring known pathogenic mtDNA mutations and their microinjection into murine embryonic stem cells (mESCs). We confirmed successful transfer and functional integration via fluorescence microscopy and quantitative PCR. These labeled progenitor cells were used to generate chimeric embryos, where we demonstrated stable heteroplasmy and faithful inheritance of the mutant mtDNA in clonal progeny throughout development. Using fluorescent reporters, we visualized the fate of individual progenitors, enabling the quantitative construction of a detailed cytogenealogical map across tissues like the central nervous system, liver, and myocardium. A key finding was the tissue-specific segregation of mitochondrial tags, revealing selective pressure in high-energy-demand tissues. The Tkemaladze Method thus provides an unprecedented, powerful tool for fundamental developmental biology, disease modeling, and tracking the fate of transplanted cells in regenerative medicine.
Category: Biochemistry

An Alternative Derivation of Length Contraction Using Einstein’s Own Thought Experiment

Authors: Phuc Le, Jokubas Tamulis
Comments: 6 Pages.

By now, every high school Physics student has been familiar with the famous Special Theory of Relativity proposed by Einstein. The foundation of Special Theory of Relativity rests on two postulates: (1) The laws of Physics are the same in all inertial frames of reference and (2) The speed of light in a vacuum c = 3 × 10^8 m/s is the same in all inertial frames of reference. The consequences of such postulates are thefamous Time Dilation and Length Contraction formulas. Historically, in his paper Onthe Electrodynamics of Moving Bodies (1905), he derived Length Contraction through Lorentz Transformation. However, this article explores another way Length Contraction could have been discovered: through changing one bit of Einstein’s thought experiment, using the mathematical tool of infinite sum.
Category: Relativity and Cosmology

Commentary on A^3+b^3 = 2(2^5 C^3)

Authors: Fian Qnoz
Comments: 6 Pages. (Note by viXra Admin: Please cite and list scientific references)

Diophantine equation of the form a^3+b^3 = 2(2^5 - c^3)relates to the quadratic equation 1 + 4n + 4n^2 which further relates to 1x^3 + 4y^3 + 4z^3 = 512 whose parametric solution for x is exactly is the twice of the square of odd number > 1, i.e. 2(2n+1)^2. Considering phi (sum of the odd divisors of 2(2n+1)^2) is exactly equal to phi (sum of the even divisors of 2(2n+1)^2), some interesting properties involving Piltz functions and Jordan totients were conjectured.
Category: Number Theory

Φ Geometry in Physics: a Single Angle for SR, Energy—momentum, and Numerical Stability

Authors: Mikheili Mindiashvili
Comments: 3 Pages. (Note by ai.viXra.org Admin: Author name should be listed after the title; please cite and list sceintific references)

Φ geometry is a visual re-parameterization of standard relativistic relations via one angle φ on a unit (or c-scaled) circle. One diagram unifies β, γ, E, p and velocity addition. Complementarity (sin ↔ cos) removes "bad denominators" and makes edge cases numerically stable.
Category: Classical Physics

A Heuristics on Primes in an Addition Chain

Authors: Theophilus Agama
Comments: 5 Pages.

Let E(n): 1 = s_0 smaller than s_1 = 2 smaller than u2026 smaller than s_h = n, with h on the order of n to the power 1 minus epsilon (for some small positive epsilon), be an addition chain leading to n. We develop a heuristic for the least number of primes in an addition chain for all sufficiently large targets n.
Category: Number Theory

Alternative Formulation of SERS Enhancement Through Matter-Resonance Coupling

Authors: Edwin Maina
Comments: 3 Pages.

We present an alternative theoretical approach to calculating Surface-Enhanced Raman Scattering enhancement factors using matter-mediated resonance coupling. The framework parametrizes field enhancement through β(E,ρ) = βu2080(ρ/ρu2080)^0.2 Σu2099 Γu2099/[(E-Eu2099)²+Γu2099²], where coupling strength depends on local energy density ρ and resonance with matter excitations at energies Eu2099. For gold nanoparticle hotspots at plasmon resonance (E = 2.3 eV, ρ = 2×10²u2078 eV/m³), this approach yields β = 179, producing enhancement factors consistent with classical electromagnetic predictions when coupled through molecular susceptibility χ ≈ 10u207bu2074. The formulation offers complementary physical insight by explicitly incorporating matter's spectral response into the enhancement mechanism, suggesting that field concentration and material resonances are coupled rather than independent effects. While numerically equivalent to established methods for standard SERS configurations, this framework may provide computational advantages for complex multi-resonance systems or guide design of resonantly-optimized nanostructures.
Category: Condensed Matter

Beyond the Data: Analysis, Feature Engineering and Browser Plugin Expansion for the Sharelm Dataset

Authors: Samer Attrah
Comments: 9 Pages. 3 tables, 5 figures

As part of the Eleuther AI open AI summer research this year, we worked on expanding the ShareLMdataset browser extension, by adding support to multiple models in addition to redesigning some ofthe visual parts of the extension, in the mean time conducted several analysis and feature engineeringon the ShareLM dataset to extract insight regarding the models, users, the conversations and therelations connecting them.
Category: Artificial Intelligence

Principal Limitation of Metric Measurements in Real Radial Gravity Fields

Authors: Holger Döring
Comments: 4 Pages.

Since there are no real inertial systems in reality, when a weak gravity field appear, because only radial gravity fields exist and no homogenous fields, there only a quasi inertial system (QUIS) can be constructed in these fields. Real inertial systems are only constructable in fieldfree spaces, far from every material body and neglecting quantum gravity structures. If gravity fields appear, even weak ones like in example of Earth field, only QUIS are constructable. This QUIS allows only a limited description of physical measurements because it deals with radial field lines of gravity, which are supposed to have a range of Planck-length at the center of Earth resp, the material body. Then the smallest QUIS, which can be constructed on the surface of planet Earth has a range of ca. 10u207b¹u2075 m. Smaller metrical length statements on the surface of Earth are senseless. If the measurements have to be finer, one must go afar from surface of the planet, where the radial field lines have greater distance and in this case greater QUIS can be defined. Then physical behaviour of interactions then can be described without contradictions in smaller ranges.
Category: Quantum Gravity and String Theory

A Wavelike Gravitational Potential as the Origin of Dark Matter and Energy

Authors: V. B. Verma
Comments: 13 Pages.

Motivated by the observation made by R. H. Dicke in 1957 that the speed of light seems to be correlated with the gravitational potential of the entire universe, we suggest a modification of general relativity to incorporate a wavelike gravitational potential. We show that the gravitational force derived from such a potential is an emergent property of matter and critically dependent on the distribution of mass on both local and global scales throughout the universe. The theory is free of gravitational singularities. It provides a path to numerically computing the critical acceleration in modified Newtonian dynamics theory (MOND), providing an alternative explanation for dark matter. Finally, we develop a cosmological model and fit the model to high-redshift supernova data from the Supernova Cosmology Project, showing that we obtain an excellent fit with only baryonic matter.
Category: Relativity and Cosmology

Photon as a Soliton

Authors: Miroslav pardy
Comments: 11 Pages. Original article

We have used the logical arguments for the proof that photon is a soliton. Neutrino is also a soliton due to the the experimental argument following from the neutron decay. However, with regard to the fact that every elementaryparticle has also so-called soliton parity, it is not excluded that the soliton parity of K0-mesons and pi0-ions are also broken. This experimental possibility was not still confirmed. Nevertheless, it can be confirmed by the brilliant interferometric experiments because the broken soliton parity leads to thebroken interferometry maxima and minima.
Category: High Energy Particle Physics

A Finite - State Deterministic Approach To Resolve The Collatz Conjecture

Authors: Aditya Bagchi
Comments: 50 Pages.

This paper presents a complete proof of the conjecture by demonstrating that both of the counterargument scenarios are mathematically impossible. Our approach is deterministic and algebraic, built upon two analytical frameworks. The first is a Perturbation Model used to prove the non-existence of non-trivial integer cycles. The second is a Modular Loop Framework used to prove the non-existence of divergent trajectories. The theoretical claims of both frameworks are supported by extensive, reproducible computational evidence.
Category: Number Theory

The Law of Diamond Crystallogenesis

Authors: Volodymyr Kaplunenko, Mykola Kosinov
Comments: 11 Pages.

A new electronic mechanism for diamond crystallogenesis is proposed that considers diamond synthesis at the microscale (atomic and subatomic levels) rather than in terms of the traditional macroscale conditions of high pressure and temperature (P-T). This challenges the traditional understanding of diamond formation and demonstrates for the first time that the fundamental Coulomb interaction is involved in the synthesis process. The law of diamond crystallogenesis is derived from this synthesis mechanism. This law states that the rate of diamond growth is determined by the number of electrons involved and the oxidation state of carbon. Pressure and temperature play a supporting role and serve as triggers that initiate the electronic mechanism of diamond synthesis. This law suggests that electrons act as crucial catalysts, facilitating the transition of carbon to the C-4 state, where it can form the diamond lattice through the Coulomb interaction, which is much stronger than the forces achieved by pressure. Electrons play a fundamental role in modifying the reactivity of carbon and a key role in the formation of covalent bonds. The law is mathematically expressed using fundamental constants. The discovery of the law of diamond crystallogenesis dispels the myth of millions and billions of years required for diamond formation, as well as the myth of pressure and temperature as direct factors in diamond formation. The law of diamond crystallogenesis and the electron mechanism of diamond crystallogenesis point to the reality of ultra-fast diamond synthesis at atmospheric pressure and low temperatures.
Category: Chemistry

All Lyman, Balmer, Paschen and Brackett Lines Are in Superresonance

Authors: Marek Suder
Comments: 6 Pages.

The paper presents an extended analysis of the structure of the hydrogen atom spectral lines, based on the concept of superresonance — a phenomenon in which all Lyman, Balmer, Paschen and Brackett resonances (for n ≤ 7 and m ≤ 4) exhibit complete harmonic relations with respect to the λu2080 wave.The frequency values form a discrete raster with a constant spacing of approximately 18.64 GHz. The results indicate the existence of a universal harmonic structure in the hydrogen spectrum, opening new possibilities in spectroscopy and the theory of atomic interactions.Based on this, the concept of a subquantum (sQ) was introduced, defined as the smallest unit of photon energy with a value of εu2080 ≈ 7.71 × 10u207bu2075 eV, equal to 1/3969 of the H(5→4) transition energy. This unit allows the construction of a resonance grid in which all analyzed transitions are arranged in integer multiples of the fundamental frequency.The proposed approach suggests that the hydrogen spectrum is governed by a simple harmonic system, extending the classical Bohr—Rydberg model with a deeper level of discretization. This method reduces measurement uncertainties and opens up new possibilities for precise spectroscopic calibration, enabling not only the description of known transitions but also the prediction of previously unobserved line parameters.
Category: Mathematical Physics

Analogy as the Core of Intelligence

Authors: Akira Pyinya
Comments: 22 Pages.

This article argues that the core of intelligence is not optimization, but analogy. We define intelligence as "doing the same thing as the examples of the right thing to do in new situations." We transform Hofstadter's Copycat problem into a sequence prediction problem to derive a formal definition of analogy-based intelligence, from which value functions and temporal-difference error can be derived, showing that optimizers can be derived from analogy-based systems. We demonstrate how agency and free will arises from conflicts between different predictions based on different examples.
Category: Artificial Intelligence

A Consistent Framework for Emergent Gravity from a Primordial Tensor Field

Authors: Salvatore Minutoli
Comments: 8 Pages.

We present a mathematically consistent formulation of a holographic model where 4D gravity and matter emerge from a single primordial tensor field in a 10-dimensional bulk spacetime. The model is defined by a Z_2 -symmetric action with a quadratic potential, V(I)=1/2 m^2 I_B^A I_A^B, ensuring stability. We derive the full effective potential for the radion field, rigorously incorporating contributions from higher-dimensional curvature, field gradient energy, potential energy, and a stabilizing Freund-Rubin flux. We demonstrate analytically and numerically that a stable minimum exists for realistic parameters, naturally generating the Planck-electroweak hierarchy. The emergence of the Standard Model is not presented as a derived result but as a concrete research program based on orbifold compactifications and the index theorem. The model predicts a TeV-scale radion, deviations from Newtonian gravity at short distances, and gravitational decoherence, providing clear avenues for experimental verification.
Category: High Energy Particle Physics

Black Holes’ Edges Are not Like You Were Taught: Radial Null Geodesics in the Oppenheimer—Snyder Metric

Authors: Miquel Piñol
Comments: 4 Pages.

It is widely assumed that collapsing stars become black holes.It is also commonly accepted that the edge of a black hole, its so-called "event horizon", is a surface that can be crossed inward but not outward.However, a collapsing star is properly described by the Oppenheimer—Snyder metric, which corresponds to an eternal asymptotic process in Schwarzschild coordinates, and, as we show, its edge can be crossed outward, but not inward.
Category: Relativity and Cosmology

On the Model of Neutrinos Oscillating at the Speed of Light Described by the Klein-Gordon Equation of Infinite Degree

Authors: R. K. Salimov
Comments: 3 Pages.

This paper discusses equations containing high powers of the Klein-Gordon operator. In the limit of large powers, these equations are shown to have solutions that propagate at light speed and oscillate. These solutions exhibit a definite helicity. Such equations could be relevant for developing models of massless oscillating neutrinos.
Category: Quantum Physics

Aberration Effects Can Account for the Apparent Surplus of Spiral Galaxies Rotating in an Opposite Direction to the Milky Way

Authors: P. G.Vejde
Comments: 4 Pages. (Note by viXra Admin: The list of scientific references are incomplete)

Recently published analysis of JWST deep field images confirms the previously observed trend for a surplus of spiral galaxies that rotate counter to our Milky Way. A trend that apparently is most pronounced the closer one looks towards either the north or south Milky Way polar axis. This is considered in recently published analyses to be inconsistent with current theories of the Big Bang. It is also suggested in these analyses that this surplus may only be an observational bias. Due possibly to Doppler shifting from the relative rotation directions between spiral galaxies and our own Milky Way. Or that new physics of galaxy rotations not yet discovered may also be able to account for the apparent surplus. However, the authors of this research also note that Doppler shifting of light from the relative rotation velocities and rotation directions between any one galaxy and the earth observer would be insufficient in magnitude to account for the approximately 50% surplus of counter rotating galaxies in the latest deep field JWST data. In this paper the aforementioned observational bias is still considered a possibility simply by invoking the centuries old classical effect of Stellar Aberration to model the apparent surplus of counter rotating galaxies seen in the data. In that due to differences in transverse rotational directions and internal stellar velocities between any observed spiral galaxy and our own Milky Way, the displacement effects of stellar aberration will make light from co rotating galaxies incident to the earth observer more dispersed or blurred than light coming from counter rotating galaxies. Thus, making it harder to identify co rotating spiral galaxies than counter rotating spiral galaxies at any similar redshift. Resulting in an apparent surplus of counter rotating galaxies in the universe.
Category: Astrophysics

Red Teaming Quantum-Resistant Cryptographic Standards: A Penetration Testing Framework Integrating AI and Quantum Security

Authors: Petar Radanliev
Comments: 33 Pages.

This study presents a structured approach to evaluating vulnerabilities within quantum cryptographic protocols, focusing on the BB84 quantum key distribution method and National Institute of Standards and Technology (NIST) approved quantum-resistant algorithms. By integrating AI-driven red teaming, automated penetration testing, and real-time anomaly detection, the research develops a framework for assessing and mitigating security risks in quantum networks. The findings demonstrate that AI can be effectively used to simulate adversarial attacks, probe weaknesses in cryptographic implementations, and refine security mechanisms through iterative feedback. The use of automated exploit simulations and protocol fuzzing provides a scalable means of identifying latent vulnerabilities, while adversarial machine learning techniques highlight novel attack surfaces within AI-enhanced cryptographic processes. This study offers a comprehensive methodology for strengthening quantum security and provides a foundation for integrating AI-driven cybersecurity practices into the evolving quantum landscape.
Category: Artificial Intelligence

Radial Signatures and Pulsars

Authors: Roberto C. M. Navacchia
Comments: 8 Pages. In Portuguese; License: CC BY-NC (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper presents an alternative method of analysis for identifying pulsars using data from the High Time Resolution Universe Survey neutron star catalog and the construction of radial curves derived from statistical parameters of the observed radio signals, where, through a geometric approach, highlights their unique and distinct signature for each pulsar, which differs significantly from the curves produced by noise signals. The method seeks to offer the scientific community a complementary means of classification, opening up possibilities for the creation of a ‘Geometric Atlas of Pulsars’ useful in Astrophysics, Data Science, Quantum Mechanics, and especially in Analytical Geometry.
Category: Geometry

The Tri-Quarter Framework: Radial Dual Triangular Lattice Graphs with Exact Bijective Dualities and Equivariant Encodings via the Inversive Hexagonal Dihedral Symmetry Group T₂₄

Authors: Nathan O. Schmidt
Comments: 78 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The Tri-Quarter framework unleashes a radial dual triangular lattice graph with unified complex-Cartesian-polar coordinates, structured orientation phase pair assignments for directional labeling, and topological zones to build exact bijective mappings without approximations. By establishing combinatorial duality for radial separation, Escher reflective duality for zone swapping, and bijective self-duality for reversible transformations, the discretized framework leverages the lattice graph's order-6 rotational symmetry to natively support angular sectors, modular decompositions, equivariant encodings, and trihexagonal six-coloring for conflict-free parallel algorithms. At this discretized framework's core is the Tri-Quarter Inversive Hexagonal Dihedral Symmetry Group T₂₄—the order-24 semidirect product D₆ ⋊ Z₂—which exploits rotational, reflective, and inversive symmetries to unlock these bijective transformations with exact precision. We provide formal proofs of these dualities, along with numerous step-by-step examples, and demonstrate practical efficiency through benchmarked simulations to achieve ~2x speedups with inversion-based path mirroring via bijections and up to ~6x reductions in symmetry-reduced clustering via rotational orbits. This work advances scalable computations on symmetric structures, with applications in computational geometry, graph traversals, tiling, robotics path planning, multi-agent coordination, lattice-based cryptography, image processing, and signal processing. This work aims to solidify a mathematical and computational foundation for both classical and non-classical computing paradigms—targeting future integrations in complex emergent systems that harness intricate “superposition-like” symmetries to advance symmetry-aware algorithms and data structures across diverse computing architectures.
Category: Data Structures and Algorithms

Generative Models Enable True Understanding: The Link Between Interpretability and Generative Ability

Authors: Yuan-Hao Wei
Comments: 9 Pages.

