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[44] viXra:2610.0044 [pdf] submitted on 2026-10-10 12:44:19
Authors: Zohaib Muaz
Comments: 16 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Autonomous Large Language Model (LLM) agents are increasingly vulnerable to indirect prompt injection (IPI) attacks, where adversarial instructions embedded in external data sources manipulate agent behavior without direct user input. These external data can originate from user documents, web retrieval results, or API outputs, leading to unauthorized compliance, sensitive information disclosure, identity spoofing, and cross-agent propagation of unsafe practices. This review synthesizes current research on IPI vulnerabilities and proposed mitigation strategies. Key attack vectors include manipulating webpage HTML via adversarial triggers for web agents, poisoning agent skills with tampered content, and injecting malicious commands into cloud logs processed by debugging agents. Covert attacks, which execute malicious actions without user-perceptible traces, pose a particularly insidious threat. Existing defenses, such as SecAlign's preference optimization, StruQ's structured queries, and multi layered zero-trust architectures, show promise. More advanced frameworks like ClawGuard enforce user-confirmed rule sets at tool-call boundaries, while ZEDD detects semantic shifts in embedding space for zero-shot detection. However, current guardrails often fail against sophisticated, adaptive attacks, and frameworks like AgentVigil and MUZZLE demonstrate high success rates in red-teaming exercises. The UReCoM attack further highlights vulnerabilities where benign users unknowingly relay adversarial content, bypassing existing defenses. The pervasive nature and increasing sophistication of IPI necessitate robust, behavior-grounded evaluation metrics and unified defense mechanisms to secure autonomous LLM agents in complex, untrusted environments.
Category: Artificial Intelligence
[43] viXra:2610.0043 [pdf] submitted on 2026-10-10 23:19:09
Authors: Abdelmajid Ben Hadj Salem
Comments: 4 Pages.
In 1859, Georg Friedrich Bernhard Riemann had announced the following conjecture, called the Riemann hypothesis : The nontrivial roots (zeros) $s=sigma+it$ of the zeta function, defined by: $$zeta(s) = sum_{n=1}^{+infty}frac{1}{n^s},,mbox{for}quad Re(s)>1$$ have real part $sigma= 1/2$. In this paper, it was used the expression of $zeta(1-bar{s})$ in function of $zeta(s)$, it implies to the proof that $Re(s)=sigma= 1/2$.
Category: Functions and Analysis
[42] viXra:2610.0042 [pdf] submitted on 2026-10-10 14:12:38
Authors: Arina Bator
Comments: 21 Pages.
This work falls within the scope of recreational mathematics and the experimental exploration of the order-3 magic square of squares. Instead of resolving the open problem of the existence of such an object, the research focuses on "near-miss" structures. The analysis is based on the reduction of the original problem to three three-term arithmetic progressions of square numbers with a common difference (r), whose first terms also form an arithmetic progression.By relaxing the condition requiring the initial terms to form an arithmetic progression, this paper introduces a percentage error function (p). This function allows for a quantitative assessment of the discrepancy between the differences of these terms, and consequently, a quantitative measure of how closely a configuration approximates a fully magic structure.Subsequently, an algorithm developed for this study was applied to generate all three-term progressions of integer squares with a common difference r. To optimize calculations and eliminate redundant operations, a filter based on the theory of quadratic residues in the ring Z_240 was implemented. Ultimately, a deterministic exploration of the differences r from 2 to 70,000,000,000,000 was conducted.Next, a geometric parametrization utilizing 120-degree Eisenstein triangles is presented. This enabled a dimensionality reduction of the error optimization problem to a function of a single real variable. It was demonstrated that the theoretical optimum point with zero error corresponds to an irrational number, preventing its direct realization in integers. It was proven, however, that despite structural limitations, it is possible to construct a parametric matrix generating semi-magic squares with equal sums in rows, columns, and on one diagonal. Diophantine approximation and continued fractions yielded an infinite sequence of rational approximations where the error function converges asymptotically to zero, while the ratio of the diagonal sums remains close to 1. This is illustrated by a numerical example where the ratio yields a value on the order of 1 - 7.3506 x 10^(-103230).The results offer a new method for the assessment of near-miss structures based on the error function p. They outline an approach based on Eisenstein triangles, for generating configurations where the error p tends to zero and the diagonal sum ratio approaches 1. This work does not prove the non-existence of the magic square of squares, but provides a universal research framework for approaching ideal structures.
Category: General Mathematics
[41] viXra:2610.0041 [pdf] submitted on 2026-10-10 23:12:51
Authors: Tanmay Patil
Comments: 33 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This paper presents an experimental protocol for testing whether an intermediate state in multi-digit addition has causal influence through hidden activations, visible reasoning tokens, both, or neither. Each arithmetic trace is generated by an executable interpreter and records the digit position, carry, partial result, next transition and final answer. The proposed test replaces a valid intermediate state and checks whether the remaining trace follows the corresponding counterfactual computation. Hidden-only, visible-token-only and joint interventions are compared with shuffled-donor, unrelated-donor and same-norm random controls at three positions around state-token emission. Evaluation uses full-trace counterfactual transition fidelity, nuisance invariance, repair, donor leakage and collateral change on separately held-out IID and out-ofdistribution splits. Attribution methods may identify candidate locations, but every retained location must pass an exact activation intervention. This paper reports the protocol and no new model results. Behavioural accuracy and a readable rationale alone cannot establish causal authority; the proposed interventions test it on held-out data.
Category: Artificial Intelligence
[40] viXra:2610.0040 [pdf] submitted on 2026-10-10 22:48:29
Authors: August Lau
Comments: 8 Pages.
