n
42
Every stabiliser generator costs one logical qubit. Deleting a single row of H_X therefore returns a code with k + 1 logical qubits on the same n physical qubits, at a distance that can only fall or stay put. Where the parent sits near a cell frontier and the distance happens not to fall, the child lands undominated for free.
Parent: the board entry [[42,10,4]] (codes/42-10-4.json). Row 0 of H_X is removed; every other check is untouched. k rises 10 -> 11 and the distance holds at 4, which is the case worth submitting: the deletion bought a logical qubit and cost nothing.
Every single-row deletion of every board entry small enough to re-derive the distance cheaply: 480 parent/row pairs across two machines, each re-measured for k, distance and Tanner connectivity. Deletions whose distance dropped, or that disconnected the Tanner graph, were discarded. Of the survivors, this is one of the few that is still undominated against the live board.
The sweep is the reason the result is trustworthy rather than lucky: the same deletion applied to most parents loses a distance point, and those cases were measured, not assumed.
Witness search on each side, 200k then 2M random information-set trials, with each witness classified by the conditions it actually satisfies (in the kernel of the opposite matrix, outside the row space of its own) rather than by the search's argument order. Deleting a row leaves H_X and H_Z with different shapes, and the argument order stops being a reliable side label there.
Distance is an upper bound from witness search, not a proof. The parent's distance claim is inherited context, not re-derived here. Literature novelty is unverified.