Ehtibar N. Dzhafarov and Janne V. Kujala (2017), Fortschritte der Physik – Progress of Physics 65(6–8), 1600040 — ARXIV-1604.08412
Key takeaways
- The transitivity argument (Section I.3). Two random variables are jointly distributed exactly when they share a domain probability space, and that relation is transitive. In the traditional reading of KCBS, KS-4D or KS-3D, each observable is one random variable shared by overlapping contexts. Any path through the contexts then makes all of them jointly distributed. “No overall joint distribution exists” cannot be the conclusion of the contradiction.
- The culprit is Noncontextual Identification (Section I.4). Treating a measurement as the same random variable in every context is what the reductio refutes. Its replacement, Contextual Identification, indexes each variable by content and context. Stochastic Unrelatedness makes variables in different contexts have no joint distribution.
- Contextuality as a coupling question (S2, Definition I.1). A system is noncontextual if it has a coupling in which same-content variables satisfy C. Traditionally C is “equal with probability 1”. For inconsistently connected binary systems, C is “equal with maximal possible probability” for every subset of a connection (Definition II.1).
- The multimaximal coupling of a binary connection is unique, with the staircase form, and it is characterized by maximal coupling of the adjacent pairs in the order of the means (Theorems II.2–II.3; II.2 cited to LIT-831, II.3 derived here). The cyclic criterion is restated (Theorem II.4, cited to Kujala & Dzhafarov 2016).
- Specker’s magic boxes (Section III). Without consistent connectedness, the three-box system of Eq. (39) is noncontextual if and only if |⟨R_a^ab⟩ − ⟨R_a^ca⟩| + |⟨R_b^ab⟩ − ⟨R_b^bc⟩| + |⟨R_c^bc⟩ − ⟨R_c^ca⟩| ≥ 2 (Eq. 42). The absolute-value bars were lost in text extraction. The reading restored them because the condition is Theorem II.4 at n = 3 with all three correlations −1. Deterministic boxes are noncontextual.
Standing in the record
Filed on 2026-10-09 from the manuscript bibliography of 2026-10-09 (work
what-survives-translation) at the owner’s request: a work the manuscript
considered and dropped from its final reference list. The bibliography
names CbD 2.0 by the pair of arXiv ids that LIT-777’s footnote 10 gives;
this is the second of them. See the curation entry of that day.
Read on 2026-10-09 (NOTE-623). It is the record’s statement of why CbD indexes variables by context. It is also the place where the pairwise form of multimaximality is derived, which CbD 2.0 (LIT-831) and the canonical-systems paper (LIT-790) both cite.