IndisputableMonolith.Acoustics.RoomImpulseResponseFromJCost
Defines an acoustic domain cost from the RS J-functional and packages a room-impulse certificate around a positive canonical threshold. Acoustics workers cite it when linking measured impulse responses to the same cost that forces the forcing chain. The module is mostly definitions plus elementary nonnegativity and positivity lemmas; no deep analytic PDE work lives here.
claimOn the acoustic domain one defines a cost $C$ built from the RS $J$-functional, proves $C\ge 0$ with equality at equilibrium, and fixes a canonical threshold $\theta>0$. A room-impulse certificate is then the structure asserting that the impulse-response cost clears $\theta$; the certificate type is inhabited.
background
Recognition Science measures mismatch by the unique cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$), forced by the Recognition Composition Law. The Cost import supplies that functional; Constants supplies the RS tick $\tau_0$.
This module lifts $J$ into an acoustic domain cost suitable for room impulse responses (the linear filter from a source impulse to a receiver in a room). Equilibrium is the zero-defect configuration of that cost. A canonical positive threshold then separates certified impulse responses from sub-threshold ones.
The local setting is certificate packaging rather than wave-equation analysis: the objects are scalar cost values and a Prop-carrying certificate record, not Green functions or modal expansions.
proof idea
Definition module with short supporting lemmas. domainCost is introduced from $J$; domainCost_nonneg and domainCost_at_equilibrium are immediate from the corresponding $J$ facts. canonicalThreshold is a positive constant (canonicalThreshold_pos). RoomImpulseCert bundles the threshold comparison; cert and cert_inhabited discharge inhabitation by constructing a witness. No multi-step tactic scripts or analytic estimates appear.
why it matters in Recognition Science
Places room acoustics on the same $J$-cost footing as the T5 uniqueness step in the forcing chain, so impulse-response quality can be scored in RS-native units rather than ad-hoc dB metrics. Downstream graph edges are empty in the current mirror, so the module is a leaf certificate surface: it exposes RoomImpulseCert for later measurement or UI layers without yet feeding a named parent theorem. It does not touch mass ladders, $\alpha$, or the eight-tick octave; its role is domain transfer of the cost, not new physics constants.
scope and limits
- Does not derive the wave equation or room Green functions from $J$.
- Does not claim measured RIRs equal a closed-form $J$ expression.
- Does not fix numerical threshold values beyond positivity.
- Does not connect to phi-ladder masses, alpha, or T6–T8.
- Does not supply DSP code or convolution implementations.