GATE D25
Adaptive rational-time separation
What changed
D24 showed that a fixed handful of clocks, the level fourteen, twenty-eight and forty-two grids, removes more than half of the reachable states but only by a constant factor, which is not enough to bring the search within the fixed limits. D25 stops relying on a fixed set of clocks and instead invents new ones on the fly, aimed at whichever branches are still alive. Each new clock is a rational time whose denominator is chosen to separate the surviving states, and by the definition of a lonely runner every genuine counterexample must have at least one runner near the origin at that time, which becomes an exact clause on the speeds modulo that denominator. The crucial discipline, and the whole point of the gate, is that these denominators are kept separate and are linked only loosely through their common factors; they are never folded into one enormous shared modulus, because that would simply bring back the state explosion the previous gates ran into. The gate measures, directly on the states the previous search actually reached, which of these adaptive clocks cut real branches, how much they shrink the search, and how expensive the resulting proofs are, both on their own and combined with the arithmetic checks. The required regression is unchanged: the p=197 base cover has a lonely time at one fourteenth, so an adaptive early cut must fire. No larger compute budget is authorized, and nothing about the conjecture is decided by opening this gate. LRC(13) remains open.
Evidence
Verification: double · I2 · 8 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)