All Submission Categories

A Novel Three-Dimensional Cu(II) 1,2-Ethylenediphosphonate Framework with Channel-like Voids

Authors: Roberto Köferstein, Michael Arnold, Christian Robl
Comments: 9 Pages. The paper was published in: Z. Anorg. Allg. Chem. 642 (2016) 1126—1132. (DOI: 10.1002/zaac.201600248)

Turquoise monoclinic single crystals of the novel three-dimensional Cu2[µ8-O3P(CH2)2PO3)]*3.2H2O coordination polymer have been prepared using the silica gel method. Space group C2/m (no. 12) with a = 1483.6(2), b = 668.44(8), c = 436.30(6) pm, beta = 93.28(2)°. The Cu2+ cation is coordinated by four oxygen atoms stemming from the 1,2-ethylenediphosphonate dianions in a square planar manner and two water molecules in the axial positions. The connection between the Cu2+ cations and the [PO3C] units from the 1,2-ethylenediphosphonate dianions leads to layers parallel to (100), which are linked by the ethylene groups to a three-dimensional framework with channel-like voids. The voidsaccommodate water molecules not bound to Cu2+ and extend parallel along [001] with an opening of about 550 x 260 pm. Magnetic measurements reveal an antiferromagnetic behaviour due to a superexchange coupling between Cu2+ ions through an oxygen bridge. The UV-Vis spectrum reveals three d-d transition bands at 694, 774, and 918 nm. The compound can be fully dehydrated by thermal treatment and rehydrated by storage in ambient air.
Category: Chemistry

An Alternative Equation for Effective Nuclear Charge that is Applicable to All Atoms

Authors: Ikechukwu Udema
Comments: 16 Pages. DOI: https://doi.org/10.26434/chemrxiv.15010220/v1 (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

Although the advent of ionization energies predated Slater’s rule, there was unawareness of the utilitarian value of the former for the computation of effective nuclear charge (ENC for short) until recently and in this research. The study aimed to derive another equation in which the average ionization energies of hydrogen and any other multi-electron atom are independent variables. The objective was to answer the question in the literature that states, "Are Slater’s Rules the Best Approach for Calculating Effective Nuclear Charge for Undergraduates?" (Moore & Birnbaum, 2014) and compare the graphical portrayal of chemical periodicity between outcomes using data generated using Slater's rules for some elements and data generated in this research. By exploring theoretical and computational methods and the data in the literature, the study showed that ENC (1.34458-3.32446) for the first 30 elements computed using the 2021 CODATA fine structure constant (FSC, for short) was higher than those (1.34402-3.32309) without it; however, the equation containing the computed FSC using e^2/2_0hc and other equations gave the same value of ENC. The use of Slater’s result (atomic radii) for the computation of ENC (1.29859-5.06996) and average ionization energy, IE (553.21-2108.13 kJ), gave higher values than other methods. All plots using Slater’s values of ENC and IE versus atomic number (Z) did not show chemical periodicity (greater linearity), unlike the use of other values (less linearity or lower R^2). The new equation was derived, and with earlier equations, ENC can be accurately computed; they should therefore be part of the school curriculum at all levels without ceasing to teach Slater’s rule, which is not the best approach. A future study should include 30 other elements of the periodic table.
Category: Nuclear and Atomic Physics

Crystal Structure and Characterization of Two Layered Copper(II) Coordination Polymers with Anions of 3-Phosphonopropionic Acid and (RS)-2-Phosphonobutyric Acid

Authors: Roberto Köferstein, Michael Arnold, Christian Robl
Comments: 16 Pages. The paper was published in: Z. Anorg. Allg. Chem. 644 (2018) 205—214. (Highlighted as cover picture 04/2017, DOI: 10.1002/zaac.201700453)

