Physical Sciences

Abstract: The observable universe has always remained below its own gravitational radius—yet it is not the interior of a black hole. This apparent paradox, derivable from the Friedmann equations, suggests that three-dimensional space is not the fundamental level of physical description. In this work: (1) we derive the global gravitational constraint R_p ≲ R_g valid in every cosmic epoch; (2) we prove with a causal no-go theorem that this constraint does not imply a black hole-type geometry; (3) we show that, within standard physics, the resolution that survives the exclusion of alternatives is holographic: fundamental information resides on a two-dimensional boundary, while the interior volume is an emergent reconstruction. The ingredients of this argument—Friedmann cosmology, covariant entropy bounds, holographic counting—are individually well established. What has been missing is their systematic combination into a closed logical chain. If this chain were trivial, holographic cosmology would already be the dominant paradigm and inflation would be recognized as optional. It is not, which suggests the synthesis itself is the contribution. The framework dissolves what we call the “spacetime island” problem: in standard physics, coordinates are treated as primitives disconnected from the informational language of quantum theory and statistical mechanics. Holographic emergence reconnects them. Giving up one or two “fundamental” dimensions is a gain in parsimony and unification, not a loss. Observable consequences follow. The Gaussianity of the CMB emerges from the central limit theorem applied to boundary degrees of freedom. Primordial gravitational waves are expected to be strongly suppressed (r < 10⁻³); a robust detection at r > 10⁻² would falsify the minimal framework. Recent observations—the absence of predicted dark matter subhalos in high-resolution lensing, the anomalous pressure in cluster mergers—provide independent hints that the standard picture has cracks where this framework offers natural explanations.

Abstract: The standard cosmological model, ΛCDM, has been very successful as a model of the cosmos, but measurements increasingly show deviations from its predictions. There is no accepted model for the asymmetry between matter and antimatter; cosmic inflation requires superluminal expansion velocities, lacks a compelling mechanism for the expansion or for shutting off that expansion, and the predicted primordial gravity waves have not been detected; there is no accepted theory for what dark matter is or its properties; and the observation of orthogonal multipole axes and time-varying asymmetry in galaxy rotation are in conflict with the expected isotropy of the universe. A Big Bang model based on the concepts of spacetime duality and generalized time, along with CPT symmetry and dimensional symmetry between time and space, leads to a model of the early universe and dark matter that resolve these concerns. The model has time starting to flow in our universe when it has cooled sufficiently for the weak, strong, and electromagnetic forces to become distinct, which means it is then possible to distinguish between matter and antimatter, each of which flows in opposite directions of generalized time, resulting in a natural separation of matter into our universe and antimatter into a universe on the “other” side of the fabric of spacetime. The universes can interact gravitationally through the fabric of spacetime. Experiments have shown that there is a flow of time in quantum/relativistic systems which cannot be measured by an external, classical clock. This is the initial flow of time when matter and antimatter separate and quantum interactions dominate. The time flow in this quantum/relativistic direction means the superluminal expansion velocity in cosmic inflation is actually subluminal when measured in generalized time. The quantum state produces the homogeneity seen in the CMB, and energy considerations preclude magnetic monopoles from becoming entrained in the flow of time in our universe. If time has three dimensions symmetric with space, then six universes result from cooling after the Big Bang, with our universe as one of them. The other five universes explain the 5:1 ratio of dark matter to matter, and the two types of “dark universes”, three antimatter and two matter, explain how dark matter can be both compact in a galactic center and have a halo extending out from the galactic plane. CPT considerations explain the high rotation asymmetry of early galaxies, and subsequent gravitational interactions with the dark universes, which in aggregate have the opposite rotation asymmetry, explain why that asymmetry is decreasing with time. Those ongoing gravitational interactions with the dark universes explain why the observed multipole features in galaxy rotation are not observed in the CMB – those multipole features may require a significant amount of time to interact with the dark universes, and the CMB reflects an early time in our universe where those interactions would have been minimal. The model makes testable predictions for the amount of dark matter in dark matter halos, interacting dark matter halos, and galaxy rotation.

