Transport Closure in Cosmological Inference and the Hubble Tension (Parameters)

Overview This record contains the manuscript and supporting archive for Transport Closure in Cosmological Inference and the Hubble Tension: A Certified Redshift-Active Analysis of Planck, DESI, Pantheon+, and SH0ES. The paper develops a constraint-based analysis of cosmological parameter inference under the AASC framework, where AASC stands for Admissibility And Standing Constraint. The central question is not whether a numerical value of (H_0) can be shifted by adding phenomenological freedom, but whether the early-universe and late-universe determinations can be certified as the same transported parameter-object under a fixed admissibility, standing, reference, and transport ledger. Central Result The manuscript constructs a declared redshift-active AASC transport theorem object with a three-coefficient transport correction entering late-sector SN and BAO observables. The retained primary run uses a de-overlapped data stack: native Planck validation likelihood configuration, DESI DR1 BAO information, calibrated Pantheon+/SH0ES covariance, no separate explicit SH0ES Gaussian summary term. The completed five-chain redshift-active posterior yields [ H^{AASC}_{0,\mathrm{RA}} = 68.7319 \pm 0.3675 \ \mathrm{km,s^{-1},Mpc^{-1}}, ] with all three redshift-active transport coefficients statistically consistent with zero: [ dT_{a0}=0.0144\pm0.0590, \quad dT_{a1}=-0.0181\pm0.1063, \quad dT_{a2}=0.0051\pm0.0669. ] The posterior therefore does not activate a SH0ES-scale same-parameter transport correction. Seven-Coordinate Certificate The paper supplies a restricted seven-coordinate AASC certificate for the declared finite redshift-active theorem object. The certificate closes the following coordinates: anchor preservation, tensor-witness transport, quotient-observable closure, continuation consistency, boundary-record identity, estimator identity, hidden-remainder closure. The Jacobian/SVD hidden-remainder audit clears: [ \operatorname{rank}(J_\Pi)=6, \quad \operatorname{nullity}(J_\Pi)=0, \quad \operatorname{rank}(\text{transport subspace})=3, \quad C_M=0. ] Thus, within the declared redshift-active theorem object, all three transport coefficients are standing-bearing, observable-facing tensor witnesses, and no hidden observable-invisible transport direction remains. Interpretation Conditional on the imported AASC dependency stack, the result is stronger than a failure to find a numerical bridge. The paper constructs an admissible redshift-active transport channel, audits that channel with the full seven-coordinate certificate, verifies observable leverage, and still finds that the posterior does not occupy the SH0ES-scale transport role. Accordingly, the SH0ES-scale late-sector determination is not certified as the same transported expansion parameter from the early-universe anchor within the declared redshift-active AASC comparison. This is a transport-status result, not a conventional fit-improvement claim. Scope and Non-Claims The manuscript does not claim that SH0ES is false. It does not claim that (\Lambda)CDM is beaten by Bayesian evidence, AIC/BIC, or model-selection criteria. It does not exclude all possible new physics, all possible redshift-active bases, or all possible cosmological extensions. The result is restricted to the declared finite theorem object, data ledger, transport basis, and AASC certificate architecture described in the manuscript and archive. Formalization and Audit Support A standalone Lean 4 audit accompanies the manuscript. The Lean archive machine-checks the typed theorem-object layer, certificate assembly, AASC-class instantiation, kernel import, recognition theorem, and formal scope boundary. Numerical posterior statistics, convergence diagnostics, covariance calculations, and Jacobian/SVD values are imported as externally verified certificate evidence; Lean does not rerun Cobaya, CAMB, MCMC, covariance whitening, or SVD. Lean audit DOI: 10.5281/zenodo.20807195 AASC Dependency Stack This manuscript is downstream of the following public AASC records: Non-Degenerate Construction and the Kernel of Admissibility DOI: 10.5281/zenodo.19324199 The Structure of Admissibility DOI: 10.5281/zenodo.19198249 The Exhaustion Theorem DOI: 10.5281/zenodo.18682423 Admissibility and Constraint-Induced Rigidity of Physical Quotient Structure DOI: 10.5281/zenodo.18630901 On the Structural Origin of Cosmological Parameter Tensions and Transport-Induced Divergence DOI: 10.5281/zenodo.19907827 Record Contents This archive includes: final manuscript PDF, LaTeX source files, computational configuration files, redshift-active AASC chain outputs, posterior summaries and convergence diagnostics, matched (\Lambda)CDM comparator outputs, seven-coordinate certificate ledgers, Jacobian/SVD hidden-remainder audit files, figures and plotting outputs, verification reports, project manifest and checksum files, Lean formalization references and audit documentation.