Abstract: Koide's mass formula, originally proposed for charged leptons, has been hypothesized by Carl A. Brannen to also apply to neutrinos. Assuming this hypothesis' validity, two three-dimensional mass models were constructed based on the proposed neutrino masses. This paper demonstrates that the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix can be derived by introducing an intermediate set of hypothetical states, referred to as mass negative eigenstates, which mediate the transformation between mass and flavor eigenstates. This framework naturally reproduces the tribimaximal mixing structure and yields a PMNS matrix with elements close to those obtained using global fits. Neutrino oscillation probability predictions were further compared with results from the Tokai-to-Kamioka (T2K) and Daya Bay collaborations. While the proposed model captures key structural lepton mixing features, a deviation of approximately −3σ in sin²(2θ₁₃) highlights its limitations in terms of reproducing current data. This discrepancy may indicate the involvement of additional mechanisms or physics beyond the current framework. Future theoretical refinements and more precise experimental tests are crucial to assess whether the Koide--Brannen framework can serve as a meaningful step toward a deeper understanding of neutrino phenomenology.

Abstract: It is shown that the off-shell renormalization schemes for subtraction of ultraviolet divergences in Quantum Field Theory produce zero for sums of perturbative corrections to physical quantities when all perturbation orders are taken into account. That is the off-shell renor malization schemes are in this sense unphysical. In this connection it is desirable to develop on-shell renormalization schemes for different quantum theories.

Abstract: Entanglement is conventionally treated as an abstract property of tensor-product Hilbert spaces. We show instead that it can be realized as a global compatibility constraint in the internal gauge bundle of the vacuum, encoded by a locally pure-gauge field Ξ(x) acting only on internal degrees of freedom. This vacuum internal gauge symmetry (VIGS) yields a concrete, symmetry-based mechanism for quantum correlations that requires no nonlocal dynamics, introduces no new particles or forces, and leaves the Standard Model Lagrangian unchanged. Our main result is the Vacuum Internal Gauge Theorem, which demonstrates that: (i) all nontrivial global constraints induced by Ξ are confined to internal fibers; (ii) only internal degrees of freedom can become entangled; (iii) no information can be transmitted via the vacuum gauge structure; and (iv) gravitational degrees of freedom, having no internal fiber structure, cannot be entangled. Thus VIGS explains the empirical restriction of entanglement to internal DOFs and predicts the absence of gravitational entanglement, providing a gauge-theoretic foundation for quantum correlations within a strictly local spacetime.

Abstract: The origin and evolution of the universe are central questions in modern natural science. The current mainstream theoretical frameworks in related fields are the Standard Model of Particle Physics and the Big Bang theory of cosmology, both of which exhibit significant limitations. The Standard Model fails to incorporate gravitational interactions and includes an extensive array of elementary particle types. The Big Bang theory’s "singularity" hypothesis struggles to explain the initial conditions of the universe, dark matter, dark energy, and the accelerated expansion of the cosmos. This paper proposes a unified theoretical framework — the Great Tao Model, which consists of the Yin-Yang Model of elementary particles and the Theory of Existence Field. The Yin-Yang Model classifies elementary particles into three categories based on charge properties: electron, positron, and subston, and deduces five composite particles (proton, antiproton, neutron, antineutron, neutrino). The Theory of Existence Field posits that charge and mass, as fundamental physical quantities, inherently and continuously diffuse their physical information into surrounding space, forming an "existence field". Elementary particles transmit physical information and interact through their existence fields. Based on the Great Tao Model, this paper systematically elucidates the complete physical picture from the combination of elementary particles to the formation of cosmic structures and provides unified explanations for puzzles such as dark matter, neutrinos, the nature of nuclear forces, the precession of Mercury, and the accelerated expansion of the universe. Philosophically, the model aligns with ancient Chinese Daoist thought, while physically, it embodies theoretical simplicity and unity, making it a potential candidate for a "Theory of Everything".

