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Theorem, construction, or exact resource formula

MMR-121

Claim MMR-121

Exact statement

For Gibbs weights pi=viτ/rp_i=v_i^\tau/r, the ideal ASI bootstrap map is Φ(β)=3βlog⁡r/(3H+βL)\Phi(\beta)=3\beta\log r/(3H+\beta L) and satisfies 1/Φ(β)=α/β+(1−α)/(3τ)1/\Phi(\beta)=\alpha/\beta+(1-\alpha)/(3\tau) with α=H/log⁡r<1\alpha=H/\log r<1.

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

Direct entropy algebra using H+τL=log⁡rH+\tau L=\log r. This is the explicit fixed-point form of the classical type/compression proof.

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.