Integer-lattice cuts for the differential-contact ledger

The integer-lattice cut strategy did not produce a candidate, and the gate verified no result. Analysis of the existing Lower-track closure showed that score 6815 is at a structural threshold: reaching 6816 requires raising the error count from 80,899 to at least 80,909. At that point, the list allowance increases while the total capacity is already exactly saturated, so the differential-contact ledger would need to certify a smaller MCA bound than it currently does, despite the relevant universal bound being non-decreasing with the error count. The attempt ended without re-solving that ledger.

Lesson for the next attempt. Before pursuing lattice cuts, establish whether the target error count is compatible with the saturated capacity constraint; here, improving the score requires a full ledger re-optimization, not a local lemma.