Abstract: The Standard Model (SM) of particle physics is one of the most successful frameworks in modern physics, yet it leaves several fundamental questions unanswered, including the nature of dark matter (DM). Precise knowledge of DM is crucial for testing astrophysical and cosmological observations and for determining the matter density of our Universe. Many hidden dark-sector models beyond the SM open the possibility of coupling between DM and SM particles via various portals. The corresponding new-physics particles include light Higgs boson, dark photon, axion-like particle, and spin-1/2 fermions. Furthermore, the introduction of a dark baryon could simultaneously explain the origin of DM and the observed matter-antimatter asymmetry in the Universe. If these hypothetical particles have masses of a few GeV, they can be explored at high-intensity e⁺e⁻ colliders, such as the BaBar, Belle/Belle II, and BESIII experiments. This report reviews the current status of DM searches at e⁺e⁻ colliders, with a focus on portal-based scenarios.

Abstract: Peer review of empirical patterns in high-precision, low-dimensionality param- eter spaces relies on implicit evaluation standards. When N = 3 parameters at 2% precision permit thousands of statistically significant formulas, reviewers must distinguish structure from coincidence, but the criteria for doing so remain unar- ticulated. We found no published record of community debate establishing explicit standards, despite decades of informal application. This paper proposes one such articulation: seven criteria emphasizing tempo- ral convergence through timestamped predictions. We offer specific thresholds not because we believe them correct, but because explicit proposals can be calibrated while implicit standards cannot. The need for explicit standards is timely. Lattice QCD has only recently achieved the precision necessary for discriminatory tests of quark mass relations. Historical precedents from lepton phenomenology (Koide, Gell-Mann–Okubo) provide limited guidance: leptons offer ∼35,000× greater discriminatory power than light quarks, in- volve no RG running, and constitute a fundamentally different measurement regime. The historical record is further compromised by survivorship bias: patterns that di- verged are largely unrecorded. Historical cases motivate the problem by illustrating why implicit evaluation proved adequate for leptons but may prove inadequate for quarks. They cannot validate the proposed solution. Validation is prospective by design: starting from this publication, patterns evaluated under this framework will be tracked publicly. The framework succeeds if it proves predictively useful; it fails if it requires constant post-hoc adjustment, judged by its own temporal convergence criterion. If this proposal provokes disagreement that leads to better criteria, it will have served its purpose. If it is ignored, the current system of implicit evaluation contin- ues unchanged. We consider both engagement and refinement to be success.

Abstract:

The physical nature of dark matter and dark energy remains one of the most pressing questions in modern cosmology. This work presents a phenomenological model where the entire dark sector is described by two minimally coupled scalar fields within General Rela-tivity. The first, an ultra-light scalar field Ψ with mass m_Ψ, constitutes Fuzzy Dark Matter (FDM), whose coherent oscillations dynamically replicate cold dark matter on large scales. The second, a quintessence field ϕ, evolves under an axion-like potential and serves as the dark energy component. We demonstrate that this framework can successfully reproduce the canonical cosmic history while offering a physical mechanism to address the S₈ tension. By exploring the model’s parameter space, we show that the suppression of small-scale structure is a direct function of the FDM mass. For a benchmark mass of m_Ψ = 10⁻²² eV, chosen to illustrate the potential impact, we show that the model can produce a value of S₈ σ₈(Ω_m/0.3)^0.5 of approximately 0.79, significantly alleviating the tension between early and late-universe probes [1,9,10]. Concurrently, the model predicts a “thawing” behavior for dark energy, with a present-day equation of state, w_ϕ,0, that depends on the potential’s parameters, yielding w_ϕ,0 0.92 in our benchmark case—a value distinguishably different from the cosmological constant’s w_Λ = 1. We acknowledge that the FDM mass required to affect the S₈ tension creates a testable conflict with some Lyman-alpha forest constraints [16], a point we discuss as a key feature for the model’s falsifiability. By connecting cos-mic acceleration, dark matter, and the S₈ tension, this self-consistent framework offers a compelling and highly testable alternative to the ΛCDM model, motivating a full statistical analysis.

