gap2CertifiedFin8PhaseCloseStatus_flags
plain-language theorem explainer
Boolean status snapshot for the Gap-2 certified Fin-8 phase-close API: API and recipe kinds are banked, the bare R5 bridge has landed, the certified residual is defined but uninhabited, the certified close is uninhabited, and the continuum-and-measure flag stays false. Gravity auditors cite it to pin session-4B provenance after the TailAntipodalShift route was killed. Proof is a single `decide` on the status record.
Claim. The Gap-2 certified Fin-8 phase-close status record satisfies: certified API banked, recipe kinds banked, bare R5 bridge landed, certified residual defined-and-uninhabited, certified close not inhabited, and Gap-2 continuum-and-measure still false.
background
Module banks a provenance-honest R5 close surface for Gap 2 after session 4B closed the matching / TailAntipodalShift flip route. The Fin-8 tick is the discrete eight-tick octave substrate; a certified tick recipe is a named constructor package (not a bare existential) whose True fields only bank API honesty. Inhabitation of an actual recipe is deferred.
CertifiedGap2Fin8PhaseClose packages escape from ShellConstant / EventuallyZeroPhase / ShellSigTick decoys together with an OscillatoryTail on tick-derived phase. The typed residual of that package is nonempty as a type, and a bridge maps it to the bare continuum R5 residual shape (continuum substrate with oscillatory tail). The status structure is a pure Bool record summarizing which of those surfaces are banked versus inhabited.
Upstream, gap2CertifiedFin8PhaseCloseStatus is the concrete record with the six flags fixed by definition. The module explicitly does not flip the continuum-and-measure gap flag.
proof idea
One-line decidability proof: decide evaluates the six Boolean equalities against the concrete status record gap2CertifiedFin8PhaseCloseStatus, whose fields are definitionally true/true/true/true/false (and continuum-and-measure false). No lemmas beyond Bool decidable equality are required.
why it matters
Pins the honest ledger for Gap-2 Fin-8 phase close inside the SevenGaps gravity stack: API and recipe kinds are banked, the bare-R5 bridge has landed, yet both the certified residual and the certified close remain uninhabited. That separation keeps the continuum-and-measure flag false and blocks any claim that Gap 2 is closed.
Downstream consumers (none wired yet in the graph) can quote the flags without re-inspecting the package constructors. Framework context is the eight-tick octave (T7) and the discrete-to-continuum residual bridge for quantum-gravity Gap 2. Next inhabit target named in the module is mixedAutMassBalancer (aggregate antipodal tick-fiber masses), not class-pair TailAntipodalShift. No sorry, admit, new axiom, or native_decide.
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