IndisputableMonolith.Acoustics.RS_ACS_Cert_008
Acoustics certificate 008 packages a domain cost, a positive canonical threshold, and an inhabited certificate record for RS acoustic recognition. Anyone checking the ACS cert suite or wiring cost bounds into acoustic claims would cite it. The module is mostly definitions plus elementary nonnegativity and positivity lemmas over the imported J-cost and constants.
claimDefine a domain cost $C$ on the acoustic side, prove $C \ge 0$ and evaluate it at equality cases, fix a canonical threshold $\theta > 0$, and assemble an inhabited certificate record $\mathrm{RSACSCert008}$ bundling these data for the ACS-008 acoustic recognition check.
background
Recognition Science measures mismatch with the J-cost $J(x) = (x + x^{-1})/2 - 1$ from the Cost layer (the unique cost forced by the Recognition Composition Law). Constants supplies the RS-native tick $\tau_0 = 1$. This module sits in the Acoustics domain and turns those primitives into a named ACS certificate.
Sibling definitions introduce a domain-level cost, its value at equality, nonnegativity, a canonical threshold with a positivity proof, and the certificate type RSACSCert008 together with an inhabited instance. The setting is certification scaffolding: pin a cost bound and a threshold so downstream acoustic claims can quote a single cert object rather than re-deriving inequalities.
proof idea
Definition-heavy module. Domain cost and canonical threshold are introduced as defs; nonnegativity and positivity are short lemmas over the imported Cost and Constants facts. The certificate record is assembled and shown inhabited. No deep tactic proof; the argument is packaging plus elementary sign checks.
why it matters in Recognition Science
Gives the Acoustics lane a numbered ACS-008 certificate object so cost and threshold data travel as one unit. No downstream consumers are wired in the graph yet (used_by is empty), so the module is a leaf cert package rather than a step in the T0–T8 forcing chain. It still matters for the RS acoustic audit trail: any later theorem that needs a positive threshold or nonnegative domain cost against J can import this cert instead of rebuilding the interface. Touches the Cost layer and RS-native constants only; it does not itself force $\phi$, the eight-tick octave, or $D = 3$.
scope and limits
- Does not derive the J-cost or prove RCL uniqueness; those live upstream in Cost and forcing.
- Does not claim a physical acoustic spectrum or measured dB bound.
- Does not force phi, eight-tick structure, or spatial dimension D = 3.
- Does not list downstream theorems; the dependency graph currently shows no used_by edges.
- Does not replace a full ACS proof suite; it packages cert data for certificate 008 only.