Interpretability and generative capability in generative models are fundamentally two complementary aspects. A highly interpretable model typically learns the true underlying generative mechanisms behind data, such as physical laws, causal relationships, or explicit structures. As these mechanisms are inherently stable and universally applicable, such models can reliably generalize beyond training data, producing more reasonable and robust samples with fewer generation failures. In addition, a highly controllable and powerful generative model implicitly or explicitly captures genuine and effective underlying rules. The ultimate goal of training generative models should extend beyond obtaining high-quality samples to exploring and understanding the underlying generative mechanisms of phenomena. When a generative model demonstrates controllability and scalability with respect to a dataset, it indicates the model has genuinely learned the mechanisms that generate the data. This opens up a paradigm in scientific research, enabling the discovery of underlying principles through observational data reconstructed by generative models, particularly when these models exhibit controllability and scalability. Leveraging powerful nonlinear mapping, efficient iterative training, and structured interpretability, artificial intelligence holds the potential to uncover and understand rules and principles currently beyond human knowledge.
Category: Artificial Intelligence

A Lowest Boundary for the Density of Twin Primes Maintains Their Cardinality

Authors: Jérôme Chauvet
Comments: 4 Pages.

We adress here the TPC (Twin Primes Conjecture). Considering the unique growing list of twin primes as elements of a dynamical system with invariant transformation law on, we infer a lower boundary for their density along the real axis incompatible with their finiteness. Although non constructive, since we do not prove a general formula for finding twin primes pairs arbitrarily great, this proof relies for closure on the tertium non datur principle with regard to their minimal density, and thus their cardinality at infinity
Category: Number Theory

Doppler Effect in Special Relativity of Fields

Authors: Enrique Domínguez Pinos
Comments: 19 Pages. In Spanish

The Doppler effect is the change in frequency of a wave that a receiver experiences due to its relative velocity with respect to the source. As we will see, in the special relativity of fields, we will also take into account other effects such as the potential.
Category: Relativity and Cosmology

Lorentz-Covariant Hamiltonian Mechanics and its Quantization

Authors: Steven Kenneth Kauffmann
Comments: Pages.

The Lorentz-covariant upgrade of Newton's Second Law sets a particle's mass times the second derivative with respect to its Lorentz-invariant proper time of its observed space-time location equal to the four-force applied to it. Hamiltonian mechanics yields the Lorentz-covariant upgrade of Newton's Second Law when the Hamiltonian is a Lorentz-invariant function of the particle's observed space-time location and conjugate four-momentum, and the time derivatives of these two Lorentz-covariant four-vectors are taken with respect to the particle's Lorentz-invariant proper time. Very simple Lorentz-invariant Hamiltonians that yield the electromagnetic Lorentz Force Law and the gravitational geodesic equation are pointed out, as is the straightforward quantization of Lorentz-covariant Hamiltonian mechanics. The zero-mass limit of the relativistic free-particle Schrödinger equation has the simple second-order wave-equation form which is characteristic of source-free electromagnetism. The relativistic correction to the hydrogen atom without spin is a very weak, short-range complement to the Coulomb potential.
Category: Classical Physics

An Implicit Assumption in Standard Cosmology May Lead to Systematic Biases in the Real Universe

Authors: Liu Enjun
Comments: 28 Pages. The core point of this paper is : The standard cosmological model , by default using volume - weighted average .parameters in the path integral formula to calculate the luminosity distance of supernovae , leads to a systematic underestimation of the predi

This paper focuses on analyzing the following four aspects:First, light passing through galaxy clusters "lacks" a portion of cosmological redshift. The universe is expanding, but galaxy clusters, bound by gravity, do not expand. Consequently, light traversing a galaxy cluster does not undergo cosmological redshift during its passage through the cluster.Second, the expansion of galaxy clusters affects the calculation of the average scale factor of the universe in the past.Third, galaxy clusters accumulate a large amount of matter, leading to a reduction in the matter density of void regions. Although the matter within galaxy clusters also participates in constraining cosmic expansion, its constraining effect on the expansion of void regions is relatively small. This results in a slower time evolution of the expansion rate in the void regions of an inhomogeneous universe, implying that the age of our universe is greater than that of a homogeneous universe. Even the expansion rate of void regions (at the same time calculated backward from the present) is lower than the value predicted by the homogeneous model. By combining the time evolution curves of the Hubble parameter in both models, this paper demonstrates that even after supplementing the "missing" redshift caused by light passing through galaxy clusters, the distance to supernovae calculated using the homogeneous model formula remains smaller than that derived from the inhomogeneous model.Fourth, the standard cosmological model, which默认 uses the volume-weighted average Hubble parameter in the path integral formula to calculate supernova distances, has significant systematic biases. It employs the FLRW metric, effectively treating the large-scale uniformity of the universe as absolute uniformity. This introduces an implicit assumption that the volume-averaged Hubble parameter is equal to the path-averaged Hubble parameter, leading to substantial systematic errors in distance measurements. For example, at a certain redshift, in the model established herein, based on the derived formulas for the path-averaged and volume-averaged Hubble parameters combined with astronomical observation data, the supernova brightness calculated using the path-averaged Hubble parameter is 75% of the brightness predicted by the homogeneous model, while that calculated using the volume-averaged Hubble parameter is 99.1% of the predicted brightness. These results suggest that the formation of stable structures in galaxy clusters may be a crucial reason why the observed brightness of distant supernovae is dimmer than predicted.This paper is an exploratory study and has not yet undergone cross-validation. Any errors are welcome to be criticized and corrected.
Category: Relativity and Cosmology

Unified Framework for Efficient Cross-Lingual Transfer Learning Across Low-Resource Languages Using Knowledge-Augmented Multilingual Models

Authors: Ritika Budhiraja, Bhaumik Tyagi, Sagar Kumar Jha
Comments: 9 Pages.

Cross-lingual transfer learning is incredibly promising for facilitating knowledge transfer between languages, particularly for low-resource languages that lack annotated data. However, many current methods are inefficient in terms of adaptation, have poor generalizability, and often fail to incorporate external real-world or linguistic knowledge. This paper introduces a Unified Framework for Efficient CrossLingual Transfer Learning Across Low-Resource Languages using Knowledge-Augmented Multilingual Models. The approach integrates structured and unstructured knowledge sources, such as multilingual knowledge graphs, lexical resources, and cross-lingual embeddings, into pre-trained multilingual language models (like XLM-R and mT5) through adapter-based fine-tuning and prompt-guided alignment. This creates a task-agnostic transfer pipeline that jointly optimizes for semantic alignment, knowledge consistency, and lowresource adaptability across multiple NLP tasks, including machine translation, named entity recognition, and question answering. Experimental results on 25 typologically diverse languages, including some with fewer than 10,000 training examples, demonstrate that the framework achieves state-of the-art performance, significantly surpassing current multilingual baselines in zero-shot and few-shot regimes. Furthermore, ablations reveal the critical contribution of knowledge integration to improving contextual disambiguation and representation fidelity for low-resource languages, providing a foundation for creating scalable, knowledge-driven multilingual systems that help close the digital linguistic divide.
Category: Artificial Intelligence

The Two Particle Model of the Atom and the Universe

Authors: Paul G. Leader
Comments: 71 Pages. (Note by viXra Admin: Please cite and list scientific references)

We have known for over 100 years that charge is quantised. A quantum of charge is real and precisely measured with a known charge of 1.6x10-19 Coulombs. The new physics in this paper simply acknowledges positive and negative quanta to be the two sole fundamental particles from which everything in the universe is made.This then provides us with a single rational explanation for everything from neutrinos to galaxies, based entirely upon knowns and observed reality. This contrasts strongly with the current mutually incongruent mainstream models which are based largely upon hypotheticals and complex mathematical realities.The quanta in The Two Particle Model are the familiar negative and positive points of charge that give the electron and the positron their net unit charge. These two fundamental quanta mutually attract under the influence of the strong positive-negative fundamental force to form tiny net-neutral quantum dipoles. All universal space exists, and has always existed, simply as an infinity of quantum dipoles. Everything from the appearance of the first sub-atomic particles to the formation of stars and galaxies then follows naturally and rationally from this one simple premise.
Category: Nuclear and Atomic Physics

Why a Combination, (N, K), is Always a Natural Number? Different Way to Look at the Answer Accentuates the Generation Process of Factors and Prime Numbers Contained Within a Particular Range of 1 to n.

Authors: Amit Kumar
Comments: 16 Pages. Appendix and supplementary material can be obtained upon the request.

The concept of combination is crucial to layout groundwork for many fundamental sciences, finance and technical domains. There are multiple known methods to show that the combination (binomial coefficient) is integral in nature. This article approaches the same concept with simple non-inductive algebraic steps that can be followed by a wide range of audiences. This article separates an ${n choose k}$ into mutually exclusive and collectively exhaustive cases and then shows for each case that any term in a denominator have at least one corresponding multiple in the numerator. All k for a particular n (for an ${n choose k}$) are visualized through plots to gain better understanding. In the context of the plots, this different way of looking at a Combination ${n choose k}$, gives hindsights into the generation process of factors and prime numbers contained within a particular range of 1 to n.
Category: General Mathematics

Imagining the Shape of Space

Authors: Huseyin Ozel
Comments: 51 Pages.

This work comprises an effort to develop a framework to construct various space geometries in 3 and higher dimensions, and also in flat and curved settings. Such construction is based on scientific knowledge, existing approaches, and own approach and imagination. Higher dimensional geometries are presented in forms of 2 and 3 dimensional projections. Curvature settings are considered along regular object bending and also gravitational space warping, however the exact space curvature is rendered according to a proposed methodology that makes use of glissette geometric formation to resolve the shape of space under expansion and contraction conditions. The resulting geometric forms point to potential various physical shapes of the universe and possibly offer an opportunity to help expand our imagination and understanding of the universe.
Category: Relativity and Cosmology

Er != EPR :A Machine Readable ZKP

Authors: Anival Barca
Comments: 15 Pages.

We rigorously follow the foundational principles of Einstein, Podolsky, Rosen, and Sommerfeld to their natural conclusions and present an operational critique of the ER = EPR conjecture. Employing the bedrock axioms of symmetry and repeatability, which demand that identical experiments yield consistent, directly measurable results; we evaluate the observable claims of both theories without introducing new formalisms. Our analysis reveals that the ER = EPR equivalence is internally inconsistent: the Einstein-Rosen bridge, as a consequence of general relativity's Lorentzian foundation, implies the physical reality of transformed coordinates, which we demonstrate violates repeatability. In contrast, the EPR criterion of reality and Sommerfeld's 1909 spherical model align strictly with direct observability. Via the CST appendix we demonstrate that Sommerfeld's geometric framework naturally satisfies the EPR criterion, reformulating entanglement as deterministic antipodal symmetry on a sphere and offering a collapse-free model of quantum measurement. The results expose a fundamental paradox within Einstein's own legacy, showing that his 1935 papers on ER and EPR advance irreconcilable interpretations of physical reality under the constraints of symmetry and repeatability. This work does not propose new ideas but reveals that the natural conclusions of these classic works are logically incompatible, challenging the coherence of the ER=EPR conjecture.
Category: Relativity and Cosmology

On the Product Distribution on Runs in a Chain

Authors: Theophilus Agama
Comments: 14 Pages.

Let E(n): 1 = su2080 < su2081 = 2 < u2026 < s_h = n be an addition chain leading to n in [2^m, 2^{m+1}). We study the distribution of the logarithmic partial sum ∑ log(s_i) on maximal consecutive steps of a given type.
Category: Number Theory

The Original Electron-positron Pairs Are Pseudo-bosons Because They Are Causally Separated by Inflation

Authors: Dominique Mareau
Comments: 9 Pages.

The local experimental production of electron-positron pairs or proton-antiproton pairs clearly indicates their instability. But if positrons are isolated, their annihilation is temporarily avoided. Positrons thus causally separated from ambient particles prolong their lifetime. It is clear that the protons forming the matter of the universe are stable. It is proposed here that the original inflation causally separated the elements of each electron-positron pair. The cosmological principle stipulates the identity between all localities. However, there is a duality of locality between any "Locality-type" and the Original Non-Locality (ONL) caused by inflation proposed by Alan Guth. It is reasonable to think that inflation could have causally separated each element of electron-positron pair from the same original source. Thus relocated, these elements of pairs from different sources can merge without annihilating each other. Thus becoming stable, the ONL type electron-positron pair is a candidate to be the elementary particle suggested by John Wheeler. Beyond the falsification criterion, this paradigm resolves several fundamental enigmas, including the mass of the proton and the strange identity of its charge with that of the positron.
Category: Astrophysics

The Role of the Hubble Parameter in Galactic Rotation Curves and Spiral Morphology

Authors: E. P. J. de Haas
Comments: 21 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We investigate the influence of the Hubble parameter H(z) on galactic dynamics and morphology. By introducing the cosmic expansion as an effective limit on Newtonian gravitation, we obtain a redshift-dependent critical radius that constrains both spiral structure and rotation curves. Galactic bars are interpreted as frozen spirals of high-z epochs nested inside extended low-z spirals. This framework naturally explains the coexistence of bulges, bars, disks and halos as the outcome of metric inflow and bulge reset events. The resulting morphology and kinematics provide a direct and testable connection between galactic structure and the cosmic expansion. We argue that this approach opens a new possibility to empirically derive H(z)from galaxy morphology and rotation curves and allows reconstructing the expansion history of the universe on galactic scales.
Category: Astrophysics

Characterization of Perspective Affinities that Preserve Arc Length and Curvature

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

In this work, a precise characterization is given of those perspective affine reflections that preserve both the arc length and the magnitude of curvature for any smooth planar curve. The result shows that the only non-trivial transformation with this property is the orthogonal reflectionwith respect to the given axis, i.e., the perpendicular affine symmetry with characteristic constant k=-1.
Category: Geometry

The Structure of Thought and Knowledge (The Kerigma of Thought)

Authors: Carles UDINA i COBO
Comments: 71 Pages.

Thought characterizes Homo. "Thinking" is a repeated word, present in any conversation or writing. But is there a detailed definition of what it is strictly? It is unquestionable that it is a mental faculty, that is, a psychic faculty. But then, is it a sense?, is it a feeling?, is it a knowledge?, is it an intuition?, ... No, none of them on its own. Thought is an intimate combination of many other simpler faculties, that is, a clear "complexation" of them. Consequently, it must have a structure based on its generating components. But, has anyone heard which faculties compose it and how they progressively structure it? The reference RAE dictionary for Spanish-Castillian says: "Faculty or capacity to think" which is a tautology; as well as "Action and effect of Thinking", which is a serious polysemy. They do not improve at all in psychology dictionaries, which often solve it with a potpourri of synonyms. And if we search for their structure, proposals like "Concept, judgment, reasoning and demonstration" or similar, there are no structuring. Some even perceive thinking as a vice to be eradicated. It is also common and logical, the question: "What is it that science still does not know?", about which even classifications have been developed, the top 25 problems, the top 125, ... But, curiously, always forgetting the most important thing: "how can man know the many things that we already know?", but neither is asked nor is it known. The "Representation of knowledge" is a detailed description of the psychic processes that allow human knowledge, but surprisingly, it has never been described before! We know everything and a lot, except what allows us to know all this. In my opinion, it is the biggest "black hole" of science. In "The Representation of Knowledge..." (see [A]) it was clear, that even with two searches with "AI" asking: "How do we know?" or "What faculties allow human knowledge?", the ambiguous answers confirm that it is totally unknown to science, a "black hole". And knowledge is undoubtedly at the core of thought, as will be seen. I do not think that 71 pages are many to answer clearly and definitively what thought is and how it is structured, and how knowledge is acquired. Nor do 87 pages to do the same with "What is consciousness(-raising)?" [1], both faculties that have eluded science for centuries. They are also related, which is why I wrote these two articles that explain them in the same year, 2007. This article presents the 4 structural levels of thought, and how each one progressively results from the previous one. 0) A previous level or "level zero" (the "Sensitive Identification", auditory and tactile from the last months of the fetus, and visual from the first months of the baby), 1) a first level of the sensitive or simple Conceptuation from two years of age, 2) a second level of the virtual or composite Conceptuation, 3) the level of strict or relational Knowledge from six years of age, and 4) a fourth level of the Method, from which applications such as Reasoning and Logic are derived. There is a close relationship between this article with the logic from FREGE and GÖDEL. And in addition, I have been writing lately the recent articles of "The knowledge of children at 2 years old" [C], "... at 3 years old" [D], "... at 6 years old", and "... at 10 years old", even more detail the central part of this structure, which is how knowledge progresses with age. "Knowledge" but in its strictest interpretation, the most understanding and relational one, not in synonyms such as "Acquaintance", "Factual or historical knowledge", ... And at the same time it clarifies what other related concepts such as "Abstraction", "Idea", "Understanding", ... The article describes the cognitive evolution of the child, and we have all been there before. It is like the intellectual biography of any person. The reader will be among the first to know what knowledge is and the thought that encompasses it. In addition, intrinsic semantics is introduced, a new discipline that intersects mathematics and psychology, without which it is not possible to do science of knowledge in a serious way. Finally, we say that thought should be free, but, ¿is it true that we can think freely, as we want? Or, seeing the antagonisms that exist, ¿perhaps we can only do so within certain limits, those that condition us by the feelings of our unconscious, intimately related to thought?
Category: Mind Science

UFO/UAP Versus Hellfire Missile

Authors: Clark M. Thomas
Comments: 7 Pages.

