What died: the v0.4.1 proposal that adjacent Menger factors are "glued" by a phase prescription (BII). The proposal's phases are a coboundary — gauge-equivalent to zero — so the entire Menger factor shears out of any observable built on it.
Mechanism-level point [F]: in a gauge theory, a "gluing rule" that is a coboundary is not a weak gluing; it is no gluing. Any physical content of such a prescription must live in the cohomology class, which here is trivial. This is why the program re-founded flatness on explicit H₁ holonomy instead.
Downstream: every subsequent flat-bundle result uses cocycle (cohomology) language with exact flatness checks. Nothing currently in the registry depends on BII.