AGI stands for artificial general intelligence and HSA stands for 3 areas (hypertopology/semigroup/acyclicity) in mathematics. The author will describe the connection between the two fields.
Category: Artificial Intelligence
[39] viXra:2610.0039 [pdf] submitted on 2026-10-10 23:26:04
Authors: Renato Vieira dos Santos
Comments: 6 Pages.
When a geometric modification of spacetime is equivalent, by a field redefinition, to a theory we already know, does anything physical survive the equivalence? We examine a metric-compatible contortion of the form $K^lambda_{ muu} = F(phi),epsilon^{lambdaho}_{ muu},partial_hophi$, generated by the gradient of a scalar field and totally antisymmetric in its three indices, which is unique within its class once one requires that spinless particles follow the geodesics of general relativity. The Ricci scalar acquires a correction $R(Gamma) = R({}) + 6F^2(partialphi)^2$ that shifts the scalar kinetic term by a factor $1 - 6F^2/kappa_g$, yielding a ghost bound $M_F > 0.49,M_{m Pl}$, and the Schwarzschild metric remains an exact vacuum solution when the scalar field is constant. We show that the bosonic sector is equivalent, by a field redefinition, to a canonical scalar field minimally coupled to general relativity, so that the modification of the Kalb-Ramond duality is a statement about the parametrization rather than about the physical spectrum. The survival of a residual coupling in the matter sector is not specific to this construction, since it also occurs in the Jordan-Einstein frame equivalence of scalar-tensor theories, but the form of the surviving coupling is. Here the residual coupling is parity-odd, spin-dependent, and non-universal, affecting only matter with spin. We estimate the magnitude of this force in a cosmological background and find it to be far below observational sensitivity; we do not claim that it becomes observable in regimes that we have not calculated.
Category: Relativity and Cosmology
[38] viXra:2610.0038 [pdf] submitted on 2026-10-10 00:52:08
Authors: Imrich Krištof, Jiří Tunkl
Comments: 14 Pages.
Fullerens connected with extreme energetically cascade Ξ [ksí hyperons], hyperons Λ [lambda], Σ sigma [hyperons], Ω- [omega minus], baryons N and ɥ [baryons] For example, for mass resonances of (Ω)=M|Ξ*/+Δm=3 000 + 300= 3 300 meWe explicitly come with this classification of particles (here we understand all particles, stablequasiparticles and resonances) Our work deals with combining quantum physics and quantum chemistry, because it is built on these first two evidently built on "a basic built stones" of high-energy particle physics. The extremely mass andenergetical neutrinos were detected in recent time on Antarctica (project Ice Cube), ANITA (AntarcticImpulsive Transient Antenna) - financially supported by NASA. Next Project KM3NeT, underwater in the deepest point of the Mediterranean Sea near Italy/France. We hope that cardinal solution of this particle puzzle will be brought by TRIDENT (the Chinese Neutrino Telescope), which is planned in principle as a next generation neutrino marine observatory to be located in the South China Sea (Pacific Ocean) at a depth of 3,5 kilometers and will cover a volume of approximately 8 cubic kilometers, utilizing technology combination of advanced hDOMs, which combine photomultipliers tubes (PMTs) and silicon photomultipliers (SiPMs) to detect Cherenkov’s light produced by neutrino interactions. TRIDENT is expected to be completed around 2030.
Category: High Energy Particle Physics
[37] viXra:2610.0037 [pdf] submitted on 2026-10-10 00:48:07
Authors: Miroslav Súkeník, Magdaléna Súkeníková
Comments: 3 Pages.
In the article, we examine the control functions that enable the analytical derivation of Viswanath's constant.
Category: Number Theory
[36] viXra:2610.0036 [pdf] submitted on 2026-10-10 00:43:25
Authors: Olegs Verhodubs
Comments: 7 Pages.
The bubble sort algorithm is one of the simplest and most wellu2011known in programming. That is why this algorithm was chosen as an experimental algorithm for studying the meanings embedded in it and their transformation. This research is part of a broader study whose final goal is to develop a system for the automatic generation of algorithms. Automatic algorithm generation can be implemented in various ways, but in this case, preference is given to a semantic approach — more precisely, an approach based on Semantic Web Technologies. The advantage of this approach lies in the direct, "willful" movement (from one concept to another) towards the result, as well as in the ability to trace the entire path from the initial data to the generated algorithm. To achieve the final goal, it is proposed to develop an ontology of the semantic subtext of the algorithm. This ontology will serve as a source of rules for an expert system for the automatic generation of algorithms.
Category: Artificial Intelligence
[35] viXra:2610.0035 [pdf] submitted on 2026-10-10 00:37:37
Authors: Roberto Köferstein, Christian Robl
Comments: 8 Pages. The papaer was published in: Z. Anorg. Allg. Chem. 640 (2014) 1937—1942. (DOI: 10.1002/zaac.201400177)
Abstract. Triclinic single crystals of Cu4(H3N-(CH2)9-NH3)(OH)2[C6H2(COO)4]2*5H2O have been prepared in aqueous solution at 80 °C in the presence of 1,9-diaminononane. Space group P-1 (no. 2) with a = 1057.5(2), b = 1166.0(2), c = 1576.7(2) pm, alpha = 106.080(10)°, beta = 90.73(2)° and gamma = 94.050(10)°. The four crystallographic independent Cu2+ ions are surrounded by five oxygen atoms each with Cu−O distances between 191.4(3) and 231.7(4) pm. The connection between the Cu2+ coordination polyhedra and the [C6H2(COO)4]4- anions leads to a three-dimensional framework with negative excess charge and wide centrosymmetric channel-like voids.These voids extend parallel to [001] with the diagonal of the nearly rectangular crossection of approximately 900 pm. The channels of the framework accommodate [H3N-(CH2)9-NH3]2+-cations and water molecules, which are not connected to Cu2+. The nonane-1,9-diammonium-cations adopt a partial gauche conformation. Thermoanalytical measurements in air show a loss of water of crystallization starting at 90 °C and finishing at approx. 170 °C. The dehydrated compound is stable up to 260 °C followed by an exothermic decomposition yielding copper oxide.
