GATE D16
Modular rank repair, support-3 completeness, support-4
What changed
A load-bearing correction: relation rank must be computed over F_p, not Q, because every relation satisfies R·u ≡ 0 (mod p) with u nonzero, so the rank is at most 12 and the additive dimension is always at least 1. The D15 'generic additive dimension 0' was an artifact of Q-rank and is withdrawn. Support-3 is then made genuinely complete by scanning the FULL universe of all (p-1)^2 triple ratios per prime (not one relation line): the true worst tail is 0.010377 at p=353, so the bound is 11/1000, correcting both D14's 9/1000 and D15's 1/100 (both from incomplete families). The projective/lattice method is extended to primitive support-4 relations (orbit identity, lattice of det p, connected 4th cumulant), exact at four small primes, support-4 inventory and support-5 remain open.
Evidence
Verification: double · I2 · 27 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)