IndisputableMonolith.Physics.RS_PHY_Structural_003
Structural physics module packaging a domain cost functional, its nonnegativity and evaluation identities, and a positive canonical threshold into an inhabited certificate. Physicists tracking RS structural constraints cite it when a domain-level cost bound or threshold gate is needed. The module is mostly definitional: lemmas discharge elementary algebraic and positivity facts from the Cost and Constants layers.
claimThe module introduces a domain cost $C_{\mathrm{dom}}$, proves $C_{\mathrm{dom}}\ge 0$ and an evaluation identity at equality cases, defines a canonical threshold $\theta_{\mathrm{can}}>0$, and packages these into an inhabited structural certificate $\mathrm{Cert}_{003}$.
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 and its elementary calculus; Constants supplies the RS-native tick $\tau_0=1$ and related units.
This module sits in the physics structural layer. It lifts the scalar cost to a domain-level cost $C_{\mathrm{dom}}$, records that the cost vanishes or matches under equality of arguments, and fixes a positive canonical threshold used as a gate in structural claims. The certificate bundle $\mathrm{Cert}_{003}$ is the export surface for downstream physics lemmas that need those facts without reopening Cost.
proof idea
Definition-heavy module. domainCost and canonicalThreshold are introduced as defs; domainCost_at_eq and domainCost_nonneg are short algebraic or Cost-library appeals; canonicalThreshold_pos is a positivity check. RSPHYStructural003Cert, cert, and cert_inhabited assemble and inhabit the certificate record. No deep tactic proof; structure is package-and-discharge.
why it matters in Recognition Science
Gives the physics tree a reusable structural certificate for domain cost and a positive threshold, so later RS physics results can assume nonnegativity and a canonical gate without re-deriving Cost facts. No downstream edges are recorded yet in the mirror graph; the natural consumers are higher structural or mass/threshold lemmas that need a certified domain cost bound. Ties to the J-uniqueness landmark (T5) only indirectly, through the Cost import.
scope and limits
- Does not derive J-uniqueness or the Recognition Composition Law; those live upstream in Cost/Foundation.
- Does not fix numerical values of masses, alpha, or rung gaps.
- Does not claim a unique physical domain; only packages cost and threshold data.
- Does not discharge open scaffolding outside the listed sibling lemmas.
- Does not assert dynamical evolution or eight-tick timing laws.