Context
The research record preserves failed approaches when they expose a model boundary, an invalid transfer, or an unsupported strengthening.
Proof or evidence
a scalar multiplication may overwrite a last-use operand, while a recursive child must retain its input blocks and create a fresh output. Exact search finds minimum recursive-call frontier five, so the recursive base uses six stored scalars rather than the Run 1 scalar peak five.
Verification notes
The failure status and preserved lesson are recorded in the cumulative failure ledger.
Limitations
- a recursive receipt must distinguish ordinary liveness from values pinned across a call.