Abstract: We introduce a path-based curvature method for the gravitational bending of light in black-hole (BH) spacetimes. The construction is structurally distinct from the two standard routes. The deflection is not read off from an asymptotic comparison of incoming and outgoing geodesic directions (Bozza-Tsukamoto), and it is not a two-dimensional Gibbons-Werner Gauss-Bonnet (GB) surface integral. It is built instead as a one-dimensional line integral of the optical Gaussian curvature $\Kopt$ along the photon trajectory, weighted by a geometric kernel $W(r,b)$. The framework itself is generic in scope. The closed-form simplification $W=\sqrt{r^{2}-b^{2}}$ delivers the weak-field regime: it reproduces $\hat{\alpha}=4M/b$ for every static, asymptotically flat metric (Theorem~1), and the curvature integral evaluates analytically for Schwarzschild, Reissner-Nordström (RN), and equatorial Kerr. Effectiveness is quantified: agreement with the exact geodesic is $\sim 4\%$ at $b/M=100$ and degrades smoothly as $b$ approaches the photon-sphere edge, locating exactly where path-deformation corrections matter. The strong-deflection regime enters through a winding-sum continuation that maps onto the Bozza-Tsukamoto logarithm. Finite source-observer distances are handled through the Ono-Ishihara-Asada (OIA) construction. The deflection becomes a directly plottable cumulative quantity along the path, a feature both standard routes hide.

Abstract: We present a unified theoretical framework in which particle physics, gravity, and cosmology emerge from a common hypercomplex steering–spinor algebra. The theory is based on a sixteen-dimensional algebra generated by basis elements e₀,…,e₁₅, organized into five spinor sectors Γ, Θ, U, V, and W. Within this structure, the gauge interactions of the Standard Model arise naturally from spinor products: the electromagnetic interaction from the Γsector, the weak interaction from the Θsector, and the strong interaction from cross-sector couplings between Γand U. The three fermion generations correspond to the spinor sectors U, V, and W, providing a geometric interpretation of the generation structure. The electroweak mixing angle and the approximate mass ratio of the W and Z bosons follow from the normalization of the spinor sectors. A key feature of the framework is the non-associative structure of the algebra, whose associator generates corrections to the gravitational connection and curvature. In the weak-field limit this produces a Yukawa-type modification of the Newtonian potential that can reproduce flat galaxy rotation curves without invoking dark matter particles. The vacuum curvature of the spinor manifold yields an effective cosmological constant, providing a geometric origin for cosmic acceleration. The resulting cosmological dynamics reproduce the phenomenology of the ΛCDM model while introducing scale-dependent corrections that may help explain the observed Hubble tension. These results suggest that gauge interactions, gravity, and cosmological dynamics may arise from a common hypercomplex algebraic structure.

Abstract: We propose a unified theoretical framework for observed redshift phenomena in astrophysics, in which gravitational and cosmological contributions arise from distinct but coexisting physical mechanisms. In this model, the gravitational field itself carries an effective mass, leading to a nontrivial field–mass structure that naturally identifies halo mass with the gravitational field mass outside baryonic sources. Independently, a cosmological redshift mechanism is derived from a relativistic quantum treatment of coherent photon propagation through an effective medium, resulting in a nonlinear closed-form energy-loss law characterized by a single effective parameter with units of Hubble’s constant. Through the definition of redshift, these two mechanisms combine multiplicatively, yielding a mathematically consistent total-redshift expression. The framework provides a unified mapping between distance and redshift for both galaxies and quasars without assuming a single dominant redshift cause. The model is constructed from explicit assumptions grounded in relativistic field dynamics and quantum coherence, and its internal consistency is demonstrated through analytic solutions and calibrated examples. Although parameter calibration is used for illustration, it does not constitute empirical validation; the focus is on formal structure, logical coherence, and theoretical plausibility. The proposed framework serves as a basis for future observational tests and theoretical refinement, illustrating how alternative physical interpretations of redshift can be formulated within a consistent relativistic setting.

