The case
Manuscript §3: “take three binary observables solidarity S, condemnation M, and humor H, available in pairs {S,M}, {M,H}, and {H,S}. Constraints S=M, M=H, and H≠S are individually pairwise satisfiable but admit no common global assignment. This parity example demonstrates an obstruction, not a claim about actual judgments.”
What it can show
That local consistency need not glue (CLAIM-037). It changes CASE-008 from a probabilistic question about data into a logical example. It cannot show that pragmatic judgements behave so (CLAIM-009).
First stated at A78 (U29), with the constraints S=M, M=H, H≠S: “This example illustrates a logical obstruction to global assignment. With suitable measurement-consistency conditions and probability models, analogous constructions yield formal contextuality tests.” A78’s diagram labels a different but equivalent set (S=M, M≠H, S=H); its caption notes the difference. It is the example for CLAIM-038.
“Local consistency need not glue” holds in two readings, which should be kept apart.
- Over the supports. Here no compatible family of support sections exists at all. That is strong contextuality, the grade this case has; the weaker possibilistic grade is a locally possible section that belongs to no compatible family (TERM-042).
- Over the distributions. Here a compatible family of distributions has no global joint.
The weighted version is CASE-037 (A129 §2, A161, and A178’s negative control).