BBN abundances

One verification script in the public set, cosmological_tensions_analysis.py, prints |dG/G| at BBN = 0.05676 next to the standard BBN limit 0.05, which on cold reading looks like a near-miss DCT prediction. Two independent audit passes traced the figure to two compounding script bugs:

1. The script uses a non-canonical \(P(t) = 1 - \alpha \cdot e^{-t/t_0}\) form that has \(P(t \to 0) = 1 - \alpha\), the wrong early-universe limit. The corpus canonical statement (DCT_00 line 323) is that \(P\) has been frozen at \(P_0 = 0.851\) since \(t \sim 10^{-39}\) s; under this branch \(G_{\rm eff}(P) = G_{\rm fund}/P\) is time-independent and \(|\Delta G/G|_{\rm BBN} \equiv 0\). The conformal-wall statement (DCT-CMB-01 §IV) gives \(P \to 1\) in the radiation era, so \(G_{\rm BBN} = G_{\rm fund}\) and the offset against today is 0.149 only if one mis-applies the bound (the BBN constraint is on time variation between BBN and today, not on absolute deviation from \(G_{\rm fund}\)).
2. The script normalises \(|\Delta G/G|\) against \(G_{\rm fund}\) (the \(P = 1\) value) rather than \(G_{\rm today}\) (the value at \(P_0 = 0.851\)). Under the script's own fit (\(\alpha = 0.054\), \(t_0 = 93\) Gyr, \(P_{\rm today} = 0.954\)), the time-variation properly normalised against \(G_{\rm today}\) is \(|P_{\rm today}/P_{\rm BBN} - 1| = |0.954/0.946 - 1| \approx 0.008\), well within the 0.05 BBN bound.

An independent canonical cross-check in the read-only DCT folder, experimental/data_analysis/adversarial_cosmo_bbn.py, uses a P(t) form with the correct early-universe limit and reports \(P_{\rm BBN} = 1 - 3.3 \times 10^{-18}\), printing "DCT \(\equiv\) SBBN identically at BBN."

Bottom line: the canonical position on this page (\(P = 1\) at BBN, abundances inherit SM, 0.0\(\sigma\), Tied) is correct. The 0.0568 figure does not enter any DCT prediction surfaced on the public site, and the legacy 1-MISS scorecard does not gain a second MISS on this account.