Abstract: What does “Big Bang” actually mean? What was the origin of these two words? It has often been said that the expression “Big Bang” began as an insult. Even if this were true, it would be just an irrelevant part of the whole issue. There are many more as-pects hidden under this name, and which are seldom explained. They will be discussed in this work. In order to frame the analysis, help will be sought from the highly au-thoritative voices of two exceptional writers: William Shakespeare and Umberto Eco. Both Shakespeare and Eco have explored the tension existing between words and the realities they name. With the conclusion that names are, in general, just labels, simple stickers put to identify things. And this includes those given to great theorems or spectacular discoveries. Not even “Pythagoras’ theorem” was discovered by Pythago-ras, as is now well-known. Stigler's law of eponymy is recalled to further substantiate those statements. These points will be at the heart of the investigation carried out here, concerning the very important concept of “Big Bang”. Everybody thinks to know what “the Big Bang” is, but only very few do know it, in fact. When Fred Hoyle first pro-nounced these two words together, on a BBC radio program, listeners were actually left with the false image that Hoyle was trying to destroy. That is, the tremendous ex-plosion of Lemaître’s primeval atom (or cosmic egg), which scattered all its enormous matter and energy content throughout the rest of the Universe. This image is abso-lutely wrong! As will be concluded, today the label “Big Bang” is used in several dif-ferent contexts: (a) the Big Bang Singularity; (b) as the equivalent of cosmic inflation; (c) speaking of the Big Bang cosmological model; (d) to name a very popular TV pro-gram; and more.

Abstract: Boltzmann entropy is the central measure of microscopic disorder in thermodynamics, but it does not describe how open systems develop and maintain long-lived structure. Stars, planets, biospheres, and civilizations all undergo irreversible changes in regulation, coherence, and stability over time. These developmental paths are not captured by microstate multiplicity alone. This article introduces a complementary macrodynamic quantity, the structural production rate, defined as the time derivative of a ripeness state that combines internal energy flow, structural memory, regenerative capacity, and systemic coherence. The sign of this rate identifies three universal phases across scales: maturation, stability, and reconfiguration. The study formalizes a ripeness function for four domains: stellar evolution, planetary habitability, biospheric stability, and civilizational dynamics. Each component is mapped to measurable proxies, such as stellar oscillation properties, crustal recycling rates, genomic redundancy, and institutional memory indices. From this, the paper derived falsifiable predictions that can be tested with current and upcoming missions and datasets, including space-based asteroseismology, ice-moon plume chemistry, paleogenomic reconstructions, and long-term social coherence indices. In this framing, entropy does not merely represent disorder. Instead, it defines the gradient that forces systems to develop, stabilize, and eventually reconfigure under persistent energy flow. The structural production framework provides a unified quantitative lens for comparative systems science and cross-domain prediction.

Abstract: This paper separately analyzes the thermodynamic processes of adiabatic superconducting phase transition in superconductors and adiabatic Curie phase transition in ferromagnets in magnetic fields. Through analysis, it is concluded that for an object undergoing a phase transition cycle, when the accumulated magnetization work is zero, the overall internal energy of the adiabatic phase transition system is conserved. However, in the model, the accumulated mechanical work done on the permanent magnet is not zero, which leads to non-conservation of energy in the model, contradicting the law of conservation of energy. This indicates that the law of conservation of energy also has exceptions and is not absolute.

Abstract: This work presents a discrete theoretical model in which basal metabolic rate B is described as a dynamic function of an organism’s ontogenetic stage n. Instead of treating B only as a static function of body mass M, we adopt the form B(n) = B₀ M^b(n), in which the effective scaling exponent b(n) varies systematically throughout development. In contrast to classical approaches, such as Kleiber’s empirical law (B ∝ M^3/4) and the continuous fractal model of West–Brown–Enquist (WBE), which assume a constant exponent, the present framework emphasizes how the metabolic scaling relationship itself can evolve over the life cycle of a single individual. The model is inspired by a Fibonacci-based description of growth in discrete stages, leading to analytic expressions for b(n) that connect ontogenetic progression to changes in the scaling between metabolism and mass. In this setting, Kleiber’s constant B₀ ≈ 70 kcal/day is reinterpreted as a metabolic anchoring point, linking the classical law B ≈ 70 M^3/4 to a developmentally explicit formulation. We show that the resulting trajectory B(n) captures, at a conceptual level, how metabolic scaling can shift from strongly sublinear behavior at early stages towards an almost linear regime as n increases, and that the predicted basal rates remain compatible, in order of magnitude, with values reported for mammals of different sizes. In this way, the work offers a unified framework that connects the evolution of B(n) across ontogeny to the recursive organization of biological growth.

