GATE D24

Early cuts on reachable states

partialEvidence I2Verify: doublePublic claim: No2026-07-19

What changed

D23 proved that its early cuts are safe and showed, on a bounded pilot, that they prune strongly before reconstruction. The pilot numbers, every sampled candidate and every sampled cover removed, are measurements on a sample, not a statement about the whole search. D24 tests the proved cuts where it actually matters: on the real states the global master reaches, rather than on random candidates. The engine carries a single shared clock, one global residue pattern modulo eighty-four, the least common multiple of the level fourteen, twenty-eight and forty-two grids, and it never re-chooses that pattern separately at each prime, so the level constraints stay one common global object. On this real reachable-state stream it measures how much the proved cuts prune, the branching they introduce, the certificate cost and the projected campaign cost. No larger compute budget is authorized, and nothing about the conjecture is decided by opening this gate. LRC(13) remains open.

Evidence

check 1Apply the D23-proved early cuts (Branch A arithmetic realizability + Branch B refinement 14/28/42) to the REAL reachable states enumerated by the global master, not a random sample

check 2Carry ONE global residue multiset modulo 84 = lcm(14,28,42), a single common small-modulus clock; never re-choose the level residues independently at each prime

check 3D24-PARTIAL (measured on the reachable distribution): global mod-84 semantics and refined CRT coupling proved and double-verified; the exact t=1/14 cut fires on the p=197 witness; the fixed refinement cuts at 14/28/42 remove 55.3% of reachable states. 190-plus corruption rejected. But the reduction is a constant factor: mod-84 space about 2^84, residual about 2^83 versus caps about 2^42, a scale indicator for the current architecture not a hard floor. Exact closures on tested branches; certified OPEN branches remain; the frontier moves to D25 adaptive rational-time separation. LRC(13) OPEN

Verification: double · I2 · 8 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)

Graph impact

introducedC-D24-REACHABLEProved (internal)introducedC-D24-COUPLINGProved (internal)introducedC-D24-PRUNINGValidated (bounded)introducedC-D24-CLOSUREOpen changedC-D23-CAMPAIGNOpen

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