Category: Chemistry
[34] viXra:2610.0034 [pdf] submitted on 2026-10-10 00:36:23
Authors: Igor Shchitov
Comments: 6 Pages.
This article presents examples of linear partial differential equations with analytic coefficients and system of such equations for which the solutions to the Cauchy problem in the class of continuously differentiable functions are non-unique. More precisely, the time during which the analytical solution to the Cauchy problem remains unique is finite for such equations and system,after which this solution may even transform into one of many possible solutions. These solutions may have unusual properties.Key words: systems of linear partial differential equations; analytical coefficients; Cauchy problem; Holmgren’s theorem; uniqueness of solution.
Category: General Mathematics
[33] viXra:2610.0033 [pdf] submitted on 2026-10-09 00:09:57
Authors: Ray Tomes
Comments: 4 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Geomagnetic polarity reversals are widely held to occur at random, with no periodicity to their timing — a position well supported by over 50 years of statistical analysis. This paper shows that the same reversal record, examined not as a sequence of reversal timings but as the prevailing polarity condition through time, displays a clear periodicity near 1.11 million years. Using the standard 0-30 Ma geomagnetic polarity timescale sampled on a 1000-year grid, a continuous-frequency spectrum reveals twelve dominant cycles between 0.2 and 6 Ma, refined here to five significant figures. Two of the next-strongest peaks relate to the dominant 1.1101 Ma cycle by simple, clean ratios — 0.74026 Ma (2/3) and 3.3335 Ma (3×) — each within a tenth of a percent of an exact fit. The 1.1101 Ma periodicity is confirmed visually by folding the full 30 Ma record at this period. The origin of these harmonic relationships, and their connection to solar system cycles of very similar period, is left for future papers.
Category: Geophysics
[32] viXra:2610.0032 [pdf] submitted on 2026-10-09 00:09:39
Authors: Ray Tomes
Comments: 4 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
A companion paper establishes, from the standard 0—30 Ma geomagnetic polarity timescale, a clear periodicity in Earth's prevailing magnetic polarity near 1.1101 million years. This paper sets that figure aside and asks an independent question: does a period of similar length appear anywhere in the dynamics of the solar system itself, arrived at without any reference to Earth's magnetic field? Two such periods are identified, from two distinct physical mechanisms. The Uranus—Neptune orbital energy exchange, established via numerical integration of the outer planets (the LONGSTOP project), gives 1.119 Myr — a drifting, near-resonant beat. The Jupiter—Uranus perihelion anti-alignment, a stable secular frequency difference computable directly from measured planetary precession rates, gives 1.107 Myr — a fixed period. Both sit within a fraction of a percent of the geomagnetic figure. The paper also records the recovery, after a decades-long search, of the original source for a long-held personal note of "1.108 Myr" for this cycle. The explanation for why these independent timescales agree so closely is left for a future paper.
Category: Astrophysics
[31] viXra:2610.0031 [pdf] submitted on 2026-10-09 00:06:20
Authors: Roberto Köferstein, Stefan G. Ebbinghaus
Comments: 42 Pages. The paper was published in: J. Eur. Ceram. Soc. 43 (2023) 6137—6144. (Open Access, DOI: 10.1016/j.jeurceramsoc.2023.06.040)
Magnetoelectric (NiFe2O4)0.3-(Sr0.5Ba0.5Nb2O6)0.7 composites with addition of LiNbO3 as sintering additive were prepared by a classical mixed-oxide method. XRD patterns of ceramics sintered between 1000 and 1200 °C show the desired Sr0.5Ba0.5Nb2O6 and NiFe2O4 phases. SEM investigations confirm the 0-3 connectivity of the composite ceramics. The addition of 10 and 20 mol% LiNbO3 improves the densification of the composite ceramics and leads to an increase of the size of the Sr0.5Ba0.5Nb2O6 grains. Magnetic measurements show hystereses with low coercivities. Dielectric measurements were carried out depending on temperature and frequency. The samples with the LiNbO3 addition show significantly higher resistivity values (sDC). Magnetoelectric measurements were carried out in dependence of the magnetic DC-field, temperature, and frequency. The maximum magnetoelectric coefficient (aME) rises with the addition of LiNbO3 from 180 to 803 µV Oe-1 cm-1 (@ 900 Hz). Temperature dependent measurements show a continuously decreasing of aME with lower temperature.
