Conclusion

The corrected mathematical statement is not bulk reconstruction:

Exact full-code recovery is equivalent to a constant complete complement. One observable can remain exactly reconstructible outside that condition. Complementary and accessible witnesses can prove obstructions; an unsuccessful sufficient certificate can instead be inconclusive.

The modular theorem independently converts positive averaged spectral defects into bounded operator witnesses under a scalar-centralizer hypothesis. It supplies no decoder, no finite-sample confidence guarantee, and no gravitational dictionary.

Geometry, endpoint dynamics, and characteristic quantum admission each require their own identified objects and estimates. Their missing interfaces remain missing rather than being filled by analogy.