cert_inhabited
plain-language theorem explainer
The Module 11 forcing-chain certificate is inhabited: there exists a witness packing diagonal vanishing of the domain cost, its non-negativity on positive arguments, and positivity of the canonical threshold. Anyone citing the RS rung-spacing structural package uses this existence fact. The proof is a one-line term that exhibits the prebuilt certificate value.
Claim. The type of Module 11 certificates is nonempty: there is a witness packing (i) $\mathrm{domainCost}(r,r)=0$ for all $r\neq 0$, (ii) $\mathrm{domainCost}(m,e)\ge 0$ whenever $m>0$ and $e>0$, and (iii) the canonical threshold is strictly positive.
background
Module 11 of the RS forcing chain treats rung spacing: consecutive rungs on the $\varphi$-ladder differ by the golden-ratio factor $\varphi\approx 1.618$. The module is marked structural (zero sorry, zero axioms).
The certificate structure packages three elementary cost facts used by that spacing story. The domain cost vanishes on the diagonal: equal positive arguments give cost zero. It is nonnegative for strictly positive measure and expectation arguments. The canonical threshold (the positive scale against which rung steps are compared) is strictly positive.
These three fields are exactly the hypotheses a downstream consumer of Module 11 needs before invoking the spacing arithmetic; the inhabitedness theorem asserts that package is realizable.
proof idea
One-line term proof. The certificate value cert (assembled earlier in the module from the three proved field lemmas) is exhibited as an explicit inhabitant of RSForcingChain011Cert, which immediately yields Nonempty.
why it matters
Closes the structural certificate for Foundation Module 11 (RS rung spacing by factor $\varphi$). In the forcing chain this sits with the $\varphi$-ladder mass formula and the T6 self-similar fixed point: consecutive rungs are separated by $\varphi$, and the cost package guarantees the comparison scale is well-defined and nonnegative. No downstream consumers are wired yet in the graph; the theorem is the existence seal that later modules can import when they need a single named witness rather than three separate lemmas. It does not itself derive the spacing law; it only certifies the cost side-conditions.
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