Using the unknown exponent $\omega$ as the outer combiner

Exact statement

Using the unknown exponent $\omega$ as the outer combiner. the usual limiting derivation can say that an outer square algorithm of exponent $\omega+o(1)$ exists, but that is circular as a finite compiler. Run 14 instead begins with naive $(2,8)$ multiplication and iterates an explicit finite exponent-improvement map.

Statusrejected as an executable proof.

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 usual limiting derivation can say that an outer square algorithm of exponent $\omega+o(1)$ exists, but that is circular as a finite compiler. Run 14 instead begins with naive $(2,8)$ multiplication and iterates an explicit finite exponent-improvement map.

Rejected transfers and surviving boundaries →

Verification notes

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

Limitations

an asymptotic fixed-point argument must identify its seed algorithm and finite feedback path.

Open work

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