Gap2TickPhaseSubstrateStatus
plain-language theorem explainer
Status record for the Gap-2 exact-shell tick-phase enrichment residual (Wave C1 R2). Four booleans track whether the schema closed, an escaping witness landed, the strengthened late-block balance remains open, and whether the continuum/measure flag flipped. Gravity auditors cite it as the single dashboard for R2 progress. It is a plain structure definition with no proof content.
Claim. A status bundle of four booleans for the Gap-2 tick-phase substrate: (i) R2 schema closed, (ii) escaping witness landed, (iii) strengthened balance still open, (iv) Gap-2 continuum-and-measure flag. Instantiated downstream as $(\mathrm{true},\mathrm{true},\mathrm{true},\mathrm{false})$.
background
Gap 2 in the Seven Gaps gravity program concerns continuum and measure structure on exact shells. Wave C1 R2 banks an exact-shell tick-phase enrichment schema: path classes are already the GlobalEquivalent quotient of shell signatures, so a tick map into $\mathrm{Fin},8$ is well-posed on classes. Dead classes (shell-constant phase, eventually-zero phase) are blocked upstream; escape needs genuine intra-shell tick variance.
The eight-tick API supplies only a $\mathrm{Fin},8$ trace hypothesis, not equidistribution. Equidistribution is stated here as equal fiber cardinalities inside each shell, independent of amplitudes. Mass-balanced fibers cancel by eighth-root orthogonality and yield vanishing shell amplitude. A concrete signature-vertex-count mod 8 witness escapes both dead classes; a raw complexity tick $2\pi\cdot(n\bmod 8)/8$ is shell-constant and therefore dead.
This structure does not prove those facts. It only packages four progress flags so the residual DAG can be read without scanning the whole module.
proof idea
No proof. The declaration is a four-field structure of booleans. The sole downstream instance sets schema-closed and escaping-witness to true, strengthened-balance-open to true, and continuum-and-measure to false, matching the module's theorem list and open list.
why it matters
Gives a single typed dashboard for the R2 residual named in the Wave C1 Gap-2 design notes. Downstream gap2TickPhaseSubstrateStatus freezes the current ledger: schema and escaping witness closed, strengthened contiguous late-block balance still open, and gap2_continuum_and_measure not flipped.
In the Recognition chain this sits under gravity's seven-gap program and uses the eight-tick octave (T7) only as a $\mathrm{Fin},8$ phase substrate, not as a continuum measure theorem. It records that per-shell equidistribution and shell-amplitude vanishing are banked, while uniform block cancellation and the analytic oscillatory-tail claim for the signature witness remain open (R4). Auditors use the flags to separate closed schema work from the still-open continuum flip.
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