logAPosteriorMedian
plain-language theorem explainer
Records the posterior median of the GWTC-3 ringdown amplitude column logA_t_0 for event S190727h as the real constant −22.211884808706. Verification and phenomenology work cite it when comparing the one-member sample to the RS structural target log(φ^{−44}). It is a literal numeric definition, not a derived theorem.
Claim. The posterior median of the ringdown log-amplitude samples $\log A_{t_0}$ for GWTC-3 member S190727h is the constant $-22.211884808706$.
background
This module freezes one explicitly RS-referenced amplitude statistic from a range-read GWTC-3 ringdown posterior table. The member is rin/rin_S190727h_pyring_DS_1mode_10M.h5, dataset /EXP6/posterior_samples, column logA_t_0.
The RS structural target on this scale is $\log(\varphi^{-44}) = -44\log\varphi \approx -21.173320302623$. Sibling constants in the same file record the posterior mean ($\approx -22.2446$), standard deviation ($\approx 0.3983$), quantiles, residual and $z$-score relative to that target, and the sample fraction above target ($\approx 3.3\times 10^{-4}$).
The setting is one-member amplitude-scale comparison only: no archive-wide likelihood and no claim that $\log A_{t_0}$ is the final RS echo amplitude observable.
proof idea
There is no proof. The declaration is a bare real definition equal to the precomputed posterior median $-22.211884808706$ taken from the HDF5 sample summary for this event. Downstream residual and interval statements simply read this constant.
why it matters
It anchors the median side of the one-member RS amplitude check against $\log(\varphi^{-44})$. Together with the mean, std, and quantile siblings it supports the module claim that the RS target lies outside the central 68% and 90% posterior intervals and sits roughly $2.69,\sigma$ above the mean for this event.
In the broader Recognition ladder, $\varphi$-powers set mass and amplitude yardsticks; here $\varphi^{-44}$ is the structural amplitude scale under test. The module is marked structural closure (0 sorry, 0 new RS axioms) but remains a single-member freeze, not a population inference. Open questions it does not close: whether $\log A_{t_0}$ is the correct echo observable, and what an archive-wide likelihood would say.
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