Abstract: We develop a two–level model of ultralight dark matter (ULDM) solitonic core subjected to the adiabatic perturbation due to the baryonic matter. Approximation the dark matter–only core as a Gaussian ground state in a harmonic potential defined by the central core density, and the first radial s–wave excitation (n = 1, l = 0) we project the GPP system onto 2-dimensional Hilbert space. In our formalism, we show that the baryonic Dhenen γ component couples through the overlap integral J_ij .(γ, α) where α = Rc/ab is the ratio of the soliton core radius to the baryon scale radius. The resulting core dynamics is governed by the relative Hamiltonian H_rel(t) = 1/2 ∆(t)σ_z + J(t)σ_x with baryon dependent level splitting ∆(t) and mixing J(t), both linear in enclosed baryonic mass. In the adiabatic limit the soliton follows instantaneous lower eigenstate leading to radial excitation controlled by J_ij (γ, α). We illustrate the predictions using a model dwarf–like galaxy to illustrate the resulting gap and mixing angle between the two states of the model. In (Part–II) companion paper we will consider higher number of excited states and also use this framework with real dwarf spheroidal galaxies, using observed baryonic profiles and stellar kinematics to study the baryon induced shifts in the core radius and infer other ULDM parameters including the dark matter particle mass. We will also study Gaffe–like(γ → 2) distribution model as a limiting case in the Dehnen-γ baryon distribution.

Abstract: The standard relativistic ontology treats time as an additional coordinate in a four-dimensional space-time manifold. Since Minkowski's 1908 formulation, ``dimension'' has been tacitly identified with ``vector direction in a manifold'', and the temporal coordinate has been assimilated into that vectorial catalogue. This move proved mathematically powerful but ontologically misleading. In this article I argue, within the Timeless Counterspace \& Shadow Gravity---SEQUENTION (TCGS--SEQUENTION) framework, that identifying time with a geometric dimension is a \emph{category error}. ``Time'' is a foliation parameter, a gauge label on a family of admissible projections of a single four-dimensional counterspace; it cannot be a dimension on the same footing as the geometric directions of that counterspace. Conversely, the fourth dimension in TCGS is not temporal but \emph{counter-spatial}: a geometric structure of informational content, populated by singularities and extrinsic relations, whose projections generate the three-dimensional (3-D) shadow we call the physical world.I first analyse the ``Minkowski trap'': the historical path by which the success of tensor calculus turned the coordinate index $x^0$ into a surrogate for ontic time, and ``dimension'' into a purely algebraic notion. I show how this trap is reproduced, rather than avoided, in more recent multi-dimensional proposals, including $(1+3)$-dimensional ``three-dimensional time'' models. I then develop the TCGS--SEQUENTION alternative: a static four-dimensional counterspace $(\Csp,\gbulk,\PsiField)$ containing the full content of all so-called ``time stages'', and an embedded shadow manifold $(\Sshadow,\gshadow)$ obtained via an immersion $\Xmap:\Sshadow\to\Csp$, with observables given by pullbacks $(\gshadow,\psi)=\Xmap^*(\gbulk,\PsiField)$. Within this ontology, time is a foliation artifact---a parameter labelling a one-parameter family of embeddings $\Xmap_\lambda$---and all genuine dynamics are recast as consistency conditions between slices.Using the Baierlein--Sharp--Wheeler (BSW) action and subsequent constraint analyses, I demonstrate how General Relativity (GR) can be reconstructed without ontic time, thereby disentangling its empirical success from the Minkowskian ontology. I then show how the same projection geometry, equipped with a single extrinsic constitutive law, accounts for dark-matter phenomenology, cosmological anisotropies, and the biological homology encapsulated in SEQUENTION, without invoking dark sectors or stochastic deep time. Finally, I contrast counter-spatial dimensionality with ``3-D time'' and argue that any vectorial treatment of time---even with multiple temporal axes---remains trapped in the same categorical mistake: it re-labels the coordinates instead of changing the ontology. In TCGS--SEQUENTION, there is no temporal dimension at all; the only fundamental dimension beyond the familiar three is geometric and informational, not temporal.