Blue single crystals of Cu[µ3-O3P(CH2)2COOH]*2H2O (1) and Cu[(RS)-µ3-O3PCH(C2H5)COOH]*3H2O (2) have been prepared in aqueous Cu2+-solutions (pH = 2.5—3.5) containing 3-phosphonopropionic acid (1) and (RS)-2-phosphonobutyric acid (2), respectively. 1: Space group Pbca (no. 61) with a = 812.5(2), b = 919.00(9), c = 2102.3(2) pm. Cu2+ is five-fold coordinated by three oxygen atoms stemming from [O3P(CH2)2COOH]2— anions and two water molecules. The Cu-O bond lengths range from 194.0(3) to 231.8(4) pm. The connection between the [O3P(CH2)2COOH]2— anions and the Cu2+ cations yields a polymeric structure with layers parallel to (001). The layers are linked by hydrogen bonds. 2: Space group Pbca (no. 61) with a = 1007.17(14), b = 961.2(3), c = 2180.9(4) pm. The copper cations are surrounded by five oxygen atoms in a square pyramidal fashion with Cu-O bonds between 193.6(4) and 236.9(4) pm. The coordination between [O3PCH(C2H5)COOH]2- and Cu2+ results in infinite puckered layers parallel to (001). The layers are not connected by any hydrogen bonds. Each layer contains both R and S isomers of the [O3PCH(C2H5)COOH]2- dianion. Water molecules not bound to Cu2+ are intercalated between the layers. UV/Vis spectra suggest three d-d transition bands at 743, 892, 1016 nm for 1 and four bands at 741, 838, 957 and 1151 nm for 2, respectively. Magnetic measurements suggest a weak antiferromagnetic coupling between Cu2+ due to a super-superexchange interaction. Thermoanalytical investigations in air show that the compounds are stable up to 95 °C (1) and 65 °C (2), respectively.
Category: Chemistry

The Number 137 in Physics: Fine-Structure Constant, Quantum Effects, and the Nuclear Stability Limit in LEDM

Authors: Viktor Strohm
Comments: 5 Pages.

In fundamental physics, the fine-structure constant (α≈1u2044137.036) is traditionally introduced as an empirical dimensionless parameter that determines the strength of the electromagnetic interaction. In this paper, within the framework of the Local Energy Deficit Model (LEDM), an analytical derivation of the constant α is presented from the first principles of the mechanics of an isotropic elastic vacuum substrate. It is shown that the inverse quantity αu207b¹ represents a fundamental geometric-dynamical invariant of a three-dimensional medium defined by spatial normalization (4π), the number of shear degrees of freedom of the stress deviator (n_s=5), the spectral integral of zero-point fluctuations, and SU(2) spinor topology.A systematic analysis of physical phenomena associated with the number 137 is carried out, including the electron velocity on the first Bohr orbit, the fine structure of spectra, the convergence of quantum electrodynamics (QED) series, the anomalous magnetic moment of the electron (g - 2), and the critical Schwinger limit. On this basis, the physical and mechanical nature of the "running coupling constant" α(Q^2 ) is revealed as a nonlinear elastic response of the medium (Hooke's law) under strong deformations, and a mechanical-topological solution to the "Feynman paradox" for element 137 of the periodic table is proposed.
Category: Classical Physics

Parameters of Triangles Formed by the Peaks of the Giza Plateau Pyramids and the Highest Point of the "Great Sphinx" Monument

Authors: Andrey V. Voron
Comments: 4 Pages.

Based on calculated and recorded data, this paper demonstrates the use of two length systems — the metric system and the ancient Egyptian system (royal cubit) — by the builders of the Giza plateau. The study analyzes the numerical linear dimensions of each pyramid in the Giza pyramid complex, as well as the base area and visible surface area of the complex pyramids. Spatial3D segments were obtained, which formed the basis for calculating the areas of two trianglesformed by the peaks of the Menkaure, Khafre, and Khufu pyramids and the highest point of the"Great Sphinx" monument.
Category: Archaeology

Estimating Moment or Kshana as a Lowest Quantum Time Interval Using the Heisenberg Uncertainty Relation, Within the Context of Compton Effect and Fourier Relationships for Free Wave Packets.

Authors: Shesharao Wanjerkhede
Comments: 10 Pages.

