GATE D10
Moment duality & signed cancellation
What changed
Encode the signed cancellation as factorial moments of N (the number of forbidden runners): u proper iff some time has N=0. An exact rational moment dual certifies properness per vector (closes 60/60 proper vectors). A clean pair theorem is proved-in-direction: large pair-correlation deviation forces a low rational ratio height. But the uniform generic dual is refuted, an intrinsic small-time spike (all runners cluster) inflates the higher moments 15-95x, independent of ratio height, re-encoding the D9 cancellation barrier.
Evidence
check 1Exact factorial-moment dual: per-vector LP dual closes 60/60 proper vectors (integer-coeff Bonferroni valid)
check 2Pair theorem proved-direction: deviation > 0.03 ⟹ ratio height ≤ 2 (interval/lattice overlap)
check 3Generic uniform dual REFUTED (intrinsic spike inflates μ4~15x, μ5~95x), two verifiers, 30/30 corruption
Verification: double · I2 · 14 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)