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Theorem, construction, or exact resource formula

MMR-071

Claim MMR-071

Exact statement

Evaluated tensor-power SLPs obey the literal addition recurrence (9.14); interpolation adds at most ke (dim⁡C)kke\,(\dim C)^k vector additions, preserves O(k)O(k) dependency depth when each evaluated recursion has O(k)O(k) depth, and preserves O((dim⁡C)k)O((\dim C)^k) serial storage when each evaluated recursion has such a schedule.

StatusProved in the FPRD research record
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

Run 9 equations (9.14)--(9.16) and serial evaluation. Depth/storage are conditional transfer statements, not consequences of border rank alone.

Mathematical overview and evidence boundary →

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.

Open work

Independently re-audit the complete derivation before any further promotion.