Context
The research record preserves failed approaches when they expose a model boundary, an invalid transfer, or an unsupported strengthening.
Proof or evidence
hardwired algebraic circuits can omit zeroed sources and outputs at zero arithmetic cost, but the mask, address map, strong-disjointness proof, and constituent isomorphisms still need description or generation.
Verification notes
The failure status and preserved lesson are recorded in the cumulative failure ledger.
Limitations
- “zero arithmetic gates” and “zero realization cost” are different claims.