GATE D14
Connected-support purity, TRUE_RELATION vs puncture
What changed
The connected correlation of each support set is separated by an EXACT identity: a primitive additive relation (the true structural signal) plus the deterministic F_p* puncture term -(1/(p-1))(1-β)^s. Decomposable frequency patterns cancel in the cumulant, so the relation hyperedges are pure. Every connected triple is then either a low-height primitive relation or has a uniformly small high-height tail (< 9/1000), audited at representative inventory primes 191/439/877 where the tail is 0.0080/0.0047/0.0048 and decreasing. Support-4/5 remain the open residual, the all-109-prime summed budget is the remaining step to a full pass.
Evidence
check 1Purity lemma proved as exact identity: κ_direct = κ_fourier at p=191/439/877 (rational)
check 2TRUE_RELATION cleanly split from exact puncture -(1/(p-1))(1-β)^s, decomposables cancel
check 3Support-3 tail audited 191/439/877 (later superseded by D15: 1/100 over all 109), 2 verifiers, 40/40 corruption
Verification: double · I2 · 13 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)