dsPooledFractionBelowTarget
plain-language theorem explainer
Records the empirical pooled fraction 0.560888 of GWTC-3 DS_1mode_10M ringdown posterior samples lying below the RS damping target 1/φ. Anyone citing the controlled-family damping check against φ^{-1} uses this constant. It is a literal numeric definition, not a derived theorem.
Claim. For the GWTC-3 ringdown family with model DS_1mode_10M (22 events, 643624 pooled posterior samples of damping-per-cycle), the fraction of samples strictly below the Recognition Science target $1/\varphi \approx 0.618034$ is the constant $0.560888$.
background
This module freezes a controlled-family scaling of the one-member QNM damping statistic on GWTC-3. The family is model DS_1mode_10M only: 22 HDF5 files, 22 events, 643624 pooled posterior samples. The observable is damping per cycle, $\mathrm{damping_per_cycle} = \exp(-1/(f_{t_0}\tau_{t_0}))$.
Recognition Science predicts a Berry-scale damping target at $\varphi^{-1}\approx 0.618034$ (the reciprocal of the golden ratio fixed by the T6 self-similar fixed point). Sibling constants in the same module record the pooled mean, std, median, and quantile envelope of that posterior cloud; the target sits inside both the pooled 68% and 90% intervals.
The present declaration is the single scalar summarizing how much of the pooled mass lies below that target. It is structural bookkeeping for the verification certificate, not a likelihood or model-mix result.
proof idea
No proof body: the declaration is a bare def equating the name to the decimal literal 0.560888. Downstream, ds_fraction_below_target_valid unfolds the definition and discharges $0 < 0.560888 < 1$ by norm_num.
why it matters
Supplies the numeric payload for the family certificate GWTC3RingdownDS1Mode10MDampingFamilyCert and for the range sanity theorem ds_fraction_below_target_valid. Together with the pooled mean/median/quantile siblings, it documents that the RS target $\varphi^{-1}$ is not an outlier of the DS_1mode_10M damping posterior: more than half the mass sits below the target while the target remains inside the central 68% and 90% bands.
In the broader RS chain this is empirical verification infrastructure, not a forcing step (T0–T8). It checks consistency of the predicted damping scale against a single controlled waveform family. The module status is structural closure (zero sorry, zero new RS axioms); it does not claim a full-archive likelihood or cross-model meta-analysis.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.