cert_inhabited

Module RS_MTH_Structural_008 records the structural side of Recognition Science rung spacing: adjacent rungs differ by the golden ratio $\varphi\approx 1.618$. Status is a closed structural theorem (no sorry, no axioms).

The certificate structure bundles three elementary cost properties. Domain cost is the local cost functional on a pair of positive reals (measure versus expectation). It is required to vanish when the two arguments coincide and to stay nonnegative when both are positive. The canonical threshold is a fixed positive real used as a cutoff in the same module.

Those three fields are exactly the hypotheses that later structural or mass-ladder arguments may assume as a single package rather than three separate lemmas.

Term-mode one-liner. The module already defines a concrete value cert of type RSMTHStructural008Cert (built from the sibling lemmas that domain cost vanishes on the diagonal, is nonnegative, and that the canonical threshold is positive). The proof is the standard Nonempty introduction ⟨cert⟩.

Closes the inhabitation obligation for the module-8 structural certificate so downstream code can assume a single witness rather than three separate facts. In the Recognition framework this sits under the phi-ladder and rung-spacing layer (adjacent rungs scale by $\varphi$), which feeds mass formulas of the form yardstick times $\varphi$ to a rung offset. No used-by edges are recorded yet; the declaration is the terminal packaging step of this structural file. It does not itself invoke T5--T8 or the Recognition Composition Law, but it keeps the cost side of the ladder axiomatically tidy.