Abstract: This article is a clarification and admissibility paper within the Infinite Transformation Principle (ITP) and Cyclical Infinite Organic Universe (CIOU) program. It does not derive a quantum-gravity bounce, prove physical cyclic cosmology, claim observational confirmation of prior-cycle fossils, or replace branch-specific physical models. Its narrower purpose is to define what the terms "infinite", "organic", "cycle", "inheritance", and "ripeness" are allowed to mean once finite memory, finite saturation, and falsifiable branch projections are imposed. Infinite transformation is defined as non-final composition of finite, memory-bounded, saturating transformation sectors, not as infinite storage, exact recurrence, or immortality of form. Organicity is defined as structural admissibility for nested, disequilibrium-sustaining, memory-bearing systems, not as biological literalism or cosmic intention. Ripeness is introduced only as a candidate homeostatic-maturation weighting, not as a validated universal variable. The paper includes minimal synthetic tests of saturating growth, auxiliary-memory localization, finite cycle filtering, and filter-horizon sensitivity. These tests are internal consistency and null-separation checks; they are not empirical evidence for CIOU. Physical realization is deferred to branch-specific papers that must supply concrete transfer operators, data mappings, likelihoods, independent observables, and microphysical mechanisms. The resulting claim is deliberately limited: ITP is finite in every local model and infinite only in its refusal to treat any finite form as absolute finality.

Abstract: We discuss gravitational concepts and candidate dark-matter specifications that can help explain eras in the rate of expansion of the universe and known ratios of dark-matter effects to ordinary-matter effects. Regarding gravity, we deploy multipole-expansion methods that combine two-body Newtonian gravity, aspects of the motions of sub-objects of gravitationally interacting objects, and Lorentz invariance. We suggest, for example, how gravitational repulsion arises. Regarding dark matter, we reuse, with variations with respect to the masses of charged lepton elementary particles, the set of known elementary particles. An outgrowth from our work suggests relationships among some physics constants. As well as suggesting explanations for known data, we make predictions regarding future data.

Abstract:

