Does the chromatic/anonymous discriminator turn the false-friends list into a decision procedure?

Status: open · laid 2026-09-14 · type: structural

Statement. "Consistent on every local view, inconsistent globally" is not one phenomenon but a symptom with two distinct mechanisms, and there is a single question that tells them apart before any mechanism is sought: do the local observers act on the coefficients?

• No → chromatic. The obstruction is a cycle in a labelled nerve. Instances: FLP impossibility, k-set agreement, Fekete's read-only anomaly, Borromean rings, Massey products, Rédei symbols.
• Yes → anonymous. The obstruction is a fixed-point failure of a group action. Instances: Angluin, Yamashita–Kameda, Grunwald–Wang, Tate's H³.

Friction. The project's false-friends section (the §4 of the old map-index, and its successor role in the current false-friends log) is a list of rejected identifications — it records that two things sharing a word do not share a theorem. This discriminator is stronger: it claims to convert part of that list into a decision procedure that says which kind of local-to-global failure you are looking at before you go hunting for the mechanism. If it holds, the false-friends log stops being a graveyard of coincidences and becomes an instrument that classifies a new collision on sight. That is a structural change to how the log is used, not another entry in it.

Question. Does the coefficients-action test actually partition the known local-to-global impossibility results cleanly into the two classes, with no result landing in both or neither? And is the partition predictive — does it correctly pre-sort a result the discriminator was not built from? A satisfactory answer either exhibits the clean two-class partition over the full instance list and one held-out case, or names the result that straddles the boundary and breaks it.

Why this probe. The 2026-09-12 project-file sweep singled this out as the one item in it that "could force a revision" — its author's own top pick and the strongest signal in the document. It is filed here rather than acted on so the claim is on record with a test attached rather than adopted because it is attractive.