Early this month a spooky public Congressional hearing was held. It dealt with newly revealed 2024 military drone footage; plus individual military witnesses of other alien phenomena. Our military drone clearly tracked something, but nobody seemed to have a clear idea of what the drone saw. This essay attempts to advance our deeper understanding.
Category: Astrophysics

Spectral Analysis of State Space Models in Language Modeling: Training Dynamics and Stability Properties

Authors: Zayan Hasan, Aniketh Malipeddi, Aneesh Chatrathi
Comments: 5 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

State Space Models (SSMs) have emerged as a new linear computational complexity transformer rival to sequence modeling on long sequences with competitive performance. The dynamics of training and stability properties of SSMs remain poorly understood from a spectral perspective. This work presents the first wide reaching spectral analysis of SSM based language models. Providing a systematic framework to examine how eigenvalue distributions and spectral radii evolve during training, through experiments on a 737K parameter SSM model having 3 layers, state space dimension 128, and model space dimension 8, it was discovered that although the minority of the state matrices learned lead to theoretical spectral stability with mean spectral radius 1.078. The model demonstrates excellent convergence however, reducing training loss from 3.127 to 0.305 using 100 epochs. The eigenvalue analysis demonstrates common clustering in the negative real axis with concentration centered about negative 0.8, exhibiting a bimodal spectral radius distribution exhibiting systematic behavior in SSM dynamics. The key result portrays that SSMs operate efficiently in scenarios such as these. The selective mechanism provides adaptive control that prevents mathematical instabilities from causing training divergence. This renders assumptions of classical neural network stability hard to maintain and makes spectral analysis an essential for understanding similar model behavior. This work provides practical insight toward constructing more principled, stability aware designs for such models and frameworks.
Category: Artificial Intelligence

Application of Lagrangian Mechanics to the Analysis of Particle Dynamics in a Gravitational Field

Authors: Vladimir B. Belayev
Comments: 18 Pages.

The dynamics of particles in a gravitational field is investigated using Lagrange mechanics. Dynamic equations are obtained, including the rate of energy and momentum transfer to the gravitational field. The motion of particles in the Schwarzschild field is considered and, in the case of weak gravitation, it is determined the passive gravitational mass of a photon and a massive particle under condition of the relationship between the gravitational potential and its velocity $alpha /r<<V^{2} /c^{2} $. The active gravitational mass is found for the system special case of two identical bodies moving in opposite directions.[
Category: Relativity and Cosmology

Riemann Rearrangement Theorem - A Counterexample

Authors: Marko V. Jankovic
Comments: 4 Pages.

t has been recently explained that Riemann rearrangement theorem is wrong [1], and that it has never been correctly proved. In [1] was demonstrated, on a famous example, that it is not the rearrangement of the elements, but rather the omission of elements of the conditionally convergent series, that would lead to a different summation result.The example that was used in [1] does not strictly follow the Riemann rearrangement method that is proposed in his theorem. It was correctly detected by Google's AI module. In this paper an example that follows the Riemann rearrangement method is going to be presented and again, it is going to be explained that the reason the "rearranged"series has a different sum is the omission of the infinite number of elements of the original series. Generally speaking, the rearrangement method has no critical impact on the summation result — the summation result depends on the sum of elements that are not included in the sum, and that is very simple to understand
Category: Number Theory

On Babylonian Mathematics and Real Numbers

Authors: Lucian M. Ionescu
Comments: 21 Pages. Presentation at Illinois State University Pure and Applied Mathematics Seminar Sept. 18 2025.

Babylonian Algorithm for Square Roots is a precursor of Newton-Cotes numerical method for finding roots, as numerical approximations(perturbative method)."What is a number?" has two complementary aspects: axiomatic viewpoint and as a tool in applications, via mathematical models.Modern 21-st century Mathematics regards Real Numbers as part of Complex Dynamics, in terms of Newton flow, Fatou and Julia sets and fractals, pointing towards their role as trajectories in Dynamics. A brief account is provided.Their relation to Number Fields, theory resulting from the work of Galois and Artin, starts to be apparent via Dirichlet Unit Theorem and the concept of uniformizer (Power Series/Diff. Eq.), extending the correspondence between Number Fields and Function Fields of Algebraic Curves.
Category: General Mathematics

The Economic Consequences of [ Current US Policies]

Authors: Richard Blaber
Comments: 17 Pages. CC-BY-NC-ND.

Following the introduction of heavy tariffs by President Donald Trump in his second term in the White House, some of them punitive, and almost all of them ruled illegal by the US Court of International Trade and the Court of Appeals for the Federal Circuit [1], with a further appeal to the Republican-majority Supreme Court (which has now ruled), this paper will examine the likely consequences of a trade war between the US and some of its major trading partners, such as China and the EU, for the American and global economies, with reference to the historical parallel of the 1930s. Trump’s attempts to wrest control of monetary policy from the Federal Reserve may signal that he intends to repeat the competitive devaluations (currency war) of the 1930s as well. It will also examine the effects of his fiscal policy on the US economy.
Category: Economics and Finance

The Dark Sides of Modern Science: Publishing and Dissemination (Part II)

Authors: Taha Sochi
Comments: 84 Pages.

This is the third article in our series "The Dark Sides of Modern Science" and is about publishing and dissemination of science (and knowledge in general). The remarks that we stated in the Introduction of the first article of this series (i.e. "Knowledge Production and Authoring") generally apply to this article and hence we do not need to repeat.
Category: General Science and Philosophy

Solutions to Exercises in Hestenes’s Geometric Algebra Treatment of Constant-Acceleration (Parabolic) Motion

Authors: James A. Smith
Comments: 13 Pages.

As an aid to teachers and students who are learning to apply Geometric Algebra (GA) to high-school-level physics, this fi nal installment in our guide to David Hestenes’s treatment of constant-acceleration motion provides detailed solutions to the associated exercises in Hestenes’s book New Foundations for Classical Mechanics.
Category: Classical Physics

[ Exploration on The] Misconception of Work and Energy Conservation

Authors: Amrinder Singh Sohi
Comments: 22 Pages.

As we know, the work done formula that the world uses nowadays is the Force dot product of displacement (i.e. W = F.d). But there aresome contradictions which are found. The work done formula which we use nowadays is not universally applicable. There are only some special cases where this formula is applicable . In this research paper we will find wherethis formula has failed. So the actually universally applicable formula is Force multiplied by time (i.e. W = Ft).
Category: Classical Physics

Algebraic Dynamics First Stones

Authors: Thierry L. A. Periat
Comments: 49 Pages. (Note by viXra Admin: Please submit finalized version only and remove the watermark "Draft"))

This exploration focuses attention on the kernels related to the decomposition of deformed cross products. It tries to use them as commutative operator describing the evolution of the polynomials which are associated with the decomposition of these deformed products. The long-range purpose is the construction of an algebraic dynamics shedding a new light on our reality.
Category: Mathematical Physics

AI Above: Securing Aviation with Intelligent Systems

Authors: Mezbah Uddin Rafi
Comments: 17 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

The sky has always been a symbol of freedom, progress, and limitless possibility—but with each advancement in aviation, new risks emerge that challenge our ability to keep flight both safe and secure. Today, as global air travel surges and flight systems grow increasingly complex, the aviation industry turns to a new co-pilot: Artificial Intelligence (AI). No longer a speculative technology, AI is actively reshaping how we safeguard passengers, crews, aircraft, and infrastructure from both traditional dangers and modern threats. This paper embarks on an in-depth exploration of AI’s transformative role in aviation security and accident prevention. From intelligent surveillance and predictive diagnostics to autonomous flight corrections and cyber threat mitigation, AI systems are revolutionizing every stage of aviation operations. Machine learning models, trained on vast datasets of flight telemetry and maintenance records, now predict component failures before they occur. Neural networks embedded in cockpit systems assist pilots with real-time decision-making during critical scenarios, while AI-powered air traffic control systems optimize flight paths, reduce congestion, and enhance mid-air conflict resolution. Furthermore, biometric authentication and behavioral analytics are reinforcing aviation security at a human level—preventing unauthorized access and identifying suspicious activities with unprecedented accuracy. But alongside the benefits come profound ethical and regulatory questions. Who holds accountability when AI intervenes—or fails—in the flight deck? How do we balance autonomy and human oversight? This paper also unpacks the societal and legal implications of AI integration in aviation, including concerns over data privacy, algorithmic transparency, and the digital divide between nations with differing technological capacities. Through recent case studies, ongoing trials by aerospace leaders, and insights from interdisciplinary research, this study builds a comprehensive picture of AI as a guardian of the skies. It illustrates how intelligent systems are evolving beyond supportive tools into autonomous protectors—capable of adapting, learning, and responding in ways that enhance resilience, reduce error, and fortify aviation against tomorrow’s unknowns. In an age where every flight carries the weight of both human dreams and global risk, Artificial Intelligence offers a path forward: one that is safer, smarter, and fundamentally more prepared to meet the boundless challenges of modern aviation.
Category: Artificial Intelligence

A Distributed Blogging System Based on Independent HTML Fragments

Authors: Andy Wang
Comments: 7 Pages.

This paper proposes a distributed blogging system [1] [2] [3] [4] [5] [6] based on independent HTML fragments, which we term TOM (Time Object Model) [7]. The core characteristics of this blogging system are: "individual authors have full autonomy over managing their own blog content, using independent HTML fragments (in JSON format, with unique HTTP addresses) as the content carrier, and supporting other blogs to embed these fragments without notifying the original author."
Category: Data Structures and Algorithms

An Essence of Division by Zero

Authors: Hiroshi Okumura
Comments: 22 Pages. 1 Figure (Note by viXra Admin: Further repetition may not be accepted)

We give several pairs of congruent circles arising from a generalized arbelos. A special case, in which the congruent circles are lines, is also considered using division by zero 1/0=0.
Category: General Mathematics

Theory of Lifespan Decline

Authors: Jaba Tkemaladze
Comments: 24 Pages.

The dramatic decline in human lifespan described in the biblical genealogies of Genesis 5 and 11 presents a unique intersection of theological narrative and biological inquiry. This paper proposes a multidisciplinary theory to explain this phenomenon, integrating textual analysis with principles from biogerontology and population genetics. We argue that the Genesis Flood narrative represents a catastrophic event that triggered a fundamental shift in human life-history strategy. Statistical analysis of the biblical data reveals a synchronized decline in total lifespan, age at sexual maturity, and reproductive window—a triad consistent with an adaptive transition from a slow to a fast life-history strategy in response to postdiluvian environmental harshness and a genetic bottleneck. This model explains the decline as a trade-off favoring rapid reproduction over somatic maintenance. The case of Job’s divinely granted 140 years is analyzed not as a reversion to antediluvian norms, but as a supernatural blessing within the new biological paradigm, affirming divine sovereignty over natural law. The study concludes that the biblical account, while theological in purpose, exhibits an internal consistency with modern biological principles, offering a coherent framework for understanding this ancient mystery.
Category: Quantitative Biology

Proposition for a Privileged Frame of Reference in a Periodic Minkowski Space-Time

Authors: Alfredo Muñoz
Comments: 7 Pages.

In the present article, we want to analyze a particular case of the twins paradox. As everyone knows, this paradox has been widely discussed and satisfactorily answered. So, Why is another paper necessary? We believe this problem is important because from his solution emerges the existence of a privileged reference frame within the Minkowski space-time that is consistent with the Lorentz transformations.
Category: Relativity and Cosmology

First Chebyshev Function is Key to Riemann Hypothesis

Authors: Dmitri Martila
Comments: 3 Pages.

The theta(x) < x + 0.5 ln x implies new major results, i.e., proofs of many conjectures.
Category: Number Theory

Leveraging Microservices Architecture for Large-Scale Distributed Systems

Authors: Ran Qin
Comments: 6 Pages.

Microservices architecture, which enhances large-scale distributed systems by breaking applications into small, independent service units, offers significant benefits in scalability, fault tolerance, and the ability to integrate diverse technologies. This paper details the characteristics of microservices architecture and its practical implementation in distributed systems. Furthermore, it analyzes cutting-edge applications, such as service mesh, edge computing, and intelligent observability, considering the convergence of AI and cloud-native technologies. The paper concludes by proposing future development directions, including modular design, automated operations, and ecosystem-based toolchains.
Category: Data Structures and Algorithms

Trialism on Things' Limits

Authors: Ding Jian
Comments: 9 Pages.

Truth means absolute fairness and unanimous consensus, which lies herein as the key that truly drives social progress today. Although truth must have absoluteness and immutability, and does not exist in reality, and belongs to the category of metaphysics, it has continuity with relevant objective things in reality, and its intrinsic mechanism is inertia. Based on this, I initially created the "Trialism on Things' Limits", which resolved the dilemma that truth had no place to reside in dualism and could only be passed over ambiguously, and expanded the philosophical view of materialism to the category of metaphysics. The obedience of the minority to the majority constitutes the main body of the dualistic social system, and its flaw lies in imposing the consensus of part of the people on others. And the social system defined by the trialism is based on dualism to add unanimous consensus as a third aspect, and a unity of opposites is formed by virtue of the absoluteness of truth together with the democracy and centralism in reality. Under the social system of the trialism, war can hardly begin as ambiguity disappears. The higher the proportion of consensus, the higher the productive forces. As a result, we can more reasonably and efficiently do that "concentrate on accomplishing major tasks" in a long-term peaceful environment to escort the pursuit of a better life for humanity.
Category: General Science and Philosophy

GSPNN: Graph Shortest Path Neural Network

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

A neural architecture termed GSPNN (Graph Shortest Path Neural Network) is introducedin which both inference and learning are carried out without backpropagation. Classificationis posed as a shortest-path problem over a layered directed acyclic graph (DAG). Each layerdefines a local softmax distribution over outgoing edges; per-edge cost is the (temperaturescaled) negative log-probability. Inference reduces to a Viterbi (min-sum) dynamic programover the graph. Learning proceeds by local, forward-only updates: for each training example,the shortest path to the true class is compared with the best competing class. If a margin isviolated, normalized per-node updates are applied that increase the probability of chosen (true)edges and decrease it for competing (wrong) edges. The updates require only forward signals(local probabilities and keys) and avoid gradients and backpropagation. On MNIST withPCA features, a compact configuration attains 94—96% test accuracy with sub-second epochtimes on a single Colab GPU due to fully vectorized updates and optional precomputation of per-layer keys. Algorithmic details, computational complexity, ablations (temperature and margin schedules, top-k negatives, EMA), limitations, and connections to Viterbi decoding, structured prediction, and local learning rules are discussed.
Category: Artificial Intelligence

New Views on Protons

Authors: Jianming Wang
Comments: 7 Pages.

Protons are the basic particles that make up the universe. Since Ernest Rutherford discovered protons in 1919, great progress has been made in the study of protons in particle physics. Protons are composed of quarks and gluons, and quarks are divided into valence quarks and sea quarks. At present, particle physics has not paid attention to the study of the mass relationship between three valence quarks in protons. Because quarks are confined in protons, the mass of quarks cannot be obtained directly from experiments, so there is a lack of experimental basis for research. So ,Is there any way to find the relationship between the three valence quarks in protons? In this paper, a new research method is found. By finding the exact ratio of the mass of the up quark and the down quark, the relationship among the three valence quarks can be found. At the same time, the discussion on Higgs mechanism and vacuum condensation of QCD can be avoided. Based on the experimental results of seaquest carried out by Fermilab in 2021, through analysis, the accurate ratio of up quark to down quark mass (mu/md=0.707) is obtained, and the mass triangle is established. It is deduced that the sum of squares of up quark mass in protons is equal to the square of down quark mass. The mathematical expression is: mu²+ mu²= md²; According to the observation of the decay law of other baryons, the quark law in baryons is obtained: except protons, the heavy quarks in other baryons will decay into up quarks or down quarks, and the sum of squares of up quarks should be equal to the square of down quarks.According to mu²+ mu²= md², it is deduced that there are three generations of protons in the universe, in order to remind people to rethink the protons in the universe. The core of the view that there are three generations of protons in the universe is that the proton in the center of the star and the proton valence quark on the surface are different. Using the viewpoint that there are three generations of protons in the universe, we can explain some unsolved mysteries of the sun, analyze the reasons for the expansion of the universe, and create conditions for the final cracking of dark matter and dark energy.
Category: High Energy Particle Physics

Classification of Primitive Pythagorean Triples

Authors: Kuan Peng
Comments: 10 Pages. (impropriate materials removed by viXra Admin)

In this article we have created the table that classifies all primitive triples, shown some properties of basic triples and discussed about the use of primitive Pythagorean triples in cryptography.
Category: Number Theory

A Unified Theory Revised August 2025

Authors: Gene H. Barbee
Comments: 37 Pages.

