QUESTION-018: When a generator receives several conditions, what determines whether it preserves their conjunction and relational bindings?

Why it is a question

A110 §IX.4: “When a generative model receives multiple conditions, what determines whether it preserves their conjunction and relational bindings? Compare constraint satisfaction, local empirical distributions, and compatibility across measurement contexts.”

Where it stands

The manuscript §7 says each condition can be met while the conjunction fails (CLAIM-321), and that score addition composes conditions only under conditional independence at the noisy state. CLAIM-123, corrected on 2026-10-19, states the exact condition: the scores add when p(y₁,y₂|x)/(p(y₁|x)p(y₂|x)) does not vary with the noisy state x, which conditional independence is sufficient for but does not require. C7 Appendix D adds that the identity “is not a generic identity for arbitrary prompt embeddings or finite-step diffusion implementations”, and that failures “may reflect estimator error, model misspecification, or sampling limitations”. Which of these explains a given relational failure is the open part. CASE-004 is the case.

Note of 2026-10-11: material in the record that may bear on this

A synthesis review of 2026-10-11 found these entries bearing on this question without being linked to it. Each is listed for what its title says; none has yet been assessed as an answer, and none is linked by answers.

• THEORY-117: Compositional generalization comes from diversity of combinations, not data volume: in vision models…
• CLAIM-097: T2I-CompBench is not purely object-centered: its non-spatial relation category already probes…
• CLAIM-013: Existing text-to-image benchmarks evaluate object presence and attributes, and need extending to…

Note of 2026-10-14: a measurement of the failure

THEORY-250, filed from LIT-938, measures that DALL-E 3’s relational bindings fail when an asymmetric relation is reversed and when relations are combined, and that the failures are mostly wrong or role-swapped relations, not missing objects. Low prior plausibility correlates only weakly (r = 0.09). It does not separate the candidate explanations above, so it is evidence about the explanandum, not an answer, and it carries no answers edge.