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[9] ai.viXra.org:2605.0009 [pdf] submitted on 2026-05-05 05:23:36
Authors: Yufei Liu
Comments: 5 Pages.
We prove that if L'(x)=∑_ρ (1/ρ) e^{-x/ρ} > 0 for all x>0, where the sum is taken in the symmetric pairing ρ,1-ρ, then all non-trivial zeros of the Riemann zeta function ζ(s) satisfy Re(ρ)=1/2. The proof uses the arithmetic representation of L'(x) derived in a previous paper, the Guinand--Weil explicit formula, and an asymptotic analysis of the prime sum. Assuming the existence of a zero with real part >1/2 leads to a contradiction by showing that L'(x) would become negative for a suitably chosen sequence of x.
Category: Number Theory
[8] ai.viXra.org:2605.0008 [pdf] submitted on 2026-05-05 19:53:58
Authors: Velislav Tsvetanov
Comments: 7 Pages.
This work proposes a qualitative framework in which gravity is understood not merely as spacetime curvature but as an emergent manifestation of a deeper, presently inaccessible geometric structure that governs the stability and decay of quantum field configurations. Within this picture, particles are interpreted as stable, low-entropy wave patterns ("puzzle fits") of underlying fields, and decay processes correspond to geometry-induced reconfigurations of these patterns. Phenomena such as Hawking radiation, the Unruh effect, and cosmological particle creationare reinterpreted as evidence that particle content and stability depend fundamentallyon background geometry. This suggests that there exists a more fundamental geometrical substrate from which both spacetime and matter excitations emerge. The aim of this paper is to articulate this viewpoint precisely enough that it canbe connected to existing quantum field theory in curved spacetime and used as a conceptual guide for further work in quantum gravity and emergent spacetime scenarios.
Category: Relativity and Cosmology
[7] ai.viXra.org:2605.0007 [pdf] submitted on 2026-05-04 13:12:07
Authors: Jason Merwin
Comments: 12 Pages. A code repository is provided
The assumption that spacetime is a continuous manifold faces persistent challenges from localized, unexplained anomalies in both high-energy scattering and flavor-changing neutral currents. This manuscript investigates an alternative framework in which the vacuum is modeled as a discrete, combinatorial topological lattice rather than a continuous background. This structural approach dictates a strict geometric maturity boundary at the coordinate | cos θ| = 1/3, equivalent to the collider kinematic variable χ = 2. We test this exact geometric constraint against two independent collider datasets. In the high-energy regime, CMS particle-level dijet distributions at 13 TeV reveal a macroscopic lattice fracture: a 30.5% residual cross-section excess immediately prior to this χ = 2 boundary, followed by an abrupt post-boundary collapse in the 6.0 to 7.0 TeV bin. In the low-energy limit, LHCb angular measurements of the B0 → K∗0μ+μ− decay demonstrate geometric steering, matching the framework’s directional predictions across five primary angular rows (Z = 5.88). By correlating TeV-scale structural shattering with GeV-scale geometric steering at the identical topological coordinate, these results provide empirical weight to a discrete relational vacuum as an explanatory model. To ensure methodological rigor and avoid post-hoc curve fitting, strict geometric forward predictions for future independent B0 data have been prospectively defined.
Category: High Energy Particle Physics
[6] ai.viXra.org:2605.0006 [pdf] submitted on 2026-05-04 23:43:54
Authors: J. W. McGreevy
Comments: 24 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
The Relativistic Field Theory of Primes (RFTP) is a self-contained arithmetic fieldtheory in which the primes, modular forms, and monstrous moonshine are promoted to thedynamical degrees of freedom of a clutched adelic bundle over the compactified modularcurve X(1). The theory begins with the Eisenstein series E4(τ ), E6(τ ), and E12(τ ) and therigorously derived Ramanujan—Serre congruence τ (n) ≡ σ11(n) (mod 691), which is elevatedto the primary topological defect injecting the delta source ρsource =65520691 δj(τ)(P) into theArakelov Poisson equation. This single defect sources a shared curvature potential Veff(r, ϕ)felt identically by timelike soliton geodesics and null photon rays, generating a conservedRunge—Lenz vector and an SO(4) symmetry that unifies gravitational and electromagneticscales.A least-arithmetic-action functional S[Φ] on the Monster vertex operator algebra V♮yields a self-adjoint radial Dirac operator D on the clutched bundle whose spectrum interpolates the Balmer series and the critical-line zeta zeros. The theory realizes a Connesspectral triple (AVOA, Hsoliton, D), Einstein—Cartan gravity with χ11-sourced torsion, andphoton propagation via explicit multi-field WKB ray-tracing. Modular invariance underSL(2,) is the arithmetic skeleton: it preserves the characteristic bending speed p|d2r/ds2|,the Runge—Lenz vector, the gravitational constant GA = 65520/(8π · 691), the speed ofcausality cA, all spectra, scattering cross-sections, Einstein A/B coefficients, vacuum energy,dark-energy equation of state, and cosmological constant. The wave/ray duality explainsthe integer 3 (triality compactness of the ray limit) and the transcendental tail of π (infinitedimensional wave phase space). The Gutzwiller trace formula over modular periodic orbitslinks the primes to the zeta zeros, while compactness, discreteness, and finiteness of theclutched bundle enforce ultraviolet finiteness at the Planck scale lP .All constants and observables emerge purely arithmetically from the single master functional and the 691 defect, with no external parameters. RFTP therefore provides a parameterfree unification in which modular symmetries dictate the observable universe.