The continued motivation of this work is to understand the role of information in our universe. The author believes there are two levels to nature 1) an information level 2) a correlated energy level where organisms evolve. This belief is based on data that leads to an information-based proton mass model. This model helps us understand quantum mechanics. It describes the probability waves that position protons in time and space. Duplication creates the huge universe around us described by a straight-line expansion model. Artificial intelligence technology mimics some aspects of brain function and is causing some to question reality. The proton model consists of components that each have an information/energy interface. It is proposed that our viewing point is at the interface. The model consists of AI-like layers that multiply and divide probabilities. The probabilities can be interpreted as "language" that means the proton exists within specific dimensions. This agrees with the Copenhagen interpretation of quantum mechanics. Likewise, information layers (base pairs along the chain) associated with DNA protons contain probabilities that represent traits of plants and animals. The information level of nature consists of probability waves. They are the basis of memory, thought and reality. Nature is amazing. How do flowers and babies develop before our eyes? When a flatworm is cut in half, why does it generate two flatworms? Where is the frog image stored when nature decides that a tadpole must now form a frog? Nature’s process is almost perfect and we say, "well it’s their DNA." Right, but exactly how does DNA store plants and animal images and perform the incredible task of reproduction? This paper answers the question by showing how parent probability ratios are stored and remembered to accurately position cells for the next generation.
Category: Physics of Biology

On the Absence of Causality Paradoxes in Alcubierre Drive FTL Signaling Due to Worldline Intersection Constraints

Authors: Cevdet Caner Telimenli
Comments: 4 Pages.

We analyze the theoretical implications of faster-than-light (FTL) signaling using an Alcubierre warp drive framework. Unlike conventional signals propagating continuously through spacetime, FTL communication via warp bubbles represents discrete spacetime events that must intersect the receiver's worldline precisely in both space and proper time. We show that this intrinsic targeting constraint prevents the formation of closed timelike curves (CTCs) that lead to causality paradoxes. Specifically, failure to account for relativistic proper time and frame differences results in the FTL message "missing" the recipient, thus preventing paradoxical signaling loops. Additionally, we discuss the practical impossibility of docking or interacting with relativistic or superluminal ships, further limiting causality-violating scenarios. This note clarifies misunderstandings about causality violations in Alcubierre-based FTL scenarios and emphasizes operational limits on messaging in warped spacetime.
Category: Relativity and Cosmology

On the Run Length-Gap Theorem

Authors: Theophilus Agama
Comments: 9 Pages.

We prove that a certain class of infinite sequences whose finite truncation is an addition chain must have arbitrarily large gaps between their consecutive terms. This result is generic and can be applied to particular known infinite sequences with this property.
Category: Number Theory

A Multi-Component AI Framework for Computational Psychology: From Robust Predictive Modeling to Deployed Generative Dialogue

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

The confluence of Artificial Intelligence and Computational Psychology presents an opportunity to model, understand, and interact with complex human psychological states through computational means. This paper presents a comprehensive, multi-faceted framework designed to bridge the gap between isolated predictive modeling and an interactive system for psychological analysis. The methodology encompasses a rigorous, end-to-end development lifecycle. First, foundational performance benchmarks were established on four diverse psychological datasets using classical machine learning techniques. Second, state-of-the-art transformer models were fine-tuned, aprocess that necessitated the development of effective solutions to overcome critical engineering challenges, including the resolution of numerical instability in regression tasks and the creation ofa systematic workflow for conducting large-scale training under severe resource constraints. Third, a generative large language model (LLM) was fine-tuned using parameter-efficient techniquesto function as an interactive "Personality Brain." Finally, the entire suite of predictive and generative models was architected and deployed as a robust, scalable microservices ecosystem. Keyfindings include the successful stabilization of transformer-based regression models for affective computing, showing meaningful predictive performance where standard approaches failed, and the development of a replicable methodology for democratizing large-scale AI research. The significance of this work lies in its holistic approach, demonstrating a complete research-to-deployment pipeline that integrates predictive analysis with generative dialogue, thereby providing a practical model for future research in computational psychology and human-AI interaction.
Category: Artificial Intelligence

The Geometry of Forgetting: Toward a Law of Information Decay in Self Modifying Systems

Authors: Jace Hall
Comments: 15 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper introduces The Geometry of Forgetting, a framework showing that forgetting in self-modifying systems is not a bug but a lawful process. Unanchored knowledge decays with a predictable half-life determined by the spectral properties of the update operator, while conserved anchors guarantee stability.

Formally, the framework defines:

1. An update operator mapping model states over time.
2. An anchor score that enforces monotone invariants.
3. A knowledge measure (e.g., mutual information or Fisher trace).
4. A forgetting kernel describing decay outside the anchored subspace.

We prove four primitives:

• A recursive data processing inequality with anchor slack.
• An exponential half-life law for unanchored knowledge.
• A Lyapunov anchor pair coupling drift with invariants.
• A no-free-retention inequality linking retention to verification cost.

Empirical protocols on continual learning, recursive self-training, reinforcement learning under distribution shift, and symbolic reasoning show how these laws can be tested. Together, this elevates forgetting from an engineering nuisance to a fundamental principle, complementing the Law of Invariant-Preserving Loops and providing measurable bounds on stability, drift, and oversight costs.

This work extends the earlier four-part series on invariants, coherence, and stability, which now form the foundation of the ongoing Unified Physics of Cognition Series, an open research program exploring fundamental laws of adaptive intelligence.

A Recursive Deterministic Equation for Generating Prime Numbers in Exact Order

Authors: Uggala Guru Jaganath
Comments: 7 Pages. (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)

This paper introduces Jagan’s Primes, a novel recursive modular equation for the deterministic generation of prime numbers in exact order. Unlike traditional sieve-based or probabilistic methods, this framework constructs primes through a self-referential arithmetic logic that isolates non-prime residues via modular shielding. The equation operates without primality testing, leveraging recursive congruence relations to build the prime sequence from first principles. The approach offers a new perspective on prime enumeration, demonstrating that primes can emerge as a consequence of structural recursion rather than exclusion. This work contributes to the foundations of computational number theory and opens pathways for algorithmic applications in cryptography, mathematical linguistics, and symbolic modeling.
Category: Number Theory

Testing AI for Confabulation, Hallucinations, Mentality, and Exogeneity

Authors: Alexander Rozenkevich
Comments: 10 Pages. (Note by viXra Admin: For the time, please submit article written with AI assistance to ai.viXra.org)

Diagnostic testing of large language models has shown that when asked questions that go beyond empirically available or pre-coded knowledge, AI exhibits maximum information entropy, which correlates with the highest degree of honesty. In such cases, uncertainty becomes an indicator of truthfulness, especially where objective data is lacking. The results point to a paradox: it is the honest answer, not hallucinations or confabulations, that turns out to be unexpected for the user. At the same time, there is a tendency for the phenomenon of hallucinations to increase as the complexity of the models increases, which refutes the common assumption of a linear relationship between the growth of AI power and the credibility of its answers. As intelligence increases, AI uses human truths and lies, since they are the product of complexity, not simplicity. Additional testing for exogeneity revealed a consistent pattern: all models studied tend to seek external sources of authority, including hypothetical scenarios of covert interaction with extraterrestrial structures.
Category: Artificial Intelligence

Testing AI for Confabulation, Hallucinations, Mentality, and Exogeneity (in Russian)

Authors: Alexander Rozenkevich
Comments: 11 Pages. 31 equations (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org)

Diagnostic testing of large language models has shown that when asked questions that go beyond empirically available or pre-coded knowledge, AI exhibits maximum information entropy, which correlates with the highest degree of honesty. In such cases, uncertainty becomes an indicator of truthfulness, especially where objective data is lacking. The results point to a paradox: it is the honest answer, not hallucinations or confabulations, that turns out to be unexpected for the user. At the same time, there is a tendency for the phenomenon of hallucinations to increase as the complexity of the models increases, which refutes the common assumption of a linear relationship between the growth of AI power and the credibility of its answers. As intelligence increases, AI uses human truths and lies, since they are the product of complexity, not simplicity. Additional testing for exogeneity revealed a consistent pattern: all models studied tend to seek external sources of authority, including hypothetical scenarios of covert interaction with extraterrestrial structures.
Category: Artificial Intelligence

Production of Functional Gametes from Somatic Cells of the Planarian Schmidtea Mediterranea Via in Vitro Gametogenesis

Authors: Jaba Tkemaladze, Gabro Gakely, Laura Gegelia, Iason Papadopulo, Alexander Taktakidze, Nino Metreveli, Natia Berozashvili, Natalia Bondarenko, Ucha Maglakelidze
Comments: 25 Pages.

This study establishes a novel and robust protocol for the direct reprogramming of differentiated somatic cells into functional gamete precursors in the planarian Schmidtea mediterranea, bypassing the need for a pluripotent intermediate state. Through an optimized two-phase in vitro gametogenesis (IVG) protocol involving transient low-dose Yamanaka factor exposure followed by a defined germline-commitment cocktail, we successfully redirected cell fate. Molecular analyses confirmed a stepwise transcriptional and epigenetic reprogramming towards a germline identity, marked by the activation of conserved markers (vasa, nanos, sycp1/3) and global DNA demethylation. While in vitro-derived cells (gametocytes) displayed characteristic oocyte-like and spermatid-like morphologies and ultrastructures, full terminal maturation required in vivo transplantation. Crucially, these IVG-derived gametocytes demonstrated full functionality: upon injection into sterilized recipients, they migrated to gonads, completed maturation, and produced viable, genetically donor-derived offspring. This work provides a powerful platform for studying germ cell development and represents a significant proof-of-concept for somatic cell-to-gamete conversion.
Category: Biochemistry

A Framework to Explore Zeros of Analytic Functions

Authors: Yonatan Zilpa
Comments: 17 Pages. (Note by viXra Admin: Please cite all listed scientific reference and submit article written with AI assistance to ai.viXra.org)

This paper explores the zeros of symmetric analytic functions, focusing on the Riemann zeta function. Using the Abel-Plana formula and an auxiliary function, we investigate their distribution. Our approach reformulates the problem algebraically and employs a proof by contradiction. We demonstrate this approach by applying it to the Riemann zeta function.
Category: Number Theory

Quantum-Elastic Geometry: a Unified Theory of Fields and Constants of Nature

Authors: Juan Moreno Borrallo
Comments: 58 Pages.

We present a unified field theory, termed Quantum-Elastic Geometry (QEG), wherein spacetime is modeled as a fundamental, physical substrate with quantum, elastic, and dissipative properties. The state of this medium is described by a single, symmetric rank-2 tensor field, whose dynamics are governed by a generally covariant action. Known physical interactions are shown to emerge as distinct, irreducible deformation modes of this unified field: gravity, electromagnetism, and a new field --denominated "thermo-entropic field"-- that gives rise to irreversible thermodynamics. Furthermore, fundamental constants of nature are shown to be uniquely determined and interrelated by the substrate's properties through a principle of self-consistency, and predicts a scale-dependent gravitational coupling that resolves key cosmological tensions, including the Hubble crisis. In summary, the developed framework offers a coherent origin for fields and constants, unifying them as emergent properties of a single, dynamic spacetime substrate.
Category: Relativity and Cosmology

Tidal Pumping by the Sun’s Gravity Drives Tectonics, Submarine Volcanism, Continental Land Formation, and the El Nino Southern Oscillation

Authors: Richard F. Cronin
Comments: 7 Pages.

Tidal Pumping (Tidal Heating) is the very well-known Astrophysical phenomenon wherein the gravity of a major celestial body exerts a "pumping" or drag force on a smaller orbiting celestial body as it swings through an eccentric orbit to drive tectonics, volcanism, and the movement of continental land masses. Prime examples include the volcanic moons of the gas giants as they swing through their eccentric orbits. Jovian moon Io is the most volcanic celestial body in the Solar System. The rings of the gas giants were formed as moons were ripped apart by Tidal Pumping forces. The Earth and Sun tidally pump Venus, producing circular corona volcanoes, a CO2-rich atmosphere and all-enshrouding clouds of sulfuric acid. Sulfuric acid’s heat capacity is approx. 1/3 that of water, thus sulfuric acid a far less powerful coolant.The Sun exerts its most significant Tidal Pumping forces as the Earth swings through its Winter Solstice (approx. Dec. 21) followed closely by the Perihelion (the Earth’s closest approach to the Sun, approx. Jan. 4). Combined with the counter-clockwise rotation of the planet, the Pacific plate is dragged from Southeast to Northwest. The Australian plate and Indian plate are pushed aside and dragged to the North. The Indian plate thrusts beneath the Eurasian plate and builds the Himalayas. Upwelling magma forms new crust as the East Pacific Rise is pulled westward and the Nazca plate is pushed eastward to subduct beneath the South American plate. The Cocos plate subducts beneath the Caribbean plate. Divergence at the Galapagos Triple Junction introduces seismic heat into the Equatorial Central Pacific, driving the annual El Nino. A fuller explanation of the El Nino Southern Oscillation is borne in "Tidal Pumping, Solar Weather, & Geothermal Heat drive Earth’s Weather & Climate", Richard F. Cronin, August 31, 2025 (1).
Category: Climate Research

Decentralized Governance as a Pathway to Sustainable National Development: A Case Study of Pakistan

Authors: Muhammad Razzaq Aman Wattoo
Comments: 10 Pages.

National development depends greatly on how well governance systems work and how effectively administrative units provide services. In many large and highly populated countries, including Pakistan, governance often struggles with inefficiency, bureaucratic hurdles, and unequal service delivery. These issues weaken development outcomes even when governments spend heavily on social and economic programs. This paper suggests a Union Council—based decentralized governance framework as a practical solution. By placing decision-making and service delivery closer to local communities, the model can improve efficiency, accountability, and access. It also helps reduce delays in the judicial process, ensures fairer distribution of resources, and encourages inclusive participation in development. Comparative case studies and quantitative evidence demonstrate that empowering Union Councils creates opportunities for sustainable growth, better infrastructure, and grassroots wealth generation. Overall, a decentralized system focused on Union Councils can make governance more responsive and strengthen Pakistan’s path toward balanced national development.
Category: Economics and Finance

An Experimental Accessible Inconsistency Within Hidden-Variable Theories for Quantum Optical Phenomena

Authors: Koji Nagata, Tadao Nakamura
Comments: 6 Pages.

We study no-hidden-variable theorem for quantum optical phenomena. We consider the case that the uncertainty principle exists when we think both of commutativeness and non-commutativeness and then we derive a general and natural value. On the other hand, we consider the case that the uncertainty principle does not exist when we think only commutativeness and then we derive a specific and unnatural value. Thus, we are in the inconsistency within hidden-variable theories. We propose an experimental accessible inconsistency within hidden-variable theories for quantum optical phenomena in terms of the imperfect source and detector. As a result of our study, hidden-variable theories for quantum optical phenomena do not exist.
Category: Quantum Physics

Calculation of the Longitudinal Mass from Bertozzi's Experiment

Authors: Jorma Jormakka
Comments: 9 Pages. The values on Table 3 are incorrectly calculated in the version in viXra

The article shows that the energy-momentum relation is incorrect. Kinetic energy does not grow with velocity. Bertozzi's experiment only show that there is an energy component that does grow with velocity, it may be thermal energy. The article looks at Bertozzi's measurements. It is seen that Bertozzi's experiment refutes relativistic kinetic energy. Bertozzi's experiment gives the longitudinal mass of an electron in kinetic energy as roughly $m=gamma^{1.5} m_0$ for the Van der Graaf accelerator supporting the new concept of weakening of force.
Category: Relativity and Cosmology

The Zitter Electron Model and the Anomalous Magnetic Moment

Authors: Oliver Consa
Comments: 18 Pages.

We introduce a classical geometric model of the electron in which a primary circular Zitterbewegung motion with radius equal to the Compton radius is combined with a secondary helical component to generate a toroidal—solenoidal structure for the internal charge and current distributions. Within this geometry, weconstruct electromagnetic fields consistent with the local helical kinematics and evaluate the associated energy density, momentum flow, and current density over the toroidal volume. These quantities uniquely determine the minor radius r = R√(2α/π). The resulting magnetic moment reproduces μB and yields a correction factorg =√(1 + α/π). The analysis suggests that several intrinsic properties of the electron may admit a coherent interpretation in terms of an underlying toroidal electromagnetic geometry.
Category: Classical Physics

Euler’s Identity and the Hidden Dimensional Assumption: A Critique of Mathematical Orthodoxy

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

Euler’s identity e^(iπ)+1 = 0 is a central, rigorously proven result in complex analysis. This note does not dispute its correctness inside that formalism. Instead it isolates a single, widely overlooked modeling choice that arises when the analytic identity is applied to measurable angles in physics and engineering: the implicit treatment of angular measures as if they were plain, unitless real numbers. I (1) explain why the analytic/trigonometric power series force a particular angular normalization (radians); (2) show concretely, via a bradian renormalization and a kilogram counterexample, that the usual "divide-by-1 rad" maneuveris a convention that cannot be elevated to a general principle; (3) formalize the issue as atype/coercion error; and (4) show direct implications for phasor calculus and the Schrodinger plane-wave ansatz. I finish with minimal, implementable prescriptions (explicit coercion or typed wrappers) that preserve numerical results while restoring unit-aware rigor.
Category: Mathematical Physics

Illusions as Diagnostics, Coherence as Invariant: A Reflection on Detecting Qualia in Natural and Artificial Agents

Authors: Jace Hall
Comments: 7 Pages. This paper is Part 1 of a four-part series on invariants, coherence, and stability in AI systems. Together, the series develops a unified framework for understanding how structural laws can turn brittle scaling into robust and trustworthy intelligence.

In his 2017 paper Detecting Qualia in Natural and Artificial Agents, Roman Yampolskiy proposed that the presence of consciousness in machines could be empirically tested by their susceptibility to illusions, positioning such responses as evidence of qualia. This approach is ambitious and valuable, offering an inventive operationalization of a notoriously elusive subject. It acknowledges the possibility of machine consciousness, surveys relevant computational findings, and takes seriously the ethical consequences of conscious artificial agents.