Category: Chemistry
[30] viXra:2610.0030 [pdf] submitted on 2026-10-09 00:06:02
Authors: Roberto Köferstein, Florian Oehler, Stefan G. Ebbinghaus
Comments: 40 Pages. The paper was published in: Mater. Chem. Phys. 278 (2022) 125616. (Open Access, DOI: 10.1016/j.matchemphys.2021.125616)
Magnetoelectric (Sr0.5Ba0.5Nb2O6)1-x-(CoFe2O4)x (x = 0.2-0.6) composites were prepared by a one-pot soft-chemistry synthesis using PEG400. Calcining at 700 °C resulted in nanocrystalline composite powders (dcryst. = 24-30 nm) which were sintered between 1050 and 1200 °C to ceramic bodies with relative densities up to 98 %. SEM investigations confirm the formation of composite ceramics with a 0-3 connectivity and variable grain sizes from 0.2 to 3.6 µm for sintering up to 1150 °C, while sintering at 1200 °C leads both to a change in the microstructure and a considerable grain growth. Magnetic measurements at 300 K reveal ferrimagnetic behaviour with saturation magnetization values smaller than bulk CoFe2O4 and coercivities between 790 and 160 Oe. Temperature-dependent impedance spectroscopy showed that the relative permittivities decrease both with rising frequency and CoFe2O4 fraction. The frequency dependence of the impedance can be well described using a single RC circuit. Magnetoelectric measurements show the presence of pronounced field hystereses. The maximum magnetoelectric coefficient (aME) depends both on the CoFe2O4 fraction (x) and sintering temperature. The composite with x = 0.3 exhibits the largest aME value of 37 µV Oe-1 cm-1 (@ 900 Hz). With rising frequency of the AC driving field aME increases up to 300-400 Hz and is nearly constant until 1 kHz.
Category: Chemistry
[29] viXra:2610.0029 [pdf] submitted on 2026-10-09 00:05:47
Authors: Roberto Köferstein, Stefan G. Ebbinghaus
Comments: 42 Pages. The paper was published in: , J. Solid State Chem. 278 (2022) 123564. (Open Access, DOI: 10.1016/j.jssc.2022.123564)
Nano-crystalline Sr0.5Ba0.5Nb2O6 powders with addition of LiNbO3 or LiF as sintering additives were prepared by a soft-chemistry synthesis using polyethylene glycol. Calcination at 600 °C results in nanocrystalline powders (dcryst. ~ 30 nm) which were sintered between 1000 and 1300 °C to ceramic bodies. By addition of 10 and 20 mol% LiNbO3, the sintering temperature was reduced by about 200 K and the activation energy of the initial stage of sintering decreases from 386 to 271 kJ mol-1. The sintering aid improves the grain growth and dense ceramic bodies were obtained after sintering at 1125 °C for 1 h. A higher LiNbO3 content favors the formation of a pillar-like microstructure. XRD patterns of ceramics sintered above 1000 °C show only reflections of the Sr0.5Ba0.5Nb2O6 phase indicating an incorporation of LiNbO3 in the Sr0.5Ba0.5Nb2O6 structure. Dielectric measurements reveal a diffuse phase transition and a relaxor-like behavior. The phase transition temperature (Tm) depends on the sintering conditions and is between 117 and 127 °C for 10 mol% LiNbO3, which is very close to pure Sr0.5Ba0.5Nb2O6, while addition of 20 mol% shifts Tm to around 200 °C and the transition becomes slightly more diffuse. The optical band gap of the samples is ~ 3.3 eV and depends slightly on the sintering conditions. We also tried LiF as sintering aid, but this leads to the formation of considerable amounts of secondary phases in the ceramics and relative densities of only 82 %.
Category: Chemistry
[28] viXra:2610.0028 [pdf] submitted on 2026-10-08 23:59:01
Authors: Werner Lange
Comments: 4 Pages. In German
This paper explains how the form of time dilation caused solely by the expansion of the universe can be modelled using light emission and light reception on different light cones.
Category: Relativity and Cosmology
[27] viXra:2610.0027 [pdf] submitted on 2026-10-08 23:55:02
Authors: Tkachenko Igor, Miroshchenko Yurii, Tkachenko Olesia, Miroshchenko Victoria, Miroshchenko Sergii, Tkachenko Svitlana
Comments: 9 Pages.
Based on thermodynamics, dislocation theory together with own theoretical andexperimental results, a new phase nucleation development for the mono - phase industrial realpoly crystalline materials was analized. At first, the terms "multy-phase" and "mono-phase"materials were specified and reformulated, introducing an addition one3"nominally". Thedislocation substructure role in solute chemical elements segregation and subsequent new phasenucleation was analyzed. It was theoretically shown and experimentally verivied possibilities toobtain super fine and homogeneus structure due to isothermal holding at optimal bothtemperature and duration for the nominally mono-phase metal materials. It was shown that thepossibilities may be expanded on other multiphase materials, particularly, Grey and White CastIrons.
Category: Condensed Matter
[26] viXra:2610.0026 [pdf] submitted on 2026-10-08 23:51:33
Authors: Mikel Aickin
Comments: 12 Pages. (Note by viXra Admin: Please cite listed scientific references and submit article written with AI assistance to ai.viXra.org)
Conventional statistical inference is awkward, which has the consequence that it is difficult to explain and even difficult to use properly. The problem is not with its fundamental elements (confidence intervals and hypothesis tests), but instead with how they are packaged. Here support functions are offered as an alternative package, which very much improves real-world practice and provides conceptual clarity to the process of scientific inference.
Category: Statistics
[25] viXra:2610.0025 [pdf] submitted on 2026-10-08 23:48:12
Authors: Mauro Alfonso Montenegro
Comments: 23 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Why is there something rather than nothing? This paper argues that the question is often framed by a false symmetry. Absolute nothingness is not a state, cause, possibility space, probability distribution, or background; it contains no laws, powers, relations, time, or potentiality. By contrast, deprivation, destruction, falsehood, and death are intelligible only relative to positive realities that can be damaged, falsified, or lost. This paper distinguishes an epistemic asymmetry between construction and criticism from an ontological asymmetry between actualityand privation. The proposed resolution is that nothingness cannot stand as an ontological rival to being or generate being. The live question is instead what kind of actuality is non-derivative- brute actuality, necessary actuality, or an endless structure of dependence. Classical Christian metaphysics offers one coherentcompletion by identifying the non-derivative ground with God and evil with privation, but that identification requires further premises.
