The objection
The reading: “In sheaf theory, a cover is a family of domains equipped with specific compatibility and gluing conditions. In the transport proposal, a cover is operationally associated with which questions a receiver population can answer determinately. These are not automatically the same mathematical object.”
It separates “Changing the measurement domain, changing the empirical response distribution, and changing the compatibility structure”, and says: “Only the third directly engages gluing obstructions, and even there the restriction maps and admissible covers must be specified.” A target language that makes an underspecified distinction obligatory “can change the set of distinctions available to readers. But this does not establish noncontextuality, contextuality, or failure of gluing.” Low agreement “may indicate ambiguity, heterogeneity, uncertainty, or an inadequately defined response variable”, not an absent context.
CLAIM-201 already separates a change of global compatibility from local distortion. CLAIM-197 says “which families count as covers decides whether anything glues”, and CASE-048 applies it without stating the cover. Notes of 2026-10-12 on all three record the tension.
What would answer it
A stated construction of the operational cover as a family of contexts with restriction maps, shown to be a cover in the sense CLAIM-197 uses. Or a separate name for the operational notion, with each entry that uses “cover” saying which it means.
What it does not say
It does not say the operational notion is empty. The reading’s advice is to “Keep the empirical notion of accessible distinctions, but give it a different formal name until an explicit functorial or sheaf-theoretic relationship is established.”
Note of 2026-10-19: distributions do engage gluing
The reading’s “Only the third directly engages gluing obstructions” is corrected here. In the sheaf framework (LIT-016, THEORY-012) a cover is part of the measurement scenario: the observables and the family of jointly measurable contexts. A family of response distributions on it is an empirical model, and contextuality is a property of the model on a fixed cover. The CHSH cover carries both kinds. A product of local response laws is noncontextual, and the PR box is contextual. So changing only the distributions can create or remove a gluing obstruction. Changing the measurement domain changes the cover too, since a cover is a family of subsets of the domain.
So the operations are of two kinds. A change of scenario, of domain or cover, changes what gluing means. A change of empirical model on a fixed cover changes whether it fails. The claim’s point survives the correction and is sharper for it. Which questions a population answers determinately is a property of the responses, so changing it is a change of empirical model and not of cover. That is the conflation CLAIM-201’s operational “cover” risks.
Note of 2026-10-30: what holds it back
Neither answer its body names is on record: no construction of the operational cover as a family of contexts with restriction maps, and no separate name for the operational notion with each entry saying which sense it means. Promoting it makes that renaming due on CLAIM-201, and CLAIM-257, CLAIM-256 and CLAIM-125, which are Active, use “cover” in the operational sense.