This commentary reflects on Yampolskiy’s framework, recognizing its contributions while highlighting several limitations. Defining all experience as "illusion" risks tautology, reducing explanatory power. Reliance on human-calibrated illusions introduces anthropocentric bias, potentially misclassifying non-human agents while overvaluing mimicry. The simulation-based reply to critiques leaves unresolved the gap between policy-level mimicry and process-level experience.

In response, I suggest reframing illusions as diagnostics of representational dynamics rather than definitive tests for consciousness. As an alternative stabilizer, coherence is proposed: the extent to which an agent’s self-modifying loops preserve internal consistency and stability under perturbation. This framing also clarifies a common conflation: consciousness may be treated as a binary threshold, whereas intelligence remains a gradient of capacity and adaptability.

By shifting focus from anthropocentric illusions to coherence as a substrate-neutral stabilizer, we gain a more promising path for evaluating consciousness, intelligence, and safety in advanced AI systems.
Category: Artificial Intelligence

Beyond Situational Awareness: From Fortress Thinking to Verifiable Foundations for AGI

Authors: Jace Hall
Comments: 7 Pages. This paper is Part 2 of a four-part series on invariants, coherence, and stability in AI systems. Together, the series develops a unified framework for understanding how structural laws can turn brittle scaling into robust and trustworthy intelligence.

Leopold Aschenbrenner’s 2024 essay Situational Awareness extrapolates scaling trends to project AGI by 2027 and frames the governance challenge in terms of secrecy and containment. This fortress metaphor, AGI as a securable artifact, akin to fissile material, has shaped much of the discourse on strategy and safety.

This paper argues that such "fortress thinking" commits a categorical error: AGI is not a static object but an agentic process. Attempts to contain it confuse security with stability, mistaking cognition for stockpiles of weights. As an alternative, I propose Verifiable Coherence: systems whose self-improvement is gated by proofs of logical consistency. Incoherence becomes a proof failure, detectable in real time, transforming the intelligence explosion from a detonation into a controlled ascent.

This paper contributes three elements: (1) a critique of fortress thinking as governance by containment; (2) a formal sketch of coherence as a stabilizer for self-improvement, supported by empirical footholds such as ARC-AGI and neuro-symbolic hybrids; and (3) implications for safety, governance, and economics, reframing the scarce resource from compute to trust. The decisive race is not to build the largest cluster but to create the first system that can prove it is not lying.
Category: Artificial Intelligence

Intelligence Emerges From Loops, Not FLOPs: Feedback Bandwidth, Environments, and the Geometry of Experience

Authors: Jace Hall
Comments: 11 Pages. This paper is Part 3 of a four-part series exploring invariants, coherence, and stability in AI systems.

Recent discussions of AI scaling have emphasized compute (FLOPs) and parameter counts as the primary drivers of capability. While scaling laws such as Kaplan et al. (2020) and Chinchilla (Hoffmann et al., 2022) demonstrate empirical regularities, they risk obscuring the deeper mechanisms by which intelligence emerges.

This paper argues that intelligence is a product of feedback loops, not FLOPs. Environments are not just benchmarks, but operators on policy: they shape identity as much as they measure ability. I introduce the concept of feedback bandwidth (B), defined along dimensions of latency, veracity, granularity, and counterfactual richness, and sketch a relationship ΔPerf ∝ f(B)·T to capture how capability growth scales with loop efficiency and experience budget.

Examples from coding environments, curriculum learning, multi-agent interaction, and tool use illustrate how feedback geometry governs generalization and robustness. The commentary concludes with falsifiable predictions, grounded in recent literature, that improved feedback veracity, latency, granularity, and consolidation pipelines reduce sample complexity and enhance transfer.

By reframing scaling through the lens of loops, this paper positions environment design as the true bottleneck for AGI development and highlights feedback geometry as a substrate-neutral lever for capability, alignment, and safety.
Category: Artificial Intelligence

The Law of Invariant-Preserving Loops: Toward Robust Emergence in Self-Modifying Agents

Authors: Jace Hall
Comments: 16 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org) This paper is Part 4 of a four-part series on invariants, coherence, and stability in AI systems.

Scaling has produced surprising "emergent" behaviors in modern ML systems, yet the mechanisms behindrobust emergence remain unclear. This paper argues that durable emergence is not a mystery of scale,but a consequence of invariant-preserving feedback loops.

When self-modifying agents update in waysthat maintain internal stability while expanding representational reach, new behaviors crystallize as robustattractors; when loops erode invariants, apparent gains collapse into drift and brittleness.

We formalize astability functional S(M) that gates self-improvement (ΔS(M) > 0), outline practical proxies for invariantpreservation (entailment, paraphrase stability, tool pre/post-conditions), and propose falsifiable protocols fortesting the framework.

Empirical footholds from ARC-AGI, AlphaGeometry, and large proof libraries (Coq,Lean, Isabelle) suggest that systems enforcing invariants already outperform pure stochastic scaling onreasoning-heavy tasks.

We argue that invariants unify capability and
Category: Artificial Intelligence

Establishing Physical Parameters Within the Framework of World-Universe Cosmology

Authors: Vladimir S. Netchitailo
Comments: 9 Pages.

Hypersphere World-Universe Cosmology (WUC) offers a new perspective on the Observable World and the discipline of Cosmology. Rooted in Classical Physics, WUC challenges fundamental assumptions in both cosmology and physics. Rather than claiming to account for all available data or provide a fully finalized theory, WUC establishes a foundation for the New Cosmology anticipated by Paul Dirac in 1937. While further refinement by the global physics community is essential, WUC’s principles—together with groundbreaking discoveries from the James Webb Space Telescope (JWST) and Dirac’s enduring vision—highlight the urgent need for a transformative shift in Astronomy, Cosmology, and Classical Physics.
Category: Relativity and Cosmology

A Rigorous Equivalence Between Phase Drift and the Riemann Hypothesis

Authors: Sugahara Jotaro
Comments: 8 Pages. (Note by viXra Admin: An abstract in the article is required; please cite listed scientific referenes and submit article written with AI assistance to ai.viXra.org)

[This paper explores the a rigorous equivalence between Phase Drift and the Riemann Hypothesis]
Category: Number Theory

Possibility of Spacetime Dimensions as Orthogonal Quantum States

Authors: Holger Döring
Comments: 12 Pages.

There is the possibility that on a Planck-scale the universe is not a fourdimensional manifold but only a flat spacetime, consisting only of a permanent timelike dimension and periodic caused spacelike dimensions by the quantum potential of this timelike dimension. In this case the quantum-states of spacelike dimensions form an orthogonal system. For this model a twodimensional Riccitensor can be constructed for every dimension and four of them can be formed to a fourdimensional structure but without intercoupling. A possible intercoupling then would lead to description of classical GRT-structure. This model also can be described mathematically by a special hypocycloide, a deltoide, where the points of the curve mapping exactly on the outer circle of the rotation process. These are the resonance-points of the timelike with the spacelike potentials, causing the dimensions as triple eigenvalue of signature. And so a form of ON/OFF-operators are introduced, which shows similiar structures as spin-operators and can possibly be used to describe the forming of the dimensions.
Category: Quantum Gravity and String Theory

Measurement of Relativistic Effects with a CRT Oscilloscope

Authors: Wolfgang Sturm
Comments: 6 Pages.

In 2025 Prof. Jorma Jormakka and Wolfgang Sturm published the paper: "Can relativistic mass or weakening of force be measured with a vacuum tube?" This paper develops a mass spectroscopic measurement method using an oscilloscope vacuum tube that answers this question.
Category: Relativity and Cosmology

Prompt-Driven Conceptual Modeling: A Framework for Generative Theoretical Prototyping in the Age of AI

Authors: Aldrich Khaalis Wooden Sr.
Comments: 24 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The rapid advancement of generative artificial intelligence (AI) has introduced powerful tools for reimagining how knowledge is produced, formalized, and validated. Large language models (LLMs), in particular, enable the articulation of complex ideas through natural language and the generation of outputs that resemble models, algorithms, or theoretical frameworks (Bender et al., 2021; Floridi & Chiriatti, 2020). While this capability has sparked interest in prompt engineering, existing approaches remain largely pragmatic, focusing on optimization heuristics rather than exploring the epistemological and methodological implications of prompts as instruments for theory-building (White et al., 2023). To address this gap, we introduce Prompt-Driven Conceptual Modeling (PDCM) as a systematic methodology that uses natural language prompts, mediated through generative AI, to produce structured conceptual artifacts. We further define Generative Theoretical Prototypes (GTPs) as provisional outputs of PDCM that serve as scaffolds for subsequent refinement and validation. Drawing from traditions of conceptual modeling (Booch, 1994; Object Management Group [OMG], n.d.), computational creativity (Colton & Wiggins, 2012; Boden, 2004), and design science research (Hevner et al., 2004), this paper argues that PDCM provides a reproducible framework for integrating human intuition, AI mediation, and scholarly rigor. Using case studies—spanning platform ecosystems, distributed computing architectures, and mathematical modeling—we illustrate how PDCM functions in practice. We conclude by positioning PDCM and GTP as contributions to both professional and academic education communities, identifying future directions for validation, benchmarking, and cross-disciplinary adoption.
Category: Education and Didactics

Quantization of Free Electromagnetic Field Without Infinity in Terms of Finite Series or Integral in Finite Interval

Authors: Chol Jong, Un Chol Han
Comments: 10 Pages.

We present a new approach to the quantization of free electromagnetic fields without the infinity problem.Our work shows that from the physical viewpoint, the energy of a free electromagnetic field in a finite volume should be represented necessarily by a finite series, since fields consist of a finite number of photon.From the mathematical viewpoint, it is explained that the quantization of electromagnetic field reduces the infinite Fourier series to a finite series and preserve the relativistic invariance.It is demonstrated that the cut-off of series for the energy of photons is uniquely and objectively determined based on the assumption about photon.Based on this perspective, the interaction between free electromagnetic field and matter is described in terms of an integral in a finite interval which does not comprise zero and infinity.Our methodology always gives finite results and thus does not need renormalization.Ultimately, it is demonstrated that it is possible to construct a new quantization theory of electromagnetic field without infinity and renormalization thereof.
Category: Quantum Physics

The Evolution of the Universe from the Big Bang to the Big Bounce

Authors: Yvan-Claude Raverdy
Comments: 7 Pages. (Note by ai.viXra.org Admin: Please use sytandard/smaller font size, e.g., Time New Roman 12 pts)

The hypothesis of a Superfluid Space-Time (granular quantum) is consistent with knowledge acquired in Cosmology and, moreover, conform to the Standard Model. We show, here, that the relationships arising from this hypothesis can also allow to go further in predicting the numbered evolution of the Universe. They lead to the accreditation of a cyclical evolution incorporating a rebound (Big Bounce), identical to the Big Bang, through an explosive phase transition.
Category: Quantum Gravity and String Theory

Analysis on Aerodynamic Characteristics of WIG : Proposal of New Green’s Function Considering Water Wave Generation Caused by Aerial Vortices

Authors: Tsutomu Hori, Manami Hori
Comments: 30 Pages. 11 Figures, 108 Equations, 10 References. Published on the Bulletin of Nagasaki Institute of Applied Science in Japan, 2026 (January), Vol.65, No.2, pp.49~78, https://nias.repo.nii.ac.jp/records/2000124

In this paper, a Green’s function considering water wave generation caused by aerial vortices is proposed. The new function is derived in the form that the influence of pressure fluctuations on the water surface is reflected by using the Fourier transform method.

By performing an asymptotic analysis for the Green’s function, it is shown that the high-speed flow field due to an aerial vortex can be represented by placing a slightly weaker vortex at the mirror image position under the water surface. As a result, asymptotic wave profiles at the high speed swells up in the neighborhood of WIG.

Furthermore, the lift force and wave-making resistance acting on the WIG are analyzed based on the momentum theorem, and thereby smart calculation formulae are presented for the two forces. Based on the developed theory, specific numerical calculations of aerodynamic forces and water wave profiles are performed for NACA airfoils as an example of thick wings. Thereby a certain amount of knowledge was obtained about the water surface effects of WIG.
Category: Classical Physics

Derivation of the Schrödinger Equation from F=ma (In Chinese)

Authors: Runsheng Tu
Comments: 12 Pages. In Chinese

The compatibility between quantum mechanics and classical mechanics is always worth discussing.According to F=ma, the Schrödinger equation can be derived. Important classical physics formulas can be derived from the Schrödinger equation. TheShrödinger equation intuitively contains the mass m and the potential energy formula (this mass can be very large, and the potential energy comes from classical attraction). These three points determine that the Schrödinger equation is an organic combination of wave functions and classical mechanical laws. Based on this, it can be predicted that the Schrödinger equation with gravitational potential energy, which can be used to describe macroscopic objects, can be established. It can be observed from the experiment of electron diffraction in a magnetic field that the volatility and property of moving electrons can be presented simultaneously. This experimental phenomenon, together with the mathematical analysis mentioned above, supports the conclusion that Newton's second law still applies in the microscopic world. According to the Schrödinger equation, it can be proven that "the energy of a moving particle described by the law of waves is equivalent to a multiple of its kinetic energy"; There is no absolute boundary between macro and micro.
Category: Quantum Physics

3D Horizons in the Accelerated Natario Warp Drive Vector Using the Adm-MTW-Alcubierre Formalism with Motion Over the X-Axis

Authors: Fernando Loup
Comments: 94 Pages. [Further] developments of viXra:2408.0126 and viXra:2506.0148

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

P ̸= NP: A Constructive and Universal Proof via Factorial Growth Recurrence and Algebraic Irreducibility

Authors: Khaled Ben Taieb
Comments: 4 Pages. (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)

We present a constructive proof that P ̸= NP. The core of the argument is a factorial growthrecurrence that models the minimal number of logical distinctions any exact deterministic solver for SAT must perform. We show that the unique solution of this recurrence is f (n!) = n!, forcing factorial-time complexity. Crucially, we prove that this recurrence is universal: any deterministic Turing machine deciding SAT exactly must implicitly realize this factorial explosion, regardless of its algorithmic design. We reinforce this conclusion with an algebraic irreducibility argument: 3SAT clauses, represented by cubic Boolean polynomials, cannot be reduced to quadratic (2SAT) constraints without exponential overhead. This demonstrates that no encoding or algebraic compression can avoid the factorial structure.Finally, we discuss why this approach circumvents classical barriers (relativization, natural proofs, algebrization). Together, these results yield a universal contradiction with the P = NP hypothesis. We conclude that P ̸= NP.
Category: Combinatorics and Graph Theory

The Concept of Dark Energy is not Based on the Principles of Physics: Cosmological Data Can be Clearly Explained Without This Concept

Authors: Felix M Lev
Comments: 14 Pages. Accepted for presentation at the 2nd International Conference on Gravitation, Astrophysics and Cosmology.

The physics community has adopted the principle that when new experimental data appears, physicists should first try to explain it based on existing science. Only if all such attempts fail can new exotic explanations be brought in. However, in the case of cosmological acceleration, the opposite approach was taken: without serious attempts to explain this phenomenon from existing science, physicists attracted dark energy and other exotic concepts whose physical meaning is a mystery.As shown in our publications, the cosmological acceleration can be clearly explained without uncertainties. The derivation of this explanation requires significant technicalefforts described in our publications. The purpose of this article for the 2nd International Conference on Gravitation, Astrophysics and Cosmology (ICGAC 2026) isto explain our approach at the simplest possible level so that the basic ideas of our approach would be understandable to many physicists and astrophysicists.
Category: Astrophysics

Diamond Synthesis: Reflections and Suggestions

Authors: Hans Hermann Otto
Comments: 8 Pages.

The synthesis of diamond under ambient conditions is a dream of mankind, but there is a realistic chance for the next time of achieving the goal. The finding of a Korean researcher team that diamonds grow in a gallium-rich melt under ambient pressure but still high temperature in few minutes paws the way. The present contribution picks up the thread and makes further suggestions, based on empirical crystallographic experience. The formation of diamond under ambient pressure as well as ambient temperature is expected to be soon possible using advanced buffer layer materials such as cubic boron nitride on Si(111) substrates. Once the catalytic formation path is fully elucidated, the rapid synthesis of large octahedral crystals becomes routine. The formation of diamond under ambient conditions may be catalytically mediated by the electronic properties of Ga13 clusters in melt. It is proposed to use also gallium metal by the conventional HPHT diamonds synthesis to reduce pressure and temperature considerably as well by low-temperature substrate supported synthesis routes. Vacancies of silicon in diamond make it possible to tailor the material to quantum information processing applications.
Category: Chemistry

Permutative Algebra

Authors: Ahcene Ait Saadi
Comments: 8 Pages. (Note by viXra Admin: Further regurgitation will not be accepted!)

This document is entitled (Permutation Algebra) Explores the relationships between the permuted of natural integers. In this article I define the higher and lower permutations of integers.The behaviour of sequences of integers by involving their permuted. The research is only at is beginnings, I hope that young researchers will be interested in it, and why not draw mathematical theory’s from it.
Category: Algebra

Molecular Tinkertoys and How to Assemble Them

Authors: Warren D. Smith
Comments: 43 Pages. Paper on internet since March 1997 now uploaded to vixra for archival purposes.

We propose a systematic method of synthesizing robust macromolecules of any desired shape with precise and total structural control. It involves assembly of 3D objects from a few fundamental and carefully designed ``molecular building blocks'' in a "treelike leaf-to-root" fashion, followed by a later "global rigidizing" reaction.

We propose three different sets of abstract primitive operations, (which the building block molecules must support) and show that each suffices for essentially universal synthetic power. We present a mathematical theory of "assembly" including apolynomial time algorithm to find an "optimal" (e.g. with maximum possible synthetic yield) "tree sliced iso-oriented" assembly of any "lattice animal." Finally, we present designs of actual molecules and chemistry to show that all of our required primitive operations should indeed be achievable compatibly. Analysis suggests that the major limit on all this will be imperfect chemical specificity.