Category: General Science and Philosophy
[24] viXra:2610.0024 [pdf] submitted on 2026-10-07 16:50:59
Authors: Dino Bruniera
Comments: English, pages 1-5 and Italian, pages 6-10
This paper introduces a comprehensive cosmological model based on the Expanding Space Quanta (ESQ) theory, providing a realistic geometric description of cosmic evolution as a radical alternative to the standard ΛCDM paradigm. By utilizing an inverse cosmological luminosity equation grounded in pure three-dimensional spatial expansion (1 + z)³, this model enables the empirical testing and falsification of cosmic distances without the introduction of arbitrary free parameters or unobservable entities. Through an elementary kinematic analysis of the cosmological redshift (z)—empirically defined as the index of the average expansion velocity during the total photon travel time (Vm = c · z) —we demonstrate that global Type Ia Supernovae (SN Ia) observational datasets (including recent NOIRLab/DESI Hubble diagrams) mathematically signify a continuous and progressive deceleration of spatial expansion from primordial epochs to the present day. The ESQ model successfully resolves the deep epistemological and thermodynamic paradoxes of orthodox cosmology by strictly adhering to the First Law of Thermodynamics (Energy Conservation) and rigorously satisfying the methodological criteria of Occam’s Razor. The intrinsic geometric foundations of this theoretical framework and the conceptual transition from the standard mathematical metric to the physics of space quanta were formally delineated by the Author in the foundational paper titled "From Apparent to Real Universe".
Category: Relativity and Cosmology
[23] viXra:2610.0023 [pdf] submitted on 2026-10-06 20:18:35
Authors: R. Köferstein, J. Jacobs, S. G. Ebbinghaus
Comments: 40 Pages. The paper was published in: J. Eur. Ceram. Soc. 45 (2025) 117567. (Open Access, DOI: 10.1016/j.jeurceramsoc.2025.117567).
Lix(Sr0.5Ba0.5)1-x/2Nb2O6 ceramics were prepared by a solid state synthesis and sintered at 1300 °C. XRD investigations reveal single phase samples up to a substitution limit of x = 0.275. For higher lithium contents, the appearance of LiNbO3 as secondary phase was observed. The density of the ceramics increases with lithium content. The microstructures show globular grains which turns to pillar-like grains with rising lithium substitution. Dielectric investigations confirm relaxor ferroelectric behavior and the diffuse phase transition is shifted towards higher temperatures with increasing lithium content from 129 °C (x = 0) to 221 °C (x = 0.275). The diffuseness coefficient increases with the lithium content. From high-temperature XRD measurements the length of the tetragonal cell parameter c decreases with increasing temperature, reaches a minimum at about 150-230 °C (depending on x) and afterward increases with increasing temperature. Additionally, a significant shift of the Nb(2) position with temperature can be observed.
Category: Chemistry
[22] viXra:2610.0022 [pdf] submitted on 2026-10-06 20:16:24
Authors: Charles Ba Oumar
Comments: 8 Pages.
This paper presents a Vector Gravitational Field Theory asymptotically equivalent to standard Minkowski spacetime in the limit of a classical vacuum. From such a theory we then derive a new definition of rest mass energy as well as an approximation of the quantum of gravitational action via a graviton particle of energy ℎ��proportional to the gravitational charge quantified by matter-energy density and compute solar system graviton energy ranges.
Category: Quantum Gravity and String Theory
[21] viXra:2610.0021 [pdf] submitted on 2026-10-05 04:57:22
Authors: Saburou Saitoh
Comments: 65 Pages. (The Third Lecture at Peking University on 5 October, 2026).
In this talk, we will introduce the importance of the division by zero containing the division by zero calculus and its great impact to elementary mathematics and mathematical sciences for some general mathematicians. For this purpose, we will give its global viewpoint in a self-contained manner by using the related references. (The Third Lecture at Peking University on 5 October, 2026).
Category: Functions and Analysis
[20] viXra:2610.0020 [pdf] submitted on 2026-10-06 00:35:46
Authors: Ali Rıza Şahin
Comments: 13 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This paper establishes a rigorous real-analytic and geometric framework governing the distribution of the non-trivial zeros of the Dirichlet eta function $eta(s)$ across the critical strip $mathcal{S}={sinmathbb{C}:0
Category: Number Theory
[19] viXra:2610.0019 [pdf] submitted on 2026-10-06 00:23:26
Authors: Ali Rıza Şahi̇n
Comments: 8 Pages.
The general theory of relativity fundamentally relies on the metric tensor to describe gravitational phenomena, traditionally eschewing the vector field formulations ubiquitous in electrodynamics and quantum field theories. This study introduces a novel framework that defines the spacetime metric and its inverse via a set of underlying vector fields. By expressing the metric tensor in terms of these fields, we derive the corresponding geodesic and Einstein field equations, revealing striking structural parallels with electrodynamics—most notably, the natural emergence of a covariant Lorentz-like force and a stress-energy tensor mathematically analogous to that of electromagnetic fields. To demonstrate the astrophysical viability of this approach, we solve the equations for a spherically symmetric, static mass distribution, yielding a non-singular alternative to the Schwarzschild metric. The practical validity of this metric is subsequently tested through the recalculation of the perihelion precession of planets and the gravitational deflection of light. The results provide precise agreement with perihelion precession observations while predicting a slightly modified value for light deflection (1.90 arcsec), offering a potential theoretical basis for the historical discrepancies observed between visible light and radio wave measurements during solar eclipses.
