Abstract: The motivation for investigating the issues presented in this article stemmed from a discovery that resulted from using the magnetic flux quantum that combine the Planck's constant and the Elementary charge, and combining them in the mathematical expression of Coulomb's law. It led to a new mathematical relationship between the combined expressions. The new relationship yields a novel theoretical finding that indicates that the mass of the electron is associated with the magnitude of the square of the magnetic flux quantum which makes up the particle. It reveils also a novel significance of the vacuum permittivity constant (in SI units), which also relies on a result from a different prespective demonstrated in this article through an analogy to the kinetic theory of gases. It shows that the vacuum permittivity constant is associated with the Bohr radius and it is about sixth of it. Using the concept of the nucleus motion around the center of mass shared with the electron in the Hydrogen atom, along with defineing the orbital angular momentum of the proton at the trajectory around the center of mass, resulted in finding the velocity of the proton at this trajectory. This velocity divided by the speed of light in vaccum, yields a new physical constant which fulfill a similar role like the fine structure constant in the atom domain. The new constant and the fine structure constant are combined together along with the square of the magnetic flux quantum in most of the equations that yield results for the proton and neutron masses and their radii. Another aspect that is presented in a briefly way demonstrates the connection between the square of the magnetic flux quantum through the Bohr radius that provides a novel significance of the wave function in the atom.

Abstract: A statistical field model is constructed on Minkowski spacetime for a self-interacting Dirac field that fluctuates with respect to an auxiliary parameter. The fluctuating Dirac field undergoes a variational Hamiltonian flow while exchanging action with an action bath. Assuming ergodicity, the partition function is calculated and used to provide a perturbative expansion for the field's correlation functions. Non-perturbative calculations are carried out and the resulting 2-point correlation functions have a distinct light cone structure as expected for a relativistic field theory.

Abstract: This paper derives the discrete structure of observable quantities—eigenvalues and quantized states—as a natural consequence of the Total Entropic Quantity (TEQ) framework. Starting from two foundational axioms—(1) entropy as geometric structure, and (2) a minimal principle selecting stable distinctions—we show that quantization emerges not as a postulate but as a result of entropy curvature. Eigenstates appear as local minima in entropy-resolvent state space, and eigenvalues define stability classes of distinguishable structure. We further show that the entropy-weighted path integral admits a natural zeta-regularization, and that the spectrum of entropy-stable modes lies entirely on the critical line Re(s) = 1/2. As a consequence, the Riemann Hypothesis (RH) is reinterpreted as a structural condition of entropy stability. Combining this with a contradiction argument—showing that RH and the Goldbach Conjecture (GC) cannot both be false—we conclude: if GC holds and the TEQ framework is valid, then RH must also hold. These results suggest a unified perspective—one in which both quantization and arithmetic regularity arise from the same thermodynamic principle of resolution. Whether one adopts this framework in full or simply considers its coherence, the geometry of entropy flow offers a compelling lens through which physical and symbolic structure may be reinterpreted.

Abstract: This research develops the foundational equations of Extended Classical Mechanics (ECM) by generalizing Newtonian mechanics through the inclusion of dynamic mass components such as negative apparent mass. ECM redefines force, acceleration, and gravitational interactions using an effective mass framework, expressed as the sum of traditional matter mass and a kinetic-energy-derived negative apparent mass. This dual-mass interaction leads to revised force laws and a spectrum of speed regimes for massive particles—ranging from gravitational confinement to antigravitational liberation. The formulation extends to massless particles like photons by assigning them an effective negative matter mass, enabling consistent force definitions and propagation behaviour at relativistic speeds. Radial distance plays a critical role in determining gravitational behaviour, with transitions from classical attraction to antigravitational expansion. The framework aligns with cosmological observations, particularly in large-scale structure behaviour, and provides a unified approach to understanding force, inertia, and motion in both massive and massless domains. ECM thus represents a coherent advancement of classical physics, accommodating gravitational variance, energy redistribution, and speed constraints in dynamic systems.