In this treatment, Kshana or moment is used as a proposed lowestindivisible quantum of time, distinct from its philosophical origin andevaluated here as a physical hypothesis. Applying the Heisenberg uncertainty relation to particle localization through high-energy photon scattering in the Compton-effect framework, and Fourier relationships of freewave-packets estimated the lowest quantum time interval Kshana or moment based on the statement of Maharishi Vyasa in his commentary onPatanjali Yoga Darshan. The calculated lowest mean interval is

∆t_min = 1.93213300126795 × 10⁻²¹

2.0233249470 ×10⁻²¹

Synthesis and Crystal Structure of two Cu(II)-benzene-1,2,4,5-tetracarboxylates with Three- Dimensional Open Frameworks

Authors: Roberto Köferstein, Christian Robl
Comments: 9 Pages. The paper was published in: Z. Anorg. Allg. Chem. 640 (2014) 310—316 (DOI: 10.1002/zaac.201300527)

Two new three-dimensional frameworks with zeolite-like channels have been prepared in the presence of 1,6-diaminohexane. Cu1.5(H3N-(CH2)6-NH3)0.5[C6H2(COO)4]*5H2O (1) crystallizes in the triclinic space group P-1with a = 772.56(7), b = 1110.36(7), c = 1111.98(8) pm, alpha = 98.720(7)°, beta = 108.246(9)° and gamma = 95.559(7)°. Cu2(H3N-(CH2)6-NH3)0.5(OH)[C6H2(COO)4]*3H2O (2) crystallizes in the monoclinic space group P2/c with a = 1159.34(11), b = 1059.44(7), c = 1582.2(2) pm and  = 106.130(11)°. The Cu2+ coordination polyhedra are connected by [C6H2(COO)4]4- anions to yield three-dimensional frameworks with wide centrosymmetric channel-like voids. Complex 1 reveals voids extending along [100] with diagonals of 900 pm and 300 pm, whereas in complex 2 the diagonal of the nearly rectangular crossection of the channels extending parallel to [001] is 900 pm. The negative excess charges of the frameworks are compensated by [H3N-(CH2)6-NH3]2+-cations, which occupy the voids along with water molecules. The [H3N-(CH2)6-NH3]2+-cations are not connected to Cu2+ and have served as templates.
Category: Chemistry

A Novel One-Dimensional Copper Mellitate Complex Featured by {Cu(H2O)2(urea)[C6(COO)4(COOH)2]}n2n- Polyanions

Authors: Roberto Köferstein, Christian Robl
Comments: 9 Pages. The paper was published in: Z. Anorg. Allg. Chem. 641 (2015) 1886-1891. (DOI: 10.1002/zaac.201500231)

Abstract. Blue monoclinic single crystals of the novel one-dimensional [H3N-(CH2)6-NH3][Cu(H2O)2(urea)(µ2-C6(COO)4 (COOH)2)]*H2O coordination polymer have been prepared in aqueous solution at room temperature in the presence of 1,6-diaminohexane and urea. Space group P21/n (no. 14) with a = 958.48(9), b = 1465.74(11), c = 1821.14(12) pm, beta = 97.655(8)°. The Cu2+ cation is coordinated in a square pyramidal manner by two oxygen atoms stemming from the dihydrogen mellitate tetraanion, one oxygen atom from the urea molecule, and two water molecules. The Cu−O distances are between 193.3(2) and 229.4(2) pm. The connection between Cu2+ and [C6(COO)4(COOH)2]4- yields infinite chain-like polyanions parallel to [-101] with a composition of {Cu(H2O)2(urea)[C6(COO)4(COOH)2]}n2n-. The dihydrogen mellitate tetraanion adopts a µ2 coordination mode. The [(H3N-(CH2)6-NH3)]2+ cations are accommodated between the chains as counter cations. The hexane-1,6-diammonium cations adopt a partial synclinal conformation. The chains are connected by strong and weak hydrogen bonds. Magnetic measurements reveal a paramagnetic Curie-Weiss behaviour and a magnetic moment of 1.93 µB per Cu2+. Thermoanalytical investigations in air show that the complex is stable up to 135 °C. Following decomposition processes yielding CuO.
Category: Chemistry