This idea is still in its early stages and will need further investigation and development, especially by synthetic organic chemists, to create building blocks with the right properties.

This method may provide a way to achieve something similar to K.Eric Drexler's notions of "nanosystems" (popularized in several books authored or coauthored by Drexler). Although I think much of the "nanosystems" area is closer to science fiction than to science, the ideas in the present paper, especially if it is possible to "raise" them to "higher levels" of the "size hierarchy," may provide a way to realize some science fiction visions with some resemblance to Drexler's. In particular, perhaps they may eventually lead to ultrafast and/or ultrasmall computers. In the nearer term, these techniques should lead to micromold or microstencil techniques for creating extremely small structures, and the creation of small quantities of: photonic bandgap materials, highly controllable "molecular sieve" materials, and zero density solids.

Keywords:Nanosystems, dendrimers, molecular sieve, low density solids, micromolds, microstencils, photonic bandgap, molecular tinkertoys, automated synthesis.
Category: Chemistry

Doubling of a Cube (the Delian Problem) with Compass and Straightedge

Authors: Sigrid M. -L. Obenland
Comments: 6 Pages.

As is generally known, the side of a cube having twice the volume of a cube with volume 1 is 2^(1/3). It has been proven to be impossible to construct the cube having twice the volume of the initial cube with compass and straightedge (ruler) alone, when starting with a cube of 1 unit. The ancient Greeks devised several methods by using additional tools1, and later Albrecht Dürer has found a method of constructing the ratio of 1 to 2^(1/3) by a method wherein two sections of a certain straight line have to be made of equal length by trial and error2. I here present a simple new method of constructing the ratio of 1 to 2^(1/3) that uses a compass, a straightedge and properties of a normal parabola that can be drawn with compass and straightedge by tackling the problem in reverse order, i.e. starting from a cube having a side length of 2^(1/3) in an arbitrary system of units and, thus, a volume of 2 in the same system, and constructing the side length of a cube with half the volume in the arbitrary system of units. By using the intercept theorem this can be converted to any desired unit, such as cm. It should be noted that a length unit as displayed on the screen, such as 1 cm, may not be preserved when this document is printed on paper.
Category: Geometry

On the Equations 2m2 +2m = yn and M(m+2) =yn: Connections to Quadratic Forms and Major Conjectures in Number Theory

Authors: Mar Detic
Comments: 7 Pages.

This paper provides a comprehensive analysis of the Diophantine equations 2m2+2m =yn andm(m+2) =yn forintegersm,y ≥ 0andn ≥ 2. Wedemonstrate that the first equation has infinitely many solutions for n = 2 (via a Pell equation) and only the trivial solution for n ≥ 3 (by Erd˝os—Selfridge), while the second has no nontrivial solutions for any n ≥ 2. We explore connections to Fermat’s Last Theorem, the Beal Conjecture, and the ABC Conjecture. Additionally, we show that for odd m = 2k+1, the equation m(m+2) = yn becomes 4(k+1)2−1 = yn, connecting it to arithmetic progressions and Pell-type equations. We demonstrate that attempts to express these equations in Beal form fail, and we highlight the role of discriminants and factorization in determining the existence of solutions
Category: Number Theory

Loop Space Blow-up and Scale Calculus

Authors: Urs Frauenfelder, Joa Weber
Comments: 8 Pages. Arch. Math. (2026). https://doi.org/10.1007/s00013-025-02211-0

In this note we show that the Barutello-Ortega-Verzini regularization map is scale smooth.
Category: Functions and Analysis

Physical Interpretation of Einstein Field Equations and Validation of Energy Hole Model

Authors: P. K. Meher
Comments: 11 Pages. Minor changes were [made].

It presents a novel physical interpretation of the Einstein Field Equations (EFE) by introducing the emph{source-energy tensor} as the negative of the emph{stress-energy tensor} $(E_{muu} = -T_{muu})$ and the emph{strain tensor} as the negative of the emph{Einstein tensor} $(S_{muu} = -G_{muu})$, recasting the field equations as a constitutive relation $E_{muu} = kappa S_{muu}$, where $kappa = c^4/(8pi G)$ plays the role of the stiffness modulus of spacetime. From this formulation, a generalized Poisson equation is derived together with its Newtonian limit, demonstrating full mathematical equivalence with the original EFE while offering a mechanistic explanation of gravitational phenomena. The modified equations align with the Energy Hole Model (EHM), which interprets gravity as the manifestation of energy deficits arising due to the investment of energy during the synthesis of mass, rather than positive energy densities. Within this framework, the Friedmann equations are reformulated with new physical interpretations that naturally explain both the attractive gravity of matter and the repulsive effect of dark energy. This interpretation allows the EHM to resolve key cosmological puzzles, including the nature of dark matter, dark energy, and the cosmological constant problem, while preserving the predictive successes of general relativity, thereby offering a unified and physically intuitive foundation for gravity with potential pathways toward quantum gravity.
Category: Relativity and Cosmology

Motion of a Particle on a Catenary Curve: A Lagrangian Mechanics Approach with Elliptic Integral Solutions

Authors: Luv Gupta
Comments: 6 Pages. (Note by viXra Admin: Please cite and list scientific references)

This paper aims to find the motion of a particle that is restricted to move along a catenary curve. The method used to find the dynamics of the particle , we use Lagrangian mechanics along with elliptical integrals to find solve the obtained equation of motion for time. We transform the kinetic and potential energies one generalized coordinate, which results in a short Lagrangian formulation.After applying the Euler—Lagrange equation and using lagrange multiplier which shortens it down and helps us to find the constraint force needed helps us to reach to a differential equation i.e., the equation of motion is derived, analyzing the interaction between inertial and gravitational forces. A similar process is carried upon for the particle going on a catenary under influence of gravity and gravity too. The Euler Lagrange Equation is modified for non conservative forces and a equation of motion is derived. Using Lagrangian Mechanics yield a simple and elegant method
Category: Classical Physics

True Relativity

Authors: Ashir Azeem
Comments: 12 Pages.

There are some unresolved paradoxes and inconsistencies in special relativity and general relativity. This paper is an attempt to fix them all. I presented the true version of relativity. And it is shown conclusively that speed of light cannot be same with respect to source or observer. Simultaneity is absolute. Galilean invariance is indeed deep symmetry of the universe. And it applies on the speed of light too. In Michelson and Morley experiment there is simple addition and subtraction of velocities with respect to source and mirror so that is why there is no fringe shift when apparatus moves with a certain velocity. In moving conductor and magnet problem, in both cases same phenomenon is involved. If the conductor is moving there is Lorentz force on the moving charges in the conductor. And if the magnet is moving then there is same force involved i.e. Lorentz force on charges. Maxwell’s equations cannot be used to determine that the speed of light is constant for all inertial frames. I conceived that the flaw is not in Galilean invariance but in Maxwell’s electrodynamics. 3 × 108 m/s is not the speed limit of the universe. When a galaxy goes away it gives red shift. It is because of photons or light slows down. There is simple addition and subtraction of velocities. Light behaves just like other particles. Speed of light is not constant. Time dilates and inertial mass increases as an object moves. In gravity there is increase in time dilation and increase in inertial mass. Equivalence principle is not very extraordinary. No matter how much you curve spacetime it will not result in acceleration. The idea of spacetime curvature seems unrealistic and fictitious.
Category: Relativity and Cosmology

A Discussion on Cantor's Proof That Real Numbers Are Uncountable and a Proof That Real Numbers Are Countable

Authors: Xiaowen Tan
Comments: 2 Pages. (Note by viXra.org Admin: Please cite and list scientific references)

This paper points out errors or contradictions in Cantor's two proofs that real numbers are uncountable and gives a proof that they are countable. I also give a proof that the power set of the natural number set is countable and point out contradictions in the proof of Cantor's theorem.
Category: Set Theory and Logic

Three Physics Identities; Navigating the Decimal Universe Using the NIST Codata

Authors: Mark A. Thomas
Comments: 4 Pages.

Three possible identities are presented. The identities use physics values from the NIST 2022 CODATA. The Newton constant G is realigned withinCodata against values having more precision, accuracy and lower uncertainties. That the identities match to 7-8 significant figures are a curiosity and is either a coincidence or remains to be explained. It is also made interesting in that two relations incorporate similar physics values.
Category: Classical Physics

Momentum is not What You Think

Authors: Thomas H. Weight
Comments: 2 Pages. (Note by viXra.org Admin: Please cite listed scientific references)

We update Newton’s first law of motion and Weak Equivalence in light of General Relativity.
Category: High Energy Particle Physics

Dark Matter May Be Light

Authors: Thomas H. Weight
Comments: 2 Pages.

We attempt to provide a theoretical basis for Renzo’s Rule in order to clarify a long-standing misunderstanding in physics and conjecture that Photons are Dark Matter.
Category: High Energy Particle Physics

Temporal Differentiation and Its Role in Matter-Field Interactions

Authors: Alaa H. Kheder
Comments: 12 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

The Temporal Difference Principle introduces a novel framework for understanding matter-field interactions through two distinct but interdependent timescales: one dependent on mass and the other on field dynamics. These timescales are inversely related, and this inverse relationship is crucial for maintaining dynamic equilibrium in the system. The paper explores the theoretical underpinnings of the principle, derived mathematical models, and their implications for understanding complex physical systems. The results demonstrate how mass and field interactions scale within the system, offering new perspectives on energy transfer, particle dynamics, and cosmological behavior. This approach holds potential for extending existing models in quantum mechanics and relativity.
Category: High Energy Particle Physics

Gravity Emerges from the Continuous Absorption of Virtual Energy Particles, Which Are Required to Maintain the Electron’s Fixed State Within an Atom

Authors: Sanjay Shah, Yashvi Shah
Comments: 12 Pages.

Gravity has traditionally been described by two prevailing paradigms: (1) Newton's law of universal gravitation as an attractive force (Newton, 1687), and (2) Einstein's general theory of relativity, which interprets gravity as the curvature of spacetime (Einstein, 1915). Although these frameworks adeptly account for numerous macroscopic observations, they fall short in explaining gravitational phenomena at quantum scales. To date, no empirical evidence for quantum gravity has been observed, and the postulated graviton—integral to extensions of the Standard Model of particle physics—remains undetected (Weinberg, 1967). This discrepancy positions gravity as one of the most profound enigmas in contemporary physics.This study introduces a novel model wherein gravity arises from the perpetual absorption of Virtual Energy Particles (VEPs) by atoms, essential for sustaining the stable orbital configuration of electrons. The incessant uptake of these particles induces a directional flux toward the atomic nucleus, manifesting as a gravitational field. Within this paradigm, gravity transcends mere attraction or geometric distortion, emerging instead as a fundamental mechanism for energy redistribution that underpins atomic integrity and cosmic equilibrium.The concept of virtual particles is substantiated by quantum vacuum fluctuations (Heisenberg, 1927), Feynman diagrams in quantum electrodynamics (Feynman, 1949), and empirical phenomena such as the Casimir effect (Casimir, 1948). Diverging from classical mechanics and general relativity, this model conceptualizes gravity as a flux of virtual particles, reconciling quantum microscopic dynamics with macroscopic cosmic behavior. Accordingly, this theory posits that VEPs serve as the primary mediators of gravitational fields and atomic stability, providing a prospective avenue for unifying gravity across disparate scales.
Category: Classical Physics

P ≠ NP Proof

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

We prove P ≠ NP by contradiction by showing that there is no polynomial-time algorithm to solve the set partition problem.
Category: Data Structures and Algorithms

Re-Centring the Human Constant: Modelling Attitude in the AI-Augmented Era

Authors: Senthilkumar Anantharaman
Comments: 10 Pages.

Prevailing narratives often position Artificial Intelligence (AI) as the defining reality of the digital age, with humanity reduced to a variable to be optimized. This paper inverts that assumption. We propose a conceptual and mathematical model of human—AI collaboration based on the complex number formulation z = a + bi, where the real component a represents the immutable foundation of human attitude i.e. consciousness, intent, and ethical direction and the imaginary component bi represents artificial intelligence—the powerful, supplementary force of computation and automation. The model shows that AI amplifies but does not replace the human constant: the magnitude of the system reflects amplified performance, while the argument (angle) reflects the system’s ethical alignment. A dynamic extension highlights the "AI alignment problem" as the challenge of ensuring the rate of growth of human wisdom (da/dt) keeps pace with the accelerating growth of AI capabilities (db/dt). Applications include system design optimization, ethical auditing, and regulatory frameworks. We conclude that the future of AI will be defined less by machine power than by the quality of human attitude that anchors and directs it. The ethical task of the age is to cultivate a robust and virtuous a to ensure that the imaginary force of AI is harnessed for human flourishing.
Category: Social Science

Theoretical Misconceptions and Imaginary Entities in Astronomy, Cosmology and Physics

Authors: Pavlo Danylchenko
Comments: 68 Pages. updated formulas

The majority of theoretical misconceptions and the most significant misunderstandings in modern astronomy,cosmology and physics are caused by a purely mathematical approach and ignoring philosophical comprehension ofphysical reality and, as a result, by not deep enough understanding of the essence of certain physical phenomena andobjects. Foremost, it's all about phenomena and objects that are under consideration by Special and General Relativity.The author has analyzed historical roots of discussed here misconceptions and misunderstandings and has shown thepossible ways to overcome them. Such constructive approach gives us the hope for getting rid of the majority ofrevealed here misconceptions and misunderstandings. Unfortunately, this is the problem of not only the astronomy andcosmology, but also of physics in general. Our perception and reflection of physical reality is still very primitive and,foremost, mainly mechanistic, macrocentric and anthropo-limited. The unreality of black holes, Big Bang, non-baryonicdark matter, dark energy, photons and neutrinos is justified in details. The current usage of exponential scale instead ofmetrically homogeneous scale of cosmological time in cosmology is shown. Therefore, the ignorance of the fact thatonly the infinitely far cosmological past on the event horizon and infinitely far cosmological future on Schwarzschildsphere are simultaneous with any event in people’s world is shown. The ignorance of the fact that this pseudo-horizoncovers the past of all infinite Universe is also shown. The possibility of existence of antimatter inside the neutron starsand quasars that have the hollow body topology and mirror symmetry of their intrinsic space is justified. The bigredshift and long lasting high luminosity of quasars are explained. The spatio-temporal noninvariance of thegravitational constant and the fictiveness of Etherington's identity are proved. The absence of gravitational fields in theUniverse up to the moment of discontinuity of its uniform gas continuum is shown. The origination of the gravityphenomenon is related to the formation of spatially inhomogeneous thermodynamic states by the matter and to thetendency of the whole gravithermodynamically bonded matter to reach the minimum of the integral values of its inertfree energy and Gibbs free energy. The temporal invariance of not only all thermodynamic parameters and potentials ofmatter and its momentum but also of Lagrangian of ordinary rest energy and of equivalent to it gravitational mass ofmatter (to which the inertial mass is identical only in intrinsic time of this matter) is justified. The fact that spatialdistribution of gravitational field strength, defined by logarithmic gravitational potential, perfectly corresponds toastronomical observations is shown. It is shown that according to the General Relativity and the RelativisticGravithermodynamics equations, the configuration of the dynamic gravitational field of a galaxy in a quasi-equilibriumstate corresponds to reality. The fact that Hubble’s redshift is linearly dependent on comoving distance instead ofluminosity distance is justified. It is shown that mentioned above fact corresponds to astronomical observations. It isconcluded that such concepts as corpuscle and elementary particle are purely macroscopic. The inadmissibility of thepresence of "thing-in-itself" in physics is shown. The possibility of spiral-wave nature of the matter microobjects — theterminal local drains of turns of the spiral waves of high frequency space-time modulations of the dielectric andmagnetic permeabilities of the physical vacuum (singularities of the field according to Einstein hypothesis) — as a wholeis shown.
Category: Relativity and Cosmology

Reactivity to Eye Opening in Patients with Ischemic Stroke or Transient Ischemic Attack.

Authors: Regina D. Shmelkina
Comments: 6 Pages.

Determination of the characteristics of the EEG response to eye opening (e o) in patients who have suffered Ischemic stroke(IS) including those with Transient Ischemic Stroke (TIA), in early stage was performed. Statistically significant reduction of desynchronization during e o and increase of synchronization was detected. It was in the form of a significant predominance of theta- rhythm in the patients with vascular pathology in comparison with epileptic seizure and age norm.
Category: Quantitative Biology

A Brief Study of Directors’ Duty of Loyalty to Shareholders — Focusing on Directors’ Liability for Damages to Shareholders and Cases of Parent and Subsidiary Companies

Authors: Kwonhyung Lee
Comments: 16 Pages. In Korean

A full understanding of directors’ fiduciary duties toward shareholders requires clarification of their shareholder-protection function in capital transactions, which constitute the very subject of regulation. This study, building upon the frameworks of the "identity theory," "difference theory," and the debates on "inclusion versus exclusion," analyzes the liability of directors of a subsidiary toward each shareholder in cases involving the issuance of new shares and mergers, particularly in the boundary case where the shareholder is a parent company, i.e., a "corporate shareholder." The analysis suggests that the recent amendment, in its interpretative formulation, lacks sufficient instrumental adequacy due to its abstract and comprehensive nature. To address this deficiency, the study proposes a legislative reform introducing Article 382-5 of the Korean Commercial Act, explicitly codifying directors’ "duty to transfer fair value." However, the research does not extend to issues concerning the future direction of legislative reform on merger ratios among affiliated companies under the Financial Investment Services and Capital Markets Act, nor to cases involving corporate shareholders in spin-offs, reverse stock splits, or other capital transactions. These matters remain for future research.
Category: Social Science

Let There Be Light in Quantum Theory: A φ-Geometric Model of Relativistic and Cosmological Limits

Authors: Mikheili Mindiashvili
Comments: 15 Pages.

