Manuscript En05-C@1 · En05-C.tex · remark · aa213ea6
Remark: Countable locally finite substrates
Stage E: one-layer locality without product channels › Partitioned layers · lines 1407–1417
If finite-region algebras generate a quasi-local global algebra and every finite region meets only finitely many blocks, the same formula defines a layer on the local union. Enlarging a region adds only devices that fix the smaller calculation, so the definition is consistent. The finite compositions are UCP contractions at every matrix level; norm completion gives a UCP global map. Finite horizons still have finite backward regions under the usual finite-ball and finite-block hypotheses. No infinite-past network semantics is inferred.