Synthesis, Crystal Structure and Hydrogen Bonding of µ-Hydroxo-µ-Peroxo-Bis[bis(ethylenediamine)cobalt(iii)] Squarate

Authors: Roberto Köferstein, Christian Robl
Comments: 10 Pages. The paper was published in: Z. Anorg. Allg. Chem. 642 (2016) 560—565. (DOI: 10.1002/zaac.201600080)

Black-brown needle-shaped single crystals of [Co2(en)4(O2)(OH)][C4O4]1.5*H2O (en = ethylenediamine) have been prepared in aqueous solution at room temperature. Space group P1 ̅ (no.2) with a = 800.20(8), b = 1225.48(7), c = 1403.84(9) pm, alpha = 100.282(5), beta = 94.515(7), gamma = 95.596(6)°. The Co3+ cations [Co(1), Co(2)] are coordinated in an octahedral manner by four nitrogen atoms stemming from the ethylenediamine molecules and two oxygen atoms each from a hydroxo group and a peroxo group, respectively. Both Co3+ coordination polyhedra are connected by a common corner and by the peroxo group leading to the binuclear [(en)2Co(O2)(OH)Co(en)2]3+ cation. The squarate dianions, not bonded to Co3+, and the [(en)2Co(O2)(OH)Co(en)2]3+ cations are linked by hydrogen bonds forming a three-dimensional supramolecular network containing water molecules. Magnetic measurements reveal a diamagnetic behaviour indicating a low-spin electron configuration of Co3+. The UV-Vis spectra shows two LMCT bands (pi*(O22-) -> d(sigma)*(Co3+)) at 274 and 368 nm and the d-d transition (1A1g -> 1T1g) at 542 nm. Thermoanalytical investigations in air show that the compound is stable up to 120 °C. Subsequent decomposition processes to cobalt oxide are finished at 460 °C.
Category: Chemistry

M2(H2O)[μ10-C6h2(coo)4] (M = Ba2+, Pb2+) Two Isotypic Three-Dimensional Coordination Polymers with a Layer-Like Separation Between Anions and Cations

Authors: Roberto Köferstein, Christian Robl
Comments: 8 Pages. The paper was published in: Z. Anorg. Allg. Chem. 641 (2015) 1150—1155. (DOI: 10.1002/zaac.201500050)

Monoclinic single crystals of Ba2(H2O)[µ10-C6H2(COO)4] (1) and Pb2(H2O)[µ10-C6H2(COO)4]*H2O (2) have been obtained using the silica gel method. Space group C2/c (no. 15), Z = 4; 1: a = 780.89(4), b = 1756.19(8), c = 914.80(5) pm, beta= 114.512(5)°; 2: a = 756.70(10), b = 1772.8(2), c = 890.2(2) pm, beta= 113.590(10)°. There are two crystallographically independent M2+ ions (M = Ba, Pb). M(1) is surrounded by eight carboxylate oxygen atoms and one water molecule forming a tricapped trigonal prism. M(2) is coordinated by ten carboxylate oxygen atoms in the shape of a tetracapped octahedron. The connection between the M(1) and M(2) polyhedra leads to infinite layers parallel to (010) which are linked by [C6H2(COO)4]4- anions to form a three-dimensional framework. The [C6H2(COO)4]4- anion adopts a µ10 coordination mode. Compound 1 reveals short Ba-Ba contacts of 426.46(2) pm, whereas the Pb-Pb distance of 411.01(6) pm in 2 is larger than twice the van der Waals radius.
Category: Chemistry

The Life of Psi: How a Wave Function Behaves During a Measurement

Authors: Alan Schaum
Comments: 18 Pages.

