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; no four-register association found. Does not cover shared cross-output linear circuits or recomputation.
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.