status_substrate_measure_open

Lane 2 of the Seven Gaps program builds a proved path-sum measure for the Recognition Science partition sum $Z_{RS}$ over a scoped class of bounded combinatorial complexes. The module already discharges several layers: the configuration class is finite, the relabeling quotient is finite, the symmetry factor $\mu(K)=1/|\mathrm{Aut},K|$ is positive and at most one and relabeling-invariant, and the weighted path sum $Z$ is a finite sum with modulus bounds and unitary weights $w=e^{iS}$.

Those achievements are summarized in the status record pathSumMeasureStatus, whose proved fields include count finiteness, quotient finiteness, measure definition, positivity, and modulus bounds. One further flag on that record tracks whether a nonuniform measure has been derived from the recognition substrate itself (as opposed to the combinatorial symmetry factor). The module documentation marks that substrate-derived measure as still open.

Term-mode reflexivity. The status definition sets the substrate-derived flag to false by construction; the theorem is rfl against that field projection. No lemmas are applied.

Recognition Science gravity work needs an honest ledger of what is closed versus open in the path-sum construction for $Z_{RS}$. This declaration freezes the open bit in Lean so downstream gap reports cannot silently claim a substrate-derived nonuniform measure. It sits beside the proved combinatorial measure $\mu(K)=1/|\mathrm{Aut},K|$ and the finite path sum, without overclaiming a derivation from the recognition substrate or from the forcing chain (T0–T8). No parent theorems currently depend on it; its role is status hygiene for the Seven Gaps audit trail.