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← Claims

Theorem, construction, or exact resource formula

MMR-019

Claim MMR-019

Exact statement

Fixed-base literal recursion obeys Mk=rkM_k=r^k, Ak=rAk−1+ab2(k−1)A_k=rA_{k-1}+ab^{2(k-1)}, and Ck=rCk−1+cb2(k−1)C_k=rC_{k-1}+cb^{2(k-1)}.

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

Block-size accounting and induction in Run 2; no cross-call sharing.

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.