Through this paper we analyze from first-principles, high-precision derivation of the spectral shape, characteristic amplitude, and unique observational signatures of the stochastic gravitational wave background (SGWB) generated during the primordial first-order topological phase transition that is a fundamental prediction of the Expanded Quantum String Theory with Gluonic Plasma (EQST-GP) framework. The transition corresponds to the spontaneous symmetry breaking \( SU(4) \to SU(3)_C \times U(1)_{\text{DM}} \) within the gluonic plasma confined to M5-brane world-volumes in the specific compactification geometry \( M_4 \times \text{CY}_3 \times S^1/\mathbb{Z}_2 \) with Euler characteristic \( \chi(\text{CY}_3) \approx -960 \). We move beyond generic parameterizations to perform a complete microphysical calculation. Starting from the finite-temperature effective potential for the symmetry-breaking scalar field \( \Phi \), where the coefficients \( D, T_0, E, \lambda \) in \( V_{\text{eff}}(\Phi, T) \approx D (T^2 - T_0^2) \Phi^2 - E T \Phi^3 + (\lambda/4) \Phi^4 \) are not free parameters but are explicitly computed from the underlying M-theory parameters: the M5-brane tension \( T_{M5} = (2\pi)^{-5} l_P^{-6} \), the volumes of the wrapped 2-cycles \( \text{Vol}(\Sigma_2) \), the stabilized values of the Kähler moduli $T_i$ from the KKLT-inspired potential \( V_{\text{up}}(\phi) \), and the thermal contributions of the confined \( SU(4) \) gluon degrees of freedom and the associated moduli fields. This derivation yields a highly specific set of phase transition parameters: a critical temperature \( T_c = 1.04^{+0.06}_{-0.05} \times 10^{16} \, \text{GeV} \), a nucleation temperature \( T_n = 0.971 \times 10^{16} \, \text{GeV} \) (corresponding to a Euclidean action \( S_3(T_n)/T_n = 138.2 \)), a transition strength parameter \( \alpha = 0.42 \pm 0.03 \) defined as the ratio of latent heat density to radiation energy density \( \alpha = \epsilon / \rho_{\text{rad}} \), and an inverse transition duration relative to Hubble \( \beta / H_* = 94.7 \). The bubble wall velocity \( v_w \), determined from the balance of the vacuum driving pressure against the friction from the strongly-coupled (2,0)-theory plasma on the M5-branes, is calculated to be \( v_w = 0.27 \, c \), characteristic of a deflagration mode. We then compute the gravitational wave spectrum \( \Omega_{\text{GW}}(f) h^2 \) from the three principal sources—scalar field bubble collisions \( (\Omega_\phi) \), sound waves in the post-collision plasma \( (\Omega_{\text{sw}}) \), and magnetohydrodynamic turbulence \( (\Omega_{\text{turb}}) \)—using the most advanced hydrodynamic simulations and envelope approximations, adapted for the specific relativistic degrees of freedom \( g_* = 187 \) of the EQST-GP plasma. The total spectrum exhibits a distinct, multi-peak fingerprint: a primary peak from sound waves at \( f_{\text{sw}} = 1.87 \times 10^{-3} \, \text{Hz} \) with amplitude \( \Omega_{\text{GW, sw}} h^2 = 6.31 \times 10^{-14} \), a secondary, broader peak from turbulence at \( f_{\text{turb}} \approx 3.2 \times 10^{-3} \, \text{Hz} \) with \( \Omega_{\text{GW, turb}} h^2 \approx 1.2 \times 10^{-14} \), and a high-frequency tail from bubble collisions. Crucially, we establish a detailed discrimination strategy demonstrating that the EQST-GP signal is distinguishable from inflationary tensor modes, cosmic string networks, and generic first-order phase transitions through multi-messenger consistency with predictions for ultra-heavy Majorana gluon dark matter, Hubble tension resolution, and fundamental constant derivation. We present a comprehensive detection blueprint for LISA, demonstrating that a signal-to-noise ratio $\text{SNR} > 8$ is achievable over a 4-year mission with optimal template-based analysis, and outline how cross-correlation with future CMB B-mode polarization measurements and 21-cm cosmology observations can further isolate this signal from astrophysical foregrounds.

Abstract: We investigate a possible connection between early central activity in galaxies and present-day large-scale stellar kinematics. Recent observations from the James Webb Space Telescope have revealed both a population of apparently massive galaxies at high redshift and compact luminous sources (“little red dots”, LRDs), challenging standard hierarchical formation scenarios. While the former suggest rapid early mass assembly, the latter are commonly interpreted as systems dominated by intense nuclear activity. At the same time, analysis of Gaia DR3 data reveals non-zero Galactocentric radial velocity components in the Milky Way, indicating large-scale non-equilibrium motions. We develop a phenomenological framework linking AGN-driven outflows, star formation, and stellar kinematics, in which stars form in dense clumps within multiphase outflows and inherit a small fraction of the outward velocity. Using characteristic values v_out∼10³kms⁻¹ and v_R∼1–10kms⁻¹, we derive a coupling factor f∼10⁻³–10⁻², consistent with Gaia DR3 observations. The model predicts star formation rates of 1–100M_⊙yr⁻¹ and growth timescales of 10⁷–10⁹yr, consistent with JWST constraints. Within this framework, LRDs may represent an early phase of centrally driven evolution, while present-day radial motions may reflect a long-term kinematic imprint of similar processes.

Abstract:

We present a mathematically rigorous formulation of the Fundamental Speed Theory (FST), a dimensionally consistent vector–tensor theory featuring a dimensionless vector field \( \nu^{\mu} \). We introduce characteristic scales \( L_0 = 10 \) kpc and \( M_0 = \hbar/(cL_0) \) and keep \( \hbar \) and \( c \) explicit throughout. In dimensionless form, the galactic field obeys

