GATE D20

Simultaneous prime-product lift, blocked at scale

blockedEvidence I2Verify: doublePublic claim: No2026-07-19

What changed

D20 built the full prime-product lift machinery and then hit a computational wall. The D6 finite reduction and D7R alignment were frozen and independently replayed with no predicate mismatch, so no restart. The key correction, O-A, is that a local cover at one prime is a necessary but not sufficient sign of a global counterexample: the exact p=197 witness covers at the base level yet is proper one refinement level up, so a base cover can be broken by refinement. That makes the base-cover compatibility search a sound one-way filter, and every survivor only a candidate that must still pass the refinement tower. On that footing the applicability, normalization and reconstruction rules were proved: a prime is applicable exactly when it divides no speed, sign is removed by squaring, the one global scale acts as a single unit per prime with no independent per-prime scaling, the global object is the monic polynomial in the squared speeds, and a certified inventory of 294 primes crosses the reconstruction threshold. The compatibility engine, the complete projective atlas over every coefficient stratum, the three-valued cover oracle and the complete exact-cover generator were all built and double-verified. But the decisive fact is measured, not assumed: complete local-cover enumeration does not terminate within the resource caps for the inventory primes, so every campaign block is open and nothing is certified closed. This is D20-BLOCKED, an honest negative-capability result driven by cost, exactly like the earlier D6 non-tight campaign. It is not a compatibility claim, not a counterexample, and not a solution. LRC(13) remains open.

Evidence

check 1D6/D7R reduction frozen and independently replayed (V1/V2 ACCEPT), no predicate mismatch, no restart; O-A resolved: base cover is necessary not sufficient (p=197 witness proper at level 14), so the base-cover search is a sound one-way filter with mandatory refinement escalation
check 2Applicability, QR-projective normalization and CRT reconstruction proved (O-B/O-C/O-D); projective atlas over all strata, three-valued oracle and complete exact-cover generator built and double-verified with full corruption suites
check 3D20-BLOCKED (measured): complete local-cover enumeration does not terminate within caps at inventory scale, every campaign block OPEN, certified-closed product zero. Honest cost-driven negative capability, not a compatibility claim or counterexample. LRC(13) OPEN

Verification: double · I2 · 34 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)

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