30.5 carries V30’s early_growth_window from BBN into a toy CMB phase-damping ledger: using Planck PR3-like TT/TE/EE spectra, a softened shared likelihood, and identical sampling resources, the report lands at Δχ² = 0 and ΔBIC < 2, so ΛCDM uniqueness is not preserved in this observable, while the toy-data scope and the slight EFT α_phase R-hat miss remain explicit.
Use this section as a compact machine-readable EFT reference.
30.5 keeps the CMB-facing side of Volume 30 deliberately bounded. Using Planck PR3-like TT/TE/EE toy spectra, the report compares ΛCDM with the Energy Filament Theory (EFT) under symmetric priors, one shared likelihood family, and identical sampling resources. Because the reported outcome is Δχ² = 0 with ΔBIC below 2, the window lands in the report’s statistical-equivalence regime and therefore denies uniqueness for this observable without claiming ownership of CMB ontology.
The setup is narrow on purpose. The data are preprocessed TT/TE/EE CSV spectra in (ℓ, C_ℓ), and the likelihood is a softened χ² with toy noise σ_ℓ so the comparison stays numerically stable without pretending to be the full Planck machinery. Both models are written in the same phase-shift / damping language, k_damp is fixed to 0.10, and the EFT side adds one report-local tension parameter, eft_phase_tension with prior [-1,1]. That is the real frame of 30.5: a fair, compressed phase-damping comparison window.
The reinforced audit layer is visible rather than hidden. MCMC uses 32 walkers, 8000 steps, burn-in = 2000, and thin = 2, with R-hat ≤ 1.1 and ESS ≥ 200 as the stated targets. The standard α_phase chain clears cleanly, and EFT eft_phase_tension does as well; EFT α_phase keeps ESS around 1.25×10^3 but reports R-hat around 1.21, slightly above the threshold. Even with that mild slippage, the report still records identical minimum χ² and places ΔBIC below 2, so 30.5 reads as reinforced statistical equivalence rather than as a fully green-lit convergence triumph.
The report’s scientific implication is deliberately modest. In this phase-shift plus damping-tail observable, the data admit more than one explanatory path, and EFT is framed as compatible rather than as a wholesale rejection of standard cosmology. But that implication is bounded twice over: the spectra are toy-level preprocessed inputs rather than a full mission likelihood, and one EFT diagnostic target is missed slightly. For Volume 30, this means 30.5 is strong as a support-and-bridge report window, not as a sovereign CMB verdict.
30.5 is easy to keep as a bridgeable report asset because its reproducibility block is explicit: sampler_mcmc.py, likelihood_phase_damp.py, run_mcmc_standard.ps1, run_mcmc_eft.ps1, and run_diagnostics.ps1 generate the saved chains and diagnostics JSON outputs. Inside Volume 30, that block lets the section function as the earlier linear-physics leg of the early_growth_window, carrying the line forward from 30.4’s primordial-abundance ledger into 30.6’s RSD fσ8 growth window without claiming object-level ontology authority.