Context
The research record preserves failed approaches when they expose a model boundary, an invalid transfer, or an unsupported strengthening.
Proof or evidence
two-node interpolation literally creates ten rank-one terms, but global algebraic simplification or a different exact algorithm can use fewer. The checker proves identity, not minimality.
Verification notes
The failure status and preserved lesson are recorded in the cumulative failure ledger.
Limitations
- distinguish literal debordering cost from exact tensor rank and from optimized executable arithmetic.