Codimension-Two Cut Coherence Is Koszul Exact
Entry 441 proves the eight individual six-by-four Cut squares after the cellular sheet transform. Coherence requires comparing both restriction orders whenever two physical Cut divisors meet.
Among the 28 unordered pairs of the eight physical octagon cuts, 12 are compatible and 16 cross. Each compatible pair partitions the octagon into three quadrilaterals. Its common link is therefore
The link has face counts , 125 loaded cells, and loaded chain ranks
The two restriction orders are not equal as unoriented operations. Normal contraction along the first Cut followed by the second differs from the reverse order by exactly the Koszul sign . The audit checks this on all 324 underlying common-link faces, equivalently all 1,500 loaded cells across the 12 compatible pairs.
Entry 87's exact certificate gives zero compatible double residue in every ordered channel pair. Exact additive transport through the octagon conductor kernel preserves those zeros. Thus all 24 ordered transformed double residues vanish, and the required anticommuting square is exact rather than merely equal after forgetting orientation.
Consequently codimension-two Cut coherence holds in the cellular fs/Kato sector. The next nontrivial arity test is codimension three: on a complete quadrangulation of the octagon, compare all six orders of three compatible Cut restrictions and verify the full alternating sign representation.
The executable audit is research/voevodsky/check_n8_codimension_two_cut_coherence.py.