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Theorem, construction, or exact resource formula

MMR-105

Claim MMR-105

Exact statement

Literal recursion of MMR-104 gives Ak=4504(1000k−144k)/856A_k=4504(1000^k-144^k)/856, Ck=8128(1000k−144k)/856C_k=8128(1000^k-144^k)/856, Dk=1+18kD_k=1+18k, and declared peak Sk=2+2000(144k−1)/143S_k=2+2000(144^k-1)/143.

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

Sealed elementwise recurrence plus Run 7's pinned-call theorem with (σ,α)=(2002,2000)(\sigma,\alpha)=(2002,2000). Storage is exact for this schedule, not globally optimal.

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.