cert

Physics RS Module 3 records the neutron-lifetime match $\phi^{17}\cdot 0.246,\mathrm{s}=878.5,\mathrm{s}$ against PDG $878.4,\mathrm{s}$, marked RS_PASS as a structural theorem (zero sorry, zero axiom).

The certificate structure demands three properties of the module's domain cost: it is zero when the two arguments coincide (and nonzero), it is nonnegative on the positive orthant, and a fixed positive threshold exists. Upstream, recognition cost is already known to be nonnegative: "The cost of any recognition event is non-negative," via nonnegativity of the J-cost on positive states.

Sibling lemmas supply the three concrete facts wired here: diagonal vanishing of domain cost, its nonnegativity for positive inputs, and positivity of the canonical threshold.

One-line structure construction. Each field of the certificate is filled by the corresponding sibling lemma: diagonal vanishing by the domain-cost-at-equality fact, nonnegativity by the domain-cost nonnegativity lemma, and threshold positivity by the canonical-threshold positivity lemma. No further rewriting or case analysis occurs.

Gives Module 3 a single named inhabitant of its certificate type, so downstream code (and the module status line) can treat the three cost axioms as one package rather than three free-floating lemmas. The module itself is the neutron-lifetime rung check on the phi-ladder; this certificate is the structural wrapper that the status banner relies on. No parent theorems currently depend on it in the graph, so its role is local packaging inside the physics module rather than a link in the T0–T8 forcing chain.