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03_SNela: Hubble-diagram redshift spine
V30-30.3 · F 证据节 / 显影节 ·
30.3 fixes Volume 30’s SN Ia redshift-distance spine with a 277-object Pantheon+SH0ES Hubble-flow window: under the same diagonal χ², equal parameter count, and a TPR-only EFT test that removes PER, it records near-zero ΔIC rather than uniqueness, while keeping the unfinished MCMC / PPC layer visible as a boundary instead of hiding it.
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Keywords: Energy Filament Theory, EFT, TPR, PER, SN Ia, Pantheon+SH0ES, Hubble diagram, standard-candle ledger, geometry_redshift_window, equivalence verdict, diagnostic boundary, BAO handoff, geometry audit
Section knowledge units
thesis
Section 30.3 fixes the SN Ia side of Volume 30’s geometry-redshift window. Using the Pantheon+SH0ES Hubble-flow subsample (277 SNe), the report compares flat ΛCDM with a TPR-only Energy Filament Theory (EFT) model under the same diagonal χ² likelihood, symmetric priors, and equal parameter count. The reason to keep this section is not to declare a one-probe ontology of redshift. It is to preserve a clean standard-candle ledger inside the bundle: when a TPR-only test with PER removed lands in equivalence rather than uniqueness, the SN Hubble diagram becomes a support-and-bridge spine that later geometry windows must reckon with.
mechanism
30.3 is methodologically narrow on purpose. It uses only the Hubble-flow part of Pantheon+SH0ES, removes calibrators, standardizes the table to z, μ, and μ_err, and compares the models under one shared diagonal χ². Flat ΛCDM carries {H0, Om0}; the EFT side is a TPR-only construction with {H0_TPR, alpha}, explicitly removing PER so the window tests only the endpoint tension-potential leg rather than a full redshift stack. Equal parameter count is therefore not decoration; it is the fairness condition that lets the section function as a report ledger instead of a flexibility contest.
evidence
The headline numbers are deliberately plain. In the maximum-likelihood table, flat ΛCDM returns χ² = 119.846, AICc = 123.889, and BIC = 131.094, while TPR-only EFT returns χ² = 119.859, AICc = 123.903, and BIC = 131.107. The reported differences are Δχ² = 0.014, ΔAICc = 0.014, and ΔBIC = 0.014 (EFT − ΛCDM). Under the report’s equivalence criterion v1.3, |ΔIC| < 2 is enough to reject uniqueness, so this section does not claim that the SN Hubble diagram prefers EFT; it claims that the diagram does not make ΛCDM unique within this controlled window.
boundary
The strong version widens the audit frame but keeps its unfinished parts visible. It specifies an MCMC layer with four chains, R-hat and ESS thresholds, a posterior predictive check (PPC) built on Hubble-diagram residual statistics, and additional prior-sensitivity, subsample-robustness, and outlier checks. But the same report states that the full MCMC / PPC numerical diagnostics were not executed in the present run. That boundary matters for Volume 30: 30.3 is strong because it exposes the diagnostic scaffold and its thresholds, not because it pretends those posterior outputs are already in hand.
interface
Within Volume 30, 30.3 should be kept as the standard-candle leg of the geometry_redshift_window. Its job is to hand a controlled SN redshift-distance ledger forward to 30.7, where a BAO standard-ruler window will supply a complementary probe, and then to 30.8, where a geometry-consistency audit can recollect the redshift story at bundle level. The reproducibility block—standardized sample file, fit outputs, and scripts—helps this section function as a bridgeable report asset rather than as free-floating rhetoric. It supports and routes; it does not acquire object-level ontology authority.