IndisputableMonolith.Physics.RS_PHY_Structural_001
Certificate module for RS structural physics claim 001: a nonnegative domain cost functional and a strictly positive canonical threshold. Physicists citing the structural layer of Recognition Science use it to pin a cost-versus-threshold comparison. The module packages definitions, elementary positivity lemmas, and an inhabited certificate record; no deep forcing argument lives here.
claimDefine a domain cost $C$ on the RS cost structure, prove $C \ge 0$ and an evaluation identity at equality cases, fix a canonical threshold $\theta > 0$, and package these into an inhabited structural certificate record for PHY-Structural-001.
background
Recognition Science measures mismatch with the J-cost from the Cost module (the unique symmetric cost forced by the Recognition Composition Law, $J(x)=(x+x^{-1})/2-1$). Constants supplies the RS-native tick $\tau_0=1$. This module sits in the Physics domain and introduces a domain-level cost functional built on that infrastructure, together with a fixed positive threshold used as a structural comparison scale.
Sibling definitions name the objects: domainCost and its nonnegativity and evaluation lemmas, canonicalThreshold with positivity, and the certificate bundle RSPHYStructural001Cert with an inhabited instance. The local setting is bookkeeping for a numbered structural claim rather than a derivation of $\phi$, $D=3$, or the eight-tick octave.
proof idea
Definition-and-certificate module. Domain cost is introduced as a def on the imported cost structure; nonnegativity and an at-equality evaluation are short lemmas from Cost properties. The canonical threshold is a positive constant def with a one-line positivity proof. The certificate record packages these facts; inhabitation is by constructing that record from the lemmas. No multi-step forcing or analytic argument.
why it matters in Recognition Science
Gives the Physics layer a named, machine-checkable stub for structural claim 001: cost stays nonnegative and sits against a fixed positive threshold. Downstream used-by edges are empty in the graph snapshot, so this module is a leaf certificate rather than an input to T5–T8 or the mass ladder. It still matters for audit trails: any later theorem that quotes PHY-Structural-001 can point here for the cost and threshold side conditions instead of re-proving elementary Cost facts. It does not itself force $\phi$, close the alpha band, or derive $D=3$.
scope and limits
- Does not derive J-uniqueness, phi, eight-tick structure, or D=3.
- Does not prove any mass, coupling, or spectroscopic numerical claim.
- Does not connect domain cost to Berry threshold or dream fraction.
- Does not supply downstream theorems; used-by count is zero in this snapshot.
- Does not replace the Cost module; it only specializes and packages it.