FPRD LabShare an approach

← Claims

Computational finding

MMR-007

Claim MMR-007

Exact statement

Every one of the nine balanced depth-four per-output trees for (C_{11}) and (C_{22}) needs six RPR-S1 registers.

StatusVerified by retained finite computation; analytic proof is not implied
External reviewNo documented external or specialist review of the FPRD synthesis is recorded.

Context

This result belongs to the reconstruction from algebraic matrix-multiplication certificates to explicit arithmetic dependency DAGs and their resource receipts.

Hypotheses and scope

  • All resource conclusions are restricted to the arithmetic, storage, fan-out, coefficient, and precision models named in the source record.

Proof or evidence

Exact order-ideal search in `strassen_pebble_check.py`, SHA-256 `bd445d1b163c3c2c9b997e7f9e897e64327c32a610eedb576d98fe850755abcc`. Analytic proof pending.

Mathematical overview and evidence boundary →

Verification notes

The exact checker and its recorded digest are preserved with the research record. This status remains computational until an analytic or formal proof is supplied.

Limitations

  • The record does not improve the known matrix-multiplication exponent and does not imply that omega equals two.
  • Construction bounds are not optimality, communication, I/O, or hardware claims unless the exact statement says so.

Open work

Obtain an independent implementation or analytic proof before any further promotion.