IndisputableMonolith.Acoustics.RS_ACS_Cert_007
Acoustics certificate module RS-ACS-007 packages a domain cost, a positive canonical threshold, and an inhabited certificate record for the Recognition Science acoustics layer. Workers citing acoustic recognition bounds or cost-threshold comparisons use it as a self-contained cert bundle. The module is mostly definitions plus elementary nonnegativity and positivity lemmas over the imported J-cost and RS constants.
claimModule defining an acoustics domain cost $C_{\mathrm{dom}}$, equality at a reference point, nonnegativity $C_{\mathrm{dom}}\ge 0$, a canonical threshold $\theta>0$, and an inhabited certificate record $\mathrm{RSACSCert007}$ bundling these facts for the RS acoustics layer.
background
Recognition Science measures mismatch with the J-cost from the Cost module, $J(x)=(x+x^{-1})/2-1$, forced unique by the T5 step of the unified forcing chain and obeying the Recognition Composition Law. Constants supplies the RS-native tick $\tau_0=1$.
This acoustics certificate sits in the Acoustics domain. It introduces a domain-level cost functional (domainCost) together with a canonical threshold against which acoustic recognition events are compared. Sibling lemmas record evaluation at a reference point, nonnegativity of the cost, and positivity of the threshold.
The certificate record RSACSCert007 and the inhabited cert value package those facts so downstream acoustics arguments can assume a single named bundle rather than re-proving elementary cost properties.
proof idea
Definition-heavy certificate module. domainCost and canonicalThreshold are introduced as defs; domainCost_nonneg and canonicalThreshold_pos are short nonnegativity/positivity lemmas over the imported Cost and Constants infrastructure. cert and cert_inhabited assemble an inhabited record RSACSCert007. No deep tactic development; structure is package-and-discharge elementary inequalities.
why it matters in Recognition Science
Supplies a named, inhabited acoustics certificate (RS-ACS-007) so later acoustics or multi-domain arguments can cite one object for domain cost, threshold positivity, and nonnegativity. No downstream used_by edges are recorded yet; the module is a leaf cert bundle in the Acoustics domain. It ties local acoustic cost comparisons to the global J-cost and RS tick without reopening T5 uniqueness or the forcing chain.
scope and limits
- Does not derive the J-cost uniqueness or RCL; imports Cost as given.
- Does not prove physical acoustics PDEs or wave equations.
- Does not fix numerical SI values for thresholds beyond RS-native units.
- Does not claim downstream consumers; used_by is empty.
- Does not address other ACS certificate indices beyond 007.