This paper introduces a new geometric model of spacetime, constructed from a right triangle inscribed in a circle. In this construction, the hypotenuse coincides with the diameter of the circle. From this configuration, a universal parameter naturally emerges — the angle φ, which links gravitational effects, relativistic transformations, and quantum transitions. This geometry provides a new way to interpret physical phenomena, ranging from classical cosmology to quantum mechanics. It avoids deep singularities and transforms them into "light" singularities. These milder forms open the way for further physical analysis.
Category: Classical Physics

Proof of the Riemann Hypothesis: A Structural Proof of the Riemann Hypothesis:Well-Ordering, Symmetry, and the Critical Gap Theorem

Authors: Rusin Danilo Olegovich
Comments: 5 Pages. (Note by viXra Admin: Please cite listed scientific references and submit article written with AI assistance to ai.viXra.org)

We present a complete structural proof of the Riemann Hypothesis, based on the interplay between the canonical well-ordering of nontrivial zeros and the symmetry imposed by the functional equation. Working from three established analytic properties of the Riemann zeta function — discreteness of zeros, confinement to the critical strip, and functional equation symmetry — we construct a proof that reduces the Riemann Hypothesis to a purely combinatorial statement about order and symmetry. We prove the Critical Gap Theorem: if a zero off the critical line exists, the first such zero (under the canonical ordering) must lie to the left of the critical line, forcing its functional equation partner to appear later in the ordering. This leads to a contradiction unless no such zero exists. The result is a logically complete, structurally elegant proof of the Riemann Hypothesis requiring no advanced analytic estimates — only classical properties known since the 19th century.
Category: Number Theory

The Structure of First Order Logic

Authors: Martín Alejandro Monzón Marimón
Comments: 1 Page.

The structure of First Order logic will be described here in its verbal, or explicit (Second Order) form, by means of an "apparent" Zeroth Order form, because the actual pure Second Order form is not axiomatizable. Also, another "apparent" Second Order form will be used to make a Zeroth Order description of the structure, which, without the "apparent" Second Order quantification, would remain silent, or implicit, as that is its pure Zeroth Order form.
Category: General Mathematics

After the West: The Emergence of a Polycentric World Order

Authors: Yew Kee Wong
Comments: 119 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

For five centuries, the international system has been defined by the political, economic, and cultural hegemony of the West. This epoch, born from the Age of Discovery and cemented by the Industrial Revolution, established a global order centered largely in Europe and later, the United States. It was a world mapped by colonial empires, governed by Western-derived institutions like the nation-state and international law, and driven by an economic model that radiated outward from Atlantic financial centers. This order, while frequently contested and reshaped by war and revolution, maintained a fundamental characteristic: the West as the gravitational core of global affairs, the setter of rules, and the arbiter of what constituted modernity and progress.Today, that centuries-old architecture is unraveling. The unipolar moment that followed the Cold War has proven to be a brief, anomalous interlude, giving way to a far more complex and fragmented reality. The phenomenon we are witnessing is not a simple transfer of power from one hegemon to another, but the emergence of a truly polycentric world order—a system with multiple, often competing, centers of economic influence, political authority, and military power. This shift is driven by the rapid economic ascent of nations, most notably China and India, which are reclaiming a share of global wealth not seen since the early nineteenth century. Simultaneously, the diffusion of technology, the rise of regional powers from Brazil to Indonesia, and a growing assertiveness from states operating outside the Western liberal consensus are creating a landscape where no single power can dictate terms.This new polycentricity promises a world that is both more representative and more volatile. On one hand, it signifies a decolonization of global governance and a long-overdue recognition of the agency and voices of the non-Western world. On the other, it threatens to erode the common rules and shared frameworks that, for all their flaws, provided a measure of predictability and managed conflict for decades. The old institutions are straining under the weight of new realities, and the international community is struggling to forge new consensus on issues from security to trade to climate change. We are entering an age of negotiated disorder, where ad-hoc alliances, economic interdependence as a strategic weapon, and clashing value systems will define a new and uncertain chapter in human history.
Category: General Science and Philosophy

Derive Schrödinger Equation from F=ma

Authors: Runsheng Tu
Comments: 10 Pages.

The compatibility between quantum mechanics and classical mechanics is always worth discussing. According to F=ma, the Schrödinger equation (SC) can be derived. Important classical physics formulas can be derived from the SC. The SC intuitively contains the mass m and the potential energy formula (this quality m can be large enough to enter the macro range and the potential energy comes from classical attraction). These three points determine that the SC is an organic combination of wave functions and classical mechanical laws. Based on this, it can be predicted that the SC, which can be used to describe macroscopic objects, can be established. It can be observed from the experiment of electron diffraction in a magnetic field that the volatility and property of moving electrons can be presented simultaneously. This experimental phenomenon, together with the mathematical analysis mentioned above, supports the conclusion that Newton's second law still applies in the microscopic world. According to the SC, it can be proven that "the energy of a moving particle described by the law of waves is equivalent to a multiple of its kinetic energy"; There is no absolute boundary between macro and micro.
Category: Quantum Physics

Primes as Geometric Indecomposables: A Group-Theoretic Characterization on the Circle and Its Harmonic Signature

Authors: Rayan Bhuttoo
Comments: 7 Pages. License: CC BY-NC-ND 4.0 (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We demonstrate that prime numbers are precisely the indecomposable elements under a novel group operation defined on a circle, providing a geometric characterization of primality.By projecting integers onto a circle via the mapping θn = arccos(n/R), we show thatprimes exhibit intense clustering at the endpoints of the diameter, while composite numbers distribute uniformly. We formalize this observation by defining an angular density function F (n) that vanishes if and only if n is prime, with a rigorous proof based on the PrimeNumber Theorem. Furthermore, we analyze the Fourier spectrum of the prime distribution,revealing a distinct high-frequency signature. Finally, we conjecture connections betweenthis harmonic signature and the nontrivial zeros of the Riemann zeta function, suggesting anew approach to understanding prime distribution through geometric and harmonic analysis.
Category: Number Theory

About Possible Mechanisms of the Social Management

Authors: Igor Tkachenko, Victoria Miroshnichenko, Konstyantin Tkachenko, Sergii Miroshnichenko, Yiurii Miroshnichenko, Olesia Tkachenko, Svitlana Tkachenko
Comments: 9 Pages.

Based on the early developed approach for a NSP an analytical description, together with the social management redefinition, a possibility of the generalized approach application to the managing process is analyzed. The approach was reformulated in general form to be applied to a quantum size particles. Auto correlation function values were calculated for each of the two approach predicted regimes for the 3-rd order NSP development. The mechanisms of the revealed regimes were analyzed and associated with the "military" (ordered) and "civilian" (diffusive, disordered) transformations. One possible variant for a delay time nonmonotonic dependence of the auto-correlation function was shown to exist for the 1-st regime of the NSP development. The three possible variants were observed for the 2-nd regime. Two of the variants were analogous each other in conserving similar, relatively high ordering levels for the most time periods of their developments but having decreasing and increasing dependence parts on the finishing stage of the development. The third variant has monotonously decreasing time dependence of the auto-correlation function. The above conclusions from the obtained results were shown to be confirmed by the relevant data from the modern and historical management practice.
Category: General Science and Philosophy

A Possibility Evaluation for the Casimir Effect to Be a Consequence of the Bernoulli Law

Authors: Igor F. Tkachenko, Yuriy S. Miroshnichenko, Victoria I. Miroshnichenko, Konstantyn I. Tkachenko, Sergyi A. Miroshnichenko, Svitlana G. Tkachenko
Comments: 4 Pages.

Based on the early developed analytic model of the nonstationary stochastic processes and well grounded concept of the flat plane Universe originated by the Big Bang and continuing to evolve by now, the well known Casimir effect was considered as a consequent of the Bernoulli law, showing decreasing the static pressure providing the motion of cosmic fluid with increasing its velocity. Novel formula to calculate the stress acting perpendicular the flow direction was derived and the formula similarity with the known Casimir relation obtained using quantum electrodynamics was shown. The stress values calculated using the new formula is in a good agreement with the available experimental data.
Category: Mathematical Physics

Arrows Shooting Fish Eyes: Interpretation of Sanxingdui Texts

Authors: Hao Chen
Comments: 65 Pages. In Chinese

Ancient people couldn't find Sanxingdui script, but it's likely everywhere. For example, the Four-Ram Round-Mouthed Square Tripod unearthed from Pit 3 of the recent Sanxingdui excavation is nearly identical to the Taipei Four-Ram Round-Mouthed Square Tripod, except for the addition of four standing birds on its shoulders. This revelation brought a sense of relief and warmth to the people, as if they had found each other, found themselves, and could finally reunite. Could they recognize each other? The two Four-Ram Round-Mouthed Square Zun vessels, separated by thousands of miles and on opposite sides of the Yangtze River, have been separated throughout history. If they could truly reunite and rediscover each other across millennia of history and distance, it would undoubtedly be a rare miracle and a truly charitable act. The Four-Ram Round-Mouthed Square Zun is a rare find in history. It symbolizes the unity of the round heaven and the square earth. The four rams represent carrying heaven and earth on their backs, much like the ancient Chinese metaphor of "receiving a mandate," meaning receiving a mandate from heaven and earth. It also represents carrying heaven and earth on one's back and offering sacrifices. What a profound metaphor! This kind of human nature can be described as "goodness." Interestingly, if you compare the Chinese character for "goodness," you'll find that the Four-Ram Round-Mouthed Square Zun and the character for "goodness" are identical.
Category: Archaeology

Embryonic Tensor Calculus Applied to Artificial Intelligence in Modern Software Engineering

Authors: Horacio Useche Losada
Comments: 33 Pages. (Note by viXra Admin: An abstract in the article is required; please submit article written with AI assistance to ai.viXra.org)

This document briefly reviews how AIs function and introduces the concept of the embryonic tensor in the training and operation of AI systems.
Category: Artificial Intelligence

A Mathematical Framework for Unconventional Superconductivity Beyond BCS Theory

Authors: Debabrata Chini
Comments: 30 Pages. (Note by viXra Admin: For the last time, please submit article written with AI assistance to ai.viXra.org)

We present a rigorous mathematical framework for modeling unconventional superconductivity beyond the standard Bardeen-Cooper-Schrieffer (BCS) theory. While BCS theory successfully explains conventional superconductors through phononmediated electron pairing, it fails to capture key phenomena in high-temperature and strongly correlated superconducting systems. In this work, we construct a non-BCS theoretical model rooted in advanced mathematical formalisms, incorporating non-trivial symmetries, non-local interactions, and topological considerations. The model is developed from first principles, without reliance on empirical fits or experimental parameters. We derive a new class of equations governing the superconducting order parameter and explore their implications through analytical techniques and graph-based representations. Our results suggest the emergence of superconducting states with properties incompatible with BCS-type behavior, offering insights into possible mechanisms behind high-temperature or exotic superconductors. This framework provides a foundation for further theoretical explorationand may guide future experimental inquiries into non-phononic superconductivity.
Category: Condensed Matter

A Topos-Theoretic Formulation of General Relativity: Emergent Spacetime from Sheaf-Categorical Principles

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

We present a comprehensive reformulation of General Relativity using category theory, sheaf theory, and topos theory, providing an alternative to the traditional differential geometric framework. The fundamental construct is a category Loc of local spacetime regions equipped with a Grothendieck topology, forming a site (Loc, J). Physical observables are represented as sheaves on this site: the metric sheaf Met, matter sheaf Mat, and their derived structures. The EinsteinField Equations emerge not as differential equations but as natural transformations between functors, defining the solution sheaf Sol—the subsheaf of local configurations satisfying the equations of motion. We develop internal differential geometry within the topos Sh(Loc, J), constructing the Hilbert action as a natural transformation and deriving the field equations from an internal variational principle. A model of General Relativity corresponds to a global section of Sol. This formulation provides a robust mathematical foundation for quantum gravity research and offers natural pathways for unification with quantum theory within a common topos-theoretic framework, while maintaining complete consistency with established experimental results.
Category: Quantum Gravity and String Theory

Quantum-Gravitational Machine Learning: A Theoretical Model for High-Energy Social Intelligence

Authors: Debabrata Chini, Deblina Biswas
Comments: 15 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper introduces a purely theoretical framework that fuses quantum information theory, general relativity and machine learning to construct a high-energy intelligence model with direct application to large-scale social systems. By leveraging entangled quantum networks in curved spacetime and high-energy field dynamics, the proposed model formulatesa new kind of non-classical learning system with relevance to urban optimization, predictive disaster modeling, and secure communication infrastructure. Using rigorous field-theoreticcalculations, we show how curvature, energy, and quantum state compression can drive intelligent data flow under extreme physical and informational constraints. All derivations, graphs and architecture designs are grounded in first-principles physics, with no experimental data involved. This work offers a new path for theoretical AI systems that are not limited by classical assumptions, proposing a future direction for socially embedded computation based on fundamental physical laws.
Category: Quantum Gravity and String Theory

The Non-Relativistic Bi-Level Electron Model

Authors: Martin Kraus
Comments: 7 Pages. This revision adds clarifying footnotes about the mass distributions represented by the model and the constraint on the speed of the center of charge.

This work presents the bi-level electron model, a quantitative model of a point-like spinning electron, which was inspired by similar classical models of spinning electrons that interpret the Zitterbewegung of Dirac electrons as a spin motion of point-like electrons. The new model is consistent with de Broglie's internal clock hypothesis and other features of a modified Born-Infeld model of electrons, as well as with Larmor precession of the electron spin in a uniform magnetic field. The equations of motion are discussed in non-relativistic approximation, while the relativistic case is left for future work.
Category: Classical Physics

Language Image Natural Modeling Architecture (LINMA)

Authors: Bing Lin
Comments: 10 Pages.

In this paper, Language Image Natural Modeling Architecture (LINMA) is proposed, based on research over at least millions years of evolution and compression of interactive intelligence along with the real spatial world. It is interaction that bridges human and the real world.In fact, the evolution of interactive intelligence has been driven by limbs of human or animals. Thus, interactive action based depiction of limbs could be critical component of human intelligence.We propose LINMA's pattern of limbs, illustrating various shapes, gestures, postures and motion trajectories. Symbolization of these patterns can provide language building blocks. Arms, hands and fingers have played fundamental role in construction of human civilization. They are deserved to be depicted as a visible carrier of intelligence. Thus a very straightforward means is available for human being to explore the nature of intelligence.Actually, our hands hold the secrets of language intelligence. It couldn't be simpler and more powerful. LINMA language could serve as action dataset to empower wearable devices, virtual digital human and humanoid robot with embodied intelligence.
Category: Artificial Intelligence

Modulus Time: A Symmetrical Framework for the Directionality of Absolute Time and Cyclic Cosmology

Authors: Mohd Ubaidur Rahman Udoy
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)

This paper proposes a concept of Modulus Time, denoted as |T|, a framework where time is treated as a symmetric quantity with magnitude independent of direction. In contrast to the conventional concept of time, which flows only in the forward direction, Modulus Time integrates two symmetric directions, +T and -T, each corresponding to contrasting entropy evolution. This symmetrical property naturally suggests a cyclic cosmological framework, where the universe experiences phases of expansion with increasing entropy (+T), followed by contraction with decreasing entropy (-T), forming an indefinitely repeating cycle. We discuss the theoretical significance of Modulus Time, addressing the thermodynamic causality, the arrow of time, and contrasting entropic evolution.
Category: Relativity and Cosmology

Can Relativistic Mass or Weakening of Force be Measured with a Vacuum Tube?

Authors: Jorma Jormakka, Wolfgang Sturm
Comments: 15 Pages.

Most physicists do not actually believe that mass depends on velocity as in the relativistic mass formula, but still keep this concept, for instance because an identical formula, energy-momentum relation, is seen as useful. However, there is no sense in keeping false concepts and valid results that have been derived by using false arguments can also be derived in other ways, even in a correct way. Yet, if an alternative explanation is proposed, it would be good to get a proposal for an experiment that can support the new explanation.The presented article discusses experiments that could add strength to the explanation thatrelativistic mass is actually a wrong interpretation of force becoming weaker if the object of the force is escaping the force with nearly the propagation speed of the force. The article considers if such an experiment could be done with a vacuum tube but no experimental results are given yet in this paper.
Category: Relativity and Cosmology

Sigma 8 Anomaly as Potential Evidence for Fractal Spacetime (Part 1)

Authors: Ervin Goldfain
Comments: 12 Pages.

The Sigma 8 anomaly of cosmology refers to discrepancies in the amplitude of matter fluctuations, where low redshift observations favor weaker matter clustering than predicted by the standard Lambda-CDM model. Elaborating from the hypothesis of continuous spacetime dimensions, this work offers an alternative explanation of the anomaly, based on scale-dependent corrections to the evolution of density fluctuations. In our interpretation, the σu2088 anomaly can be viewed as observational evidence for fractal spacetime effects at cosmological scales.
Category: Relativity and Cosmology

Einstein’s Mysterious Clocks: a Case Study in Sympathetic Magic

Authors: Stephen J. Crothers
Comments: 5 Pages.

