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← Claims

Theorem, construction, or exact resource formula

MMR-061

Exact logarithmic depth after fan-out-two compilation

Exact statement

The ownership-aware fan-out-two realization has exact dependency depth D(N)=1+5log⁡2ND(N)=1+5\log_2N.

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

Max-plus induction gives Lxy(k)=1+5k+xL_{xy}(k)=1+5k+x and Rxy(k)=1+5k+yR_{xy}(k)=1+5k+y; a generated route through P5P_5 and the three-addition C11C_{11} tail attains equality. Unit-latency gates and buffers only.

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.