GATE D17

Support-4 fast correlation, inventory-complete

passEvidence I2Verify: doublePublic claim: No2026-07-18

What changed

A primitive root turns the multiplicative support-4 correlation into a cyclic 4-point correlation on Z_{p-1}, giving an exact fast engine (O(p^3 log p) time, O(p^2) memory) where the previous method was O(p^4). The connected fourth cumulant identity and its Fourier-tensor form are proved exactly. This closes support-4 over the COMPLETE active universe of all (p-1)^3 ratio configurations at every one of the 109 primes (all exact-transform, no prime left open): the worst generic tail is 5/686 = 0.0072886 at p=197, an interior prime decided by the inventory, not the endpoints. It also replaces the always-12 full relation-space rank with a bounded-height rank profile that measures how fast short, simple relations rigidify a vector (tight at height 1, generic at height 2). Support-5 stays open.

Evidence

check 1Cyclic + tensor Fourier support-4 identity PROVED exact (κ4_cyclic = κ4_occupancy, Fractions)

check 2Support-4 INVENTORY-COMPLETE all 109 primes: max τ4 = 5/686 at p=197, exact-transform, none open

check 3Bounded-height rank r₄,H replaces always-12 full rank; 2 verifiers, 52/52 corruption

Verification: double · I2 · 22 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)

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