Manuscript Oai280-B@1 · Oai280-B.tex · section · 6d92ab75

Decision maps and the distinction between exclusions

Decision maps and the distinction between exclusions · lines 1908–1963

On the simultaneous event of Theorem thm:main, a threshold $ε$ gives:

Certified implemented reconstruction: the access contract is independently supported and $U_{A} \leq ε$ .
Excluded for this implemented channel: $L_{A} > ε$ .
Inconclusive: neither inequality separates the threshold.

An unsupported audit or validation contract is reported as “contract not established”, not as statistical certification.

The ideal small-region error $3/4$ , its robust version in Proposition prop:robustnegative, and the specified streaming floor $1/2$ are uniform decoder exclusions in their own interfaces. The finite-data $L_{A}$ is ordinarily not.

A release should print one row per predeclared task:

Task	Ideal recovery	Access and resource audit	Error interval	Decision
$A_{1}, D_{1}$	From Theorem thm:idealaccess	Supported / unsupported	$[L_{A_{1}}, U_{A_{1}}]$	Certified / excluded / inconclusive
$A_{2}, D_{2}$	From Theorem thm:idealaccess	Supported / unsupported	$[L_{A_{2}}, U_{A_{2}}]$	Certified / excluded / inconclusive

No entries are assigned numerical values here because no validation records were supplied.

For all $32$ single-block regions, $K = 32$ . For the ten triples plus a specified collection of negative controls, $K$ is the total number of tested tasks, not merely the number expected to pass.

Equal-size region comparisons, connected versus disconnected subsets, controlled errors, and compiled decoder depths are legitimate descriptive comparisons when their interfaces and confidence allocation are fixed. On one ideal pentagon the threshold is cardinality. Geometry-dependent code properties in larger models require actual network calculations, not a reinterpretation of this table PastawskiPreskill.