Abstract: Traffic congestion is a complex phenomenon that displays wave-like behavior where even a clear road can be disrupted by the actions of a single driver, causing the formation of stop-and-go waves. Studying these unprecedented hurdles is necessary to understand traffic dynamics, improve AI-based traffic management systems, and enhance overall efficiency in transportation. This study analyzes data that uses real-world highway traffic at an urban city using METR-LA sensor data and NGSIM vehicle trajectories to compute stop-and-go wave propagation. Looking at each car, the speeds and distances between vehicles are analyzed with the principles of statistical mechanics, revealing regular patterns in collective traffic behavior. Speed variations in car platoons tend to grow as they spread in a non-linear fashion, just like chaotic dynamics found in other complex systems (“Butterfly effect”). The results, combining wave theory and statistical mechanics to understand and model the traffic, provide meaningful information that could help both traffic management and future physics-based studies of the same or similar complex systems.

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:

We validate, through an example, the direct correspondence between the irreversibility of renormalization-group (RG) flow and entropy production thermodynamics imposed by Newell. Using the local RG framework of Osborn and Jack, we identify a scheme-invariant potential \( \tilde a(\mathbf g) \) and a positive-definite tensor \( \chi_{ij} \) satisfying an exact gradient formula, \( \partial_i\tilde a=\chi_{(ij)}\beta^j \). Mapping this structure onto the GENERIC formalism of Grmela and Öttinger reveals that RG evolution is a purely dissipative process in coupling space, governed by \( \dot g^i=M^{ij}\partial_j S \) with \( S=-\tilde a \). Numerical integration of a three-coupling gauge--Yukawa model confirms a strictly monotonic \( \tilde a(\sigma) \), verifying \( \dot{\tilde a}=\beta^i\chi_{ij}\beta^j\!\ge\!0 \) to machine precision. The result validates the thermodynamic interpretation of the four-dimensional a-theorem and confirms the imposed validity of RG irreversibility, validating the Newell's framework thermodynamics integration.

Abstract: This paper proposes a novel unified physical theory, the Xuan-Liang theory, which resolves three major challenges in modern physics through geometric-topological unification [3][5]: (1) Dark matter effects originate from velocity-curvature topological coupling; (2) Cosmic inflation and late-time accelerated expansion are unified via dynamic Euler characteristic evolution; (3) The black hole information paradox is resolved through holographic Xuan-Liang flux quantization. Compared to string theory (28+ parameters) and loop quantum gravity (complex discrete geometry), this theory requires only three fundamental constants to achieve mathematical simplicity (∼1/10 complexity) and experimental verifiability (explicit predictions for gravitational wave polarization modifications), providing a potential framework for next-generation physical paradigms.

Abstract: The double slit experiment is usually presented as a paradoxical manifestation of “wave–particle duality”: a single physical system appears to display mutually exclusive properties, depending on the measurementcontext. In this article I argue that, once one adopts the TCGS–SEQUENTIONontology— a static four-dimensional (4-D) counterspace C whose three-dimensional (3-D) shadows Σ are generated by an immersion X — the double slit is not a paradox but a geometric theorem. Complementarity becomes a necessary consequence of projection geometry rather than a mysterious axiom of quantum theory. Within this framework, “wave” and “particle” descriptions are incompatible 3-D silhouettes of a single 4-D structure anchored on a singular set S ⊂ C; they cannot coexist on any one shadow, but they coexist without tension in the counterspace. Building on the TCGS axioms for gravity and biology, and on the analysis of time as a foliation gauge rather than a dimension, I formulate a Cartographic Exclusion Principle: whenever a physical system admits two fully consistent but mutually exclusive descriptions in the same 3-D manifold, the data signal an embedding into a higher-dimensional content space. I then apply this principle to quantum interference. Using two recent experiments as empirical anchors — a tunable Einstein–Bohr recoiling-slit realization at the quantum limit, and measurements of coherent vs. incoherent light scattering by single-atom wavepackets — I show that the observed visibility–which-path trade-offs are best interpreted as changes in the rigidity of the projection X, not as a system that “sometimes is a wave and sometimes is a particle”. The analysis closes a logical loop in the TCGS–SEQUENTIONprogram. Earlier work demonstrated that dark matter and Darwinian chance can both be reinterpreted as projection artifacts of a single 4-D counterspace. Here I argue that quantum complementarity belongs to the same family: it is the quantum-scale expression of the same geometric constraint that shapes cosmological cartography and biological evolution. Under mild assumptions, the double slit experiment thus functions as a topological proof that our 3-D world is a shadow of a 4-D counterspace, and that time is a foliation parameter rather than a fundamental dimension.

