GATE D13
Connected hypergraph, tight rank-1 recovered
What changed
The higher residual left by D12 is expressed as EXACT connected correlations, and the pair graph is extended to a relation hypergraph. The support-3 inverse is proved-in-direction: a large connected triple correlation is always backed by a bounded-height support-3 additive relation. Adding these support-3 hyperedges completes the structure the pair graph missed, the tight class is now recovered as additive rank 1 (the exact D5 anchor), by exact linear algebra, not hyperedge count. Scope note: the support-3 inverse profile is measured at p=191 and the support-4/5 profile is evidence, not an all-prime theorem.
Evidence
check 1Exact connected partition identity, punctured Fourier correction -1/(p-1) kept exactly
check 2Support-3 inverse: large connected triple ⟹ bounded-height support-3 relation (frozen before order 4)
check 3Hypergraph recovers tight class = additive rank 1 (Q-rank, not edge count), 2 verifiers, 36/36 corruption
Verification: double · I2 · 8 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)