GATE D27

Orbit-compressed unlabeled CRT: BLOCKED

blockedEvidence I2Verify: doublePublic claim: No2026-07-20

What changed

D26 proved the direct coordinate CRT threshold but measured the labeling obligation as a net-negative cost. D27 keeps the lower reconstruction threshold while removing the permanent per-prime labels, holding the global state as an unordered multiset of CRT root classes together with its stabilizer. Merging a new prime is done by enumerating matching orbits, that is transport matrices over the compatibility graph, rather than raw permutations. The orbit quotient is proved exact, with no false merge and no false split, and the sign-lift factor of 2^13 per prime is itemized for the first time. The decisive result is a certified obstruction, not a worst-case proxy: a single generic distinct-residue merge already produces 25,505,877,196,800 orbit children, about 2^44.5, which exceeds the frozen 2^42 state ceiling at merge depth one. The gate closes the forward orbit-enumerative unlabeled root-CRT architecture under the frozen caps. It does not rule out bidirectional or hybrid methods, and it does not decide the conjecture. LRC(13) remains open.

Evidence

check 1Orbit quotient theorem: child unordered CRT states correspond bijectively to transport matrices; raw matchings per orbit equal the exact multinomial. Proved and independently verified, no false merge or false split, repeated roots and non-free stabilizers handled

check 2Shallow-zone theorem: below the certified threshold zone the available arithmetic and rational-time cuts are pairing-blind, so the reachable width is the exact product of orbit counts; one generic merge is 2^44.5, above the 2^42 ceiling at depth one

check 3D27-BLOCKED (measured, certified at depth one). Verifiers V1 19/19 and V2 15/15 ACCEPT, corruption 255/255. The threshold theorem stands; the forward orbit-enumerative architecture does not fit the caps. No BASE-SURVIVOR, no GLOBAL-WITNESS. LRC(13) OPEN

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

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