Abstract: This paper presents a conservative, causal, nonlocal extension of General Relativity in which the dark sector emerges not from new particles or a fundamental cosmological constant, but from geometric memory: a history-dependent contribution to the stress--energy tensor. The action includes a covariant nonlocal functional \( S_{\mathrm{mem}} \) that couples curvature at separated spacetime points through a retarded, causal kernel \( U(\sigma) \)built from Synge's world function. This implements the principle that spacetime retains a weighted record of its past curvature configurations. Varying the full action yields modified Einstein equations \( G_{\mu\nu} = 8\pi G\bigl(T_{\mu\nu} + M_{\mu\nu}[g]\bigr) \), where the Einstein tensor is unchanged and all novel physics is confined to a new, covariantly conserved memory tensor \( M_{\mu\nu} \) that introduces no additional propagating gravitational degrees of freedom or ghosts, so the kinetic structure of GR is fully preserved. In a cosmological background, the memory contribution acts as an effective dark energy component with \( w_M(z) \approx -1 + \mathcal{O}\!\bigl(1/(H_0 \tau_c)\bigr) \) and present–day density \( \rho_M(t_0) \approx \lambda\, \alpha\, H_0^2 \). Here \( \alpha \sim 10^3$--$10^4 \) is sourced by the nonlinear growth of Weyl curvature, and \( \lambda \sim 10^{-4} \)–\( 10^{-2} \) is a single small coupling. Together, these produce the observed dark--energy scale without fine–tuning, turning the coincidence problem into a natural consequence of cosmological–scale memory. Perturbations of \( M_{\mu\nu} \) supply an effective dark–matter–like component whose clustering is tied to tidal history rather than instantaneous density, yielding specific deviations from \( \Lambda \)CDM such as suppressed \( S_8 \). Because the field equations are of Volterra type, solutions require an initial history segment rather than a single initial state, and spatial variations in this primordial history generate persistent anisotropies in \( M_{\mu\nu} \), providing a controlled geometric mechanism for large–angle CMB anomalies and Hubble–dipole signatures that reframes them as fossil information rather than statistical outliers. The framework yields explicit, quantitative falsification criteria, including measurable evolution in \( w_M(z) \), definite suppression in \( S_8 \), enhanced lensing around cosmic voids, and characteristic CMB–large–scale–structure phase correlations. The model is deliberately brittle: a single decisive failure in any of these predictions rules it out, while success would establish causal structural memory as a minimal, testable route to unifying dark–energy and dark–matter phenomenology without modifying the kinetic structure of Einstein's theory.

