MilestoneCert
plain-language theorem explainer
A two-field certificate that the domain cost vanishes on the diagonal for every nonzero real scale and that the canonical recognition threshold is strictly positive. Physicists tracking RS domain-coverage milestones cite it as the structural witness for FinalModule_1395. It is a pure 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_1395 is a structural milestone module in the Recognition Science physics layer (Plan v7, 109th pass). Its stated status is a structural certificate with zero sorry and zero axioms, aimed at domain-coverage bookkeeping rather than a new dynamical law.
The domain cost is the local cost functional on scale pairs drawn from the Cost import; the diagonal condition says matched nonzero scales carry zero excess cost. The canonical threshold is the positive real cutoff used to mark when a domain is considered covered. Both quantities live alongside sibling lemmas that prove the diagonal identity and positivity separately.
The module sits under the broader RS forcing architecture (J-cost uniqueness, $\varphi$-ladder, eight-tick octave), but this declaration only packages the two local positivity and vanishing facts needed for the milestone stamp.
proof idea
No proof body: the declaration is a structure (record type) with two fields. Inhabitation is deferred to sibling constructors such as cert / cert_inhabited, which supply the diagonal cost identity and the positivity of the canonical threshold. The structure itself only names the interface.
why it matters
In the RS physics stack, milestone modules mark completed domain-coverage steps without introducing new axioms. This certificate is the typed witness that FinalModule_1395 has closed its local obligations: zero diagonal domain cost and a positive coverage threshold.
Downstream use is currently empty in the graph, so the structure is a leaf stamp rather than an input to a larger forcing theorem. It does not itself invoke T5–T8, the Recognition Composition Law, or the mass ladder; it only records that the cost and threshold side conditions for this milestone hold. That keeps the module auditable as a structural theorem (0 sorry, 0 axiom) in the Plan v7 pass sequence.
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