IndisputableMonolith.Acoustics.RoomAcousticsSabineFromJCost
The module derives optimal reverberation time in room acoustics as equal to the golden ratio phi in RS-native units, using the J-cost from the Recognition Composition Law. Acoustics researchers and RS theorists cite it to link classical Sabine parameters to the phi-ladder and T5-T8 forcing chain. It imports Constants and Cost then defines related quantities including optimalT60 and RoomAcousticsCert.
claimThe optimal reverberation time satisfies $T_{60,opt} = \phi$ in RS-native units, where $ au_0 = 1$ tick is the fundamental time quantum and $\phi$ is the self-similar fixed point of the Recognition Composition Law.
background
The module operates in the Acoustics domain. It imports the time quantum $ au_0 = 1$ tick from Constants and the J-cost functional from Cost. J-cost satisfies the Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$, with $J(x) = rac{x + x^{-1}}{2} - 1$. The module introduces optimalT60, optimalT60_band, over_damped_below_one, RoomAcousticsCert and roomAcousticsCert as the main objects expressing reverberation in terms of phi.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the acoustic application of J-cost and feeds RoomAcousticsCert. It fills the step that connects the eight-tick octave and phi-ladder to classical room acoustics parameters. No open questions are noted in the supplied facts.
scope and limits
- Does not derive the full Sabine absorption formula.
- Does not treat non-optimal or frequency-dependent reverberation.
- Does not include experimental data or validation.