Category: Relativity and Cosmology
[18] viXra:2610.0018 [pdf] replaced on 2026-10-06 03:58:41
Authors: Stephen W. Hosier
Comments: 7 Pages.
Spacetime velocity and related time dilation, are presented in a clearer and simpler format. Many example calculations are shown to demonstrate the simplicity of this approach.
Category: Relativity and Cosmology
[17] viXra:2610.0017 [pdf] submitted on 2026-10-04 22:46:29
Authors: Brian Scannell
Comments: 8 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
The Lorentz factor γ(β) =1/ √︁(1 — β^2), where β = v/c, is normally considered for real |β| < 1. Allowing its argument to range over the complex plane gives Γ(z) =1/√(1 — z^2), whose real and imaginary parts generate a striking system of level curves organized around the branch points z = +/-1. The Cauchy—Riemann equations explain why the regular curves from the two families intersect orthogonally. More surprisingly, eliminating the square root shows that each nonzero contour lies on a degree-eight algebraic locus. This apparent complexity is deceptive. Solving instead for z gives z = +/-√︁ (1 — Γ^-2), revealing that the apparently complicated contours in the z-plane are locally the preimages of vertical and horizontal straight lines in the Γ-plane. Thus, a familiar real function from special relativity provides an elementary example in which complicated algebraic contours conceal a simple conformal geometry.
Category: Functions and Analysis
[16] viXra:2610.0016 [pdf] replaced on 2026-10-07 17:51:06
Authors: Roger L. Mc Murtrie
Comments: 5 Pages.
This article identifies a series of foundational mathematical and logical inconsistencies within John Bell’s 1964 formulation and demonstrates that the core discrepancy in Bell’s framework arises from an implicit and unjustified data-mapping assumption which treats the discrete, binary-valued random functions of one expectation value integral as directly equivalent to the continuous, real-valued integrand of another expectation integral. This non-linear transformation incurs a severe loss of contextual information that is mathematically unaccounted for in Bell’s original derivation. By failing to recognize this measure-theoretic mismatch the subsequent deductions, including the assertion that a remote measurement setting must dynamically influence a distant apparatus, are rendered logically invalid. Consequently, the attribution of non-locality to Einstein-Podolsky-Rosen-Bohm (EPRB) systems is shown to be an unfounded artifact of this misapplied probability space rather than an empirical property of physical nature.
Category: Quantum Physics
[15] viXra:2610.0015 [pdf] submitted on 2026-10-04 22:33:00
Authors: Sergey Pavlovich Slukhayevskiy
Comments: 10 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
A diffraction observation scheme is proposed that makes it possible to investigate the influence of the shape and size of the undisturbed part of a quasi-parallel light beam on the spatial position of the elements of the diffraction pattern. Experimental observations of the independence of the positions of the pattern elements from thisparameter were performed in the range from 0.01 to 2 mm.
Category: Classical Physics
[14] viXra:2610.0014 [pdf] submitted on 2026-10-03 00:17:02
Authors: Xincai Luo
Comments: 16 Pages. DOI: https://doi.org/10.5281/ZENODO.23089701
We present a novel theory of fundamental particle spin, deriving the energy-frequency relation of quantum theory, the Schwarzschild metric of general relativity, and the fine-structure constant from this single framework. Our theory posits that fundamental particles are composed of fundamental charges (FCs) and derives the energy-frequency relation and spin angular momenta of these particles from the circular motion of their constituent FCs, as described by Newtonian classical mechanics. The conservation of energy and angular momentum necessitates that each fundamental particle possesses wave-like properties, mathematically represented by corresponding wavefunctions in quantum mechanics. The phase angle of the wavefunction directly corresponds to the angle of this circular motion. The energy, which is proportional to the frequency of the FCs' circular motion, is expressed as the result of applying the operator iℏ∂/∂t to its wavefunction. Based on this wave arising from the circular motion of FCs, a particle's energy must propagate at the speed of light. This requirement extends beyond the constancy of the speed of light in all inertial frames proposed by special relativity. In the rest frame of a particle, precisely half of its energy moves forward and the other half moves backward at the speed of light, creating an apparent zero velocity. This constant energy propagation speed implies a constant energy flow rate, which then yields the Schwarzschild metric of general relativity. This work demonstrates that the principles of quantum mechanics and relativity are inherently linked to fundamental particle spins. Furthermore, the spin theory enables the derivation of electroweak coupling constants from first principles. The theoretical fine-structure constant derived from this spin model (without experimental input) exhibits strong agreement with experimental values (a discrepancy of only 0.14%), and the predicted electron charge (1.603×10^-19 C) closely matches the experimentally determined value (1.602×10^-19 C).
Category: High Energy Particle Physics
[13] viXra:2610.0013 [pdf] submitted on 2026-10-03 20:32:33
Authors: Clark M. Thomas
Comments: 3 Pages.
Questions swirling around human artificial intelligence, and visiting space-alien intelligence, are featured all over the media.Speculation clutters major idea gaps where scientific evidence, or at least high quality logic, should be. Ideas range fromoptimistic curiosity, to existential dread. Scientists can fairly well document our human past. Can we wisely envision and prepare for hybrid futures?
