Installed finite catalogue

Choose a finite catalogue with classical index $i\in \mathcal{I}$. An entry records:

• the test and source-description identifiers;

• the regulator $\rho$, scale $\mu$, and cutoff;

• the observation operator $D$ and smooth weight $a$;

• the selected signs and slot multiplicities;

• supplied pairings or certified enclosures and the remainder bound in (eq:certificateerror).

Only finitely many choices occur in one experiment. An arbitrary smooth function or real parameter is not claimed to have been acquired or exactly encoded by finitely many bits.

A finite report word $r(k,i)$ stores the installed data selected by a clock code $k$. It may include symbolic identifiers and rational interval endpoints. Its meaning is a certificate about supplied comparison data, not an observation of an unknown field or of the residue itself.