logAPosteriorMean
plain-language theorem explainer
Records the empirical posterior mean of the ringdown amplitude column logA_t_0 for GWTC-3 member S190727h as the real constant −22.244585483768. Anyone comparing that one-event posterior to the RS structural target log(φ^{−44}) cites this value. It is a literal numeric definition, not a derived theorem.
Claim. The posterior mean of the sampled ringdown log-amplitude $\log A_{t_0}$ for event S190727h is the fixed real $-22.244585483768$.
background
The module freezes a single range-read GWTC-3 ringdown posterior: member rin/rin_S190727h_pyring_DS_1mode_10M.h5, dataset /EXP6/posterior_samples, column logA_t_0. Recognition Science supplies a structural amplitude-scale target $\log(\varphi^{-44})=-44\log\varphi\approx-21.173320302623$ on the $\varphi$-ladder (with $\varphi$ the golden ratio fixed by the self-similar fixed-point step of the forcing chain).
Sibling constants in the same file hold the matching posterior std, median, quantiles, residual-from-mean, $z$-score, and fraction above target. The comparison is deliberately one-member and amplitude-scale only: it does not identify $\log A_{t_0}$ as the final RS echo observable, nor does it build an archive-wide likelihood.
proof idea
Definitional constant: the body is the literal real literal $-22.244585483768$ with no proof obligations, lemmas, or tactics. The value is the precomputed sample mean of the HDF5 posterior column, imported as a frozen statistic rather than recomputed in Lean.
why it matters
Gives the mean anchor for the first explicitly RS-referenced GWTC-3 ringdown amplitude statistic in the verification layer. Downstream residual and $z$-score siblings measure how far this mean sits from $\log(\varphi^{-44})$ (about $2.69$ posterior std below the target, with sample fraction above target $\approx 3.3\times 10^{-4}$). That places a concrete observational check next to the $\varphi$-ladder mass/amplitude scaffolding without claiming a full echo model or multi-event likelihood. Status is structural closure: zero sorry, zero new RS axioms.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.