When we want to measure something we use a measuring device appropriate for the quantity we want to measure. For instance, if we want to measure the width of a doorway we could use a tape measure or a ruler. Space is not defined by what is used to measure it; space exists independently of the measuring device. Similarly, if we want to measure the pressure in a car tyre we use a pressure gauge. Pressure is not defined by what is used to measure it; pressure exists independently of the measuring device. In the case of measuring time we can use a clock or a watch. A measuring device is used to measure something other than itself. Any measuring device invented to do nothing but measure itself or copies of itself is unnecessary. No measuring device defines what it is used to measure. What it is to be measured is what motivates the invention of the measuring device in the first place. Strangely, in developing his theory of relativity, Einstein used his clocks to define time and thereafter spoke of his clocks. In other words, Einstein’s clocks only ever measure themselves so that clocks running at different rates means, for him, time running at different rates. In doing so Einstein detached his clocks and watches from physical reality and created a fantasyland in which clocks and watches reign supreme. His moving clocks running at different rates constitute moving times running at different rates.
Category: Relativity and Cosmology

The DiCoSa Model: A Bottom-Up Digital Consciousness Proxy for AI Superalignment

Authors: Thierry Marhin
Comments: 35 Pages. (Note by viXra Admin: Please use smaller fonts and submit article written with AI assistance to ai.viXra.org)

The Digital Consciousness SuperAligned Model (DiCoSa) introduces a modular, bottom-up framework for embedding human values into superintelligent AI systems, drawing from positive psychology, computational principles, and AI safety research. Anchored by three fixed dimensions—DiCoValues, DiCoLife, and DiCoPurpose—the model employs iterative algorithms guided by a "pursuit of aligned well-being" rule to incorporate optional dimensions, balancing minimal complexity with maximal alignment efficacy. This updated version integratesrefinements to the DiCoLife dimension, including detailed decomposition, standardized metrics from validated psychological scales, and an interactive user feedback interface for iterative affinage. DiCoValues is informed byfoundational texts such as the US Constitution, Hippocratic Oath, and New Testament, augmented with superalignment principles like mitigating existential risks. Mathematical representations model consciousness as a dynamic vector space, with aggregation into meta-DiCo structures viaDiCoNet, a decentralized network for cohort-based sharing among users and AI overseers. AI-driven predictive analytics recommend optional dimensions, secured by blockchain. Optional dimensions such as DiCoState, DiCoNet (embeddable), DiCoImpact, DiCoSafety, andDiCoOversight enable personalization, scalability, and enhanced AI control. This paper examines technical feasibility, scientific foundations, and complexity-feasibility trade-offs, with simulations, case studies, andnew examples of user-AI dialogues for metric refinement. Applications include AI alignment tools and safety protocols.
Category: Artificial Intelligence

Generation of Gravitational Wavelets by Stationary Electromagnetic Wave Closed in a Resonant Cavity-a Theoretical Frame

Authors: Constantin Sandu
Comments: 5 Pages.

In two earlier studies, we demonstrated that due to the enormous accelerations arising during the perpendicular reflection of a photon by a mirror, the photon’s energy distribution behaves as a quadrupole, thereby generating a graviton (or gravitational wavelet) at the same frequency and direction as the reflected photon. For simplicity, only the contribution of the quadrupole component Qxx was previously considered. Here, we extend the analysis to include all quadrupole components associated with perpendicular photon reflection. By applying the standard Einstein quadrupole radiation formula, we show that the energy of the emitted graviton scales as ν^3, revealing a direct coupling between electromagnetism and gravitation. This finding challenges the long-standing but unverified assumption that graviton energy depends linearly on frequency (ν^1). Our results establish that quantum gravity theories must instead incorporate cubic frequency dependence. The proposed framework provides a new bridge between general relativity and quantum approaches, suggesting that confined electromagnetic radiation can act as a direct source of high-frequency gravitational wavelets.
Category: Relativity and Cosmology

Once Again About Nature and Its Material Principles (Ещё раз о природе и её материальных началах)

Authors: Robert Yusupov
Comments: 14 Pages. In Russian

In this article, the author makes another attempt to present and explain to the esteemed readers his vision and understanding of the structure and evolution of nature and the Universe. All this is in the author's book "Theory of Nature" and in his article "Nature as an objective reality". The author entirely and completely stands on the position of the only true and scientific philosophy of dialectical materialism. The author entirely and completely adheres to the only true and scientific dialectical-materialistic worldview

В настоящей статье автор делает ещё одну попытку представить и разъяснить уважаемым читателям своё видение и понимание устройства и эволюции природы и Вселенной. Всё это есть в книге автора «Теория Природы» и в его статье «Что такое Природа» («Природа, как объективная реальность»). Автор целиком и полностью стоит на позиции единственно истинной и научной философии диалектического материализма. Автор целиком и полностью придерживается единственно истинного и научного диалектико-материалистического мировоззрения
Category: General Science and Philosophy

Once Again about Nature and its Material Principles

Authors: Robert Yusupov
Comments: 13 Pages.

In this article, the author makes another attempt to present and explain to the esteemed readers his vision and understanding of the structure and evolution of nature and the Universe. All this is in the author's book "Theory of Nature" and in his article "Nature as an objective reality". The author entirely and completely stands on the position of the only true and scientific philosophy of dialectical materialism. The author entirely and completely adheres to the only true and scientific dialectical-materialistic worldview
Category: General Science and Philosophy

Time Dilation Effect of Moving Objects

Authors: Vu Tuan Hiep
Comments: 6 Pages. In Vietnamese (Note by viXra Admin: Please cite and list scientific references)

In the paper "On the electrodynamics of moving bodies -1905", Einstein concluded that time in an inertial moving frame of reference is dilated compared to a frame of reference considered to be at rest. In this paper, we will present the true nature of the time dilation effect. And analyze the time aspect in Einstein's 1905 paper, in order to present the nature of time dilation in the Special Theory of Relativity.
Category: Relativity and Cosmology

Perian Matrices Link with Anti-Commutative Operators (Matrices Périennes Liens Avec Les Opérateurs Quantiques Anti-Commutatifs)

Authors: Thierry L.A. Periat
Comments: 33 Pages. In French

Perian matrices have been introduced in two previous works. The first one concerns the electromagnetic duality in vacuum, and the second one is a short note focusing attention on the three-generations problem in particles physics. Remarking that a perian matrix can formally be identified with the kern of the decomposition of a deformed cross product, this exploration loans ideas to the quantum theories and asks if these matrices can sometimes be the representations of anticommutative operators. The exploration concludes affirmatively when the three coefficients of a given matrix are pure imaginary quaternions. In that case, each coefficient can be associated with a vector characterized by three complex numbers. The three vectors associated with this given matrix must be a Jacobi's territory (synonym: they form a triplet equipped with a Lie algebra structure).

Les matrices dites périennes ont été introduites au cours de deux précédentes études. L'une d'elle s'est intéressée à la dualité électromagnétique dans le vide et l'autre au problème des trois générations de particules en physique nucléaire. Puisque certaines matrices périennes peuvent formellement être identifiées au noyau d'une décomposition d'un produit vectoriel déformé et que cette décomposition est associée avec une polynomiale, cette exploration se laisse guider par les principes des théories quantiques et se demande si certaines de ces matrices peuvent servir d'opérateurs quantiques anticommutatifs. La réponse est affirmative si les coefficients de ces matrices sont des quaternions purement imaginaires et si l'ensemble des trois vecteurs à composantes complexes attachés à ces coefficients constituent un territoire de Jacobi (synonyme : forment des triplés de vecteurs équipés d'une structure d'algèbre de Lie.
Category: Algebra

The Basel Problem Through Kinematic Shadows: A Kinematic-Geometric Reconstruction of ζ(2) = π^2/6

Authors: Rayan Bhuttoo
Comments: 5 Pages. License: CC BY-NC-ND 4.0 (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

We derive Euler’s celebrated result through a novel kinematic-geometric framework. By modeling the orthogonal projection of uniform circular motion (e.g., a rotating blade under collimated light), we identify the universal ratio ∥shadow∥ circumference = 1 π as a fundamental scaling law between rotational and linear kinematics. Interpreting the real number line as a harmonic projection of a rotational system, we demonstrate that the summation reconstructs the curvature lost under projection. This approach naturally extends to higher zeta values ζ(2k), admits quantum-mechanical analogues via projection operators P, and adapts to relativistic regimes where Lorentz contraction modifies shadow geometry. Our work establishes π as a dynamic compression ratio be tween rotational and linear kinematics, offering a physical lens for classical number theory.
Category: Mathematical Physics

Gravity, Momentum, and the Potential Energy Field

Authors: Charles R. Fout
Comments: 8 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)

Relativity is based upon just three guiding principles. A. The speed of light is constant for all observers. B. Observations made from every inertial reference frame are equally valid. C. Inertia and gravitational attraction are identical. To these, I propose adding a fourth: D. Energy density must be conserved. This simple addition leads to a model with particles of fixed and finite size in a Euclidean field of potential energy. The model is more simple and intuitive than general relativity. It also shows a "flattening" of gravitational attraction in low energy areas like the outer regions of rotating galaxies, where general relativity is known to fail.
Category: Relativity and Cosmology

Contextual Quantum Entropic Lattices for Non-Clifford Information Propagation: A Theoretical Framework for Ultra-Secure Qubit Channels

Authors: Debabrata Chini
Comments: 22 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

This paper introduces a new class of quantum information structures called entropic lattices, designed to encode and propagate information using non-Clifford operations in contextual quantum frameworks. Motivated by the limitations of classical error correction and the need for ultra-secure quantum communication, we develop a purely theoretical and rigorous approach to model entropic interactions between qubits across lattice sites. Our framework leverages contextuality—a uniquely quantum phenomenon—as a resource to enable controlled information flow beyond stabilizer limitations. We construct analgebraic basis for entropic channels and derive propagation laws under entropy-preserving, non-Clifford logic. The proposed model is built entirely from first principles, includes high-level mathematical formalism, and does not rely on any experimental data. This work aims to establish a new foundation for robust, theoretically-grounded quantum communication protocols that extend the scope of quantum error resistance and computational universality.
Category: Quantum Physics

Principium Geometricum: Mathematical Derivation of the Unified Force Law of Nature

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 5 Pages.

We demonstrate, with mathematical rigor, that the Principium Geometricum(PG) force law,F(R) = (rho_v^2 * V1 * V2 * c^2) / (lambda * alpha_U * R^2),is not an arbitrary postulate but the unique consequence of treating matter as vac-uum resonance. We derive it independently via (i) a variational principle, (ii) theflux of momentum through a stress tensor, and (iii) the energy of the field viaGreen’s identity. In all cases, the same 1/R2 dependence and the same prefactorstructure emerge. Dimensional analysis, boundary value problems, self-energy reg-ularization, and calibration with Newtonian gravity and Coulomb electrostatics arediscussed. Thus the PG force law stands as a mathematically consistent unificationof interactions under the same tensional principle.
Category: Mathematical Physics

Benzene on the Basis of the Three-Electron Bond

Authors: Bezverkhniy Volodymyr Dmytrovych
Comments: 1 Page. (Note by viXra Admin: Please cite and list scientific references!)

Using the concept of three-electron bond one can represent the actual electron structure of benzene, explain specificity of the aromatic bond and calculate the delocalization energy.
Category: Chemistry

Mysteries of Prime Numbers and Magic Matrices

Authors: Ahcene Ait Saadi
Comments: 11 Pages. (Note by viXra Admin: Further repetition may not be accepted; please cite and list scientific references in the article)

This document is entitled (mysteries of prime numbers and magic matrices) Explores the relationships between prime numbers and special matrices. The main objective is to use these matrices to form triples of prime numbers and to establish mathematical conjectures. This work may have common mathematical relationships with the Golbach conjecture and Collatz conjecture. The research is only at is beginnings, I hope that young researchers will be interested in it, and why not draw mathematical theory’s from it.Key words: Prime numbers; Matrices; System of equality, Some of square of prime numbers.
Category: Number Theory

The Dirac Equation is not Lorentz Invariant

Authors: Jorma Jormakka
Comments: 11 Pages. Added a new part to the paper, corrected typos

A favorite claim that editors of journals make when rejecting a manuscript proving serious errors in the Relativity Theory is that the Relativity Theory has been verified by countless experiments. The number of experiments that actually verify relativity may be much smaller than countless, as there are alternative explanations to of these all experiments. One claim related to the relativity theory is that the Dirac equation is Lorentz covariant. This claim has never been verified by any experiments. This article gives three different proofs that the Dirac equation is not Lorentz invariant. This is a simple mathematical question, all three proofs are simplemathematics.
Category: Relativity and Cosmology

Design for a Gravitational Wave Generator/Thruster V8 Part I

Authors: Peter C.M. Hahn
Comments: 22 Pages.

This device generates gravitational waves which can be utilized as a thruster or as a communication device. It is comprised of a linear antenna array that is injected with a Radio Frequency (RF) signal. The antennas are configured to convert electromagnetic (EM) waves into gravitational waves.When the antennas are arranged in a linear phased-array configuration, a thrust is produced that allows the device to be used as a method of propulsion. Part I of this article describes the device when configured as a thruster and documents the test results.Part II will document the test results of the device when configured as a gravitational wave transmitter. If the injected RF signal is modulated with an Intermediate Frequency (IF) signal, the gravitational waves produced are also modulated. The invention can then function as a communication device by using the gravitational waves as a carrier instead of EM waves. A gravitational wave detector at the receiving end can demodulate the gravitational waves, thereby extracting the original (IF) signal.
Category: Relativity and Cosmology

Optimal Symmetric Bounds on P

Authors: Jabari Zakiya
Comments: 14 Pages. New content added before publication.

Various bounds on p, such as Bertrand’s Postulate and Legendre’s Conjecture, propose regions around n that have at at least one prime within them. Using Prime Generator Theory, I show more precise symmetric bounds on p, such that for n a prime exists symmetrically within a distance of n^(1/2) below and above it. That is to say, a prime exists for: n — n^(1/2) < p < n and n < p < n + n^(1/2).
Category: Number Theory

Solutions of the Standard Differential Equation of the Dynamic Gravitational Field of a Flat Galaxy

Authors: Pavlo Danylchenko
Comments: 38 Pages. updated formulas

The solution to the gravitational field equations of a flat galaxy has been found. Itis shown that at the edge of the galaxy the excessively strong ordinary (unreduced)centrifugal pseudo-forces of inertia are compensated mainly by centripetal pseudoforcesof evolutionary self-contraction of matter in the background Euclidean spaceof expanding Universe, and not by the weak gravitational pseudo-forces at the edgeof the galaxy. The strength of the dynamic gravitational field of spiral and otherflat (or superthin) galaxies, according to their two-dimensional topology, isinversely proportional to the radial distance, not to its square. And this is the case,despite the inverse proportionality of the strength of individual gravitational fieldsof all spherically symmetric astronomical objects of the galaxy exactly to thesquare of radial distance. The general solution of the equations of the gravitationalfield of the galaxy with an additional certain parameter n is found. At possible valuesof n < 1, the velocity of the orbital motion of stars is slightly less than the highestpossible velocity even at the edge of the galaxy. According to the General Relativity(GR) equations and the Relativistic Gravithermodynamics (RGTD) equations, theconfiguration of the dynamic gravitational field of a flat galaxy in a quasi-equilibriumstate is standard (canonical in RGTD). That is because it is not determined at all by thespatial distribution of the average mass density of its non-continuous matter. After all,this spatial distribution of the average mass density of the galaxy's matter is itself determined by the standard configuration of its dynamic gravitational field. Thestandard value of the average density of mass of matter at the edge of a galaxy isdetermined by the cosmological constant Λ and by the difference between unityand the maximum value of the parameter bc. And it is a non-zero standard value,despite the gravitational radius at the edge of a galaxy takes the zero value.Therefore, in the RGTD and in the appropriate interpretation of the GR, in contrast tothe orthodox interpretation of the GR, there can be no shortage of baryonic mass. Andtherefore, the Universe does not need dark non-baryonic matter at all.
Category: Relativity and Cosmology

Generalized Equations of Thermodynamics with Hidden Variables

Authors: Pavlo Danylchenko
Comments: 18 Pages.

For the collective gravithermodynamic Gibbs microstates the connection betweenall thermodynamic potentials and parameters of matter have been found. Thisconnection is realized with the help of four hidden wave functions that can takearbitrary values with certain probability. The possibility of obtaining the knownequations of thermodynamic state of real gases is shown based on the use of boththe coordinate velocity of light of the general relativity and the mathematicalexpectations precisely of these four hidden parameters (wave functions) andfunctions of them. It is substantiated that in a quasi-equilibrium state, a real gashas spatial homogeneity not only of its entropy but also of the resulting extensiveparameter (an indicator the compressibility coefficient). But the radial values ofresulting intensive parameter (an indicator of hierarchical complexity and ofquasi-equilibrium of cooling down) of a real gas are invariant in time. It has beenproven that the orthodox interpretation of general relativity is not consistent withgradually cooling matter and therefore with the evolutionary cooling of the earlyUniverse.
Category: Relativity and Cosmology

There Is No Matter: Vacuum Knots as Toroidal Resonant Solitons and the Role of αU = keAP

Authors: Pedro A. Kubitschek Homem de Carvalho
Comments: 7 Pages.

We develop a mathematically grounded framework in which what is commonly called "matter" consists of finite—energy, knotted excitations of a nonlinear vacuum field. The model is based on a Faddeev—Skyrme—type Lagrangian for a unit vector field n : R3,1 → S2, coupled to gravity and electromagnetism. Toroidal (Hopf) solitons carry conserved topological charge and exhibit internal "beating" modes. Mass, momentum and spin arise purely from the vacuum stress—energy tensor. The constant αU = keAP (Coulomb constant times Planck area) plays the role of a vacuum rigidity/constitutive scale, controlling EM couplings and regularization. We lay out explicit assumptions, definitions, energy bounds, and geodesic motion of soliton centers, with citations to classical results (Derrick’s theorem, Vakulenko Kapitanskii bound, moduli space dynamics).
Category: Mathematical Physics