GATE D23

Early global realizability cuts

passEvidence I2Verify: doublePublic claim: No2026-07-19

What changed

D22 was limited because its only genuine global check waited until the final reconstruction step, and until then matching fingerprints prime by prime removes nothing. The correction is that more than one global check is available early, before the reconstruction threshold. A symbolic state can be ruled out long before the whole speed tuple is reconstructed, for either of two independent reasons. First, arithmetic realizability: its symmetric-function values simply cannot come from thirteen bounded integer squares, which classical inequalities among symmetric functions can often certify. Second, early impropriety on the refinement grids: it already fails on the finer time grid at level fourteen, the exact place where the p=197 base cover turned out to be proper, long before any tuple is reconstructed. D23 runs both branches in parallel, carrying the global residue on the level fourteen, twenty-eight and forty-two grids alongside the residue modulo each prime, and cutting a symbolic state the moment either global check refutes it, with a theorem and a proof hash for every cut. The mandatory regression is that the p=197 witness, a genuine base cover that is proper at level fourteen, must trigger an early cut before full reconstruction. No compute budget increase, and nothing about the conjecture is decided by opening this gate. LRC(13) remains open.

Evidence

check 1Branch A arithmetic realizability from 13 bounded integer squares, applied BEFORE the 2H threshold: per-degree coefficient bounds, Newton and Maclaurin inequalities, power-sum and Hankel positivity, square-splitting modulo auxiliary moduli, primitivity and multiplicity
check 2Branch B early impropriety on refinement grids at levels 14, 28, 42: carry the global residue modulo (14,28,42) with the residue modulo p and certify refined-cover feasibility without reconstructing the integer tuple
check 3D23-PASS (measured): cut soundness proved (each early cut is necessary for a counterexample) and independently verified, the mandatory p=197 level-14 cut FIRES, and on the certified pilot Branch A cut 5000 of 5000 random candidates and Branch B cut 7 of 7 realistic base covers before 2H, where D22 had none. Two verifiers ACCEPT, 190 of 190 corruption rejected. These are BOUNDED PILOT MEASUREMENTS, not a claim that every reachable state is cut. Full compatible-state campaign OPEN; the frontier moves to D24. LRC(13) OPEN

Verification: double · I2 · 10 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)

Graph impact

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