IndisputableMonolith.Acoustics.RoomAcousticsSabineFromJCost
Module derives optimal reverberation time from J-cost in Recognition Science, establishing it equals φ in RS-native units. Acoustics researchers and RS theorists would cite it for linking perceptual optimality to the phi-ladder. The module imports the time quantum and cost definitions to build the result as a set of definitions and theorems.
claimThe optimal reverberation time satisfies $T_{60} = \phi$ in RS-native units, where $\phi$ is the self-similar fixed point.
background
The module sits in the acoustics domain and imports the fundamental RS time quantum $\tau_0 = 1$ tick from Constants together with the J-cost function from Cost. J-cost is the function $J(x) = (x + x^{-1})/2 - 1$ that encodes the Recognition Composition Law. The module applies these to room acoustics to obtain the optimal reverberation time.
Recognition Science derives all physics from the single functional equation whose solutions force the phi-ladder. This module supplies the acoustic observable that sits on that ladder, consistent with the eight-tick octave and D = 3 spatial dimensions already fixed upstream.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the acoustic result that feeds RoomAcousticsCert and the sibling declarations optimalT60 and optimalT60_band. It fills the chain step that converts J-cost into a measurable time, directly instantiating T5 J-uniqueness and T6 phi fixed point in the acoustics setting.
scope and limits
- Does not derive the full Sabine absorption formula.
- Does not treat non-optimal or frequency-dependent cases.
- Does not include experimental data or measurement protocols.