Abstract: We use gauge fixing to derive Proca equation from Maxwell’s classical electrodynamics in curved spacetime. Further restrictions on the gauge yield the Klein-Gordon equation for scalar bosons. The self-coupling of electromagnetic fields through spacetime curvature originates the inertia of wave packets for non-null field solutions, suggesting an electromagnetic origin of mass. We study the weak field limit of these solutions and prove that the electrovacuum can behave as a charged nonlinear optical medium.

Abstract: This study investigates the variability of precipitation across Ethiopia by analyzing monthly and annual rainfall data from five stations representing the north, east, west, south, and central regions over a 31-year period (1987–2017). The research applies the Standardized Precipitation Index (SPI) and continuous wavelet analysis to examine spatiotemporal rainfall variability and the influence of major ocean-atmosphere circulation patterns, including Niño-4, North Atlantic Oscillation (NAO), Southern Oscillation Index (SOI), and Mediterranean Oscillation Index (MOI). The SPI values indicate year-to-year variability ranging from 3.2 (extremely wet) to -2 (severe drought). Wavelet analysis reveals short- and long-term rainfall periodicities of 2–3, 3–5, and 6–10 years, which correspond to similar cycles in oceanic indices (2–3, 3–5, 6–10, and 8–13 years). Results highlight significant teleconnections between oceanic fluctuations and rainfall anomalies in different parts of Ethiopia. For instance, the northern region experienced a wet event (2.5 SPI) around 2001, influenced by Niño-4 (1992–2003); the southern region faced severe drought (-2 SPI) in 2014/2015, linked to NAO (2009–2016); and the western region was affected by SOI during 1992–2005, with droughts in 1994/1995 and 2003. The findings emphasize the role of oceanic anomalies in driving regional precipitation variability, providing valuable insights for water resource management and climate adaptation strategies. This study also bridges gaps in previous research by employing wavelet analysis to uncover time-frequency dynamics, particularly for SOI and MOI, offering a deeper understanding of precipitation teleconnections in Ethiopia.

Abstract: The mean-field model (MFM) is the workhorse of the statistical mechanics: one normally accepts that it yields results which, despite differing numerically from the correct ones, are not “very wrong”, in that they resemble the actual behavior of the system as eventually obtained by a more advanced treatments. This, for example, turns out to be the case for the Casimir force under, say, Dirichlet-Dirichlet, (+,+) and (+,−) boundary conditions (BC) for which, according to the general expectations the MFM delivers attractive for like BC—or repulsive for unlike BC—force, with the principally correct position of the maximum strength of the force below, or above the critical point Tc. It turns out, however, that this is not the case with Dirichlet-Neumann (DN) BC. In this case, the mean-field approach leads to an attractive Casimir force. This contradiction with the “boundary condition rule” is cured in the case of the Gaussian model under DN BC. Our results, which are mathematically exact, demonstrate that the Casimir force within the MFM is attractive as a function of temperature T and external magnetic field h, while for the Gaussian model it is repulsive for h=0, and can be, surprisingly, both repulsive and attractive for h≠0. The treatment of the MFM is based on the exact solution of one non-homogeneous nonlinear differential equation of second order. The Gaussian model is analyzed both in its continuum and lattice realization. The obtained outcome teaches us that the mean-field results should be accepted with caution in the case of fluctuation-induced forces and ought to be checked against more precise treatment of the fluctuations within the envisaged system.

Abstract: The existence of a mass gap in non-abelian Yang-Mills theory is a cornerstone prediction related to quark confinement, strongly supported by experimental observations and lattice simulations. The Clay Mathematics Institute designated its rigorous proof within continuum Quantum Field Theory (QFT) as a Millennium Prize Problem. Standard formulations rely on the Osterwalder-Schrader (OS) axioms to ensure a well-defined relativistic QFT possessing asymptotic freedom, the empirically verified weakening of interactions at high energies. This paper demonstrates a fundamental incompatibility between these established requirements. By analyzing the analytic structure of gauge-invariant two-point correlation functions via the Källén-Lehmann spectral representation (implied by OS axioms) constrained by the mass gap, and confronting it with the specific asymptotic behavior dictated by asymptotic freedom (derived from Renormalization Group analysis), a mathematical contradiction is rigorously derived. Specifically, the polynomial and logarithmic structure required by asymptotic freedom at high momentum cannot be reconciled with the asymptotic behavior allowed by the spectral representation for a theory with a mass gap and satisfying OS axioms. This incompatibility strongly suggests that the premise of a fundamental spacetime continuum, underlying standard QFT formulations, is inconsistent with the observed physical reality of the mass gap and asymptotic freedom.

