因果輻輳重力理論 OUROBOROS Ver.2.0.0: Causal Congestion Gravity

Abstract

Abstract We formulate OUROBOROS Ver.2.0.0, Causal Congestion Gravity (CCG), a covariant endogenous-time framework in which relational clock response and Lorentzian causal geometry are treated as outputs of a common physical causal state. The central problem is to distinguish genuine physical clock generation from a mere reparametrization of evolution, and to determine under which explicit assumptions causal-state information can be completed into an effective gravitational metric without introducing an external master clock. For deterministic dynamics, we prove that multiplication of a vector field by a positive state-dependent scalar changes only the parametrization of its oriented state-space trajectories. A state-dependent rate therefore does not by itself define a new physical time degree of freedom. For Ito diffusions, covariance under the corresponding random time change additionally requires the diffusion amplitude to scale with the square root of the clock factor. In the relativistic formulation, physical time is represented by a worldline clock density rather than by a global evolution rate. In static spacetimes this reduces to a logarithmic delay potential, D = -ln N, whose gradient reproduces the standard weak-field static acceleration; the scalar delay description is not promoted to a generic theory of nonstatic gravity. CCG introduces a substrate-neutral measure over physically admissible causal extensions. Front, history, coherence, and retained-record constraints determine a surviving fraction s, and the associated causal-survival burden is defined by b = -ln s. We show that independent filters add in b and that any continuous scalar load compatible with multiplicative survival composition is necessarily logarithmic. Mapping this burden into clock response requires an additional constitutive assumption rather than following from the logarithmic theorem alone. Correlated restrictions are represented through Boolean-lattice Möbius inversion. An explicit triadic construction demonstrates irreducible three-way causal congestion with vanishing pair-connected coefficients, showing that higher-order causal restriction cannot in general be reduced to pairwise diagnostics. The relativistic construction separates candidate localization from physical history selection. Three independent front constraints in four dimensions leave a one-dimensional locus rather than an isolated event, and for three independent null fronts the residual tangent is necessarily spacelike. An additional physical history or coherence condition is therefore required before a timelike worldline can be defined. We also prove a deterministic covariance obstruction: a symmetry-invariant input state cannot select a unique element of a nontrivial transitive candidate orbit through a deterministic symmetry-preserving rule. This isolates microscopic selection as a genuine physical problem rather than a coordinate artifact. The central physical assumption of Ver.2.0.0 is the CCG self-closure postulate. Under the stated tomography conditions, the front sector determines a Lorentzian conformal class [g], while the burden sector determines an operational clock-density ray [a-hat] prior to the use of metric proper time. After a physical normalization is fixed, or modulo an admitted overall similarity gauge, a timelike clock tangent completes these data into a metric of the form g = Omega^2 g0, with Omega^2 = c^2 a-hat^2 / |g0(u,u)|. A noncircular source-state firewall requires the physical inputs used in this construction to be defined before the metric-dependent structures they generate. Compatible convergence of the conformal and clock sectors is shown to transfer to the completed metric under explicit regularity assumptions. At long wavelengths, we identify sufficient conditions for the reconstructed common-metric sector to reduce to Einstein gravity. The result assumes four spacetime dimensions and a diffeomorphism-natural, symmetric, divergence-free rank-two geometric tensor constructed locally from one common metric with differential order at most two, with no torsion, nonmetricity, or additional gravitational fields. Under these assumptions the infrared geometric sector is the Einstein sector in the Lovelock sense. This is a conditional reconstruction result, not a derivation of Einstein gravity from causal congestion alone. We further establish microscopic nonselection and scale-opacity results. Locality, covariance, reversibility, recurrence, finite-horizon predictive agreement, and related regularity conditions do not uniquely determine a microscopic CCG generator. Likewise, a numerical gravitational constant cannot be obtained from dimensionless information alone without a physical scale-bearing normalization. If a microscopic length is only a refinement parameter, no physical ell_* should be inferred from it; if it is a genuine physical scale, dimensional matching can constrain combinations such as G proportional to c^3 ell_*^2 / hbar times a dimensionless coefficient, but the coefficient and physical identification remain additional inputs. A scale-bearing isotropic six-line local-stencil realization provides an observational test through gravitational-wave dispersion. Its leading correction maps to the standard alpha = 4 modified-dispersion parameter according to A4 = -ell_*^2 / [5 (hbar c)^2], with the factor 1/5 obtained from the stencil moment structure. Using the official curated GWTC-3.0 and GWTC-4.0 modified-dispersion event kernel-density estimates, we reconstruct the combined catalog posterior directly from the released event-level KDEs. The released alpha = 4 branch contains 43 GWTC-3.0 KDEs and 41 O4a KDEs; after the released exclusion of S231123cg / GW231123_135430, the cumulative analysis contains 83 events. For the matched flat-A4 branch conditioned on A4 <= 0, direct numerical inversion of the reconstructed catalog CDF gives ell_,90 = 17.2275093 micrometres for GWTC-3.0 and ell_,90 = 10.4004957 micrometres for GWTC-4.0, an improvement factor of 1.6564123. The relevant conditional quantile is evaluated at 0.1 Q_minus, where Q_minus = F(0), rather than at the ordinary 5th percentile. These results are constraints on the explicit scale-bearing realization; they are not presented as evidence that CCG is realized in nature or that modified gravitational-wave propagation has been detected. Reproducibility is part of the release architecture. The Technical Supplement provides the source, Technical Notes, curated-KDE reconstruction code, a locked numerical certificate, deterministic mathematical and numerical verifiers, a release descriptor, and an optional external-data verifier. Given the separately obtained official MDR archive, the external verifier checks its cryptographic identity, reconstructs the catalog posterior from the event-level KDEs, and compares the result with the locked certificate. The release therefore distinguishes analytic proofs, computational consistency checks, and external-data reconstruction rather than treating software self-consistency as independent empirical evidence. OUROBOROS Ver.2.0.0 does not claim a unique microscopic quantum ontology, a unique total law of nature, a derivation of numerical G from c, hbar, and dimensionless information alone, a fundamental causal-set or fixed-graph ontology, or a proof that the observed universe realizes an exact causal cycle. Exact recurrence and Closed Causal Cyclic Cosmology are not imported as premises of CCG. The CCG self-closure relation remains a physical constitutive postulate whose empirical status must be assessed through realizations with observable consequences. The present work instead provides a controlled mathematical framework connecting endogenous time, causal-survival burden, higher-order causal congestion, Lorentzian conformal geometry, cone-clock metric completion, conditional Einstein-sector reconstruction, microscopic nonselection, gravitational-wave modified dispersion, and executable reproducibility tests.