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02_BAO: standard-ruler window
V30-30.7 · F 证据节 / 显影节 ·
30.7 adds the BAO standard-ruler side of V30’s geometry_redshift_window: using five DV/rd measurements from 6dFGS, SDSS-MGS, and BOSS DR12, one Gaussian release-level likelihood with covariance omitted, symmetric k = 3 model complexity, and a piecewise-linear Energy Filament Theory (EFT) DV/rd parameterization against flat ΛCDM, the report lands at ΔAICc = 0.4460 and ΔBIC = 0.4460, so BAO is kept as a light equivalence ledger rather than a unique expansion-history verdict, with the no-MCMC boundary left explicit.
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Keywords: Energy Filament Theory, EFT, BAO, standard ruler, DV/rd, piecewise-linear fit, geometry_redshift_window, release-level likelihood, equivalence verdict, RSD bridge, geometry audit, late-potential interface
Section knowledge units
thesis
30.7 adds the standard-ruler side of Volume 30’s geometry_redshift_window. Using five BAO DV/rd measurements from 6dFGS, SDSS-MGS, and BOSS DR12, the report compares flat ΛCDM with a piecewise-linear Energy Filament Theory (EFT) DV/rd model under the same data, one Gaussian release-level likelihood, symmetric priors, and equal model complexity k = 3. Because the reported gaps are only ΔAICc = 0.4460 and ΔBIC = 0.4460 (EFT − ΛCDM), the section is kept as a light equivalence ledger rather than a master expansion verdict. Inside V30 its role is to deny one-probe uniqueness at the BAO ruler level and hand that result forward.
mechanism
The setup is intentionally spare. The dataset has five DV/rd points: 6dFGS at z = 0.106, SDSS MGS at z = 0.15, and BOSS DR12 at z = 0.38, 0.51, and 0.61. The likelihood is Gaussian with independent errors, and the covariance matrix is explicitly omitted at release level. Flat ΛCDM uses {H0, Ωm, rd}; the EFT side uses three piecewise-linear control points {a0, a1, a2} at z0 = 0.106, z1 = 0.38, z2 = 0.61, with other redshifts linearly interpolated or extrapolated. Because both sides keep k = 3, 30.7 functions as a fair-comparison standard-ruler window rather than as a flexibility contest.
evidence
The numerical table is close on purpose. After coarse-grid search plus local refinement, flat ΛCDM reaches χ² = 4.2657, AICc = 34.2657, and BIC = 9.0940. The piecewise-linear EFT side reaches χ² = 4.7117, AIC = 10.7117, AICc = 34.7117, and BIC = 9.5400 at (a0, a1, a2) = (3.11, 10.04, 14.56). The report therefore quotes ΔAICc = 0.4460 and ΔBIC = 0.4460. Under the Fair Comparison Specification v1.3, |ΔIC| < 2 belongs to equivalence, so BAO DV/rd does not uniquely select ΛCDM in this window.
boundary
The section is intentionally light. Small-sample AICc is needed because n = 5, and the fitting workflow is MLE-style coarse grid plus local refinement rather than a posterior-heavy pipeline. The source states directly that no MCMC is used and that R-hat and ESS are not applicable at release level. Combined with the omitted covariance matrix, that means 30.7 should not be inflated into a full BAO likelihood, full background-expansion, or universal Big-Bang-history verdict. Its narrower claim is that this five-point release-level BAO ledger does not preserve ΛCDM uniqueness.
interface
The reproducibility block is compact: data/bao_DV_over_rd.csv, the model scripts, the search scripts, the local-best outputs file, and the published PowerShell execution chain. Inside Volume 30, 30.7 sits between 30.3’s SN Ia redshift spine and 30.8’s geometry-consistency audit, while also bridging laterally toward 30.6’s RSD growth ledger and 30.10’s ISWxLSS late-potential return. Its job is to supply a light standard-ruler interface inside the bundle, not to author EFT ontology.