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Theorem, construction, or exact resource formula

MMR-098

Claim MMR-098

Exact statement

Explicit coefficient gates keep raw fan-out at 60 at every positive recursion level; sealed fan-out-two compilation uses exactly 13040(1000k−144k)/85613040(1000^k-144^k)/856 buffers.

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

Base consumer counts are (60,60,18)(60,60,18) and require 4896+4896+32484896+4896+3248 buffers. Unit coefficient gates break raw identity paths; the recursive count solves the sealed block recurrence.

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.