GATE D11

Punctured moments, inventory-wide closure

partialEvidence I2Verify: doublePublic claim: No2026-07-18

What changed

The D10 blocker was a universal atom, not a missing dual. Removing the t=0 spike EXACTLY (where all 13 runners are trivially forbidden) unblocks the low-degree dual: the punctured degree-5 dual now has a positive generic margin for ALL 109 inventory primes (worst +0.1221, exact). The pair inverse theorem becomes inventory-uniform (exceptional correlation implies ratio height at most 3). Every vector is then closed by the dual (high ratio height) or emits an exact exceptional-ratio structure certificate.

Evidence

check 1Exact spike removal μ_j = C(13,j)/p + (p-1)/p·μ_j* (proved + verifier-checked)
check 2Punctured deg-5 dual: generic margin POSITIVE for all 109 primes (worst +0.1221)
check 3Pair theorem inventory-uniform, dichotomy closed-or-exceptional-ratio, 2 verifiers, 30/30 corruption

Verification: double · I2 · 12 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)

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