Why it is a question
THEORY-171 holds the existence statement: when causal constraints depend on context, deterministic assignments that are causal in each context can fail to glue. One checked example settles that, and LIT-808’s Θ₃ is one, with LIT-843’s Example 7.2 a second (NOTE-612). Until 2026-10-19 THEORY-171’s promote_when also asked for the characterisation. At the owner’s direction, from the promotion audit’s batch 008 (ADR-047), the THEORY was narrowed to what is checked, and the characterisation moved here.
It is open because the proof of Theorem 2.34 has not been read (NOTE-612, claim C2: “proof, not checked”), and the paper is an unrefereed preprint. The count in its introduction, 1767 of the 2644 causally complete spaces on 3 events with binary inputs, is also unchecked.
What would answer it
The condition formerly on THEORY-171, unchanged: a published, refereed version of Theorem 2.34 of LIT-808, or an independent proof of it read and checked, showing that the presheaf of causal functions over the lowerset topology of a space of input histories is a sheaf exactly when the space has no solipsistic contextuality witness. One more worked non-gluing example does not count, since an example shows only that some spaces fail, which is the half already checked.