IndisputableMonolith.Acoustics.RS_ACS_Cert_004
Acoustics certificate module that packages a domain cost functional, a positive canonical threshold, and an inhabited certificate record RSACSCert004. Acoustic and RS auditors cite it when they need a named, nonnegativity-checked cost-versus-threshold bundle rather than ad-hoc inequalities. The module is mostly definitions plus short positivity and evaluation lemmas over the shared Cost and Constants imports.
claimThe module introduces a domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity at equality cases, fixes a canonical threshold $\theta>0$, and packages them into an inhabited certificate record $\mathrm{RSACSCert004}$ asserting the acoustic cost-threshold relation used by later ACS checks.
background
Recognition Science measures mismatch with the J-cost from the Cost layer (the unique symmetric cost forced by the Recognition Composition Law). Constants supplies the RS-native tick $\tau_0=1$. This acoustics module specializes that cost language to a domain cost functional for acoustic observables, rather than re-deriving J from scratch.
Sibling definitions name the pieces: domainCost is the acoustic cost map; domainCost_nonneg and domainCost_at_eq record nonnegativity and the on-shell evaluation identity; canonicalThreshold / canonicalThreshold_pos fix a strictly positive comparison level. The certificate record RSACSCert004 (with cert and cert_inhabited) is the export surface: a single inhabited bundle that downstream ACS material can require instead of restating the inequalities.
proof idea
Definition-heavy module, not a deep derivation. Domain cost is introduced as a Cost-layer specialization; nonnegativity and the equality-case identity are short lemmas. The canonical threshold is defined and proved positive. The certificate structure is then assembled and shown inhabited by feeding those lemmas into the record fields. No long tactic scripts; the argument is packaging plus positivity.
why it matters in Recognition Science
Gives Acoustics a named ACS certificate (004) so cost-versus-threshold claims sit behind one inhabited record rather than scattered local inequalities. It sits on Constants and Cost, aligning acoustic checks with the same J-cost and tick conventions used elsewhere in the monolith. No downstream used_by edges are recorded yet; the module is an export surface for later ACS or phenomenology hooks that need a certified acoustic domain cost and threshold. It does not itself close a T0–T8 forcing step; it applies the cost layer inside acoustics.
scope and limits
- Does not derive J-uniqueness or the Recognition Composition Law; imports Cost.
- Does not prove a physical acoustic spectrum or measured dB law.
- Does not fix numerical SI conversion beyond RS-native Constants.
- Does not record downstream consumers; used_by is empty.
- Does not claim the threshold equals a named RS landmark unless a sibling def states it.