The claim
A86 §2: min I(U;V) − β Σ_C w_C I(V;Y_C), a bottleneck whose relevance variables are the responses Y_C in each context, with the caveat that it does “not presume that every locally contextual measurement admits a single joint assignment.” A86 used it to argue that a lexically distant refrain can be “a more efficient representation of a communicative act than a literal translation”. C6 Appendix C: “The Y_C in different incompatible contexts must not silently be collected into one globally joint random vector. An information-bottleneck objective can instead sum context-indexed mutual informations computed in distinct joint experiments, or optimize an explicitly sampled measurement-context variable.”
Where it went
The manuscript §5 keeps the caveat (“Uncritically writing I(V;Y_1,…,Y_n) would assume precisely the global representation the sheaf model is intended to test”) and drops the objective. That leaves Tishby, Pereira and Bialek (LIT-338) in the reference list with nothing citing them, as the workbench entry of 2026-10-09 found. Nothing argued against the objective.
Correction, 2026-10-09
The bottleneck is in C7, in Appendix C, which the extracted manuscript omits: “A weighted bottleneck objective may sum information terms across separately elicited contexts, but that sum is a designed scalar objective, not an assertion that the Y_C admit a common joint distribution.” So Tishby, Pereira and Bialek are cited by the full draft’s appendix, though not by name and not in its body. What was dropped is the objective’s place in the main argument, not the objective.
The nearest precedent, and what it implies
Zaslavsky et al. (LIT-810, THEORY-163) apply the bottleneck to word meanings, with one relevance variable rather than a context-indexed one. Their formulation also sharpens this claim’s defeat condition. Once meanings are distributions and distortion is KL divergence, the bottleneck is rate–distortion with that distortion. A context-indexed bottleneck therefore adds something only if the indexing changes the distortion.
Note of 2026-10-30: what holds it back
Read literally, the defeat condition is met by an identity. When the context C is sampled independently of the source, Σ_C w_C I(V;Y_C) = I(V; C, Y_C), so the context-indexed objective is an ordinary bottleneck with relevance variable (C, Y_C). By this entry’s own note on Zaslavsky et al., that makes it rate–distortion with the fixed distortion Σ_C w_C KL(p(y_C|u) ‖ m̂_C). The identity was checked at the status review (p17/claim092_identity.py). Before a ruling, the condition needs restating against a named rival that indexing could beat, such as the joint objective I(V; Y_1,…,Y_n), which the indexing avoids presupposing.