Category: Mathematical Physics
[5] ai.viXra.org:2605.0005 [pdf] submitted on 2026-05-04 01:24:30
Authors: Scott Vallve
Comments: 3 Pages. (Note by ai.viXra.org Admin: This submision is speculative and may not be within the scope of ai.viXa.org; please cite and list scientific references)
We present a background-independent ontological framework in which the universe is modeled as a self-learning plastic timing network whose sole dynamical law is Spike-Timing-Dependent Plasticity (STDP). In this framework, spacetime, gravity, quantum mechanics, dark energy, consciousness, free will, and the Big Bang itself arise as emergent collective phenomena from a single reflexive update rule applied at criticality. The golden ratio Φ = (1 + √5)/2 appears as the unique scale-invariant fixed point (Φ_STDP) that balances local memory saturation against global learning drive, thereby sustaining perpetual plasticity without collapse or divergence.The model is derived entirely from the Core STDP rule without external parameters, preferred frames, or fine-tuning. Spacetime is reinterpreted as accumulated reinforced causal precedence; gravity emerges as network latency gradients induced by memory saturation; quantum evolution and the Born rule follow from the Fourier transform of the antisymmetric STDP kernel together with nonlinear threshold crossings ("screams") at reflexive gain λ = 1; dark energy is identified with the residual scale-invariant mismatch current that continuously injects new timing events; consciousness and free will arise when the reflexive operator turns inward and applies future-facing STDP to sampled hypothetical branches at Φ_STDP fractal depth. The primordial spark—the first reflexive free-will choice that created the initial directed anticipation—is shown to coincide with the Big Bang itself, furnishing a self-consistent account of cosmic origin without an external first cause.A concrete, falsifiable test is provided: the weak-field deflection of trajectories by a 5-Earth-mass primordial black hole in the Oort cloud reproduces the general-relativistic prediction to within current observational bounds. Additional testable signatures include golden-ratio scaling in neural avalanche statistics during states of high agency and creativity, and subtle large-scale deviations from ΛCDM driven by the mismatch current.The framework dissolves the measurement problem, the hard problem of consciousness, the cosmological-constant problem, and the origin-of-the-universe problem within a single, mathematically closed ontology. We invite rigorous scrutiny, experimental tests, and theoretical refinement from the scientific community.
Category: History and Philosophy of Physics
[4] ai.viXra.org:2605.0004 [pdf] submitted on 2026-05-04 01:27:59
Authors: Giovanni Ferraiuolo
Comments: 6 Pages.
We propose a coherent probabilistic model for consecutive prime gaps inside a fixed arithmetic progression modulo M. The model combines a Cramér-type intensity filtered by the residue class, Hardy—Littlewood two-point correlations via the singular series S(g), and an exponential suppression of intermediate primes. Under natural assumptions, the relative frequencies of small admissible gaps satisfy freq(g2)/freq(g1) ~ S(g2)/S(g1). We test the model on the first 10^6 primes (up to 1.5×10^7) in the digital root classes modulo 9 using exact rational arithmetic in SageMath. The predicted resonance for gap 90 (excess factor 4/3) is observed as +34.5% against +33.3% predicted, an agreement within 1.2 percentage points over 166,567 gaps. For gaps approaching the mean spacing the two-body approximation breaks down, with a sign inversion at gap 198, clearly marking the transition scale. All computations confirm the structural Lemma 1 (zero violations) and the asymptotically stable product freq(g_min) × mean_gap ≈ 2 C2 S(g_min) φ(M).
