Context
The research record preserves failed approaches when they expose a model boundary, an invalid transfer, or an unsupported strengthening.
Proof or evidence
a gadget can have ideals, and network product states can multiply. The theorem is an exact finite specification, not a polynomial algorithm or useful recursive asymptotic bound.
Verification notes
The failure status and preserved lesson are recorded in the cumulative failure ledger.
Limitations
- receipt compression is now the decisive obligation.