GATE D21
Signature-narrowed certified compatibility
What changed
D20 was blocked because it asked for the complete unconstrained local-cover universe before any cross-prime information had narrowed the query. D21 reverses the order: propagate a partial global signature first, then ask only for local covers compatible with that signature. Two corrections and one architectural win carry it. First, the padding correction: a full thirteen-speed cover is a minimal core plus a padding multiset, and padding is not harmless because it changes multiplicities, symmetric coefficients, the projective orbit and CRT compatibility, so the oracle must query the full thirteen-multiset, not just a minimal core. This is proved and checked against brute force. Second, the narrowed oracle: once a target signature is fixed, the squared-speed multiset is pinned up to the quadratic-residue scale action, so every matching cover is found by scanning the half-group of scales, a cost linear in the prime rather than the blocked full enumeration. Measured on the D20-hard primes up to 2267, each narrowed query terminates in a fraction of a second with a replayable certificate, exactly where the old route was blocked. Every query still returns one of matches-complete, empty-certified or open-incomplete, a solver refutation is invalid without a machine-checkable proof, and a timeout is open. The honest boundary: the per-query enumeration wall is removed, but the full campaign still needs a meet-in-the-middle seed at the first prime, so no campaign verdict is claimed yet. LRC(13) remains open.
Evidence
Verification: double · I2 · 24 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)