dsPooledQ84
plain-language theorem explainer
Records the pooled 84th percentile of damping-per-cycle for the GWTC-3 DS_1mode_10M ringdown family as the real constant 0.898893346068. Citation target for anyone checking that the RS damping value 1/φ sits inside the family's central 68% posterior band. Pure numeric definition; no proof obligations.
Claim. The pooled $84$th percentile of the observable $\mathrm{damping\_per\_cycle}=\exp(-1/(f_{t_0}\tau_{t_0}))$ over the $643{,}624$ posterior samples in the GWTC-3 controlled family with model $\mathrm{DS\_1mode\_10M}$ equals $0.898893346068$.
background
The module freezes a controlled-family scaling of the Session 123 one-member QNM damping statistic. Family membership is fixed: model name DS_1mode_10M, 22 HDF5 files, 22 events, and 643,624 pooled posterior samples. The observable is damping per cycle, $\exp(-1/(f_{t_0}\tau_{t_0}))$, extracted uniformly across members.
Recognition Science predicts a damping target of $1/\varphi\approx 0.618034$. Sibling constants in the same module pin the pooled mean, standard deviation, median, and the quantile ladder q05/q16/q84/q95. The pair (q16, q84) is the empirical central 68% interval of the pooled posterior; this definition is the upper endpoint of that interval.
The module is structural verification only: zero sorry, zero new RS axioms, and no mixing of Kerr, MMRDNP, or other waveform-model semantics.
proof idea
There is no proof. The declaration is a bare real definition binding the symbol to the decimal 0.898893346068, the precomputed pooled 84th percentile reported in the module header. Downstream theorems discharge comparisons by unfold of this constant together with the RS target and norm_num.
why it matters
Supplies the upper edge of the pooled 68% band used by ds_target_inside_pooled_68, which asserts q16 < RS damping target < q84 by direct numeric comparison. That fact is packaged into the certificate structure GWTC3RingdownDS1Mode10MDampingFamilyCert and into the one-statement family theorem gwtc3_ringdown_ds1mode10m_damping_family_one_statement, whose conjunction records member/event/sample counts plus target containment in both the 90% and 68% pooled intervals.
In the broader RS picture the target $1/\varphi$ is the Berry-scale reciprocal fixed by the golden ratio from the forcing chain (T6). This constant does not derive $\varphi$; it only anchors the empirical check that the GWTC-3 DS_1mode_10M damping posterior still covers that landmark at 68% pooled credibility under a single controlled model family.
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