IndisputableMonolith.Physics.RS_PHY_Structural_008
Module packaging the RS structural physics certificate 008: a nonnegative domain cost built from the J-cost, a positive canonical threshold, and an inhabited certificate record tying them together. Physicists citing the structural layer use it as a named bundle rather than raw Cost lemmas. Contents are mostly definitions plus short positivity and equality facts.
claimIntroduce a domain cost $C_{\mathrm{dom}}$ (nonnegative, with a pointwise equality form), a canonical threshold $\theta_{\mathrm{can}}>0$, and an inhabited certificate record $\mathrm{RSPHYStructural008Cert}$ packaging these structural facts for the physics layer.
background
Recognition Science measures mismatch with the J-cost from the Cost module, $J(x)=(x+x^{-1})/2-1$, forced unique by the T5 step of the unified forcing chain. Constants supplies the RS-native tick $\tau_0=1$. This module sits in the Physics structural series and lifts those primitives into a domain-level cost and a fixed positive threshold used by later structural claims.
Sibling definitions name the objects: domainCost and its nonnegativity and evaluation lemmas, canonicalThreshold with positivity, and the certificate type RSPHYStructural008Cert with an inhabited instance. No external physics hypotheses are imported beyond Mathlib, Constants, and Cost.
proof idea
Definition-heavy module. Domain cost is assembled from the upstream J-cost; nonnegativity and the pointwise equality lemma are short algebraic or rewriting facts. Canonical threshold is a positive constant (positivity is immediate from the Constants/Cost layer). The certificate is a structure bundling these facts, discharged by an inhabited instance rather than a deep proof.
why it matters in Recognition Science
Gives the Physics layer a single named structural certificate (008) so downstream RS physics developments can depend on one inhabited record instead of ad-hoc Cost lemmas. Feeds the structural certificate chain in the monolith; no further used_by edges are recorded on this page. Aligns with the RS pattern of packaging forcing-chain consequences (J-uniqueness, native units) as reusable physics certificates. Does not itself advance mass-ladder, alpha-band, or T6–T8 forcing steps.
scope and limits
- Does not derive J-uniqueness or the Recognition Composition Law; those stay in Foundation/Cost.
- Does not fix numerical values of masses, alpha, or rung gaps.
- Does not prove dynamical evolution or measurement postulates.
- Does not claim a unique physical interpretation of the canonical threshold beyond positivity.
- Does not list downstream consumers; used_by is empty on this page.