\( \frac{d^2\tilde{\nu}}{d\xi^2} + \frac{2}{\xi}\frac{d\tilde{\nu}}{d\xi} = \beta_{\mathrm{eff}}\tilde{\nu}^3 \),\( \qquad \beta_{\mathrm{eff}} \equiv -\frac{\lambda\nu_0^2}{6c_1} = 2.0\times 10^7 \ (\lambda<0). \)

We validate the theory on the SPARC sample using three primary hierarchical levels (Levels 1–3): Level 3 (zero free parameters) fits 65.7% of galaxies with mean \( \chi_{\nu}^{2}=0.809 \); Level 2 (estimated \( M, r_d \), no fitting) reaches 93.6% with mean \( \chi_{\nu}^{2}=0.347 \) for the 160 galaxies with \( \chi_{\nu}^2<3 \); and Level 1 (fitted \( M, r_d \)) fits all 171 galaxies with mean \( \chi_{\nu}^{2}=0.170 \) (91.2% with \( \chi_{\nu}^{2}<0.5 \)). We further report two derived formulations: Level 4 (coefficient-free) and Level 5 (unified), the latter showing that the field parameters unify into a single acceleration scale

\( A_0 = \frac{(c_1+c_3)\nu_0^2 c^2}{L_0} = 2.42\times 10^{-10}\ \mathrm{m/s^2}, \)

which reproduces the full formulation identically for all galaxies. A full three-dimensional numerical experiment with disk-like (anisotropic) boundary forcing confirms that the converged 3D field profiles and rotation-curve fits remain essentially unchanged relative to the 1D quasi-spherical approximation for the tested cases. We also perform an explicit sign-convention robustness check: running the full pipeline with the alternative (negative-sign) convention yields identical fits within numerical tolerance when implemented consistently. Solar System constraints are satisfied because the relevant acceleration arises from the galactic field gradient, giving a local FST acceleration at Earth of \( \sim 8\times 10^{-15} \) of the Newtonian value. All code is archived on Zenodo, and supplementary materials (including complete fit results and both sign-convention implementations) are provided. Extension of FST to cosmological scales is left as future work.

Abstract: We present a new cosmology model---the Eternal Universe Model (hereafter, EU-model)---that emerges from a subtle but consequential modification of the standard Friedmann--Lemaitre--Robertson--Walker (FLRW) framework. At first glance, the EU-model resembles the familiar ∧CDM concordance model; its departure, however, is philosophically and physically decisive: we relinquish the assumption of temporal homogeneity. Specifically, we allow the rate at which time progresses---encoded in the 00-component [g₀₀ = a²_t (r) c²₀ ] of the spacetime metric tensor---to vary systematically with radial position throughout the infinite expanse of the Universe. This single and seemingly banal alteration in the temporal architecture of spacetime gives rise to a remarkably new and rich cosmology. It introduces the continuous creation of matter and energy; it permits the variation of Fundamental Natural Constants (FNCs); it accommodates non-ponderable negative matter as a natural substrate for antimatter; and it endows the Universe with a fixed, absolute spatial centre from which all motion may be referenced. Furthermore, this framework offers natural explanations for the Hubble tension and the Cosmological Axis of Evil. The Universe that emerges is temporally and spatially infinite, globally unchanging, and truly eternal---with no beginning and no end.

Abstract: The Fermi Paradox (“Where is everybody?”) refers to the apparent contradiction between the visualisable abundance of extraterrestrial civilizations and the continued absence of confirmed detections. This work explores whether finite communicative lifetimes, combined with Galactic distance scales and the finite speed of light, can substantially suppress the probability of causal overlap between technological civilizations. Using a simplified stationary Galactic model (v = 0) within a Minkowski spacetime framework, technological civilizations are represented as finite world-line segments generating expanding “Information Shells” through electromagnetic signal propagation. Within this interpretation, successful detectability requires overlap between the communicative intervals of different civilizations in both space and time. For representative communicative lifetimes of order L ~ 10³ years, the effective causal reach of detectable signals remains small compared with typical interstellar separations expected in sparse-civilization scenarios. Using a heuristic overlap model, we estimate that for N = 100 contemporaneous civilizations distributed throughout the Milky Way, the effective causal-overlap probability remains below 1% . The analysis further considers long-term engineering limitations on autonomous probes and persistent signalling systems, including radiation damage, impact erosion, and power degradation, collectively described here as a “Hardware Filter.” In addition, the work distinguishes between the total biological lifetime of a civilization and its externally detectable communicative phase, suggesting that advanced civilizations may evolve toward increasingly low-leakage or radio-quiet technological states. Within this framework, the apparent “Great Silence” may emerge naturally from finite communicative windows, spacetime separation, and engineering constraints even if intelligent life itself is not intrinsically rare.