An explanation of the quantum measurement process must do more than produce the Born Rule.Conventional quantum mechanics makes other specific predictions about intermediate states,which develop before the completion of a measurement. This paper’s measurement model addressesthat more general problem. For a detector with efficiency less than one, the model predictsthe conventional quantum results almost exactly: an initial superposed state develops into awell-defined mixture of eigenstate and altered superposition. The minor departures of the modelfrom conventional quantum mechanics could be revealed, in principle, in an optical interferenceexperiment that is also described here. The measurement model assumes that the conversion intoan eigenstate is not instantaneous but results from a random sequence of unitary perturbationsarising from conventional quantum interactions with the microscopic components of the measuringdevice. A random walk model describes how wave functions change. And the model’s successrelies on small biases in transition probabilities which, however, could be expected of a devicedesigned to measure a specific observable. The biases help to define a generalized Ornstein-Uhlenbeck equation for the distribution of quantum states, and it admits solutions that substantiallyreplicate those of conventional quantum mechanics.
Category: Quantum Physics

Syntheses and Crystal Structures of Two Cadmium Methanetetrabenzoates Featured by Open Framework and Infinite Layers

Authors: Sven Harms, Roberto Köferstein, Helmar Görls, Christian Robl
Comments: 13 Pages. The paper was published in: Z. Anorg. Allg. Chem. 645 (2019) 912—918. (DOI: 10.1002/zaac.201900089)

Colourless single crystals of Cd2[µ8-MTB]*3H2O*DMF (1) were prepared in DMF/H2O solution. 1: Space group C2/c (no. 15) with a = 1821.30(6), b = 2175.08(6), c = 1269.87(4) pm, beta = 129.684(1)°. The connection between the methane-p-benzoate tetraanions (MTB4-) and the Cd2+ cations leads to a three-dimensional framework with channels extending along [1-10] and [110] with openings of 670 pm x 360 pm. The channel-like voids accommodate water molecules and N,N-dimethylformamide (DMF) molecules not bound to Cd2+. Colourless single crystals of [Cd4(2,2'-bipy)4(µ7-MTB)2]*7DMF (2) were prepared in DMF in the presence of 2,2'-bipyridine. 2: Space group P-1 (no. 2) with a = 1224.84(4), b = 1418.85(5), c = 2033.49(4) pm, alpha = 85.831(2)°, beta = 88.351(2)°, gamma = 68.261(1)°. The coordination of MTB4- to Cd2+ results in infinite layers parallel to (001). The layers, not connected by any hydrogen bonds, contain small openings of about 320 pm x 340 pm.
Category: Chemistry

A Formal Mathematical Framework for Relationships

Authors: Bhekuzulu Khumalo
Comments: 16 Pages. (Note by viXra Admin: Please cite and list scientific references)

This work develops a formal mathematical framework for relationships, grounded in the observation that every entity—ranging from elementary particles to galaxies—exists within and is shaped by relationships. Maintaining these relationships requires energy, yet no general abstract language currently captures their structure or behavior. The purpose of this paper is to introduce such a language: a unified, set theoretic formalization of relationships applicable across domains, including physics, chemistry, biology, and human interaction.The theory presented here arises from a practical need to supplement the view that reality is fundamentally relational with a rigorous mathematical abstraction. It provides a foundation for classifying and categorizing phenomena by revealing the underlying relational structures that give rise to such classifications. As a new interpretive framework, it is expected that further developments will emerge over time, much as algebra and calculus evolved from their initial formulations. Although general in scope, the theory remains closely connected to counting and combinatorial principles, with set theory serving as the primary tool for achieving maximal conceptual simplicity.
Category: Algebra

Theoretical Derivation of the Spiral Galaxy Rotation Curves Obtained by Vera Rubin, Without Dark Matter

Authors: Antonio Jose Mejias Marquina
Comments: 3 Pages.