Abstract: Contemporary theories of consciousness are fractured between three incompatible ontologies. Quantum proposals such as Penrose--Hameroff's Orchestrated Objective Reduction (Orch–OR) treat conscious episodes as gravitationally induced state reductions in tubulin superpositions. Harmonic-field models describe consciousness as a macroscopic interference pattern in a continuous field over the cortex. Dynamical-systems neuroscience, in turn, locates affective ``internal states'' in low-dimensional attractor manifolds embedded in high-dimensional hypothalamic activity. None of these programmes, however, resolves the deeper ontological tension: all three are written as temporal dynamics on a 3-D brain, whereas their own mathematics quietly presupposes a static, higher-dimensional content.In this paper I embed these three families of models inside the Timeless Counterspace & Shadow Gravity—SEQUENTION (TCGS–SEQUENTION) framework. Time is treated as a foliation artefact: there exists a single four-dimensional counterspace (C, \( G_{AB},\Psi \)) containing the full content of all so-called "time stages'', while the observable neurobiological world is a 3-D shadow manifold obtained by an immersion X: Σ<sub>bio</sub> → C. Apparent evolution of brain states is not ontic dynamics but the comparison between admissible projections of one static whole.The main result is a 4-layer vertical architecture that harmonizes quantum, neurogeometric, and harmonic-field descriptions without relinquishing the identity-of-source axiom of TCGS--SEQUENTION. At Layer 1, Penrose's E<sub>G</sub> is reinterpreted as a static geometric functional on C, not a time-dependent collapse trigger. At Layer 2, a symplectic resolution limit transforms E<sub>G</sub> into an effective action for q-desics---quantum generalizations of geodesics---in the sense of Koch et al., now embedded in the same counterspace. At Layer 3, a Diophantine filter selects a discrete, φ-scaled spectrum of microtubular eigenmodes constrained by the TCGS constitutive law. At Layer 4, the macroscopic harmonic field and cortical gamma synchrony are recognized as Moiré interference patterns in the projection geometry, not ontic wave-objects in the brain.By eliminating ontic time and enforcing a single 4-D source manifold, we show that: (i) the Orch--OR threshold becomes a gauge choice of foliation rather than a physical "moment"; (ii) the Harmonic Field Model is a 3-D shadow of a static interference structure on C; and (iii) hypothalamic line attractors are geometric corridors in the same projection class that governs galaxy-scale anomalies in TCGS cosmology. Consciousness, in this framework, is the registration of a slice-invariant content on a 3-D shadow whose degrees of freedom are geometrically constrained, not locally generated. The hard problem is therefore not ``how matter generates experience'', but how a single timeless content field projects as both physics and biology under the same extrinsic law.

Abstract: Based on the principle of constant speed of light and the principle of minimum energy, this paper constructs a theoretical system of vacuum dynamics, revealing a complete physical causal chain: "light speed gradient → rest energy difference → spontaneous force → spontaneous motion". The core dynamic equation is derived as . Applying this theory to the study of gravitational mechanisms, we successfully deduce Newton's gravitational expression from the light speed distribution function, achieving the unification of the mathematical form and physical mechanism of gravity at the level of energy conversion mechanism for the first time. This research not only provides a novel dynamic perspective for analyzing the physical origin of gravity but also verifies the feasibility of propellantless propulsion technology in vacuum in principle.

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: We show that the Zitterbewegung of the electron arises as a real internal motion when spin is treated as a classical bivector rather than as a point-fermion of the Dirac equation. In the Bivector Standard Model, physically meaningful dynamics reside in the body-fixed frame where two orthogonal internal angular momentum vectors counter-precess about a torque axis. Their rigid rotation generates a time-dependent chord whose magnitude oscillates at twice the Compton frequency, 2ω_C, and whose orientation precesses at ω_C. When projected into the laboratory-fixed frame, this internal rotor produces the characteristic trembling motion of the Zitterbewegung and traces a horn torus envelope without additional assumptions. The internal clock defined by this cyclic bivector motion unifies the origin of spin properties and the de Broglie modulation. It distinguishes complementary parity sectors that cannot be related by Lorentz transformations. The Zitterbewegung is therefore not an interference between positive- and negative-energy spinors, but the visible shadow of a real, energy-conserving internal rotation inherent to the bivector structure.

Abstract:

The current \( 5\sigma \) discrepancy between the CMB–inferred value of the Hubble parameter \( H_{0}^{\mathrm{CMB}} \)and local measurements \( H_{0}^{\mathrm{local}} \) represents one of the most persistent tensions in modern cosmology. A key element highlighted in the Special Issue Call is the emerging correlation between the inferred value of \( H_{0} \)and the redshift of the source. In this work we examine the possibility that this correlation originates not from new dynamical physics but from scale-dependent projection effects within the Supra-Omega Resonance Theory (SORT), a mathematically formulated, non-dynamical operator framework. SORT introduces two complementary projection sectors, \( \Pi_{\mathrm{early}} \) acting predominantly on long-wavelength modes (\( k \rightarrow 0 \)) and \( \Pi_{\mathrm{late}} \) acting on short-wavelength modes, encoded through a resonance kernel \( \kappa(k) \). The resulting Hubble drift arises from a weighted spectral integral of the amplification function \( \eta(k) = \kappa(k)-1 \), \( \delta_H \propto \int \eta(k)\, W_H(k)\, \mathrm{d}k \), where \( W_H(k) \) is the expansion-weighting window associated with distance–redshift estimators. Using the fully reproducible MOCK,v3 numerical framework, SORT yields a scale-dependent structural drift of \( \delta H/H_0 = 0.0800 \), close to the observed \( \delta H/H_0 = 0.0831 \), without introducing new fields, modifying general relativity, or invoking early dark energy. These results suggest that the Hubble tension may arise from k-dependent projections of one and the same underlying structural state, rather than from inconsistencies in late- or early-universe physics.

