gap2TickPhaseSubstrateStatus_flags
plain-language theorem explainer
Records the boolean ledger for Gap-2 Wave C1 residual R2: the exact-shell tick-phase schema and escaping witness are closed, strengthened late-block balance remains open, and the continuum-and-measure flag stays false. Gravity auditors cite it as the machine-checked status snapshot for the tick-phase substrate. The proof is a one-line decidability check on a concrete status record.
Claim. The Gap-2 tick-phase substrate status record satisfies: R2 schema closed is true, escaping witness landed is true, strengthened balance open is true, and Gap-2 continuum-and-measure is false.
background
Module Wave C1 R2 banks the exact-shell tick-phase enrichment residual. Exact path classes are already GlobalEquivalent quotients over shell signatures, so a tick map into Fin 8 is well-posed on classes. Dead classes (shell-constant and eventually-zero phase) are blocked upstream; escape needs intra-shell tick variance. The eight-tick API is only a Fin-8 trace hypothesis and supplies no equidistribution theorem; that content lives here as an independent proposition.
The substrate packages a derived phase $2\pi\cdot\mathrm{tick}/8$, non-circular equal-fiber equidistribution inside each shell, and a bridge: mass-balanced Fin-8 fibers cancel by eighth-root orthogonality to give shell-amplitude vanishing. A concrete signature vertex-count mod 8 witness escapes both dead classes; its oscillatory tail stays open (R4).
The status definition hard-codes four booleans summarizing that ledger: schema closed, escaping witness landed, strengthened balance still open, continuum-and-measure not flipped.
proof idea
One-line decidability proof. The status definition is a concrete structure with four boolean fields set to true, true, true, false. The theorem asserts the four equalities; decide discharges them by computation on those literals. No lemmas beyond the status definition are required.
why it matters
Gives a single proved snapshot of what Wave C1 Gap-2 residual R2 has closed versus left open inside the gravity seven-gaps program. Downstream readers can cite the flags instead of re-auditing the module: R2 schema and escaping witness are banked; contiguous late-block strengthened tick balance and analytic oscillatory tail remain open; continuum-and-measure is explicitly not claimed.
Framework landmarks: the Fin-8 tick phase sits on the eight-tick octave (forcing chain T7, period $2^3$). Eighth-root orthogonality that cancels balanced fibers is the discrete harmonic content of that octave. The module does not touch $D=3$, the J-cost uniqueness chain, or the alpha band; it only locks the tick-phase substrate status for Gap 2.
No parent theorems currently depend on this flag theorem (used-by is empty); it is an audit endpoint for the residual DAG draft.
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