IndisputableMonolith.Acoustics.RoomAcousticsFromPhiLadder
This module derives room acoustic parameters such as reverberation time from the phi-ladder in Recognition Science. It maps the J-cost function and RS time quantum to classical quantities like RT60 and acoustic regimes. Acousticians and wave physicists would cite it when connecting RS-native scales to measurable decay times in bounded domains. The module is purely definitional, importing constants and introducing sibling objects without proofs.
claimThe module defines RoomAcousticRegime as a classification on the phi-ladder and RT60 as the reverberation time RT60 = f(J, τ₀) with τ₀ the RS time quantum, together with ratio and position variants rt60_ratio and rt60_pos.
background
The module imports the RS time quantum τ₀ = 1 tick from IndisputableMonolith.Constants. It introduces RoomAcousticRegime as a classification of acoustic behavior indexed by phi-ladder rungs, with rt60 expressing reverberation time via the J-cost function J(x) = (x + x^{-1})/2 - 1. The setting follows the Recognition Composition Law and the eight-tick octave structure, placing acoustic scales directly on the self-similar fixed point phi without extra parameters.
proof idea
This is a definition module, no proofs. It imports the fundamental constants and defines acoustic quantities by direct mapping from the phi-ladder parameters and J-cost.
why it matters in Recognition Science
This module supplies the acoustic layer of the phi-ladder (T5-T8 forcing chain) by turning abstract recognition cost into observables such as RT60. It feeds the broader Recognition Science treatment of wave phenomena in bounded domains, closing the step from J-uniqueness to classical acoustics quantities.
scope and limits
- Does not derive the wave equation from the functional equation.
- Does not compute absorption or scattering coefficients.
- Does not address three-dimensional room geometry beyond the phi-ladder classification.
- Does not provide numerical values for specific materials or rooms.