gap2SignatureBlockerAttackStatus
plain-language theorem explainer
Status record for the Gap-2 signature-mass attack on the Fin-8 oscillatory-tail blocker. It marks Burnside mass packaging, fiberwise amplitude, cube mass at shell 2, and blocker reformulation as landed; the blocker itself and eventual-balance impossibility as unproved; asymptotic single-signature concentration as failed; and continuum-and-measure as unflipped. Downstream flag theorems cite it as the canonical ledger of what Wave C1 R4 actually closed.
Claim. The Gap-2 signature-blocker attack status is the boolean record with: Burnside signature-mass packaging landed, fiberwise amplitude decomposition landed, cube mass at shell $2$ landed, and blocker reformulation landed all true; the signature blocker itself and eventual fiber-mass balance impossibility both unproved; asymptotic single-signature concentration fails true; and the Gap-2 continuum-and-measure flag false.
background
Module setting is Wave C1 R4 of the Seven Gaps gravity program: a terminal attack on SignatureFin8OscillatoryTailBlocker. That blocker asserts there is no signature coloring $\sigma$ of shells such that the Burnside-weighted 8th-root shell amplitudes form an oscillatory tail. The honest status is that the blocker Prop is not proved.
Under the banked Burnside identity, signature mass equals the exact-complex cardinality divided by $v!,e!,t!$. The cube signature $(n,n,n)$ dominates shell $n$ (mass $>1/2$) only in a mesoscopic window; external enumeration shows dominance through roughly $n\lesssim 200$, then failure by $n\approx 400$. Route (c) (eventual fiber-mass balance impossibility via a $>1/8$ test) likewise fails asymptotically.
The structure Gap2SignatureBlockerAttackStatus packages eight boolean ledger fields for what has and has not closed in this attack, including the reformulation of the blocker as an explicit sequence Prop on signature-mass cancellation.
proof idea
Pure structure literal: eight boolean fields are assigned by hand. Four infrastructure flags (Burnside signature mass, fiberwise amplitude, cube mass at shell 2, blocker reformulation) are set true; the two theorem-shaped targets (signature blocker proved, eventual balance impossibility) are set false; asymptotic concentration fails is set true; gap2 continuum-and-measure is set false. No tactics, no lemmas applied at this site.
why it matters
This is the canonical ledger for the Gap-2 signature-blocker attack. Downstream, gap2SignatureBlockerAttackStatus_flags projects the eight booleans into a single conjunction that other modules can pattern-match without re-reading the attack file.
In the Recognition gravity stack it records an honest stall: infrastructure (Burnside mass, fiberwise 8th-root grouping, shell-2 cube mass, iff-reformulation of the blocker) is closed, but neither the full signature blocker nor eventual balance impossibility is proved, and single-signature concentration is refuted as a uniform large-$n$ strategy. It does not flip gap2_continuum_and_measure. The eight-tick Fin-8 phase structure from the forcing chain remains the ambient discrete clock; this status only tracks how far the oscillatory-tail obstruction has been pushed.
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