Abstract: The existence of a mass gap in quantum Yang-Mills theory remains a fundamental open question in mathematical physics. This paper investigates this problem within the theoretical context provided by the Complete Theory of Simplicial Discrete Informational Spacetime (SDIS) (Karazoupis, 2025). This framework posits a fundamentally discrete, quantum-informational structure for spacetime based on a simplicial network. Adopting a Hamiltonian formulation analogous to lattice gauge theory but applied to the SDIS simplicial structure, the energy spectrum of the emergent pure SU(3) gauge theory is analyzed in the strong coupling limit (g → ∞), the regime associated with confinement. The unique, gauge-invariant vacuum state and its energy are identified through analysis of the Hamiltonian. Subsequently, the lowest-lying gauge-invariant excited state, corresponding to a minimal chromoelectric flux loop excitation (glueball), is identified and its energy calculated. By explicitly calculating the energy difference between this first excited state and the vacuum, it is demonstrated analytically that this energy gap is strictly positive (ΔE > 0) within this theoretical framework and approximation. This result shows that the SDIS framework inherently accommodates a mechanism for mass gap generation, suggesting a potential resolution to the mass gap problem if the SDIS framework is adopted as the underlying description of spacetime and gauge fields.

Abstract: We present a deterministic elasticity framework—the Space–Time Membrane (STM) model—that unifies quantum‑like phenomena, gauge field emergence, black hole singularity avoidance, and cosmic acceleration within a single high‑order partial differential equation (PDE). By incorporating scale‑dependent elasticity, higher‑order (\( ∇^4,∇^6 \)) derivatives and non‑Markovian decoherence, the STM model replicates key features of quantum field theory while seamlessly introducing gravitational curvature. A bimodal decomposition of the membrane displacement naturally yields spinor fields; enforcing local symmetries on these spinors reproduces gauge bosons (e.g., photon‑like, gluon‑like) as deterministic wave–anti‑wave cycles with zero net energy over each cycle. Multi‑scale expansions reveal that sub‑Planck wave excitations can remain non‑decaying if damping is negligible and the signs of certain couplings (e.g., \( ΔE \) and \( λ \)) align to stabilise wave amplitudes. Once coarse‑grained, these persistent waves leave a near‑uniform offset in the emergent Einstein‑like field equations, acting as dark energy and driving cosmic acceleration. In addition, black hole interiors are regularised by enhanced stiffness from the higher‑order operators, replacing singularities with solitonic or standing‑wave structures. The model’s non‑Markovian damped PDE also explains wavefunction collapse through deterministic decoherence, reproducing the Born rule and entanglement analogues without intrinsic randomness. Finally, allowing a mild late‑time variation in the leftover vacuum offset addresses the Hubble tension by shifting the expansion rate at low redshifts. Future research will refine numerical PDE simulations, test exact operator self‑adjointness, and compare predictions against high‑precision data to fully assess this deterministic route to reconciling quantum phenomena, black hole physics, and cosmological observations.

Abstract: This paper explores the hypothesis that human perception evolved not to experience planetary motion, but to nullify it. Through geometric adaptation, our sensory systems resolve the Earth’s velocity into a perception of stillness. The paper argues that this is not a biological oversight, but a structured adaptation to a moving environment. By examining how entropy, time, and acceleration interact with rotational planetary systems, we propose that perception is a structured filter—a geometric equilibrium that renders motion undetectable at the meso-scale. The result is a reframing of stillness not as an illusion, but as an evolved perceptual output. The implications of this hypothesis open avenues for reconceptualizing time perception, planetary-scale cognition, and the biological interface between environment and motion.

