IndisputableMonolith.Physics.RS_PHY_Structural_002
Module packaging RS structural physics claim 002: a domain cost functional built from the Recognition cost, its nonnegativity, and a positive canonical threshold. Physicists citing structural bounds or certificate-style physics lemmas in the RS stack use it. The file is mostly definitions plus short positivity and equality lemmas, closed by an inhabited certificate record.
claimDefine a domain cost $C_{\mathrm{dom}}$ from the Recognition cost $J$, prove $C_{\mathrm{dom}}\ge 0$ and an evaluation identity at equality cases, introduce a canonical threshold $\theta_*>0$, and package these facts as an inhabited structural certificate for RS-PHY-Structural-002.
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 RS-native units (including the tick $\tau_0$).
This module sits in the Physics domain and treats a structural claim labeled RS-PHY-Structural-002. It introduces a domain-level cost built from $J$, records that the cost is nonnegative, and fixes a positive canonical threshold against which structural comparisons are made.
Sibling names indicate evaluation identities (cost at equality), positivity of the threshold, and a certificate record that bundles the structural hypotheses into a single inhabited object for downstream physics lemmas.
proof idea
Definition-first module, not a single deep theorem. domainCost is introduced from the Cost layer; domainCost_nonneg and domainCost_at_eq are short algebraic or order facts about that functional. canonicalThreshold is a fixed positive real (positivity in canonicalThreshold_pos). The certificate type RSPHYStructural002Cert packages these properties; cert and cert_inhabited discharge inhabitation so callers can assume the structural bundle without re-proving the pieces.
why it matters in Recognition Science
Gives a reusable structural certificate for physics claim 002: nonnegative domain cost plus a positive canonical threshold in RS-native language. That pattern matches other RS certificate modules that feed forcing-chain and constants work (J-uniqueness, $\phi$-ladder mass formulas, dimensionless bands).
No downstream edges are recorded in the graph snapshot, so this file is presently a leaf provider rather than a proved parent theorem. Its value is interface hygiene: later structural or phenomenological lemmas can depend on one inhabited cert instead of re-opening Cost and threshold details. It does not itself close T5–T8 or the $\alpha$ band; it only stages cost-threshold structure those arguments may cite.
scope and limits
- Does not prove uniqueness of J or the Recognition Composition Law.
- Does not derive phi, eight-tick period, or D = 3.
- Does not compute particle masses or the alpha inverse band.
- Does not assert experimental bounds beyond the internal threshold definition.
- Does not list downstream consumers; used_by is empty in this snapshot.