IndisputableMonolith.Acoustics.RS_ACS_Cert_002
Acoustics certificate module packing a domain cost, a positive canonical threshold, and an inhabited RS-ACS-002 certificate record. Acoustic and RS auditors cite it when they need a named, nonnegativity-checked cost gate for the second acoustics certification layer. The module is mostly definitions plus short positivity and equality lemmas over the imported J-cost infrastructure.
claimThe module introduces a domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity, fixes a canonical threshold $\theta>0$, and packages an inhabited certificate record $\mathrm{RSACSCert002}$ asserting the acoustics gate $C_{\mathrm{dom}}\le\theta$ (or the dual comparison fixed by the cert fields).
background
Recognition Science measures mismatch with the J-cost $J(x)=(x+x^{-1})/2-1$ from the Cost layer, with RS-native units fixed in Constants ($\tau_0=1$ tick, and the usual $\phi$-scaled constants). Acoustics certificates sit downstream of that cost calculus: they turn a domain-specific cost functional into a pass/fail gate against a fixed positive threshold.
This module is the second named ACS certificate package. It binds a domain cost domainCost, records nonnegativity and a pointwise evaluation identity, and exposes a positive canonicalThreshold. The certificate type RSACSCert002 is the structured witness that the cost-threshold comparison holds; cert and cert_inhabited supply a concrete inhabitant so downstream code can assume the gate is occupied rather than merely typed.
proof idea
Definition-heavy module, not a deep proof development. Domain cost and threshold are defs; nonnegativity and positivity are short lemmas over the imported Cost/Constants facts; the evaluation identity is an equality lemma. The certificate record is assembled as a structure, then inhabited by a one-shot constructor proof that discharges the gate fields from those lemmas.
why it matters in Recognition Science
Gives the acoustics stack a second named, machine-checkable cost gate rather than an ad-hoc inequality. In the RS forcing picture this is applied infrastructure (J-cost and constants already fixed by T5–T8), not a new forcing step: it specializes the cost calculus to an acoustics certification interface. No downstream consumers are wired in the current graph (used_by empty), so the module is a leaf certificate package ready for higher ACS or phenomenology layers to import.
scope and limits
- Does not derive the domain cost from first-principles wave or fluid equations.
- Does not prove uniqueness of the canonical threshold, only positivity.
- Does not connect the certificate to measured acoustic spectra or lab data.
- Does not re-prove J-uniqueness, $\phi$ forcing, or eight-tick structure.
- Does not supply numerical bounds beyond the abstract threshold comparison.