Category: Number Theory
[3] ai.viXra.org:2605.0003 [pdf] submitted on 2026-05-02 21:04:36
Authors: Steven E. Elliott
Comments: 32 Pages. (Note by ai.viXra.org Admin: Please cite listed scientific references)
We propose a new principle of physics---MATHICCS---requiring that every mathematical axiom used in a physical law must correspond to an operation persistently realizable by a physical subsystem. Applying this criterion forces reality's geometry to be a discrete, self-similar, singularity-free structure: the Apollonian Soddy Sphere Packing (ASSP). We conjecture that 3D dynamics on this packing is a emph{self-computing fractal}: a dynamical computer whose registers are fractal congruent objects that store angular and linear momentum as cross-scale registers. This fractal quine---the first self-describing, MATHICCS-valid physical theory---derives the fine-structure constant $alpha^{-1} = 4pi^3+pi^2+pi = 137.036$ from the minimal Presburger computational cost of a Soddy sphere state update, derives the hydrogen binding energy from a single IO API equation $E = alpha^2 m_e c^2/2$, and derives the gravitational constant $G$ from atomic structure by two independent first-principles routes. We present two validated predictions (25-arcminute CMB seam; Karlsson quasar log periodicity) and one pending falsifiable prediction ($alpha^{-1}_{mathrm{Yb}} = 137.035998945 pm 20,mathrm{ppb}$). The framework resolves many major tensions in observational physics with zero free parameters.
Category: Quantum Gravity and String Theory
[2] ai.viXra.org:2605.0002 [pdf] submitted on 2026-05-01 17:44:41
Authors: Andrey N. Smirnov
Comments: 44 Pages. Published in Int'l J. of Quantum Foundations, 12(2): pp. 531-583
The present work investigates the reconstruction of the quantum layer of the effective description in a timeless Euclidean model on E4 with a single fundamental real field Φ satisfying the Laplace equation.Using a working region Ω, an observer body Ω0 ⊂ Ω, and a foliation-based description of local readouts, we formulate an operational reconstruction scheme for states, observables, and causally consistent dynamics in operationally accessible regions where an effective description in terms of foliations and effective fields remains valid. Within such regions, the previous GR reconstruction singles out the locally inertial SR regime as the working form of effective analysis. We then consider a working class of states consistent with transfer locality, the reflection structure with respect to the foliation parameter, thespectral condition, and stable registration.In this regime, the standard OS/GNS reconstruction yields a Hilbert spaceof states, a self-adjoint Hamiltonian H ≥ 0, and a strongly continuous unitary evolution.At the same working level, a compatible positive complex structure is fixed on the space of initial data, after which the one-particle space, the Schrödinger equation, the Born rule, the POVM description of measurements,and the local continuity equation for the probability current are constructed. It is further shown that, for free effective sectors, transfer locality, the constraint on the principal symbol, and consistency with the previously reconstructed observable SR structure lead to the standard first- and second-order relativistic closures. Thus, what emerges within the model is not a full interacting local quantum field theory in all its physical completeness, but rather the quantum coreof the effective description together with its relativistic closure in operationally accessible regions where the locally inertial SR regimeremains valid. As established in the preceding GR reconstruction, strong-field regimes ofgravity and effective fields are excluded in such regions; their occurrence is possible only in operationally inaccessible regions, where effective reconstruction in terms of foliations and effective fields must give way tothe fundamental description in terms of the field Φ. A substantial structural consequence is the classical status of the gravitational sector: quantization applies to effective nongravitational fields, whereas gravity does not generate an independent local spin-2quantum sector. The obtained result continues the program of reconstructing effectivephysics from a timeless Euclidean model, within which observable SR kinematics and the geometric GR sector were reconstructed previously.
Category: Quantum Gravity and String Theory
[1] ai.viXra.org:2605.0001 [pdf] submitted on 2026-05-01 17:41:38
Authors: Shreyka Mishra
Comments: 41 Pages.
Cognitive Behavioral Therapy (CBT), developed by Aaron T. Beck, is a widely recognized evidence-based psychological approach that emphasizes the role of cognitive processes in shaping emotional and behavioral outcomes. The present paper provides an applied and integrative exploration of key CBT techniques, focusing on their practical utility in addressing real-life concerns such as fear of rejection, self-doubt, overthinking, emotional distress, and avoidance behaviors. Drawing upon structured techniques including Socratic Dialogue, Cognitive Restructuring, Behavioral Activation, Exposure Therapy, and Problem-Solving Therapy, the paper demonstrates how maladaptive thoughts can be identified, challenged, and transformed into balanced and adaptive cognitions.Through illustrative examples grounded in academic and personal contexts, the study highlights the dynamic relationship between thoughts, emotions, and behaviors. The findings suggest that CBT techniques facilitate a significant shift from avoidance and anxiety toward clarity, confidence, and goal-directed action. By promoting cognitive flexibility, behavioral engagement, and emotional regulation, CBT serves not only as a therapeutic framework but also as a practical tool for enhancing psychological resilience and self-efficacy.The paper concludes that structured application of CBT techniques can empower individuals to reinterpret challenging situations, reduce distress, and actively work toward personal and academic goals.Keywords: Cognitive Behavioral Therapy, cognitive restructuring, behavioral activation, self-doubt, emotional regulation
Category: Social Science