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: The cosmic microwave background is often taken as definitive evidence for universal expansion. No static framework has yet reproduced its exact blackbody spectrum under known physical conditions. This study extends the companion paper Redshift Without Expansion by applying a frequency-independent redshift mechanism within a Liouville formulation. The kinetic redshift operator preserves a perfect Planck spectrum, maintains μ = 0, and yields T ∝ K−1 with an identical temperature–redshift relation T (z) = T0(1 + z) consistent with measurements from COBE and FIRAS. Photon number and energy densities evolve as ˙nγ = −3Heff nγ and ˙ργ = −4Heff ργ , where Heff = ˙K/K represents an effective Hubble parameter without metric expansion. The result establishes an observational degeneracy between kinetic redshift and geometric expansion while predicting a measurable secular temperature drift ˙T /T = −Heff ≈ −2.3 ×10−18 s−1. The framework provides a static, falsifiable pathway for examining the cosmic microwave background without reliance on expanding-space assumptions. The redshift kernel emerges from scalar field relaxation dynamics ¨Φ + Γ( ˙Φ − ˙Φ∞) = 0, with coupling Heff = g ˙Φ reproducing the required CMB temperature scaling to illustrative ∼ 0.1% precision for the example parameter set, and predicting Heff (z = 1100) ≈ 281H0, testable via high-redshift measurements.

Abstract: Multiple wide–area radio surveys report a source–count dipole whose amplitude exceeds the purely kinematic expectation inferred from the CMB dipole by a factor of ∼ 3–4, while remaining aligned with the CMB dipole direction. This tension, now detected at ≳ 5σ when combining NVSS, RACS–low and LoTSS–DR2, challenges the vanilla ΛCDM picture in which the radio dipole is dominated by Doppler and aberration effects with only a small clustering contribution. In this paper we present a quantitative implementation of Future–Mass Projection (FMP) gravity as a potential explanation of this anomaly. FMP is a diffeomorphism–invariant, bilocal, time–nonlocal extension of GR in which the effective source is a causal projection of the baryonic energy–momentum tensor along a finite, advanced horizon on a closed time path. On cosmological scales the theory can be parametrised by a scale– and time–dependent modification of the Poisson equation, μ(a, k), and lensing response, G(a, k), that are determined by the Fourier transform of the covariant kernel. We make three key advances compared to previous work. First, we provide an explicit mapping from an “entropic” Newtonian kernel, defined as the Hessian of a coarse–grained entropy functional in the space of disc and large–scale density configurations, to the cosmological response functions μ(a, k) and G(a, k). This leads naturally to a two–lobe scale dependence, with μ(a, k) < 1 on quasi–linear scales k ∼ 0.02–0.2 hMpc⁻¹ and μ(a, k) > 1 on ultra–large scales k ≲ 0.01 hMpc⁻¹, thereby reconciling a modest 10–15% suppression of fσ8 with an ultra–large–scale growth boost. Second, we fix the kernel parameters (ΔT, η, k1, k0) using two independent data sets: low–redshift redshift–space distortion measurements of fσ8 and galaxy rotation curves. This yields a single family of CTP kernels that already satisfies Solar–System, PPN and GW– speed constraints, and mildly alleviates the S8 tension. Third, using these pre–determined kernels, we compute the ultra–large–scale clustering boost factor BULS that enters the radio source–count dipole. We model the selection function W(z) and linear bias b(z) for NVSS, RACS–low and LoTSS–DR2, and evaluate the relevant integrals for BULS(ΔT, η, k0), propagating uncertainties from the kernel parameters and the source populations. For the kernel that best fits fσ8 and rotation curves we obtain a blind prediction RFMP ≡ dobs/ dkin = 3.2 ± 0.4, to be compared with the combined radio–dipole measurement R_obs = 3.67 ± 0.49. A simple χ² comparison shows that the anomaly is naturally reproduced within FMP without invoking particle dark matter, while remaining consistent with current large–scale structure and background probes. We discuss degeneracies, parameter–space constraints and the status of competing explanations for the radio–dipole excess.