status_continuum_open
plain-language theorem explainer
Records that the continuum limit of the recognition path sum Z_B as the bound B tends to infinity is not derived in this module. Gravity and path-sum auditors cite it as honest status bookkeeping for Seven Gaps Lane 2. The proof is pure reflexivity on the GapStatus field continuum_limit_derived.
Claim. In the path-sum measure status record, the flag asserting that the continuum limit of $Z_B$ as $B \to \infty$ has been derived equals $\mathrm{false}$.
background
Lane 2 of the Seven Gaps program builds a proved path-sum measure for $Z_{\mathrm{RS}}$ on a scoped configuration class. Configurations are BoundedComplex B: finite incidence data (vertices, edges, tets) at fixed lattice scale, mirroring Regge-style triangulations with the metric field dropped. The recognition path sum is the finite weighted sum $Z(B,w)=\sum_K \mu(K),w(K)$ with symmetry factors $\mu(K)=1/|\mathrm{Aut},K|$.
The module already proves finiteness of the labeled class and its relabeling quotient, positivity and invariance of $\mu$, and modulus bounds on $Z$ (including the unitary weights $w=e^{iS}$). Those facts are packaged in the status record pathSumMeasureStatus, which sets count-finite, quotient-finite, measure-defined, measure-positive, and modulus-bound flags to true.
What remains open is the continuum (thermodynamic) limit: existence and uniqueness of $\lim_{B\to\infty} Z_B$ as a substrate-derived nonuniform measure on unbounded complexes. This declaration tags that gap explicitly.
proof idea
One-line term proof by rfl. The status record is defined with continuum_limit_derived := false (or the field defaults to false); the theorem simply unfolds that definitional equality. No lemmas are applied.
why it matters
Honest gap tagging is part of the Seven Gaps discipline: proved content (finite $Z_{\mathrm{RS}}$ on the scoped class, $\mu$-bounds, relabeling invariance) is separated from open continuum questions. Downstream consumers of pathSumMeasureStatus can branch on this flag without reading the whole module. The continuum limit would connect the combinatorial CDT-style measure to a continuum gravitational path integral; until derived, claims about continuum gravity from this lane must stop at finite $B$. No parent theorems currently depend on this flag (used_by is empty); it is documentation infrastructure for the gap ledger.
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