IndisputableMonolith.Physics.RS_Physics_Module_008
Physics module defining a domain cost functional and a positive canonical threshold, packaged as an inhabitable certificate RSPhysics008Cert. Experimentalists and RS auditors cite it when bounding recognition cost away from the vacuum. The module is mostly definitional: nonnegativity and positivity lemmas discharge the certificate fields from the Cost and Constants imports.
claimA domain cost $C_{\mathrm{dom}}$ on the recognition cost landscape, with $C_{\mathrm{dom}}\ge 0$ and an evaluation identity at equality points; a canonical threshold $\theta_*>0$; and a certificate bundle asserting these facts are inhabited.
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 T5 step of the unified forcing chain. The Cost import supplies that functional and its elementary inequalities; Constants supplies the RS-native tick $\tau_0=1$.
This module sits in the Physics layer and introduces a domain-level cost $C_{\mathrm{dom}}$ built from that J-cost, together with a canonical positive threshold used as a cutoff for recognition events. The local objects are the evaluation identity for the domain cost, its nonnegativity, positivity of the threshold, and a small certificate record that packages the proved properties.
proof idea
Definition-heavy module with short supporting lemmas. domainCost and canonicalThreshold are introduced as defs; domainCost_at_eq and domainCost_nonneg discharge algebraic identities and nonnegativity from the Cost import; canonicalThreshold_pos records positivity. RSPhysics008Cert and cert bundle those facts; cert_inhabited is a one-line inhabitant construction.
why it matters in Recognition Science
Supplies a reusable Physics-layer certificate for domain cost and a positive recognition threshold, so downstream mass, coupling, or timing arguments can assume nonnegativity and a strict cutoff without re-proving Cost lemmas. No downstream edges are recorded yet; the natural consumers are later RS physics modules that need a certified cost floor or threshold in RS-native units. Ties to the J-uniqueness landmark (T5) and the Cost infrastructure rather than to a numbered paper proposition.
scope and limits
- Does not derive the explicit closed form of domainCost beyond the Cost import.
- Does not prove uniqueness of the canonical threshold.
- Does not connect the threshold to alpha, mass rungs, or eight-tick timing.
- Does not export numerical bounds in SI units.
- Does not claim downstream use sites; used_by is empty.