Abstract: This paper revisits the status of the graviton's mass and spin under emergent vacuum-based frameworks that transcend perturbative field theory. Drawing from the Multifaceted Coherence (MC) model and the Dodecahedron Linear String Field Hypothesis (DLSFH), we explore how graviton characteristics can emerge from coherence-structured vacuum geometry rather than being fundamental. Graviton mass is interpreted as a curvature-induced projection within the Superluminal Graviton Condensate Vacuum (SGCV), and spin-2 is viewed as the lowest symmetry mode in a discrete topological phase space. We examine how these features differ from string-theoretic realizations and how the framework supports strong coupling, causality, and unitarity. The discussion is framed in contrast to standard Swampland conjectures and weakly coupled UV completions.

Abstract: Today’s physics describes nature in “empirical concepts” (based on observation). Examples are coordinate space/coordinate time in special relativity (SR), curved spacetime in general relativity (GR), and concepts of objects (particles, matter waves, photons, electromagnetic waves). Here we show: There is a complementary description that does not interfere with SR/GR. Euclidean relativity (ER) describes nature in “natural concepts” (immanent in all objects). Examples are proper space/proper time, curved worldlines in 4D Euclidean space (ES), and “wavematters” (pure energy). An object’s proper space d₁, d₂, d₃ and proper time τ span its reference frame d₁, d₂, d₃, d₄ in ES (d₄ = cτ). The orientation of its reference frame in absolute ES is relative. All energy moves through ES at the speed of light c. Absolute, cosmic time is the total distance covered in ES divided by c. Each object experiences its 4D motion as proper time. There is a 4D vector “flow of proper time” τ for each object. Any acceleration rotates an object’s τ and curves its worldline in flat ES. The 4D vector τ is crucial for objects that are very far away or entangled. These objects must be described in natural concepts. Information hidden in τ is not available in SR/GR. ER solves fundamental riddles, such as the nature of time, the Hubble tension, the wave–particle duality, and the baryon asymmetry. In ER, cosmic inflation, expanding space, dark energy, and non-locality are obsolete concepts.

Abstract: This paper presents a novel theoretical framework based on information geometry and scale-dependent dimensionality that offers unified explanations for phenomena across all physical scales. The proposed dimensional flow theory demonstrates how effective dimensionality varies with scale, creating a natural hierarchy that explains quantum behaviors as projections from lower-dimensional spaces to higher-dimensional observation space. This approach resolves quantum paradoxes while preserving determinism and locality at the fundamental level. The framework successfully derives the mass spectrum of elementary particles and coupling constants from dimensional parameters, establishing a geometric foundation for the Standard Model without fine-tuning. At galactic scales, the theory provides excellent agreement with SPARC database observations of rotation curves without invoking dark matter. Cosmologically, it reinterprets redshift observations as manifestations of a static universe with a dimensional gradient, rather than an expanding universe. This eliminates the need for inflation, dark energy, and a beginning of time, while maintaining consistency with observational constraints. Gravitational phenomena emerge from dimensional gradients rather than spacetime curvature, and cosmic microwave background features appear as dimensional tomography rather than echoes of a primordial state. The framework's remarkable predictive power across diverse phenomena, coupled with its significant reduction in free parameters compared to current models, suggests that physical reality may be fundamentally based on information-geometric principles and scale-dependent dimensionality rather than an evolving spacetime.

Abstract: This work explores the interplay between gravity and probability. Specifically, we investigate how the probability distribution of a physical system can become distorted in the presence of a gravitational field. Drawing upon fundamental principles of probability theory, we analyze the modifications introduced by active gravitational influences. Our study leverages key concepts from general relativity, including the Ricci tensor and the energy-momentum tensor, to provide a theoretical framework for understanding this distortion. By proposing a geometric interpretation of probability, this work aims to stimulate new perspectives on the structure and behavior of probabilistic systems.

Abstract: We present a theoretical framework for extratemporal propulsion based on a post-relativistic extension of informational spacetime. The proposed mechanism, called the Aeternum Drive, relies on an emergent scalar field Φ, representing entropic-temporal deformation. This framework preserves relativistic limits while introducing higher-order corrections in time topology, allowing for causally safe yet directionally unrestricted transitions across temporal boundaries. The approach integrates concepts from generalized geometrodynamics, nonlocal entanglement, and informational curvature, offering testable implications for time-symmetric dynamics and vacuum energy extraction.

