GATE D15

Projective directions, support-3 closed over all 109 primes

partialEvidence I2Verify: doublePublic claim: No2026-07-18

What changed

The homogeneous true-relation sum is regrouped into projective relation directions (scalar orbits), with an EXACT orbit-mass identity, a canonical direction height, and a relation lattice of determinant p with an exact shortest-vector certificate. Directions split short / medium / long by height. The headline result closes support-3 UNIFORMLY over all 109 inventory primes: the high-height tail is below 1/100 everywhere (worst 0.009475 at p=281). This corrects the D14 three-prime audit, whose worst case at p≈281 was missed by measuring only 191/439/877, so the earlier 9/1000 is superseded by 1/100. Support-4 and support-5 remain open.

Evidence

check 1Exact projective orbit-mass identity Σ∏B̂ = Σ_D A_p(D), direction height = primitive relation height

check 2Support-3 INVENTORY-UNIFORM: tail < 1/100 over all 109 primes (max 0.009475 at p=281), correcting D14's 9/1000

check 3Support-3 tail bound over 109 primes (later corrected by D16 to 11/1000 on the complete universe), 2 verifiers, 44/44 corruption

Verification: double · I2 · 27 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)

Graph impact

introducedC-D15-ORBIT-IDENTITYProved (internal)introducedC-D15-SUPPORT3-INVENTORYSuperseded

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