Declarations

. This single source contains the declared models, analytical proofs, and internal bibliography. No external data are needed for typesetting.

status. No compilation, numerical execution, independent symbolic execution, formal proof checking, or physical implementation is claimed.

. The general channel, recovery, entropy, concurrence, negativity, and dephasing frameworks are established. The paper proves its model-specific identities and bounds locally without using other manuscripts as premises.

physical boundary. The accessible and residual subsystems are not identified with Hawking radiation and a black-hole interior. No gravitational dictionary, Page curve, gravity-generated-entanglement test, or solution of the black-hole information paradox is established.