A finite installed dictionary

A dictionary entry specifies its smooth data, compact support contract, and report. Examples are:

1. a compactly tested component of ${s_0}^2\Phi =0$;

2. a pairing of $\mathcal{L}{\mathcal{G}}^{\mathrm{R}/\mathrm{A}}a-a=0$ with a fixed compact test;

3. a supplied value or certified enclosure of (eq:positive).

The zero identities and the strictly positive obstruction coefficient make this dictionary nonempty without a continuum acquisition claim.

An entry is a supplied mathematical evaluation. It is not measurement of Grassmann field data, a physical ghost detector, or an algorithm for evaluating arbitrary smooth descriptions. Rational reports or certified intervals are installed; arbitrary real numbers are not assumed to have finite exact descriptions.

Oai279-A's finite reversible lookup and Oai283-A's finite-channel or oracle pilots are comparisons only FiniteComparisons. A frozen finite lookup does not establish a uniform all-input field-theoretic family; a constant-error certificate does not give an all-orders completion. No such circuit is needed as a premise here.