The claim
A86 §4: “a collection of local entropies need not characterize the global compatibility structure”, and of sheaf structure and information: “Neither structure is reducible to the other.” The example, A = B against A ≠ B for fair bits. Manuscript §5: “equal entropy does not entail equal relational structure: perfect correlation and perfect anticorrelation of two fair binary observables have equal entropy yet reverse a fundamental relationship.”
What it changes
It is why the manuscript needs both a sheaf model and information measures. §11: “The discipline of keeping these notions separate is what permits their synthesis.” Granted, because it is elementary.