Abstract: Robust age measurements for isolated neutron stars (NSs) are not easily available. That is why, often the characteristic age τ_ch=P/2Ṗ is used as a proxy. Here P is the spin period of the NS and Ṗ is the time derivative of P. Additional assumptions related to the initial properties and spin-down evolution are made to derive τ_ch. As a result, it is expected that τ_ch is an upper limit for the real age τ_real. Recently, Chrimes et al. presented measurements of kinematic ages τ_kin for several magnetars. Surprisingly, for the majority of these sources τ_kin>τ_ch. We present a simple model including a realistic approximation for the magnetic field decay in magnetars and a simple phenomenological description of the field re-emergence after an episode of fallback after the birth of a NS. We demonstrate that this simple model can explain the observed relation τ_kin>τ_ch for realistic sets of parameters.

Abstract: Two geometrical problems of negative time metric and abuse of distance factors for angular coordinates and other two physical problems of revisit redshift and covariant acceleration were put forward to investigate the traditional frames of general relativity. It is found that sub-indexes of Christoffel symbols in gravitational fields are not really alterable. The concept of trajectory derivative was carried out to clarify the derivatives on motion trajectories which perform far from field derivatives. Calculations on trajectory derivatives of frequency shift and acceleration lead to conclusions that light speed keeps general covariance in gravitational fields but light energy momentum would not, may as well, the motions of massive matters in gravitational fields do not perform general covariance thoroughly. The conservativeness of light angular momentum has been discovered in most surprising forms, as well as that of massive matters. Renovated kinematic equations for light ray propagations and massive matter motions have been carried out that forcefully impact the traditional methodologies on solutions of trajectory and time spending. Dynamic models of fluid planet rings were founded to interpret the evolutions of accretions of quasars and active galactic nuclei. Consequently, the mechanism of relativistic release was raised up based on light speed covariance and energy conservation, although it has not been completely proved. But the equations on relativistic release and relativistic frequency shifts so far as the line widths of emission and absorption could be astonishingly verified in observations, especially on the predictions of the broad line regions and narrow line regions. It could be imagined that the spectrums of relativistic emission and absorption may have been involved with fantastic mystery of matter’s intrinsic structures that we know less.

Abstract: The ΛCDM cosmological model has been highly successful in describing the large-scale structure and evolution of the Universe, yet it continues to face persistent challenges, most notably the cosmological constant problem and the Hubble tension. Building upon a recently proposed conceptual framework, this work investigates the temporal evolution of the Universe’s total energy density and its constituent components—dark energy, matter, and radiation—under the assumptions that the Hubble parameter evolves inversely with cosmic time and that gravitationally repulsive dark energy remains in dynamical balance with attractive matter–radiation components. Within this framework, the Universe expands linearly with time and exhibits effective zero acceleration, sustained by a constant expectation value of an energy inflow rate attributed to gravity-driven vacuum energy fluctuations. Analytical results indicate that dark energy acts as a persistent energy reservoir, continuously supplying energy for the formation and evolution of matter and radiation throughout cosmic history. A simplified phenomenological description of the radiation–matter transition, while not derived from first principles, is shown to reproduce the broad thermal history of the Universe, yielding temperature estimates in good agreement with established cosmological epochs from the Planck era to the present day. Furthermore, the framework offers a potential pathway toward reconciling quantum field theory predictions of vacuum energy density with cosmological observations and provides a possible explanation for the unexpectedly rapid formation and maturity of early galaxies observed at high redshift. The analysis is further extended to a precritical, scale-dependent energetic regime, suggesting a unified balance principle operating across scales. The framework therefore provides a coherent phenomenological picture linking vacuum energetics, cosmic expansion, and early-Universe behavior, and offers a potential avenue toward addressing the cosmological constant problem.

