Failed approach · scope boundary

MRF-039

Interpolating the unnormalized polynomial at $D+1$ points

Exact statement

Interpolating the unnormalized polynomial at D+1D+1 points. the known factor εq\varepsilon^q can be divided out at every nonzero evaluation point. The normalized curve has degree e=D−qe=D-q, so only e+1e+1 evaluations are needed, not D+1D+1.

Statusrejected as valid but unnecessarily expensive.
External reviewNo documented external or specialist review of the FPRD synthesis is recorded.

Context

The research record preserves failed approaches when they expose a model boundary, an invalid transfer, or an unsupported strengthening.

Proof or evidence

the known factor εq\varepsilon^q can be divided out at every nonzero evaluation point. The normalized curve has degree e=D−qe=D-q, so only e+1e+1 evaluations are needed, not D+1D+1.

Verification notes

The failure status and preserved lesson are recorded in the cumulative failure ledger.

Limitations

  • normalized error degree, rather than total polynomial degree alone, is the load-bearing interpolation field.

Open work

Keep this exclusion attached to any future reuse of the corresponding construction.