Manuscript X-B-ST@1 · X-B-ST.tex · section · d03c150c

What the finite table contains

Installed evaluations and a complete clock instrument › What the finite table contains · lines 2262–2304

X-B-ST@1#eq:tableentries

Choose a finite catalogue of already supplied data: background descriptions, completion-test descriptions, smooth free-solution descriptions, and numerical reports or certified intervals for expressions such as

ev_{u_{i}} R_{1} (V_{1, g} [h_{i}]; F_{c_{i}}), ev_{u_{i}} A_{1} [h_{i}], \int f_{i} ρ_{2, g} [h_{i}, k_{i}; u_{i}] d^{4} x .

The last entry is explicitly classical. It is not an evaluation of an unconstructed second-order quantum map.

By (eq:normalization), the first entry is a well-defined classical number. Providing its finite description or an enclosure is an input to the finite encoding. No general algorithm for arbitrary smooth data and no universal finite encoding of arbitrary real numbers is asserted.

The catalogue can always be nonempty, for instance by using a zero background. Nontrivial scalar response values are possible: in the massless diagnostic of Proposition prop:input, let

C = \int (\partial_{t} r)^{2} d^{4} x > 0, a = C^{- 1} \partial_{t} r, c = P_{0} a .

Then

ev_{t} R_{1} (V_{1, g} [r η]; F_{c}) = - 1,

whereas the same specified $c$ at $h = 0$ gives zero. This is a mathematical evaluation of representatives, not a field preparation or measurement. Its supported host use requires the stated laboratory support contract.

Displayed formulas in this passage

X-B-ST@1#eq:tableentries · line 2268
$ev_{u_{i}} R_{1} (V_{1, g} [h_{i}]; F_{c_{i}}), ev_{u_{i}} A_{1} [h_{i}], \int f_{i} ρ_{2, g} [h_{i}, k_{i}; u_{i}] d^{4} x .$
unlabeled · line 2291
$C = \int (\partial_{t} r)^{2} d^{4} x > 0, a = C^{- 1} \partial_{t} r, c = P_{0} a .$
unlabeled · line 2296
$ev_{t} R_{1} (V_{1, g} [r η]; F_{c}) = - 1,$