IndisputableMonolith.Physics.GravitationalWaveEchoFromRS
This module defines parameters and relations for gravitational wave echoes in the Recognition Science setting, with the central relation giving echo delay as twice the minimum radius times the logarithm of phi. Researchers deriving observable signatures from the phi-ladder or eight-tick structure would cite these objects when connecting RS constants to waveform data. The module is built from a sequence of definitions establishing count, amplitude, and delay properties.
claimThe echo delay satisfies $Δt = 2 r_{min} log φ$, with auxiliary definitions for echo amplitude decay and parameter count on the phi-ladder.
background
The module sits inside the Recognition Science derivation of physics from the single functional equation, importing the RS-native time quantum τ₀ = 1 tick from Constants. It uses the self-similar fixed point φ together with the J-cost and defect-distance constructions that appear in the upstream forcing chain. The supplied doc-comment states the echo delay directly as Δt = 2 r_min × log(φ).
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The definitions supply the quantitative link between the phi-ladder and potential gravitational-wave observables, feeding the T7 eight-tick octave and the mass formula into waveform predictions. No downstream theorems are recorded yet, but the module closes the path from fundamental RS constants to echo signatures.
scope and limits
- Does not derive full waveform templates.
- Does not include general-relativity corrections to the delay.
- Does not assign numerical values to r_min for specific sources.
- Does not address detector noise or data-analysis pipelines.