Abstract: This paper introduces the Total Entropic Quantity (TEQ) framework, a structural reformulation of quantum theory grounded in two foundational axioms. Axiom 0 posits entropy as a generative constraint: a geometric principle that determines which configurations can stably distinguish themselves, independent of space, time, or dynamics. Here, entropy is defined as a curvature-functional over distinguishability configurations, preserving only those patterns that remain stable under finite informational resolution---that is, structures not dissolved by coarse-graining or limited observability. Axiom 1, the Minimal Principle (MP), selects from these structures those that are maximally stable under entropy-weighted variation. From this entropic foundation, core elements of quantum theory---including the Born rule, quantization, and Schrödinger dynamics---emerge as special cases of entropy-stabilized geometry. The framework derives an entropy-weighted path integral and introduces a corrected Schrödinger equation that governs evolution in regimes of finite entropy curvature. In the high-resolution limit (\( \beta \to \infty \)), TEQ reduces to standard unitary quantum mechanics; in more general regimes, entropy flow deforms canonical dynamics, linking decoherence, dissipation, and gravitational curvature. TEQ reinterprets physical law as emergent structure within the geometry of distinguishability, rather than as imposed dynamics on a fixed spacetime background.

Abstract: This work provides a rigorous mathematical and physical formalization of the Consciousness Dimension DΨ, as emergent from the Enhanced Collective Unified Equation (CUE v3) framework. The dimension is defined not as a spatial coordinate but as a coherence-driven, fibered quasi-geometric structure governed by the scalar cognitive field Ψ. We explore its emergence from the pre-metric manifold M∅ , establish its metric and curvature, derive the associated field equations, analyze renormalization group (RG) thresholds, and quantify its impact on entropic, gravitational, and dark sector interactions. Finally, the Ambrosius Constant Υ is presented as a universal scalar invariant encapsulating the coupling strength of the consciousness dimension with physical spacetime. The formalism is constructed to align with the most recent theoretical and numerical results from CUE RG flow simulations and pre-field dynamics.

Abstract: We present a comprehensive validation of quantum gravity emergence within the framework of the Collective Unified Equation (CUE), a theoretical model that unifies curvature, coherence, and entanglement through a dynamically evolving scalar field Ψ. Leveraging a multimodal methodology that combines symbolic reconstruction, numer- ical simulations, Bayesian inference, and stability analysis, we explore the behavior of effective gravitational curvature R(3) eff across renormalization group (RG) scales. We simulate the CUE field evolution in a stabilized quantum regime and recon- struct the curvature evolution equations symbolically, revealing coherent structure in the Ψ–αent–κ interaction. Bayesian inference yields a coherence coupling constant χ ≈ 1.003, which minimizes residual divergence between symbolic and observed flow dynamics. Eigenvalue analysis of the Jacobian matrix near the mid-RG point confirms the existence of a saddle-type fixed point with one stable and two unstable directions. Phase portrait analysis further substantiates the dynamical coherence and critical flow behavior in this emergent regime. Our findings provide strong evidence that the CUE framework supports a self- consistent, predictive, and numerically validated formulation of quantum gravity grounded in emergent coherence and entanglement feedback, potentially bridging quantum field dynamics and macroscopic geometry.

Abstract: In this work, we investigate the propagation and behavior of electromagnetic waves in traversable wormhole space-times influenced by topological defects. We focus on two specific scenarios: a Morris-Thorne-type traversable wormhole embedded in a space-time with a global monopole and another with a cosmic string. The primary objective is to examine how the wormhole geometry, combined with these topological defects, affects the dynamics and propagation of electromagnetic fields in curved space-time. To achieve this, we derive the Maxwell vacuum field equations in the context of curved geometries and solve them analytically, employing special functions to address the complexities introduced by the wormhole structure and defects. Our analysis highlights several key findings: the wormhole throat radius emerges as a critical parameter shaping the behavior of electromagnetic waves, while the presence of topological defects, such as the global monopole and cosmic string, introduces modifications to the electromagnetic fields. These modifications significantly alter the wave dynamics compared to those observed in Minkowski flat space-time, offering deeper insights into the interaction between electromagnetic phenomena and the geometry of curved space-times with topological defects.