Sequence lattice

Six bits, one per digit of the doubling orbit, and a polarity. Flipping any bit reaches a cell, and that cell at either polarity is a neighbour, so 6 positions become 12 moves and every one of the 128 states sits at the centre of the same figure. No state is special; the neighbours change because the centre moves.

Twelve is the kissing number, and that is what made a vector equilibrium look like the answer. It is not one. A cuboctahedron's twelve vertices carry 24 edges among themselves; these twelve carry 0, because two states reached by flipping different bits differ in two bits and two bits apart is not adjacent.

What it is, named exactly: the 6-cube with every vertex doubled into a non-adjacent twin — Q6[K̄₂]. Adjacency ignores the polarity entirely (true), the two polarities of a cell have identical neighbourhoods (true), and the whole thing inherits the cube's bipartition (true).

The correction is kept rather than deleted, because the count that suggested a vector equilibrium is real and only the conclusion drawn from it was not. A count is not a solid.

Computed by src/quantum/polarity-lattice.ts · asserted by npm run test:polarity-lattice.

Receipt: f3b11f45-05e6-82d8-b1de-21ccaa6aca61 · set f02fb883-0647-8f26-ac67-57cf88acb8a3