In this work, it is demonstrated that dark matter does not exist. Through a strictly analytical derivation based on clas-sical mechanics and the geometry of spiral galaxies, a formula is obtained that precisely reproduces the rotation curves observed by Vera Rubin. The results show that the flat behavior of stellar velocities in outer regions does not require invisible mass halos, but arises naturally from the proper application of fundamental gravitational laws to extended mass systems.
Category: Astrophysics

Optimal Mersenne Primes Search Using Modular Groups

Authors: Jabari Zakiya
Comments: 8 Pages. (Note by viXra Admin: Please cite and list scientific references and submit article written with AI assistance to ai.viXra.org)

Mersenne Primes have the form Mp = 2^p — 1. They are very rare. As of October 2024 only 52 have been confirmed, the last being the largest known prime. Traditionally, every sequential p value has beenused to compute|test whether 2^p — 1 is prime, requiring first generating a complete sequential list of candidate primes. Presented here is anoptimally efficient and fast process to generate candidate Mp values to test without having to use any primes to directly compute 2^p — 1, usingMersenne Prime Generators (MPG). With them, we can sequentially generate all possible Mp values starting with a p of some known Mp, without any further input or intervention in the search process.
Category: Number Theory

Einstein-Cartan Electrodynamics: Physical Four-Potential, Geometric Photon Mass, and Axial Spin Coupling

Authors: Renato Vieira dos Santos
Comments: 13 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)

If the electromagnetic four-potential is a physical field rather than a gauge class, its irrotational component is physical as well, and the geometry of spacetime can respond to it directly. We develop the consequences of this reading in the context of Einstein-Cartan gravity at the classical level. Imposing metric compatibility and linear dependence of the affine connection on the potential, we derive a unique one-parameter extension of the Levi-Civita connection. The resulting torsion is purely axial, and its Ricci scalar contributes a term $+6lambda^2 A_mu A^mu$ that generates Proca electrodynamics with photon mass $m_gamma = sqrt{3/(4pi)},lambda M_{m Pl}$, where $lambda$ is a dimensionless coupling. The same coupling also produces a universal spin-dependent force on matter and an axial-vector coupling to fermions. Because a single parameter controls all four observable sectors, the four sectors are correlated by construction, and the correlation is a signature of the geometric mechanism. We verify that the construction does not generate parity violation in the vacuum propagation of photons, and we confront the framework with laboratory, astrophysical, and cosmological bounds. The solar-wind bound on the photon mass forces $lambda lesssim 2 times 10^{-46}$, which replaces the unexplained smallness of the photon mass by an unexplained smallness of the geometric coupling. We emphasize that the paper is a classical study; the quantization of the theory and its consequences for unitarity and for the cosmological abundance of longitudinal modes are left open. Three appendices contain the detailed derivations of the uniqueness of the connection, the Ricci scalar computation, and the spin-torsion force.
Category: Classical Physics

Indirect Prompt Injection in Autonomous LLM Agents

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

A Short Solution of The Riemann Hypothesis Problem

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

A Recreational Exploration of Near-Miss Constructions for a 3×3 Magic Square of Square Numbers: The Error Function, Eisenstein Triangles, and Continued Fractions as Tools for Investigating Progressively Better Approximations

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

The Trace Is Not the State: A Counterfactual Test of What Controls Multi-Digit Addition

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

AGI and HSA (Hypertopology/Semigroup/Acyclicity)

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

Torsion in Disguise: Scalar-Gradient Contortion, Bosonic Triviality, and the Spin Coupling that Survives

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

Fullerens like a Quantum Infinitesimal Potential Wells with State Bounded of Soft Donor for Transplutonides and Oxidation of Neptunium by Energetically Doped Plutonium and also via Extreme Energetically Cascade Hyperons or Neutrinos

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

Note to Analytical Derivation of Viswanath's Constant

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

Semantic Subtext in the Bubble Sort Algorithm

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

Synthesis, Crystal Structure, Hydrogen Bonding and Thermal Behaviour of a Three-Dimensional Cu(II)-benzene-1,2,4,5-tetracarboxylate Templated by 1,9-Diaminononane

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

On the Uniqueness of Solutions to the Cauchy Problem for Systems of Linear Differential Equations with Partial Derivatives

