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
Lemma 2 of Run 4 partitions the frontier into gadget nonboundary, context, and boundary vertices; internal/external pending use is joined by disjunction.
Verification notes
The definitions, analytic proof chain, seam hypotheses, completion obligation, and likely failure points were reconstructed from the archived proofs on 2026-09-01. Four retained exact checkers reproduced the separator, product-state recurrence, bisimulation quotient, and stutter-trace witness with their recorded hashes. The current-label/external-pending distinction and the dead-gate boundary were checked explicitly.
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.