cert
plain-language theorem explainer
Packages the three structural properties of the physics-domain cost at recognition rung 26 into one certificate: diagonal vanishing, non-negativity for positive arguments, and a strictly positive canonical threshold. Anyone needing a single inhabited witness that the mod-26 physics structural claims hold would cite it. The body is a pure field-wiring of three already-proved sibling lemmas.
Claim. There is a noncomputable inhabitant of the structural physics certificate at recognition rung 26, whose three fields assert: (i) for every nonzero real $r$, the domain cost satisfies $C(r,r)=0$; (ii) for all positive reals $m,e$, one has $C(m,e)\ge 0$; (iii) the canonical threshold is strictly positive.
background
This module records the Recognition Science structural certificate for the Physics domain at recognition rung 26 (Plan v7, 120th pass). Status is structural theorem: zero sorry, zero axiom. The certificate is a three-field structure whose fields are the minimal positivity and normalization claims one needs before any quantitative physics prediction at that rung can be trusted.
The domain cost $C(m,e)$ is the RS cost functional specialized to a mass-like and an energy-like argument in the physics domain. Upstream, the foundation layer already proves that every recognition-event cost is nonnegative via the J-cost identity $J(x)=(x+x^{-1})/2-1$ (the unique cost forced by the Recognition Composition Law). The sibling lemmas domainCost_at_eq, domainCost_nonneg, and canonicalThreshold_pos specialize that non-negativity and the diagonal minimum to the physics-domain cost and fix a positive threshold scale.
Rung 26 sits on the $\varphi$-ladder used throughout RS mass and coupling formulae; the certificate does not itself compute a mass, it only locks the cost geometry that any such computation must respect.
proof idea
One-line structure instance. Each of the three fields of StructPhysicsM26Cert is filled by the corresponding already-proved sibling: diagonal vanishing by domainCost_at_eq, non-negativity by domainCost_nonneg, and threshold positivity by canonicalThreshold_pos. No new arithmetic is performed; the definition is pure packaging.
why it matters
Gives a single named witness that the physics-domain cost at rung 26 satisfies the three structural axioms required by the RS forcing chain (non-negative J-type cost, unique minimum on the identity ray, positive threshold). Downstream the module exposes cert_inhabited, so later physics lemmas can assume the certificate rather than re-prove the three facts. In the broader framework this is the rung-26 physics counterpart of the structural certificates that sit under mass-ladder and coupling predictions; it does not yet touch $\alpha$, $G$, or the eight-tick octave, but it is the local cost lock those predictions need before they can be stated at this rung. No external used-by edges are recorded yet; the certificate is infrastructure for subsequent physics modules.
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