cert_inhabited

The module treats recombination redshift as a structural consequence of J-cost geometry rather than a fitted parameter. In RS units the observed $z_{\mathrm{rec}} \approx 1100$ sits between $\phi^{14}$ and $\phi^{15}$ on the golden-ratio ladder ($\log 1100 / \log \phi \approx 14.7$), which the module records as consistent with the forcing chain's self-similar scale $\phi$.

Domain cost is the local cost functional on mass/energy pairs; the certificate demands it vanish when the two arguments coincide (and are nonzero) and stay nonnegative when both are positive. The canonical threshold is the positive cutoff used to mark the recombination scale in that cost landscape.

Recombin3Cert is the structure packing those three propositions. This theorem only asserts that the structure is inhabited.

One-line term proof. The concrete instance cert already assembles the three fields of Recombin3Cert; wrapping it as ⟨cert⟩ inhabits Nonempty Recombin3Cert. No tactics, no further lemmas.

Closes the existence side of the recombination-redshift certificate in the Cosmology layer (Plan v7, 116th pass). The module status is structural theorem: zero sorry, zero axiom. Downstream consumers that need a Nonempty witness for the certificate bundle can cite this rather than reconstructing the three field proofs. It sits under the broader RS claim that $z_{\mathrm{rec}}$ is forced near the $\phi$-ladder rung between 14 and 15, consistent with T6 ($\phi$ as self-similar fixed point) and the J-cost uniqueness from T5, without itself deriving the numerical placement of $z_{\mathrm{rec}}$.