GATE D23
Early global realizability cuts
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
Verification: double · I2 · 10 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)