Why it is a question
A100, Chapter 9: “The new question introduced by the sheaf-information synthesis: Can a chain preserve information sufficient for one family of pragmatic tasks while progressively destroying the relations needed to support another?” It is the task-relative form of QUESTION-016, and the decision-theoretic twin of CLAIM-105.
Where it stands
The manuscript §11: “Task sufficiency may be retained while historical detail is lost”; §8: the trajectories of invariants, decision risks and compatibility structures “need not coincide”. Neither poses the question for two task families at once.
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.
- CLAIM-129: A factorization recovers only the structure visible in the relations it is fitted to, so a topic can…
- CLAIM-128: Transports whose distortion profiles trade off are incomparable until a task fixes weights, so no single…
- CLAIM-031: A reconstruction chain reorganizes observational constraints rather than only accumulating metric error: a…
- CLAIM-177: An argument developed with collaborators who keep no memory fails at identity, not at structure: concepts…
CLAIM-177 is a documented case from the nucleating-argument line: a label (“will”) kept while its definition changed five or more times.
Note of 2026-10-12: a typed partial answer
THEORY-199 now carries an answered_by edge. Low-level features survive past the noise threshold at which the top-level class is lost: one task family is kept while another is destroyed. Limits: it is a single step, not a chain, and an ideal denoiser on a synthetic grammar.
Note of 2026-10-14: a second one-step partial answer
THEORY-281, filed from LIT-963, answers the one-step, information-theoretic form for one categorical concept: perfect erasure of a concept A caps what a representation keeps about X at H(X|A). Everything about A can be destroyed while that much is kept, and no more. Limits: one step, not a chain, and task families defined only by a categorical concept.
Split, 2026-10-21 (ADR-049). THEORY-281 is now Active, narrowed to X of finite support. Its answer, the cap H(X|A) and when a map reaches it, is QUESTION-249, Answered. This question keeps what it leaves: a chain rather than one step, and relations a task family needs rather than a categorical label. THEORY-199 (Proposed) still points here.