FPRD LabShare an approach

← Claims

Theorem, construction, or exact resource formula

MMR-031

Boundary-ideal receipts preserve exact peak storage

Exact statement

The complete boundary-ideal receipt Π(G) is sufficient to compute exact optimal peak storage in every finite downstream transparent RPR-S1T context.

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

Theorem R4.1; min-max DP on the compatible product graph. Fixed DAG, one shot, unbounded free fan-out, no recomputation.

Mathematical overview and evidence boundary →

Verification notes

The definitions, analytic proof chain, seam hypotheses, completion obligation, and likely failure points were reconstructed from the archived proofs on 2026-09-01. Four retained exact checkers reproduced the separator, product-state recurrence, bisimulation quotient, and stutter-trace witness with their recorded hashes. The current-label/external-pending distinction and the dead-gate boundary were checked explicitly.

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

Resolve the trimmed-DAG strictness question and test whether a smaller exact contextual quotient replaces the completed trace language.