A finite dictionary and its status semantics

A dictionary is a finite list of tasks. Each entry contains:

1. a quantity and prescription tag;

2. the frozen width, test-data identifier, and support contract relevant to that quantity;

3. a supplied exact finite value or rational enclosure, when a numerical quantity is available;

4. a status certificate with its quantifier;

5. any requested finite encoding and its error allowance.

Permitted entries include the following.

\begin{array}{p{.28\linewidth}|p{.60\linewidth}}
 \text{Entry type}&\text{Meaning}\\ \hline
 \text{Positive convolution charge}&
 A supplied enclosure \(0<L\le c_\varepsilon\le U\).\\[3pt]
 \texttt{\detokenize{ORBIT_CONSTANT}}&
 A specified scalar-input output is proved constant,
 for example the erasure channel below.\\[3pt]
 \texttt{\detokenize{INFORMATIVE_FORBIDDEN}}&
 The requested conjunction of full-orbit invariance
 and informativeness about \(a\) is excluded by
 Theorem~\ref{thm:orbit}.\\[3pt]
 \texttt{\detokenize{NOT_CONSTRUCTED}}&
 A named additional object, such as the independently
 charged second coefficient, has not been supplied.\\[3pt]
 \text{Amplitude witness}&
 A finite supplied evaluation or enclosure of
 \(\Delta_\varepsilon\) in \eqref{eq:TV}.
\end{array}

The status _CONSTANT is not assigned merely because several sampled values agree. For example, a complete erasure channel

has a valid universal certificate. A finite table of endpoint checks alone does not certify an all-real orbit identity.

Existence of rational $L,U$ enclosing a fixed positive finite $c_{\epsilon }$ follows from Assumption ass:convolution. An algorithm producing those enclosures from arbitrary smooth field descriptions is not assumed.

A report of the fixed charge is not a measurement of the variable orbit value $a(\lambda )$. A task label identifying a supplied value is likewise not an acquired continuum coefficient.