Field content, instrument limits, and curved backgrounds

The curved-background programme requires a category of specified causal substrates, functorial operations or observable algebras, compatible states, and a time-slice property. An arbitrary maximal antichain need not be a Cauchy cut for the networks under discussion. Neither local finiteness nor the finite cone theorem supplies that functor. Locally covariant QFT is the comparison template, not the construction here BrunettiFredenhagenVerch.

No same-model metric-response dictionary is provided. The lapse and spatial-cone dictionaries in separate manuscripts are not replacements for it CheungEm02E,CheungVIIIB.