Gap2SignatureBlockerAttackStatus
plain-language theorem explainer
Status record for the Gap-2 signature-mass attack on the Fin-8 oscillatory-tail blocker. Eight booleans mark which sub-lemmas have closed (Burnside mass packaging, fiberwise amplitudes, cube mass at shell 2, blocker reformulation) versus which targets remain open (the blocker itself, eventual balance impossibility, continuum flip). Gravity auditors cite it to read the honest tier of the Wave C1 R4 terminal attack without scanning the whole module.
Claim. A status bundle of eight booleans recording progress on the signature-mass form of the Gap-2 blocker: whether Burnside signature masses, fiberwise shell amplitudes, cube mass at shell $2$, and the blocker reformulation have landed; whether the signature blocker and eventual balance-impossibility are proved; whether asymptotic single-signature concentration fails; and whether the Gap-2 continuum-and-measure claim has flipped.
background
Gap 2 in the Seven Gaps gravity program asks whether an eight-tick (Fin-8) phase coloring of exact path classes can produce an oscillatory tail in the shell amplitudes. The module attacks the blocker statement that no such coloring exists, rewritten as a signature-mass cancellation claim: no map from shell signatures to Fin 8 makes the Burnside-weighted eighth-root amplitudes an oscillatory tail.
Under the banked Burnside identity, signature mass equals the exact-complex cardinality divided by the product of factorials of the signature coordinates. Shell mass is the sum of signature masses. The cube signature $(n,n,n)$ dominates only in a mesoscopic window; external enumeration shows dominance fails by $n \approx 400$, so uniform asymptotic concentration is not a viable route.
This structure is the module's ledger of which pieces of that attack have closed as theorems and which remain open. It sits after the mass packaging lemmas and the iff between the original blocker and the signature-mass cancellation statement.
proof idea
No proof: this is a structure definition. Eight named Bool fields package the attack checklist. Downstream, a single value fills the fields from the module's landed theorems (Burnside mass, fiberwise amplitude, cube mass at shell 2, blocker reformulation) and the honest negatives (blocker unproved, continuum unflipped).
why it matters
The parent value gap2SignatureBlockerAttackStatus freezes the Wave C1 R4 tier: reduction plus Burnside mass lemmas plus stall diagnosis, with the blocker Prop still unproved. That matches the module claim that routes (a)/(b) (uniform single-signature concentration) and (c) (eventual fiber-mass balance via a $>1/8$ test) fail asymptotically, while the honest reformulation to signature-mass cancellation has landed.
In the Recognition gravity stack this is bookkeeping for Gap 2, not a physics theorem. It does not touch the forcing chain (T0–T8), the Recognition Composition Law, or the $\phi$-ladder mass formula. Its job is to keep the continuum-and-measure flag and the blocker flag visibly false until a real proof arrives, preventing silent overclaim on eight-tick cancellation in the gravity gaps.
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