Companion separations

This section records the supplied source relationships. It does not claim a scan or verification of the complete Cheung series. Similar terminology does not identify models, cutoffs, observables, resource classes, or admission contracts.

and resource interfaces. Landmark I version 2 characterizes Born probabilities and destructive positive-branch residual rays inside its declared strategy class CheungI. En03-A records its own interface and scheduled-locality statements CheungEn03A. The present instrument and fragment are directly defined, not deduced from an unprovided larger calculus. These companion statements are not a premise.

The supplied En02-B perfect-code benchmark excludes exact recovery with one live laboratory qubit under its specific streaming contract CheungEn02B (thm:B5). En02-C distinguishes unrestricted information-theoretic availability from executable recovery and records a peak-one streaming obstruction for its own benchmark CheungEn02C (thm:C2, thm:C3). These motivate the distinction between consuming syndrome qubits and consuming the recovered quantum output. They are not resource optima for the decoder in this note and are not a premise.

En02-E's flagged-cutoff comparisons retain their commuting-state hypotheses CheungEn02E. A discarded probability is not a generic allowance for a coherent channel cutoff. No cutoff theorem is transferred into the present proofs. This comparison is not a premise.

and apparatus. Em03-B records the distinction between an effective apparatus readout, later reset, and thermodynamic costs CheungEm03B. Em03-C retains joint spectators, apparatus outputs, and references in its coherent comparisons CheungEm03C. The dilation (eq:read-dilation) is specified locally; neither apparatus is silently substituted for it. These records are not a premise.

Em03-E calculates complete channels and a complement for one designed finite dynamical model and distinguishes its declared energy conservation from physical black-hole identification CheungEm03E. Em03-H records complementary upper and lower certificates for a separately fixed quartic-bath interface CheungEm03H (thm:complementary). Neither is a Page curve or a gravitational dictionary for the present residual. These records are not a premise.

and scrambling. The supplied En04-A record separates its specified non-Clifford or non-local-magic quantities from complete residual response CheungEn04A (cor:noimplication). The present leakage definition therefore does not acquire a positive value merely because a program is called “magic” or “scrambling.” No such resource measure is used in the proofs. This comparison is not a premise.