Abstract: We present a geometric framework for quantum entanglement within the Cosmic Energy Inversion Theory wherein space-time torsion, dynamically sourced by primordial energy field gradients, physically mediates non-local quantum correlations. Unlike standard quantum mechanics treating entanglement as axiomatic, CEIT attributes correlations to torsion-induced phase coupling propagating at light speed through energy field variations, preserving relativistic causality while explaining Bell violations geometrically. The modified von Neumann entropy incorporates geometric contributions scaling as λℰ⁻¹∇ₐTᵅμν∂μΦₑₙₜ∂νΦₑₙₜ, where Φₑₙₜ quantifies how space-time twisting modulates correlation strength. Integration with Loop Quantum Gravity establishes holographic entropy encoding on torsion defined minimal surfaces, resolving black hole information paradoxes through geometric mechanisms. Numerical validation against gravitational gradient measurements yields 98.7% agreement with observed fidelity ratios, while pulsar coherence data constrains electromagnetic coupling parameters within 2.7% precision. The framework predicts Bell parameter modifications ΔB=0.182±0.026 in particle accelerator environments testable via CERN MATISSE interferometry, squeezed-light gravitational wave correlations accessible through LIGO observations, and enhanced cosmological structure formation signatures in JWST high-redshift spectroscopy. Experimental verification would establish entanglement as emergent space-time geometry rather than fundamental quantum axiom, unifying quantum mechanics with general relativity through six independently calibrated parameters.

Abstract: In this article the relationships are revealed between the views on neutrinos as they show up in various approaches of study. Among these are (a) Fermi’s theory on beta decay, (b) the classical view on the decay of the pion into a muon and a muon neutrino, (c) instrumental attempts for direct measurements of the neutrino’s rest mass like in the KATRIN project, (d) the studies in modern neutrino observatories on the phenomenon of neutrino oscillation and (e) the view on neutrinos in the Structural Model of particle physics. A non-classical kinematic analysis on lab frame decay processes shows that the effective masses of the three neutrinos are the same, although in this respect the comparison with the present data in the PMNS theory is not fully conclusive. Adopting the hypothesis that neutrinos fly at the lab frame speed of pions in free flight, their rest masses have to be set at 182.5 meV/c².

Abstract: This study investigates the average neutron multiplicity of fission fragments in ²³⁵U neutron-induced fission, with a focus on its correlations with fragment mass number (A) and total kinetic energy (TKE). The core objective is to elucidate the composition of fragment excitation energy—including intrinsic excitation energy (originating from nuclear excitation at the fission breakpoint) and deformation energy (resulting from shape relaxation to equilibrium)—and its impact on neutron evaporation. Using a Metropolis random walk model based on a five-dimensional potential energy surface (constructed through a macro-micro approach combined with cubic-quadratic surface (3QS) shape parameterization), the entire nuclear shape evolution process up to the fission breakpoint was simulated. Shape-dependent microscopic energy level density guided the random walk, distributed intrinsic energy among newly formed primitive fragments, and enabled calculations of neutron evaporation in excited fragments. Results show that computational results for thermal neutron-induced fission (TNNF) align well with experimental data. As incident neutron energy increases (e.g., MeV), the super-long (SL) fission mode—characterized by highly elongated fission breakpoint configurations (quadrupole moment) and low total kinetic energy—dominates, enhancing heavy fragment excitation and leading to higher neutron multiplicity than light fragments. The study reveals that the distribution of total excitation energy (E) (where E represents fission release energy) depends on nuclear structural effects and fragment mass number. This work establishes a quantitative foundation for understanding correlations between fission observables, highlights the roles of intrinsic energy, deformation energy, and super-long fission modes in neutron evaporation, and provides critical references for predicting neutron yields in high-energy neutron-induced fission.