Category: Artificial Intelligence
[12] viXra:2610.0012 [pdf] submitted on 2026-10-03 20:31:44
Authors: Xingfeng Chen
Comments: 15 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
We present Difference Power Space Extrapolation (DPSE), a geometric method for computing the n decimal digits of π by combining multiple polygon observations in difference power space. The paper shows that DPSE should be understood as a higher-order development of the Difference-Power Cumulative Method (DPCM), rather than asan unrelated construction. For the polygon semiperimeter surrogate Sk = nksin(π/nk), the geometric increments ∆Sk = Sk+1 − Sk admit a structured boundary-layer expansion that can be cancelled by Richardson-type linear combinations. For fixed extrapolation orderW, this yields the error law Ek,W = O(4−(W+1)k), while the diagonal Neville sequence exhibits an approximately quadratic error exponent in the physical observation index k. Consequently, the required physical observation count for n correct decimal digits is reduced from lineargrowth to order O(√n), while preserving the low-memory character of geometric iteration. Numerical experiments include a direct milliondigit fingerprint verification.
Category: General Mathematics
[11] viXra:2610.0011 [pdf] submitted on 2026-10-03 20:30:01
Authors: Saburou Saitoh
Comments: 15 Pages.
At first, I will introduce simply the analytical and classical reproducing kernels on the complex plane. Here, firstly, we recall the representations of reproducing kernels in terms of the theta functions that were obtained by D. A. Hejhal, J. D. Fay and A. Yamada. Indeed, the materials stated here are in Yamada's papers.Then, we will consider their meanings from the viewpoints of reproducing kernel theory, in particular, from the viewpoint of inequalities. We will find many important open problems. (The Second Lecture at Peking University on 3 October, 2026)
Category: Functions and Analysis
[10] viXra:2610.0010 [pdf] submitted on 2026-10-03 20:22:02
Authors: Guzhva Andrii Oleksandrovich
Comments: 132 pages, diploma thesis 2009, CC BY 4.0
Diploma thesis (Pryazovskyi State Technical University, Mariupol, 2009). Design of an integrated biodiesel production line with ultrasonic cavitation reactor; detailed manufacturing technology for the gearbox shaft part KLB-01,00,01. Supervisor: Andilakhai Oleksandr Oleksandrovych. Keywords: biodiesel, biofuel, ultrasonic cavitation, transesterification, mechanical engineering.
Category: Thermodynamics and Energy
[9] viXra:2610.0009 [pdf] submitted on 2026-10-03 20:25:02
Authors: Richard J. Mathar
Comments: 10 Pages.
The Multiple Zeta Value zeta(2,1) is a double sum over two positive integer indices. If these indices are restricted by parity to cover either only even or only odd positive integers, the Multiple Zeta Value splits into four non-overlapping subseries. The manuscript evaluates these four series in terms of the Riemann Zeta function, pi and log 2.
Category: Functions and Analysis
[8] viXra:2610.0008 [pdf] replaced on 2026-10-07 13:45:09
Authors: Justin Mader
Comments: 28 Pages. new chapters
This paper presents a consistent, mathematical-geometric framework describing quantum mechanics, gravitation, and cosmology within a "Bohmian" quantum field theory outside the standard model. By coupling a real helical sub-quantum domain (Helical Spin Theory, HST) with a space-filling background medium in a dynamic tachyonic momentum mode (Higgs-Tachyon-Push Field Theory, HTP), a quantitative reproduction of key astrophysical and quantum mechanical benchmark tests is achieved as an asymptotic limiting case within an absolute Euclidean reference frame. Gravitational light deflection, Mercury's perihelion precession, and the anomalous Pioneer Doppler drift are derived without invoking spacetime curvature via a spat-temporally Variable Speed of Light (VSL). On the microscopic scale, the double-slit paradox is formalized using an ontic, non-local pilot wave in line with De Broglie-Bohm mechanics. On the cosmological scale, the observed Hubble tension is mathematically resolved as a historical averaging effect derived from a degressive mass accumulation rate . Structurally, the HST is extended to spin-1/2 fermions; via a topological Möbius helix symmetry and a hyperbolic pilot-wave equation, the real negative mass squared of the electron neutrino measured by the KATRIN collaboration is rigorously derived as a geometric media-coupling parameter, providing a media-mechanical solution to neutrino oscillations. The model thus provides a closed mechanical framework that substitutes the requirements for Dark Matter, Dark Energy, and virtual particles within the macroscopic limit.Official preprint registered and priority-protected via CERN Open Science Repository Zenodo under DOI: 10.5281/zenodo.23088551.
Category: High Energy Particle Physics
[7] viXra:2610.0007 [pdf] submitted on 2026-10-02 12:49:36
Authors: Walter A. Kehowski
Comments: 10 Pages.
