The claim
From MOM-CLM-088, which reads the sheaf-semantics chapter of the MoM manuscript (v1 §10). The chapter states the sheaf condition in full. “If {U_i} is a cover of U”, and the predicates p_i agree on the overlaps U_ij = U_i ∩ U_j, “then there exists a unique global predicate p”. It then offers “tall” as the case that fails: “In Human-context, ‘is tall’ applies with threshold >2 meters. In Tree-context, ‘is tall’ applies with threshold >20 meters. These local definitions do not glue.”
They do. People and trees do not overlap, so U_human ∩ U_tree is empty and the compatibility hypothesis holds with nothing to check. The condition the chapter printed then gives a unique global section: apply 2 m to people and 20 m to trees. That is how gradable adjectives work, with the comparison class part of the semantics. One chapter later the same example gets the opposite diagnosis, that the two senses are “forcibly glued into an illusory global predicate”. Neither diagnosis holds. With an empty overlap there is nothing that could fail and nothing to force.
Two things follow, and they are what this record needs.
- A gluing failure needs an overlap. It is a context, or a pair of overlapping contexts, in which the sections disagree. MOM-CLM-088 supplies one for “tall”: a single conversation about both skyscrapers and houses carries two thresholds in one context, and there the restriction maps conflict.
- The cover decides. A sheaf needs a rule saying which families count as covering. On a bare order of contexts with no such rule, the sheaf condition is either vacuous or whatever is stipulated, and which families cover is what decides whether any concept glues.
Why this record holds it
The record has met the general point already. CLAIM-143 says local descriptions that disagree establish no obstruction until the correspondences are fixed, and CLAIM-144 and CASE-039 find the relativity example was never a gluing failure. This claim adds the simplest instance, and the rule that catches it: before calling anything a failure to glue, name the overlap.
It bears most on the self. The same MoM chapter (v1 §11.5) treats a person’s roles, “daughter”, “teacher” and “friend”, as sections over family, professional and social contexts, and identity as their global section. Read as written, roles in contexts that do not meet cannot contradict each other. CLAIM-153 already works with contexts that overlap in pairs. The consequence for interests over time is drawn in CLAIM-198.
What it does not say
- That context-relative meaning is never a problem. Contested evaluative vocabulary is where contexts overlap and the sections disagree, and that is the general case MOM-CLM-088 names.
- That the sheaf picture is wrong. The machinery is right. The claim is about where it has been aimed.
- What the right coverage is for meaning or for a self. That stays open here, as it is in MOM.
Note of 2026-10-12: a change of cover filed on 2026-10-10
PR #121 filed CLAIM-201 and CLAIM-257, which make a change of cover the surviving form of CLAIM-105’s headline. There a context is “a question whose answers readers give determinately”, and a rendering changes the cover when a question determinate for one side’s readers is indeterminate for the other’s. This claim says which families count as covers decides whether anything glues. CLAIM-201 says a change of cover is not thereby contextuality: it has “changed which questions can be asked, not shown that the answers cannot be glued”. The record does not say whether this claim’s coverage and PR #121’s operational cover are one notion, and the entries are not related; that is left to the owner.
Note of 2026-10-12: the interlocutor’s reading, as advice
The interlocutor’s reading of 2026-10-12 says this claim “supplies an essential mathematical correction, but it does not necessarily defeat the transport proposal”, and that the operational notion of CLAIM-201 should get “a different formal name until an explicit functorial or sheaf-theoretic relationship is established”. Filed as the counter CLAIM-251. Recorded as advice.