Conclusion

The finite feasibility question has an exact answer: reference-preserving message recovery and a specified encoded pair test can coexist in one linear unitary model when the partner is part of the radiation algebra. There is no independent second partner. Moreover, operations on that radiation can move the purifier or change the original pair statistics.

This answers an interface question, not the physical firewall question. The next indispensable result is a physical bridge connecting a constructed infalling algebra and complete detector instrument to a complete emission channel, with state regularity and backreaction controlled in the same model. The conditional theorem above specifies how such bridges would be used without substituting a spectrum, entropy curve, or finite register identity for them.