Hypothesis: C6 obs : Localized observable limit

For each scale, a represented observable algebra ${\mathfrak{B}}_n$ and local generating sets for bounded spacetime regions are specified. They satisfy:

1. generators in positively spacelike separated regions commute for all sufficiently fine scales;

2. linear comparison maps $j_n:{\mathfrak{B}}_n\to \mathfrak{B}$, into a common $C^{\ast }$-algebra, send admitted uniformly bounded generator sequences to norm-convergent sequences;

3. comparison preserves adjoints and the relevant cross-products asymptotically:

   $$\Vert j_n(a_n{b}_n)-j_n(a_n)j_n(b_n)\Vert \to 0;$$

4. the limits generate isotone local algebras $\mathfrak{A}(O)$;

5. operational effects and states have compatible realizations in this limit, not merely convergent numerical laws.

Allocation, consumed wires, dilation ancillas, and record ports belong to the declared representation.