Context
The research record preserves failed approaches when they expose a model boundary, an invalid transfer, or an unsupported strengthening.
Proof or evidence
cross-boundary common-subexpression elimination, folding, reassociation, or cancellation may delete or merge gates from the literal composition.
Verification notes
The failure status and preserved lesson are recorded in the cumulative failure ledger.
Limitations
- exact additive formulas require sealed graph substitution. With global optimization they remain upper bounds only.