IndisputableMonolith.Acoustics.RS_ACS_Cert_010
Acoustics certificate module RS-ACS-010 packages a domain cost, a positive canonical threshold, and an inhabited certificate record for Recognition Science acoustics checks. Anyone wiring acoustic observables into the RS cost stack would cite it. The module is mostly definitions plus elementary nonnegativity and positivity lemmas over the imported J-cost and constants.
claimModule defining an acoustics domain cost $C_{\mathrm{acs}}$, a canonical threshold $\theta_{\mathrm{acs}} > 0$, and an inhabited certificate record $\mathrm{RSACSCert010}$ asserting the domain-cost side conditions used by Recognition Science acoustics certification.
background
Recognition Science measures mismatch with the J-cost $J(x) = (x + x^{-1})/2 - 1$ (equivalently $\cosh(\log x) - 1$), forced unique by the Recognition Composition Law. The Cost import supplies that functional; Constants supplies the RS-native tick $\tau_0 = 1$.
This module sits in the Acoustics domain layer. It specializes cost bookkeeping to an acoustics domain cost and a fixed positive canonical threshold against which acoustic observables are certified. Sibling names indicate equality-at-evaluation, nonnegativity of the domain cost, and positivity of the threshold, then a certificate type with an inhabitation proof.
No forcing-chain step (T5–T8) is discharged here; the module is a local certification interface, not a derivation of $\phi$, the eight-tick octave, or $D = 3$.
proof idea
Definition-heavy module, not a single deep theorem. It introduces domainCost and proves evaluation equality and nonnegativity by reduction to the imported Cost layer. canonicalThreshold is defined and shown positive. The certificate bundle RSACSCert010 / cert is then inhabited by assembling those facts, so downstream code can demand a value of the certificate type rather than re-prove the side conditions.
why it matters in Recognition Science
Gives Acoustics a named, reusable certificate (RS-ACS-010) so acoustic claims can sit behind a uniform cost-and-threshold gate instead of ad hoc inequalities. Used_by is empty in the graph snapshot, so this is presently a leaf certification surface rather than a feeder of a named parent theorem. It does not advance the T0–T8 forcing chain, RCL uniqueness, or the mass ladder; it only standardizes domain-level cost checks for acoustics inside the monolith.
scope and limits
- Does not derive acoustic wave equations or dispersion relations from RS first principles.
- Does not fix numerical SI values for sound speed, impedance, or measured spectra.
- Does not prove J-uniqueness, phi, eight-tick structure, or D = 3.
- Does not claim downstream consumers; used_by is empty in the supplied graph.
- Does not replace experimental acoustics validation outside the certificate predicates.