gap2TickPhaseSubstrateStatus
plain-language theorem explainer
Status record for the Gap-2 exact-shell tick-phase substrate (Wave C1 R2). It marks the R2 schema closed, the escaping signature-vertex witness landed, the strengthened late-block balance still open, and continuum-and-measure unflipped. Downstream flag lemmas cite it as the single source of those four booleans. The body is a pure structure instance with four literal Bool fields.
Claim. The Gap-2 tick-phase substrate status is the four-field record with R2 schema closed equal to true, escaping witness landed equal to true, strengthened balance open equal to true, and Gap-2 continuum-and-measure equal to false.
background
Wave C1 R2 banks the exact-shell tick-phase enrichment residual for Gap 2. Path classes already live in the GlobalEquivalent quotient 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 genuine intra-shell tick variance.
The eight-tick API is only a Fin-8 trace hypothesis. Equidistribution is an independent Prop here: equal fiber cardinalities inside each shell, with no amplitudes. Mass-balanced Fin-8 fibers cancel by eighth-root orthogonality and yield shell-amplitude vanishing. A concrete signature vertex-count mod 8 witness escapes both dead classes; its oscillatory tail stays open (R4).
The status structure is a four-boolean dashboard: schema closed, escaping witness landed, strengthened contiguous late-block balance still open, and continuum-and-measure not claimed.
proof idea
Definitional instance, not a proof. The four fields of the status structure are filled by the literals true, true, true, and false respectively. No lemmas are applied; the downstream flags theorem re-reads these literals by decide.
why it matters
Gives a single named status object for the Gap-2 tick-phase substrate so progress can be audited without re-opening the module narrative. Downstream, the flags theorem asserts the four equalities and discharges them by decision procedure, locking the dashboard into the build.
In framework terms this sits under the eight-tick octave (T7): phase is $2\pi\cdot\mathrm{tick}/8$, and eighth-root cancellation is the bridge from equidistributed fibers to shell-amplitude vanishing. It records that R2 schema work and the escaping witness are banked, while TypedResidual_strengthened_tick_balance and analytic oscillatory tail (R4) remain open, and it explicitly refuses to flip continuum-and-measure.
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