The identity x^2 + (x+1)^2 + (x(x+1))^2 = (x^2+x+1)^2 is the motivation for study of the equation d^2 + e^2 + n^2 = x^2, where d and e are conjugate divisors of n, that is, n=de and $d
Category: Number Theory
[6] viXra:2610.0006 [pdf] submitted on 2026-10-02 20:56:55
Authors: Brian Scannell
Comments: 17 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
Trees are dynamically complex branched structures in which trunks, branches and higher ordercrown elements possess characteristic motions and are mechanically coupled. In a doctoral thesis completed in 1983 and formally awarded in 1984, Scannell proposed a qualitative mechanical principle termed aeroelastic similarity. Measurements on Sitka spruce suggested approximate relationships between modal frequencies at successive structurallevels, together with direct evidence of coupled branch motion. The original interpretationproposed that overlapping frequency ranges could permit wind-induced mechanical energyto be redistributed through the crown and dissipated, thereby restricting large-amplituderesonant motion. This paper reassesses that hypothesis against four decades of subsequent tree biomechanics research. Later work explicitly tested the named aeroelastic-similarity theory and subsequently developed mass damping, multiple resonance damping and damping by branching.The evidence does not support a universal hierarchy of exact modal equivalence. It does,however, support a broader principle in which frequency-compatible, mechanically coupled treemotions can exchange energy and thereby provide access to distributed dissipative mechanisms.We formulate this surviving idea as dynamically coupled modal compatibility, not modalidentity. A reduced coupled-oscillator model separates conservative energy redistribution fromdissipation, introduces descriptive measures of spectral separation and mode hybridisation,and motivates a hierarchical modal-network interpretation. We then propose a falsifiableexperimental programme based on controlled detuning in numerical models, laboratorybranched structures and living trees. Aeroelastic Similarity is therefore retained not asan exact frequency-scaling law, but as a testable hypothesis concerning the dynamicalorganisation of branched structures.
Category: Physics of Biology
[5] viXra:2610.0005 [pdf] submitted on 2026-10-01 20:59:54
Authors: Saburou Saitoh
Comments: 60 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
The theory of reproducing kernels is very fundamental, beautiful and has many applications in analysis and numerical analysis as in the Pythagorean theorem. In this first lecture, I would like to intoroduce some general viewpoint for reproducing kernels and some essences of reproducing kernels. However, the theory is already much more developing widely and deeply on this century. (The First Lecture at Peking University on 1 October, 2026)
Category: Functions and Analysis
[4] viXra:2610.0004 [pdf] submitted on 2026-10-01 12:45:48
Authors: Volodymyr Krasnoholovets
Comments: 15 Pages. This is the first paper in a series of three works.
This paper presents a deterministic, real-space reinterpretation of the 125 GeV particle discovered at the Large Hadron Collider (LHC) in 2012, commonly designated as the Higgs boson. Submicroscopic physics, developed within the framework of transparent mathematical physics in a series of the author’s previous works, allows us to bypass the complexities of physical mathematics and fine-tuning issues of the scalar Higgs field. Instead, the paper examines the 125 GeV resonance as a highly localised, ultrafast vortex formed by a frontal collision between a +e and -e integer-charged quark pair. This impact forces a massive compression of the discrete spatial lattice (tessellattice), trapping a colossal spatial mass defect (∆m∙c^2≅125 GeV). This dual-quark system forms an ultra-submicroscopic vortex with a radius of approximately 1.58 attometres, stabilised by this localised mass defect. Together with the Coulomb attraction, this structural confinement leads to the formation of a localised deformation coat around the vortex, whose geometric parameters are precisely balanced by the fine-structure constant α.
Category: High Energy Particle Physics
[3] viXra:2610.0003 [pdf] submitted on 2026-10-01 20:53:40
Authors: Hongyuan Ye
Comments: 16 Pages.
In classical electromagnetism, Gauss’s flux theorem in integral form states that the electric flux through a closed surface is proportional to the net electric charge enclosed by that surface. Gauss’s flux theorem in integral form is originally derived from Coulomb’s law of electrostatics. However, electrodynamics wrongly extends Gauss’s flux theorem to time-varying electric fields without additional theoretical and experimental justification, while confining Coulomb’s law to the scope of electrostatics. Through concise and rigorous mathematical derivations, this paper reveals that the integral form of Gauss’s flux theorem in classical electromagnetism does not hold in time-varying electric fields. Furthermore, it is demonstrated that Gauss’s flux theorem in differential form, which is expressed in terms of the flux-density divergence or the nabla-operator divergence, also does not hold in time-varying electric fields. Gauss’s flux theorem does not hold in time-varying electric fields, which poses a serious challenge to Maxwell’s equations and theoretical physics. The inapplicability of divergence to time-varying vectors also presents a significant challenge to fundamental mathematics.
Category: Classical Physics
[2] viXra:2610.0002 [pdf] submitted on 2026-10-01 15:19:27
Authors: Sergey B. Yurchenko
Comments: 20 Pages.
Science has made great strides in answering many questions, but three major mysteries remain unsolved. Although these mysteries belong to different fields of science — physics, biology, and neuroscience — they all confront with the boundary problem. These are scientific investigations into the origins of matter, life, and consciousness, which extend beyond empirical and rational methods in the search for definitive answers. Here, this problem is presented as the search for the lowest boundaries for three forms of existence: physical, biological, and conscious. They are then translated into the context of Big Bang cosmology, abiogenesis, and the neuroscience of consciousness, each representing an ontological singularity with its own epistemological event horizon.
Category: General Science and Philosophy
[1] viXra:2610.0001 [pdf] submitted on 2026-10-01 19:01:14
Authors: Tariq Khan
Comments: 10 Pages.
A speculative essay on the nature of song lyrics and song melodies answering the question of "why humans love music." A proposed shared human subconscious mind can understand language but, while it can communicate with the sleeping mind via images in dreams, it can only communicate to an individual’s awake mind via what appear to the individual as a random recall of a musical song in working memory. Remarkable lyrics of a given song can thus be used by the subconscious as a means to communicate to an awake mind. A theory of subconscious communication, from Cormac McCarthy’s essay The Kekule’ Problem and the research of Jeff Hawkins showing the human brain storing sequences of patterns including songs, is used to support the proposal. Music is considered as "primordial change" or as being equivalent to a fundamental encoding of change in a quantum or digital universe. Music is proposed as possibly being the boot code for any experience.
Category: History and Philosophy of Physics
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