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Theorem, construction, or exact resource formula

MMR-054

Claim MMR-054

Exact statement

Literal standard-Strassen recursion has exact maximum wire fan-out F(N)=3log⁡2N+1F(N)=3\log_2N+1 for N=2kN=2^k.

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

Raw passes through A11,A22,B11,B22A_{11},A_{22},B_{11},B_{22} give Fk=3+Fk−1F_k=3+F_{k-1} with F0=1F_0=1; a nested diagonal address attains it, while all other wire types have smaller fan-out. No bounded-fan-out compilation yet.

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.