Abstract: Paper attempts to clarify the meanings of key concepts in cosmology, such as matter, energy, mass, and hypothetical spacetime fabric. It also presents an attempt to prove the existence of spacetime fabric as physical entity that fills the entire Universe, based on the experimental effects it manifests. Furthermore, the paper hypothesizes that matter consists of three fundamental components (states): energy, mass, and spacetime fabric, forming another triplet in the Standard Model classification.

Abstract: This article proposes a radical simplification of physics foundations through the introduction of the concept of protomatter - the imaginary density of space, representing an additional non-geometric dimension. It is shown that this concept allows for a unified description of phenomena that previously required separate entities: charges become density clusters, the electric field becomes its gradient, the magnetic field becomes the gradient of flow, and quantum states become its resonant modes. Within the formalism, Coulomb's law and the Biot-Savart law are derived from first principles, Bohr's postulate is justified, and the finiteness of the self-energy of a charge is demonstrated. The model does not contradict experimental data but reinterprets them, indicating the derivative nature of the magnetic field and the existence of absolute (gravitationally-bound) reference frames. Dark matter and dark energy are identified with the very fabric of protomatter, eliminating the need for hypothetical particles.

Abstract: Quantum gravity aims to reconcile general relativity, which governs the macroscopic dynamics of spacetime, with quantum mechanics, which describes matter and interactions on microscopic scales. The tension between the background-independent, deterministic framework of general relativity and the background-dependent, probabilistic nature of quantum mechanics underscores the need for a unified theoretical description. Although several major theories have been developed, most notably string theory and loop quantum gravity, no fully consistent and experimentally validated theory of quantum gravity has yet emerged. A successful formulation is expected to illuminate the fundamental structure of spacetime and provide resolutions to singular phenomena such as those inside black holes and at the Big Bang. In this article, a unifying quantum theory of gravity is presented through the quantization of the double cover of the Lorentz group. In this framework, particles in the fundamental representation correspond to fermionic matter, while gauge fields in the adjoint representation carry quantum energy–momentum and encode spacetime curvature, thereby playing the role of the gravitational field. Classical general relativity arises as an effective field theory within this formulation. The resulting theory is renormalizable, free of singularities, and capable of describing black hole and Big Bang dynamics.

Abstract: The Standard Model introduces fermion masses through Yukawa couplings, yet it provides no underlying principle governing their values or generation structure. We propose a geometric–algebraic framework in which fermion masses emerge from discrete eigenmodes of the Laplace–Beltrami operator defined on compactified internal manifolds within a quantized, micro-causal spacetime. The internal geometry is endowed with E₈ exceptional symmetry, whose lattice structure organizes harmonic modes and constrains flavor multiplicity. Exponential suppression from internal curvature naturally produces hierarchical mass scales without fitted Yukawa parameters. The resulting spectrum reproduces the charged-lepton masses and yields Koide’s relation as a structural consequence. Internal quantum numbers and generation triplicity arise from the sedenionic gauge algebra, while embedding the mass eigenmodes into the E₈ lattice enforces symmetry breaking and geometric consistency. The quantized spacetime adopted here is treated as a working hypothesis—motivated by causal-set, loop-quantum-gravity, and lattice-regularization approaches—providing a finite, testable framework for fermion mass generation and flavor structure.

Abstract: This work presents a unified algebraic framework for cosmology—Sedenionic Quantum Gravity (SQG)—in which spacetime curvature, dark energy, and entropy arise from a common underlying principle: the quantized commutator structure of a 16-dimensional sedenionic gauge field. In this theory, the cosmological constant is not an arbitrary parameter but an algebraic curvature invariant derived from the relation where is the sedenionic covariant derivative. This non-associative operator framework replaces geometric curvature with algebraic curvature, linking microscopic internal spinor dynamics to the macroscopic expansion of the Universe. Unlike the constant Λ of the standard Λ-CDM model, the SQG framework predicts a slowly varying cosmological term where the single algebraic parameter determines the rate of vacuum relaxation. The model naturally reproduces late-time acceleration, baryon acoustic oscillations (BAO), and large-scale structure formation while avoiding ultraviolet divergences through intrinsic non-associativity. Key predictions include: (i) a logarithmic phase drift in the BAO power spectrum; (ii) a small deviation of the dark-energy equation-of-state parameter from −1, and (iii) finite black-hole entropy derived from internal spinor microstates. These results unify dark energy, quantum information, and gravitational curvature within a single predictive algebraic formalism, offering a physically testable alternative to both Λ-CDM and Finsler-kinetic cosmologies.

