gwtc3AnalyzedEventCount

The module attaches published GWTC-3 ringdown, echo, and quasinormal-mode (QNM) status facts to the Recognition Science §7 falsifier register. It is a status certificate, not posterior ingestion: the public abstract reports 15 confident O3b signals with false-alarm rates at most $10^{-3},\mathrm{yr}^{-1}$, no significant evidence beyond GR, no post-merger echoes in the analyzed events, remnant/QNM consistency with GR, and a graviton-mass bound $m_g \le 2.42\times 10^{-23},\mathrm{eV}/c^2$.

RS structural targets named in the module (echo damping $1/\varphi\approx 0.618$, rung phase delay $\log\varphi\approx 0.481$, leading-log coefficient $c_{\mathrm{RS}}\approx -0.2406$) are the quantities one would eventually test against full GWTC-3 posterior releases. This definition only freezes the published event count used by those status fields.

Definitional constant: the natural number is set to $15$ by unfolding equality. No lemmas, tactics, or algebraic reduction. Downstream positivity is discharged by decide after unfold.

Feeds the positivity lemma that $0 < 15$, the master structure GWTC3RingdownStatusCert (which requires a positive event count among its fields), and the one-statement conjunction that packages all GWTC-3 status scalars and flags. Without a fixed positive count, the certificate cannot assert that the echo/QNM dataset attachment has a nonempty analyzed sample.

In the broader framework this is bookkeeping for verification against §7, not a step of the T0–T8 forcing chain. It ties the published LIGO/Virgo/KAGRA GR-tests sample size to the RS echo-damping and rung-delay targets so later likelihood-style tests have a named, machine-checked status handle. Full confrontation with RS predictions still needs the posterior release files; this constant only records the abstract’s count.