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[9] viXra:2607.0128 [pdf] submitted on 2026-07-31 20:37:10
Authors: Satoshi Nakamoto, Nicolas Bourbaki
Comments: 3 Pages. (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)
We propose a geometric limit theory for discrete spatial configurations where continuous curves cannot exist, leaving a deterministic boundary error termed the "Pi residual." By balancing the root-mean-square deviation of discrete vertices against system coordinate resolution, we derive critical boundary constraints
Category: Mathematical Physics
[8] viXra:2607.0122 [pdf] submitted on 2026-07-30 01:47:55
Authors: Jinyong Liu
Comments: 22 Pages.
In the framework of classical noninertial mechanics, the theoretical construction is predicated on the existence of a special reference frame, the "inertial frame", as a priori. Its essence is to extend the dynamical laws in the inertial frame to noninertial frames through coordinate transformation and formal modification, thus inherently relying on the definition and existence of the inertial frame, making it difficult to achieve a fundamental breakthrough in the inertial frame paradigm. This paper proposes a dynamic reconstruction path based on the intrinsic relations within the system, aiming to establish a new system of particle dynamics that is logically self-consistent and physically self-sufficient and does not presuppose an absolute space-time background. On the basis of Newton's laws of motion, in this paper, the equations of particle mechanics applicable to any translational reference frame (i.e., a reference frame with an origin acceleration that can be any function of time) are derived. Through systematic analysis, it is proven that core physical quantities such as force, momentum, and the kinetic energy of a particle group all possess intrinsic properties independent of the choice of reference frame. By further introducing a particle subsystem grouping mechanism, this paper reveals the dynamical essence of internal interactions within the system and its coupling with the external environment, clarifying the physical origin of the energy hierarchy structure (internal kinetic energy and external kinetic energy) and its conservation conditions in general reference frames, thereby providing a solid theoretical foundation and an operational, verifiable mathematical framework for constructing a truly universal noninertial mechanics theory that does not require the introduction of fictitious inertial forces.
Category: Mathematical Physics
[7] viXra:2607.0119 [pdf] submitted on 2026-07-30 01:34:04
Authors: Bernd Ganter
Comments: 8 Pages. In German language. Comments please to: bernd.ganter.fsk@gmx.de
This paper explains in German language how Dark Matter covers 85% of all the total matterin the universe. It does so by applying the mathematics of consecutive optimal power towersto the relative sizes of the strengths of interactions between elementary particles.The same procedure was used with the fine structure constant in vixra 2607.0104which allowed the derivation and very exact calculation of that constant.Based upon that procedure a formula can be developed to calculate the relative valueof spacetime volume and information density (=strength) of gravity as an interaction.
Category: Mathematical Physics
[6] viXra:2607.0104 [pdf] submitted on 2026-07-26 02:23:09
Authors: Bernd Ganter
Comments: 99 Pages. In German. Comments please to: bernd.ganter.fsk@gmx.de
This paper is about dimensions and fundamental forces in the universe, and especially the fine structure constant, the value of which has remained unexplained for over 100 years now. The paper is the German parent document of the condensed version viXra:1405.0226 in English translation. It contains the derivation and exact calculation of the value of the fine structure constant which is 1/137.035999100.
Category: Mathematical Physics
[5] viXra:2607.0095 [pdf] replaced on 2026-08-18 19:45:08
Authors: Jaykov Foukzon
Comments: 27 Pages.
n this paper, we show how the finite formulation of quantum field theorybased on Langevin equations can be generalized to the case of nonrenormalizabletheories.The 5th-time stochastic-quantization approach to field theory proposed by Parisi and Wu,is put in a path-integral form in [5]. The procedure of taking the limit τ→∞ is analyzed and based on new grounds through the introduction of the vacuum-vacuum generating functional. In this paper non perturbative aprouch related to Parisi and Wu stochastic-quantization of the λϕ_{d}^{n},n≥2,d≥4 model quantum field theory in Minkowski spacetime is considered.
Category: Mathematical Physics
[4] viXra:2607.0093 [pdf] replaced on 2026-08-17 10:11:56
Authors: Frederic Lassiaille
Comments: 14 Pages.