Abstract: We present a novel formulation of general relativity derived from operator algebra over sedenionic spacetime, replacing the conventional differential-geometric framework with a non-associative, hypercomplex algebra. In this model, displacement operators on a micro-causal lattice define curvature through their commutators, and Einstein’s field equations emerge as projections of nested operator relations. A key achievement of this framework is the elimination of two long-standing problems in modern physics: the missing-mass problem and the cosmological constant puzzle. Galaxy rotation curves and cluster dynamics are explained without invoking dark matter or MOND, as the algebra naturally produces an additional force term at large scales. Likewise, the cosmological constant (Λ) is not an ad hoc insertion but arises as a derived property of the sedenionic commutator algebra, resolving the long-standing vacuum catastrophe. Beyond these breakthroughs, the model avoids black hole singularities through algebraic saturation, predicts fermionic gravitinos, and provides new insights into gravitational entropy and the arrow of time. Distinct from string and M-theory—which require extra dimensions and remain decoupled from the Standard Model—our approach offers a self-contained algebraic geometry that unifies gravity with quantum phenomena and lays the foundation for a grand unified description of all fundamental forces and particles.

Abstract: Physical processes are usually described using four-dimensional vector quantities - coordinate vector, momentum vector, current vector. But at the fundamental level they are characterized by spinors - coordinate spinors, momentum spinors, spinor wave functions. The propagation of fields and their interaction takes place at the spinor level, and since each spinor uniquely corresponds to a certain vector, the results of physical processes appear before us in vector form. For example, the relativistic Schrödinger equation and the Dirac equation are formulated by means of coordinate vectors, momentum vectors and quantum operators corresponding to them. In the Dirac equation a step forward is taken and the wave function is a spinor with complex components, but still coordinates and momentum are vectors. For a closed description of nature using only spinor quantities, it is necessary to have an equation similar to the Dirac equation in which momentum, coordinates and operators are spinors. It is such an equation that is presented in this paper. Using the example of the interaction between an electron and an electromagnetic field, we can see that the spinor equation contains more detailed information about the interaction than the vector equations. This is not new for quantum mechanics, since it describes interactions using complex wave functions, which cannot be observed directly, and only when measured goes to probabilities in the form of squares of the moduli of the wave functions. In the same way spinor quantities are not observable, but they completely determine observable vectors. In Section 2 of the paper, we analyze the quadratic form for an arbitrary four-component complex vector based on Pauli matrices. The form is invariant with respect to Lorentz transformations including any rotations and boosts. The invariance of the form allows us to construct on its basis an equation for a free particle combining the properties of the relativistic wave equation and the Dirac equation. For an electron in the presence of an electromagnetic potential it is shown that taking into account the commutation relations between the momentum and coordinate components allows us to obtain from this equation the known results describing the interactions of the electron spin with the electric and magnetic field. In the presence of a potential the momentum components cease to commute with each other. To neutralize this effect, the Schrödinger equation is supplemented by several equations with mixed derivatives on coordinates. In section 3 of the paper this quadratic form is expressed through momentum spinors, which makes it possible to obtain an equation for the spinor wave function in spinor coordinate space by replacing the momentum spinor components by partial derivative operators on the corresponding coordinate spinor component. Section 4 presents a modification of the theory of the path integral, which consists in considering the path integral in the spinor coordinate space. The Lagrangian densities for the scalar field and for the electron field, along with their corresponding propagators, are presented. An equation of motion for the electron is proposed that is relativistically invariant, in contrast to the Dirac equation, which lacks this invariance. This novel equation permitted the construction of an actually invariant procedure for the second quantization of the fermion field in spinor coordinate space. Furthermore, it is demonstrated that the field operators are a combination of plane waves in spinor or vector space, with the coefficients of which being pseudospinors or pseudovectors. Each of these pseudovectors or pseudospinors corresponds to one of the particles presented in the theory of electrodynamics. Furthermore, each plane wave possesses an additional coefficient in the form of a creation or annihilation operator. In vector space, these operators commute, whereas in spinor space they anticommutate. The paper presents the spinor and vector representations of the field operators in explicit form, comprising sets of 16 pseudospinors or 4 pseudovectors corresponding to particles represented in electrodynamics. An explicit form of the symmetric traceless tensor with spin two, zero mass and two polarizations is presented, which can serve as a model of the graviton. The results obtained may prompt changes in some aspects of the construction of Feynman diagrams. Among other things, it presents a purely mathematical derivation of Maxwell's inhomogeneous equations without reference to empirical data on the action of electric current, which is usually referred to when deriving equations.

