cert_inhabited

The module derives the Shannon capacity formula $C = B \log_2(1+\mathrm{SNR})$ as a structural consequence of the Recognition Science $J$-cost. In RS-native units the distinguished operating point is $\mathrm{SNR} = J(\varphi)^{-2} \approx 71.7$, giving spectral efficiency $C/B = \log_2(72.7) \approx 6.18$ bits/s/Hz, numerically near $\varphi^{2\varphi}$.

The certificate structure packages three elementary properties of the domain cost and the canonical threshold: diagonal vanishing, nonnegativity on the positive orthant, and strict positivity of the threshold. Those three facts are the only hypotheses the capacity derivation needs from the cost side.

Upstream, the structure itself is just the Prop-carrying record; the present theorem asserts that record is inhabited.

Pure term proof. Nonempty is introduced by the anonymous constructor applied to the already-built certificate value, so the goal reduces to exhibiting one term of the certificate structure. No tactics, no rewriting, no further lemmas.

Closes the structural package for Shannon capacity from $J$-cost in the Information domain (module status: 0 sorry, 0 axiom). The certificate is the single object a downstream capacity theorem would open to obtain diagonal vanishing, nonnegativity, and a positive threshold. No used_by edges are recorded yet, so the declaration presently stands as the terminal inhabitation fact for the session-3 plan.

Framework landmarks: the cost side ultimately rests on $J$-uniqueness (forcing chain T5) and the self-similar fixed point $\varphi$ (T6); the numerical SNR point $J(\varphi)^{-2}$ is the bridge from that cost to classical channel capacity. The result does not itself compute the $6.18$ figure; it only guarantees the certificate needed to state it cleanly.