Abstract: We introduce a new method of dimensional analysis based on complete systems of units, such as the metric and Planck systems, in which fundamental dimensionless constants arise naturally. In fact, it is the reformulated Planck system that communicates its dimensionless constants to the metric or any other system. The method reveals additional complex dynamical scales and physical effects beyond those amenable to conventional dimensional analysis. We formulate our strategy in simple settings involving pairs of seemingly unrelated constants, and then we extend the analysis to more complicated cases involving combinations of three to five well-known universal constants. In constructions involving several unrelated constants, the method captures increasingly complex effects and places two or more disparate physics areas into a single framework connecting them by never-before-seen combinations of fundamental dimensionless constants, such as the fine-structure constant and the gravitational coupling constant. Thus, this method provides an alternative pathway to unified descriptions of fundamental interactions that have so far eluded a consistent theoretical formulation.

Abstract: A recently proposed CMB temperature relation, obtained from applying the Stefan Boltzmann law to the Hubble sphere and from related Hawking–Planck–Hubble scale arguments, may be written in the compact form T_CMB(t) = T_P/(8π √(N_P(t))). Here N_P is the effective Poisson-shot count. In an R_H = ct cosmology, the normalization consistent with the Stefan–Boltzmann radiation density is N_P(t) = (R_H(t))/2l_P = t/2t_P = (M_c(t))/m_P, where M_c(t) = c²R_H(t)/(2G) is the critical Hubble mass. If instead one defines the doubled Hubble-sphere mass M_u(t) = c²R_H(t)/G, then M_u/m_P = 2N_P. The formula has the mathematical structure of a Poisson relative-fluctuation law, since σ_N/N = 1/√N for a Poisson count, and may equivalently be written T_CMB(t) = T_P/8π σ_NP/N_P.We call this the Poisson-shot CMB formula. Substitution back into the Stefan–Boltzmann law gives u_γ ∝ T_CMB⁴ ∝ R_H^-2, matching the critical-density scaling in R_H = ct and yielding a constant photon radiation density parameter. This provides additional blackbody support for the formula and connects it to the observed near-perfect blackbody spectrum of the CMB. By contrast, in the standard ΛCDM framework the present CMB temperature is normally an observational input: the model predicts the redshift scaling T(z) = T₀(1 + z) once T₀ is supplied, but it does not derive the absolute present value T₀ from the Planck scale and the Hubble scale.

Abstract: Background: The Gibbs Energy Redistribution Theory (GERT) program established a thermodynamic ontology for cosmology (Paper~I) and later identified the post-relativistic dissolution boundary of the relativistic ruler in the Hyperdilute Regime (Paper~II). The complementary open question is the onset of relativistic metric legibility in the early Universe. Objective: To determine, within GERT, the emergence boundary of the relativistic metric ruler and define the lower limit of validity of the effective relativistic regime. Methods: We define the metric-emergence parameter $\Xi(\alpha)\equiv\lambda_\gamma(\alpha)/d_{\mathrm{ph}}(\alpha)$, where $\lambda_\gamma$ is the photon mean free path and $d_{\mathrm{ph}}$ is the GERT particle horizon. The boundary is set by $\Xi=1$. We compute $\alpha_{\mathrm{em}}$ using two recombination treatments (Saha equilibrium and Peebles kinetics) and test robustness against the unknown Primordial Cauldron boundary $\alpha_{\mathrm{PC}}$. Results: We obtain $\alpha_{\mathrm{em}}=-3.0\pm0.1$, with uncertainty dominated by recombination kinetics (Saha vs.~Peebles). Varying $\alpha_{\mathrm{PC}}$ over 25 orders of magnitude changes $\alpha_{\mathrm{em}}$ by less than $5\times10^{-4}$, showing strong insensitivity to primordial microphysics. Together with Paper~II ($\alpha_{\mathrm{crit}}=12.88\pm0.12$), the relativistic GERT domain spans $15.9\pm0.2$ decades in $\alpha=\log_{10}(a)$. Conclusions: The relativistic ruler is an emergent operational regime, not an ontologically unlimited one. GERT now provides a complete domain map with pre-relativistic, relativistic, and post-relativistic sectors. The onset and dissolution boundaries are thermodynamically controlled, giving a symmetric validity structure for Layer 3.