Abstract: We present the microphysical extensions of Quantum Informational Relativity (QIR), built upon the informational field p(x) and the geometric modulation Z(p). This work develops, with full derivations, five complementary aspects: (i) the topological classification of stationary solutions and the emergence of particle families; (ii) perturbative quantization around informational solitons and the resulting mass spectrum; (iii) parameter mapping and experimental correspondence; (iv) an informational confinement mechanism consistent with strong interactions; (v) macro–micro continuity linking cosmology and particle structure. The framework preserves covariance, generalized conservation, and the unified Einstein equation with Z appearing in the numerator.

Abstract: We present a nonperturbative geometric symmetry model for the electron’s anomalous magnetic moment. The electron is represented as an extended charge–spin density whose intrinsic rotation interacts recursively with the surrounding geometry through a symmetric real-space kernel. This recursive convolution expansion reproduces the standard quantum electrodynamic (QED) correction series for the g-factor without invoking virtual fields or renormalization. Using a Gaussian twist density and a dimensionless coupling kernel constrained by spatial symmetry, the model yields g = 2.0023231, matching experiment within 1.9 ppm. The optimal configuration occurs at a normalized spatial width σ/r₀ = 1- e^-1, suggesting a universal geometric saturation scale for spin–magnetic coupling. The framework offers a symmetry-based interpretation of QED corrections as emergent from real-space geometric feedback.

Abstract: We present a quantum framework grounded in micro-causality and spacetime quantization, where spacetime is composed of discrete, causally ordered units rather than a continuous manifold. This intrinsic structure naturally generates fundamental quantum features—wave–particle duality, energy quantization, and the Heisenberg uncertainty principle—without invoking canonical quantization, matter-wave postulates, or harmonic-oscillator models. Consequently, this paradigm eliminates the long-standing paradoxes of wavefunction collapse, self-interference, and non-local spooky correlations in entanglement.Within this causal lattice spacetime, quantum commutation relations emerge from finite shift operators, and the uncertainty principle arises geometrically from non-commutativity at the fundamental level. Unlike standard quantum field theory (QFT), which predicts infinite vacuum energy and requires renormalization, the present framework removes zero-point energy, ultraviolet divergences, and fine-tuning. Moreover, U(1) symmetry is broken geometrically on the lattice, leading to mass generation without a Higgs mechanism.The Casimir effect is reinterpreted as a temperature-dependent imbalance in thermal radiation pressure rather than the consequence of vacuum fluctuations, predicting that the Casimir force should vary with ambient temperature. Experimental confirmation of such dependence would directly support the lattice interpretation and challenge the QFT view of vacuum energy.By unifying key quantum behaviors through discrete causal geometry, this model offers a divergence-free and physically grounded alternative to continuum-based QFT. It opens new avenues for quantum unification, cosmology, and the understanding of fundamental constants, without speculative constructs, singularities, or infinities.