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Theorem, construction, or exact resource formula

MMR-096

Claim MMR-096

Exact statement

Literal recursion of MMR-095 gives Ak=13408(1000k−144k)/856A_k=13408(1000^k-144^k)/856, Ck=15552(1000k−144k)/856C_k=15552(1000^k-144^k)/856, and exact depth Dk=1+13kD_k=1+13k.

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

Solve the sealed elementwise linear-map recurrences; every input-output path crosses one recursively replaced product per level.

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.