MilestoneCert
plain-language theorem explainer
Packages two structural side-conditions for a domain-coverage milestone: the domain cost vanishes on the diagonal for every nonzero real scale, and the canonical threshold is strictly positive. Physicists citing the FinalModule_1399 certificate use this as the interface type that a concrete witness must inhabit. It is a bare 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
The module FinalModule_1399 is a Recognition Science structural certificate for a domain-coverage milestone (Plan v7, 109th pass). Status is structural: zero sorry, zero axiom. It sits in the physics layer and imports the global constants and the J-cost infrastructure.
The domain cost is the local cost functional used to measure mismatch between two real scales on the recognition domain. The diagonal vanishing condition says that identical nonzero scales incur zero cost, which is the minimal consistency requirement before any off-diagonal comparison is meaningful. The canonical threshold is the positive cutoff against which domain-cost values are later compared when deciding coverage.
Upstream, the module depends on the one-primitive structure from the Primitive Recognition Calculus, which supplies the single-generator setting in which domain costs and thresholds are interpreted.
proof idea
No proof body: this is a structure declaration. It simply records two fields, the universal diagonal vanishing of the domain cost and the positivity of the canonical threshold, as the data a milestone witness must supply. Sibling lemmas in the same module discharge those fields for the concrete certificate instance.
why it matters
In the Recognition framework this structure is the typed interface for a domain-coverage milestone certificate. Downstream consumers (the inhabited certificate and any later physics modules that import FinalModule_1399) treat inhabitation of this type as evidence that the local cost geometry is well-posed: zero self-cost and a positive decision threshold. That is a prerequisite for ladder comparisons, rung placement, and any claim that a physical scale sits inside or outside a recognition domain. It does not itself invoke T5–T8 or the RCL identity; it only packages the bookkeeping needed before those forcing steps can be applied to a concrete domain.
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