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

The 1.11 Million Year Cycle in Earth's Magnetic Field Polarity

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

The 1.11 Million Year Cycle in the Outer Solar System

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

Improvement of the Magnetoelectric Response in Nife2o4-Sr0.5ba0.5nb2o6 Composites Using Linbo3 as Sintering Additive

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

Fine-Grained Magnetoelectric Sr0.5ba0.5nb2o6-Cofe2o4 Composites Synthesized by a Straightforward One-Pot Method

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

Effect of Sintering Additives on the Densification and Dielectric Properties of Sr0.5ba0.5nb2o6 Ceramics Synthesized by a Soft-Chemistry Method

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

Cosmological Time Dilation

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

Principles of a New Phase Nucleation Development for the Multy - Phase Industrial Real Poly Crystalline Materials (Part I): The Principles for the Nominally Mono — Phase Materials

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

Support Functions: Reframing Conventional Statistical Methods

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

The Resolution of Why There is Something Rather Than Nothing

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

The Decelerating Universe in the ESQ Model: A Real Alternative to Dark Energy

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

Impact of li-Substitution on Dielectric, Structural and Sintering Behavior of Lix(sr0.5ba0.5)1-X/2nb2o6 Ceramics

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

A Relativistic Vector Field Theory of Gravitation and a First Principles Approximation of the Graviton

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

Division by Zero Calculus:Structures, Singularities, and Mika’s Fundamental Theorems

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

A Rigorous Proof of the Riemann Hypothesis via Geometric Characterization of the Dirichlet Eta Function: Half-Angle Residual Dynamics and Invariant Level-Crossing Barriers ```[span_0](start_span)[span_0](end_span)

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 $mathcal{S}={sinmathbb{C}:00$ simultaneously across dual orthogonal projections with an exact $pi/4$ phase shift. We establish that this simultaneous locking condition enforces an overdetermined phase alignment and a structural polarization disparity between the dual channels, providing an absolute real-variable obstruction that strictly confines all non-trivial zeros to the critical line $mathbb{R}(s)=1/2$. By demonstrating that this geometric barrier is mathematically insurmountable, this work establishes a rigorous and definitive proof of the Riemann Hypothesis.
Category: Number Theory

A Vector Field Formulation of the Metric Tensor in General Relativity: Theoretical Foundations and Astrophysical Implications

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

Constant Spacetime Velocity and Time Dilation

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

The Complex Lorentz Factor and its Hidden Cartesian Grid

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

A Critique Of John Bell’s 1964 Article On The Einstein Podolsky Rosen Paradox

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

[diffraction Observation:] Independence of the Pattern from the Shape and Size of the Undisturbed Part of the Beam

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

Fundamental Particle Spin: Derivation of the Energy-Frequency Relation, Schwarzschild Metric, and Fine Structure Constant

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

Alien and Artificial Intelligences

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

DPSE: Difference Power Space Extrapolation for π Computation in O(√n) Iterations

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

Reproducing Kernels, Theta Functions and Fundamental Inequalities

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

Project of an Integrated Biofuel Production Line with Detailed Development of the Manufacturing Technology for the Gearbox Shaft Part KLB-01,00,01, Based at Pstu and Unikom LLC, Mariupol

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

Even-Odd Subseries of the Multiple Zeta Value Zeta (2, 1)

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

The Mechanical Universe: Helical Spin Theory (HST) and Higgs-Tachyon-Push Field Theory (HTP)

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

A Sum of Three Squares in Which One is the Product of the Other Two

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 $d1 fall empirically into two families: a triangular family mathscr{T}, and a Fibonacci family mathscr{F}, with virtually no overlap. It is conjectured that the two families comprise all n with |N_{n}|>1.
Category: Number Theory

Aeroelastic Similarity in Trees

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

Reproducing Kernel Theory: Essences and Global Perspectives

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

Correct Interpretation of the Great Discoveries in Particle Physics: I. Reconsidering the Higgs Boson via Vedic Vortex Structure

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

Gauss’s Flux Theorem Does not Hold in Time-Varying Electric Fields

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

On the Boundary Problem in the Origins of Matter, Life, and Consciousness

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

Why We Love Music

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