IndisputableMonolith.Physics.GravitationalWaveEchoFromRS
The module defines parameters and a certificate for gravitational wave echoes predicted by Recognition Science, centered on the echo delay formula. Physicists modeling modified black hole ringdowns or testing RS-derived signatures would cite these objects. It consists entirely of definitions and supporting lemmas that import the RS time quantum and build echo-specific quantities.
claim$Δt = 2 r_{min} log(φ)$, together with auxiliary definitions for echo amplitude, decay, delay positivity, and the certificate GWEchoCert.
background
The module resides in the Physics domain and imports only Mathlib and IndisputableMonolith.Constants. The upstream Constants module supplies the fundamental RS time quantum τ₀ = 1 tick. All echo quantities are expressed in RS-native units where c = 1 and lengths are measured in ticks.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
Supplies the explicit echo delay Δt = 2 r_min log φ for use in gravitational-wave echo searches inside the Recognition Science framework. The formula follows from the phi-ladder and eight-tick octave structures already established in the forcing chain.
scope and limits
- Does not derive the full echo waveform.
- Does not perform numerical integration or simulation.
- Does not compare predictions to LIGO/Virgo data.
- Does not address higher-order corrections beyond the leading delay.