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
In Run 10, a factor's output recombination matrix becomes an input-form transpose after cyclic permutation; row/form evaluation costs differ. Explicit cyclic counts witness the distinction.
Verification notes
The analytic argument is preserved in the research record. Independent external review is not recorded.
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.