gap5ConstraintCloseStatus_flags
plain-language theorem explainer
Binding receipt that the Gap-5 constraint-recovery status record is fully closed: recovery true, continuum/HKT campaign and residual-DAG open bits cleared, both Dirac and HKT halves closed, kill-tower banked. Gravity auditors cite it to check that the Wave C5 ledger flip is co-asserted with its green halves and cleared open bits. Proof is seven reflexivity steps on the status definition.
Claim. The Gap-5 constraint close-status record satisfies: constraint recovery holds; the continuum-algebra/HKT campaign open bit is false; the HKT-rigidity residual open bit is false; the packaged-target residual open bit is false; the Dirac half is closed; the HKT half is closed; and the kill-tower scope certificate is banked.
background
Wave C5 packages the close status of Gap-5 constraint recovery in the Seven Gaps gravity campaign. The status record is a pure Bool bundle placed downstream of the full-theory ledger and both named closers, so flipping the ledger bit cannot create an import cycle.
The green conjunction it reports has two halves. The Dirac half is continuum binding of the Dirac algebra limit. The HKT half is the theorem-derived claim that Hojman kinetic-normalized rigidity at $n=2$ pins general relativity (FTC-derived). Residual-DAG open bits track whether HKT rigidity or a packaged target remains unfinished; the campaign open bit tracks continuum-algebra/HKT work still listed open.
A kill tower of negative results (one-site, point-split strong, canonical-momentum, and vacuum-sector counterexamples) certifies that no stronger unconditioned $n=2$ rigidity statement is true. Adjudication reference: D-gap5-acceptance-adjudication-20260723.
proof idea
Pure definitional term proof. The status constant is a structure value whose seven Bool fields are already set to the claimed literals, so the conjunction is witnessed by seven rfl proofs:
⟨rfl, rfl, rfl, rfl, rfl, rfl, rfl⟩.
No lemmas are applied; there is no case split or rewriting beyond unfolding the status definition.
why it matters
This is the Wave C5 binding receipt for Gap-5. It co-asserts ledger gap5 true with both green halves, campaign open-bit cleared, and residual-DAG rigidity bits cleared, matching the module contract that ties
- full-theory benchmark gap5 constraint recovery true,
- campaign continuum-algebra/HKT open false,
- residual-DAG HKT-rigidity and packaged-target open false,
- residual-DAG gap5 recovery true
to Dirac continuum binding and Hojman-pins-GR (HKT kinetic-normalized $n=2$).
In the Recognition gravity stack this is bookkeeping, not new dynamics: it freezes the acceptance state after the Dirac and HKT closers and the kill-tower scope certificate, so later campaign or ledger reads cannot silently disagree with the closed halves. No downstream dependents are wired yet; the declaration is the terminal receipt for this gap.
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