Source
Lee-Youngzie, Tsuchiya, Robinson, Dietz & Monti (2026), Entropy 28(6), 615, LIT-1352, read in full in NOTE-1059 from the PMC deposit of the version of record: §4.1 (the framework), §4.1.5–4.1.6 (the two readings of failure), §5.2 and Appendix A. Locations are sections, since the copy read has no page numbers.
What was actually shown
Nothing was measured. The paper builds a framework and reads examples through it:
- The framework. The parts of an experience, ordered by subsumption, form a finite topology. A presheaf Q sends each part to the dissimilarity matrix of its qualia, measured by similarity judgements, and each inclusion to a restriction map that, by Definition 1, never decreases dissimilarity. For the visual field the parts are the two hemifields, their overlap at the vertical meridian, and the whole.
- Binding as gluing. “Conditions for phenomenal binding are formalized as the compatibility condition for the gluing of local sections” (§5.2). When Q is a sheaf, the broad quale is “wholly determined by, and decomposable into” the narrow ones (§4.1.5).
- Failure, read two ways. For binocular rivalry, “violation of the sheaf condition may be diagnostic of phenomenal disunity” (§4.1.5). For narrow qualia measured in isolation, a failure shows “interactions between parts that are irreducible to a predictable combination of narrower qualia considered in isolation” (§4.1.6). That is the Ebbinghaus case, an ordinary unified experience.
- A test. A consistency radius on measured matrices quantifies incompatibility on overlaps. A small radius means “we fail to reject the hypothesis that the sheaf structure formalizes the structure of experience” (§5.1).
What could have come out otherwise is all in the future: the consistency radius could be no different in rivalry than in fused viewing.
What this does not say
- It does not say that the unity of an experience is a global section. The paper assumes unity is always present (“their conjoint phenomenology always possesses the phenomenal quality of unity”, §1), and it counts a broad quale not fixed by its parts as unified (§5.2). What it formalizes as gluing is binding of narrow into broad qualia. Against QUESTION-255’s first answer, this is a case in which a sheaf failure is not disunity.
- Its global section is data, not an experience. The term is reserved for “the coherent global data that results from a sheaf” (Definition A14). That a gluing of similarity data tracks a unity in the experience is the structural approach’s premise, assumed and not tested.
- The rivalry reading does not follow from its definitions. Gluing applies to sections that “agree throughout their intersection” (Definition A15). Rivalry is sections that disagree on the overlap, so the sheaf condition is not violated. Only the tribar example, a cycle of three with pairwise agreement, is a gluing obstruction, which is CLAIM-153’s shape.
- The gluing condition, as defined, is thin. Definition 1’s restriction maps are functions on trials with an inequality on dissimilarities. Read so, the left and right restrictions of a trial are the same trial and always match. The test with content is the empirical consistency radius, which needs a definition of how a measured row restricts that the paper does not give (NOTE-1059, Key results).
- The worked topology is malformed, though repairable. Definition A7’s example lists down-sets of a diamond order as the up-sets of a chain, and omits the whole space (checked by script, NOTE-1059).
- It does not reach beyond two regions of one modality at one moment (§5.3.1), and it does not touch functional binding, which “can occur without conscious experience” (§1).
Connections
- QUESTION-255. Answered in part, negatively for the first option: within this framework a sheaf failure can belong to one unified experience. The tribar is a presheaf of interpretations with no global section, placed by the paper “at the level of cognitive interpretation”, and it is seen as one figure. Read against the question’s cover of interpretive contexts, it is a worked case for A7’s second answer. That reading is the record’s.
- CLAIM-153, CLAIM-197, CLAIM-198. The two-region examples are two-set covers, where CLAIM-153 has every agreeing pair glue. What fails there is either agreement on the overlap (rivalry) or determination of the whole by the parts (Figure 9). Neither is CLAIM-153’s monodromy. The tribar is.
- CLAIM-412. No bearing on constitution: the framework starts from phenomenal structure and measures it by report.
- THEORY-063. A rival proposal for the same phenomenal unity: a single functional cluster against a condition on measured qualia data.
- LIT-016. The sheaf account of contextuality from which the tribar’s reading comes. There the global section is a joint assignment of outcomes to all measurements, which is the sense the tribar uses.