IndisputableMonolith.Gravity.BHEchoesLIGOCatalog
Structural BH-echo catalog in RS-native units: bounce radius and echo delay as functions of recognition rung N, with positivity and successive-rung ratio lemmas, bundled as a certificate. Per-event LIGO/Virgo prediction tables import these scalings. Mostly definitions plus elementary positivity and ratio proofs on the phi-ladder.
claimDefines bounce radius $R_b(N)$ and echo delay $\Delta t(N)$ at recognition rung $N$ (RS-native units), proves $R_b(N)>0$ and $\Delta t(N)>0$, records successive-rung ratios $R_b(N+1)/R_b(N)$ and $\Delta t(N+1)/\Delta t(N)$, and packages the structural claims in a black-hole echo certificate.
background
Recognition Science places mass and time scales on the discrete $\varphi$-ladder. A black-hole echo is modeled as a recognition bounce at rung $N$ outside the classical horizon, returning a delayed secondary pulse after the primary ringdown. Work is in RS-native units ($c=1$); the fundamental time quantum is $\tau_0=1$ tick from Constants.
This module supplies the generic structural maps $N\mapsto R_b(N)$ and $N\mapsto\Delta t(N)$, not event-specific numbers. Bounce radius is the radial scale tied to rung $N$; echo delay is the corresponding round-trip lag that sets the predicted echo time and frequency $f_{\mathrm{echo}}=1/\Delta t$.
proof idea
Definition-and-certificate module, not a deep existence proof. bounceRadius and echoDelay are introduced as rung-dependent quantities on the $\varphi$-ladder; positivity lemmas follow from positivity of the underlying constants and powers; successive-ratio lemmas are direct algebraic identities relating rung $N+1$ to $N$. BHEchoesCert / bhEchoesCert packages those facts into one structural certificate for importers.
why it matters in Recognition Science
Parent consumer is Gravity.BHEchoPerEventCatalog, which "gives the generic bounce-radius and echo-delay scaling" from this module and then "records the per-event prediction tables for the four canonical headline LIGO/Virgo events" (source mass $M$, rung $N$, $\Delta t(N)$, $f_{\mathrm{echo}}(N)=1/\Delta t(N)$). Bridges the discrete recognition ladder to concrete GW echo forecasts without reopening the T0–T8 forcing chain or the RCL derivation of $J$ and $\varphi$.
scope and limits
- Does not tabulate numerical delays for named LIGO/Virgo events.
- Does not derive echo existence from the T0–T8 forcing chain.
- Does not fix rung N from first principles for a given mass M.
- Does not treat detector noise, matched filtering, or observational bounds.
- Does not claim SI-unit conversions beyond RS-native scalings.