IndisputableMonolith.Acoustics.RoomAcousticsSabineFromJCost
This module derives the optimal reverberation time in room acoustics as equal to phi in RS-native units by expressing Sabine parameters through the J-cost function. Acoustics researchers applying Recognition Science would cite it to link the forcing chain fixed point to measurable T60 values. The module consists of a chain of definitions for optimalT60 and related band quantities that rest directly on the imported Cost and Constants modules.
claimThe optimal reverberation time satisfies $T_{60, opt} = phi$ in RS-native units where $phi$ is the self-similar fixed point and the fundamental time quantum is $tau_0 = 1$ tick.
background
Recognition Science sets the time quantum $tau_0 = 1$ tick in the Constants module. The Cost module supplies the J-cost $J(x) = (x + x^{-1})/2 - 1$, which quantifies deviation from self-similarity and obeys the Recognition Composition Law. This module applies those objects to acoustics by defining reverberation time as a function of J-cost damping, with the optimum occurring at the phi fixed point.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the acoustic realization of T5 J-uniqueness and T6 phi fixed point from the forcing chain, providing the optimalT60 definition that supports RoomAcousticsCert and related certification objects in the same file.
scope and limits
- Does not derive the wave equation or modal analysis for rooms.
- Does not incorporate material-specific absorption coefficients beyond the J-cost model.
- Does not address non-diffuse or non-Sabine reverberation regimes.
- Does not compute numerical T60 for concrete room dimensions.