MilestoneCert
plain-language theorem explainer
A two-field certificate packing the domain-coverage milestone: the domain cost vanishes on the diagonal for every nonzero real scale, and the canonical threshold is strictly positive. Physicists tracking RS structural milestones cite it as the typed witness that FinalModule_1398 is closed. It is a plain structure definition, not a proved theorem.
Claim. A milestone certificate is a pair of assertions: (i) for every real $r \neq 0$, the domain cost of the pair $(r,r)$ equals zero; (ii) the canonical threshold is strictly positive.
background
FinalModule_1398 is a Recognition Science physics milestone module whose stated status is a structural theorem with zero sorry and zero axioms. It packages a domain-coverage certificate rather than a dynamical law.
The first field concerns the domain cost: a real-valued cost on pairs of scales, imported via the Cost and Constants layers. Vanishing on the diagonal ($r,r$ for $r \neq 0$) means matched scales carry no residual domain penalty. The second field is positivity of a fixed canonical threshold used as the acceptance cut for that domain.
The module sits downstream of the primitive recognition calculus and the global cost infrastructure; the certificate itself only records the two numerical/algebraic side conditions needed to mark the milestone complete.
proof idea
No proof body: this is a structure declaration. Inhabitation is deferred to a separate certificate term (and an inhabited instance) that supplies the two fields, typically by citing the sibling lemmas that the domain cost is zero on equal nonzero arguments and that the canonical threshold is positive.
why it matters
In the RS forcing and physics stack, milestone modules close discrete coverage claims so later mass, coupling, or ladder results can assume a clean domain. This certificate is the typed interface for that closure in FinalModule_1398: diagonal cost vanishing plus a positive threshold. It does not itself invoke T5–T8, the RCL, or the mass ladder, but it is the structural gate those layers expect when a domain is declared covered. With no downstream edges recorded yet, its role is local bookkeeping for the Plan v7 pass that minted this module.
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