Mathematical release and physical conclusion

The direct astrophysical content is the four-dimensional geometry, asymptotic time normalization, quantum-field source, greybody transmission, radiation-mode access, and energy ledger. The exact score and recovery results are then evaluated on supplied channels on those modes.

The construction establishes a precise limitation: even a complete late-radiation thermal marginal need not determine retrieval from the joint accessible state. Conversely, a message-dependent outgoing signal need not originate in a post-horizon mechanism. Prompt carriers, exterior couplings, early resources, and detector instruments must be included before either interpretation is justified.

A $3/4$ violation, if certified for the complete trusted measure-before-query null, excludes that null. It does not by itself establish quantum non-Markovianity, environmental quantum memory, black-hole interior escape, or a solution of the information paradox. An identity storage channel on an ordinary qubit already attains $q_{\mathrm{Q}}$, as also emphasized in Psy04-A/B CheungPsy04A,CheungPsy04B.