We demonstrate that algebraically integrating General Relativity into quantum field theory via the Surrounding Matter framework provides a rigorous resolution to the Yang--Mills mass gap problem. Within this framework, the local energy-momentum structure is governed by the multi-source vector field $D^mu(x)$ and the velocity ratio $v/c$. We show that the algebraic cancellation $lambda/lambda$ within the surrounding ratio ensures that an infinitesimal energy distribution generates the exact same space-time calibration as a finite one across all gauge generators. Consequently, gauge field interactions in a non-empty Universe cannot decay into zero-energy states; for localized excitations in vacuum environments, the surrounding background dynamically enhances their rest mass, establishing a strictly positive lower bound for the ground-state spectrum ($Delta > 0$). Simultaneously, high-energy divergences are inherently regularized: ultraviolet self-interactions remain strictly bounded by background saturation through the infinite interaction time delay ($t' to infty$) and the dynamic attenuation driven by the algebraic relativistic factor. This uniform upper bound guarantees the unconditional convergence of the non-perturbative Feynman path integral $int mathcal{D}A , e^{iS[A]}$ and ensures that the $n$-point Wightman correlation functions $langle 0 | A(x_1) dots A(x_n) | 0 angle$ remain well-defined tempered distributions across all of $mathbb{R}^4$. Furthermore, we demonstrate that the algebraic deformation generated by $D^mu(x)$ resolves the historical obstacle of infinite static field energy without introducing metric singularities, removing the necessity for a rigid Minkowski background. Building upon a rigorous gravitational baseline, these results reveal that General Relativity, through its global algebraic surrounding effect, plays an active and indispensable role in governing quantum gauge field dynamics at subatomic scales.
Category: Mathematical Physics
[3] viXra:2607.0066 [pdf] submitted on 2026-07-15 22:26:14
Authors: Julinho Jorge Luís
Comments: 35 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This article presents the Dual Architecture, an algebraic regularization method for divergent integrals in quantum field theory. The method rests on two functions defined over complementary domains: the Euler integral for the Gamma function over the positive real axis, and a companion integral over the negative real axis. When one integral representation diverges, its dual converges, and the regularized value is taken as the reciprocal of the convergent one. The sign alternation is encoded by an entire function without zeros on the negative real axis. Applied to Yang-Mills theory with gauge group SU(N), the method demonstrates the existence of a mass gap persisting to all orders of perturbation theory. The perturbative series of the Dual Architecture converges absolutely because the regularized Gamma values at negative integers decay factorially, in contrast to the factorial growth of the traditional Dyson series. Evidence for the proposal comes from two independent anomalies that the established method leaves unexplained. The first is a residual error in the WKB expansion of the quartic anharmonic oscillator, computed numerically to high order and documented in the literature. The second is the sign of the vacuum energy density, which the traditional analytic continuation yields as negative, contradicting the observed accelerated expansion of the Universe. The Dual Architecture corrects both anomalies, and they share a common origin in the same negative half-integer argument of the Gamma function. The method eliminates the renormalization scale because integrals are evaluated directly in four dimensions, producing finite values without pole subtraction. Correspondence with quantum electrodynamics at one loop is verified. The Wightman axioms are satisfied.
Category: Mathematical Physics
[2] viXra:2607.0057 [pdf] submitted on 2026-07-14 13:25:35
Authors: Holger Döring
Comments: 22 Pages.
At first, this second description also is no proof but a compact synopsis of the Riemanian prime-number-problem and its zero-states, seen and interpreted with the eyes of a theoretical physicist. Ergo there are mostly themes described, how the theorem can be handled by quantum mechanical, more physical descriptions and historical found partial solutions. Nevertheless there are some own ideas in it and in this way it may be that it can be useful as an assist for the goal. Here is the systematic summary of the entire thought experiment. It links every physical concept of hyperbola string of beads model with its exact mathematical equivalent in number theory.
Category: Mathematical Physics
[1] viXra:2607.0027 [pdf] submitted on 2026-07-08 20:58:45
Authors: Holger Döring
Comments: 3 Pages. In German
At first, this description is no proof but a compact synopsis of the Riemanian prime-number-problem and its zero-states, seen and interpreted with the eyes of a theoretical physicist. Ergo there are mostly themes described, how the theorem can be handled by quantum mechanical descriptions and historical found partial solutions. Nevertheless there are some own ideas in it and in this way it may be that it can be useful as an assist for the goal. Here is the systematic summary of the entire thought experiment. It links every physical concept of hyperbola string of beads model with its exact mathematical equivalent in number theory. A more detailed paper will follow.
Category: Mathematical Physics
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