Theorem: Extension-record separation

Fix an independently supplied extension $A\subset B$, together with its Q-system and all categorical comparison data. Under Definition def:determination, these fixed data do not determine recovery of an appended finite code, a radiation entropy history, or an assigned gravitational metric or area. They do not instantiate Definition def:dictionary.

Proof. Append the good and bad channels of Proposition prop:goodbad, leaving the extension untouched. Recovery differs. Append the histories of Proposition prop:histories. Their entropy trajectories differ while the extension remains fixed.

An independent metric or area assignment is not constrained by any map in the fixed extension record. Therefore the record does not select such an assignment. This last observation is a statement about missing identification data, not a claim that arbitrary assignments are genuine duals.