IndisputableMonolith.Acoustics.Room_Acoustics_RT60_RS
Module packaging room reverberation time (RT60) in Recognition Science units: a domain cost built from the J-cost, a positive canonical threshold, and an inhabited RT60 certificate. Acoustics workers cite it when tying classical decay-time bounds to the RS cost calculus. Structure is definitional plus elementary nonnegativity and positivity lemmas over Constants and Cost.
claimDefines a room-acoustics domain cost $C$ from the RS $J$-cost, a canonical positive threshold $\theta>0$, and an RT60 certificate type witnessing that the modeled $60\,\mathrm{dB}$ decay time sits in the certified regime relative to the RS tick $\tau_0$.
background
Classical RT60 is the time for mean-square sound pressure in a room to fall by $60,\mathrm{dB}$. This module places that observable in the Recognition Science cost calculus rather than in Sabine/Eyring formulas alone.
Upstream, Constants supplies the RS time quantum $\tau_0=1$ tick. Cost supplies the unique symmetric cost $J$ forced by the Recognition Composition Law (the T5 landmark $J(x)=(x+x^{-1})/2-1$). The module introduces a domain cost for the acoustics setting, records that it is nonnegative and agrees with evaluation at equality cases, and fixes a canonical positive threshold against which RT60-style decay is certified.
Sibling objects include domainCost, equality and nonnegativity facts, canonicalThreshold with positivity, and an RT60Cert bundle with an inhabited certificate cert.
proof idea
Definition module with thin lemma layer. Domain cost is assembled from the imported $J$-cost; nonnegativity and pointwise equality facts are short algebraic consequences of Cost. The canonical threshold is a positive RS-native constant (positivity lemma). RT60Cert packages the threshold comparison; inhabitation is by exhibiting the canonical certificate. No deep forcing-chain argument lives here.
why it matters in Recognition Science
Gives acoustics a first-class RS certificate surface: RT60 is not only an empirical room parameter but a cost-threshold witness in the same units as $\tau_0$ and $J$. Downstream graph is currently empty (used_by_count: 0), so this is a leaf domain module rather than a step inside T0–T8. It still matters for cross-domain uniformity: any later claim that ties architectural decay times, eight-tick cadence, or phi-scaled thresholds to measurable RT60 can import this certificate instead of re-deriving cost nonnegativity. Lands in the Acoustics domain alongside other applied RS bindings.
scope and limits
- Does not derive Sabine or Eyring RT60 formulas from the forcing chain.
- Does not prove numerical agreement with measured room data.
- Does not fix absorption coefficients, geometry, or modal density.
- Does not connect RT60 to alpha, masses, or D=3 beyond shared Cost/Constants imports.
- Does not supply downstream theorems; the module is presently a leaf.