IndisputableMonolith.Physics.GravitationalWaveEchoFromRS
The module defines parameters and functions for gravitational wave echoes in Recognition Science, centered on the delay formula Δt = 2 r_min log φ. Physicists modeling black-hole ringdown signals with RS modifications would cite these definitions. It is a definition module that imports the RS time quantum from Constants and introduces sibling objects such as EchoParameter and echoDelay without proofs.
claimThe echo delay is $\\,\Delta t = 2 r_{\min} \log \phi$, where $\phi$ is the self-similar fixed point and $r_{\min}$ is the minimum radius parameter; related quantities include echo amplitude decay and a certification predicate GWEchoCert.
background
Recognition Science derives all physics from the J-cost functional satisfying the Recognition Composition Law. The upstream Constants module supplies the fundamental RS time quantum $\tau_0 = 1$ tick. This module extends that foundation to gravitational-wave observables by introducing EchoParameter and the explicit delay relation $\Delta t = 2 r_{\min} \log \phi$ drawn from the phi-ladder and eight-tick octave.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the echo signatures that connect the UnifiedForcingChain (T0-T8) and the phi-ladder mass formula to observable gravitational-wave phenomena. It provides the concrete delay and amplitude expressions needed for downstream tests of RS predictions against LIGO/Virgo data, filling the gap between the abstract T7 octave and concrete waveform features.
scope and limits
- Does not derive the delay formula from the J-functional.
- Does not include waveform templates or numerical integration.
- Does not address observational bounds or detector response.
- Does not link echo parameters to specific black-hole masses or spins.