Candidate D: reference-stable complete channel tables

Candidate D consists of indexed complete channels on declared comparison interfaces, optionally supplemented by preparations, intervention settings, and complete correlation records.

Reference stability means that a channel acts as $\Phi \otimes {\mathrm{id}}_R$ on an untouched reference and that a comparison is made completely, including such extensions. For every channel,

This leaves the unconditional reference marginal unchanged. It does not imply preservation of all input-reference correlations: a replacement channel satisfies (eq:reference-marginal) while destroying those correlations. Exact logical identity transport is the stronger statement

on identified input and output spaces Watrous,CheungEn08B.

Thus the term “reference-preserving table” must distinguish unchanged reference marginals from successful reference-preserving transmission. Selective conditioning may also change the conditional reference state without signalling to the unconditional reference CheungEn09A (thm:main).

An intervention-indexed complete table may determine influence within its declared access model. A transport-only table need not. Neither observation supplies a cone-selection theorem here. En08-B supplies a later endpoint-approximation benchmark, but its metric and speed are inputs CheungEn08B (thm:main, cor:operational-limit).