StructMaterialsM93Cert
plain-language theorem explainer
Bundles the three structural obligations for the Materials domain certificate at recognition rung 93: diagonal domain cost vanishes, domain cost is nonnegative for positive mass and energy, and the canonical threshold is positive. Materials and RS auditors cite it as the interface that a concrete certificate must inhabit. It is a pure structure definition; no proof body.
Claim. A Materials structural certificate at rung 93 is a record of three facts: (i) for every nonzero real $r$, the domain cost of the pair $(r,r)$ is zero; (ii) for all positive reals $m,e$, the domain cost of $(m,e)$ is nonnegative; (iii) the canonical threshold is strictly positive.
background
Module status is a structural RS prediction for the Materials domain at recognition rung 93 (Plan v7, 120th pass): zero sorry, zero axiom. The certificate packages the minimal analytic obligations that any Materials-domain cost model must meet before it can be treated as a recognition-cost witness.
Domain cost is the Materials specialization of the RS J-cost (the unique cost forced by the Recognition Composition Law, $J(x)=(x+x^{-1})/2-1$). The diagonal condition says matched mass/energy ratios sit at the J-minimum. Nonnegativity is the domain-level echo of the foundation fact that every recognition event has nonnegative cost. The canonical threshold is the positive cutoff used to separate admissible from inadmissible structural configurations in this domain.
proof idea
No proof: this is a structure declaration. The three fields are Prop-valued obligations. Downstream, cert fills them by pointing at the sibling lemmas domainCost_at_eq, domainCost_nonneg, and canonicalThreshold_pos; cert_inhabited then packages that witness as Nonempty.
why it matters
Gives the typed interface for the Materials rung-93 structural certificate. Downstream cert is the concrete inhabitant and cert_inhabited records that the type is nonempty, closing the structural theorem for this module. In the RS stack this is the Materials-domain counterpart of the foundation nonnegativity of recognition cost, specialized to rung 93 on the phi-ladder. It does not itself derive materials phenomenology; it only freezes the three obligations that later materials predictions must satisfy.
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