cert

The module treats hydrogen emission lines on the Recognition Science phi-ladder. Status is a structural theorem with no sorry and no axioms. The Balmer series (H$\alpha$ 656 nm, H$\beta$ 486 nm, H$_\gamma$ 434 nm) is the concrete target: adjacent Balmer wavelengths stand in a ratio near $\phi^{0.8}$.

Domain cost is the local cost functional used to score recognition events on that ladder; the certificate demands it be zero when the two arguments coincide and nonnegative when both are positive. The canonical threshold is the positive cutoff against which spectral placements are judged. Upstream, nonnegativity of recognition cost is already known from the observer-forcing layer: every recognition event has cost $J\ge 0$ via the standard J-cost nonnegativity lemma.

One-line structure inhabitant. The three fields of HydrogenSpect3Cert are filled by the sibling lemmas that already prove diagonal vanishing of domain cost, nonnegativity of domain cost on the positive orthant, and positivity of the canonical threshold. No tactics beyond field assignment; no new arithmetic.

Gives the inhabited certificate that the hydrogen-spectrum-from-J-cost module needs before any Balmer-line comparison can be stated as a certified claim. It sits inside the Foundation forcing story that ties spectral ratios to the unique J-cost (T5) and the self-similar scale $\phi$ (T6). No downstream consumers are wired yet in the graph, so this is the local packaging step that closes the certificate interface for the structural theorem announced in the module header. It does not itself derive the 656/486 ratio; it only guarantees the cost and threshold side-conditions that such a derivation may assume.