IndisputableMonolith.Acoustics.RS_ACS_Cert_009
Certificate module for Recognition Science acoustics claim ACS-009: a nonnegative domain cost on the acoustic side is compared against a strictly positive canonical threshold. Downstream acoustics arguments cite the inhabited certificate bundle rather than rebuilding the inequalities. The module is mostly definitions plus elementary positivity and nonnegativity lemmas over the shared Cost and Constants layers.
claimThe module packages an acoustics domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity, fixes a canonical threshold $\theta>0$, and exposes an inhabited certificate record $\mathrm{RSACSCert009}$ asserting the certified relation between $C_{\mathrm{dom}}$ and $\theta$.
background
Recognition Science measures mismatch with the J-cost from the Cost layer (the unique symmetric cost forced by the Recognition Composition Law). Acoustics certificates specialize that cost to a domain functional $C_{\mathrm{dom}}$ rather than working with bare $J$ on dimensionless ratios.
Constants supplies the RS-native tick $\tau_0=1$ and the golden-ratio ladder used elsewhere in the monolith; this module only needs the shared numeric and cost primitives. The certificate pattern (named record plus cert inhabitant) is the local convention for pinning a single ACS claim without threading raw inequalities through every consumer.
proof idea
Definition-first module. domainCost and canonicalThreshold are introduced as defs; domainCost_nonneg and canonicalThreshold_pos discharge the sign obligations by reduction to Cost/Constants facts. domainCost_at_eq is an evaluation identity. RSACSCert009 is the certificate structure; cert and cert_inhabited package the proved fields into one inhabited record. No deep tactic proof lives here.
why it matters in Recognition Science
ACS-009 is one numbered acoustics certificate in the RS monolith. It freezes the domain-cost versus threshold comparison so later acoustics developments can depend on a single inhabitant rather than re-proving nonnegativity and threshold positivity. No downstream edges are recorded in the graph yet; the module stands as a leaf certificate ready for import by higher acoustics or phenomenology layers. It does not itself touch the T0–T8 forcing chain, RCL uniqueness, or the mass ladder.
scope and limits
- Does not derive the acoustic domain cost from the J-cost forcing chain.
- Does not prove numerical bounds on alpha, masses, or c, hbar, G.
- Does not assert experimental acoustics claims beyond the formal certificate fields.
- Does not supply downstream consumers; used_by is empty in the graph.
- Does not close any sorry outside its own elementary sign lemmas.