Abstract: We derive, from a well-defined action principle, a redshift-dependent perturbation \( \alpha(z) \) to the dark energy density that arises when a canonical scalar field \( \phi \) couples to a spontaneously confining hidden \( SU(N) \) gauge sector through a chiral anomaly portal. The ultraviolet cutoff of the effective theory is fixed, without adjustment, at Λ_UV = 13.6 TeV, consistent with the null results of the Large Hadron Collider (LHC). The confinement scale of the hidden sector is set equal to that of Quantum Chromodynamics, Λ_QCD = 300 MeV, providing the infrared anchor of the construction. A perturbative expansion around the ΛCDM background yields a closed-form ordinary differential equation (ODE) for \( \alpha(z) \), whose solution reproduces the expected transition behaviour at \( z_c \approx 0.7 \) and leaves a cosmologically small but non-zero residue at \( z=0 \) from the TeV anomaly. The resulting effective equation-of-state parameter \( w_{eff}(z) \) departs from -1 by at most \( 2\% \) at low redshift, yet generates a \( 6\% \) suppression in the matter fluctuation amplitude \( \sigma_8 \) relative to ΛCDM, in the direction required to reduce the present \( 2-3\sigma \) discrepancy with weak-lensing measurements. All parameters are either fixed by known physics or by numerical convergence criteria; none is tuned to reproduce a pre-specified output. A dedicated section on falsifiability examines experimental signatures at LHC, ALPS~II, neutron electric-dipole moment (nEDM) experiments, and the Eöt-Wash torsion balance. The scope and domain of validity of the construction are stated explicitly in a limitations section.

Abstract: Background: The late-time fate of black holes and the operational limits of General Rel ativity (GR) in the far future remain open problems in thermodynamic cosmology, and are central to the causal gap discussed in Penrose’s conformal framework. Objective: We determine, within Gibbs Energy Redistribution Theory (GERT), the lower density boundary of GR validity and the thermodynamic fate of supermassive black holes in the Hyperdilute Regime. Methods: Using the asymptotic gas-dominated GERT term, we derive the critical crossing λ_CMB(a) = H−1(a), compute acrit and ρGR,min analytically, and evaluate black-hole thermody namic states (including ∆G and inversion scales) across mass ranges, with no additional premises beyond the base framework. Results: We obtain acrit = 10^12.88±0.12 and log₁₀(ρGR,min) = −65.2 ± 0.4 kg/m³, closing the Layer 3 validity domain from Planck density to a symmetric lower operational threshold (161.9 density decades). At acrit, all black holes with M > M^∗ ≈ 1.7 × 10⁵M⊙ are in thermody namic absorption, with strongly non-spontaneous redistribution (e.g., ∆G ≈ +5800Mc² for 10⁹ M⊙). Thermal inversion occurs later in the Quasi-Vacuum, where cosmological cooling out paces Hawking thermal change by ∼ 10¹⁰⁶; at a_inv(M), supermassive-black-hole Schwarzschild radii exceed the Hubble radius by factors of 4 to 10¹⁰. Conclusions: In this regime, Hawking evaporation is not the operative end-channel for high mass black holes. GERT instead identifies a Gibbs-driven macroscopic phase transition (∆G < 0 in the Quasi-Vacuum) and establishes a symmetric but dynamically inverted boundary struc ture for Layer 3: Inward-dominated at emergence (dH/da < 0) and Outward-dominated at dissolution (dH/da > 0). This provides a quantitative thermodynamic completion scenario and a causal contribution to the CCC end-state problem.