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Theorem, construction, or exact resource formula

MMR-042

Completed stutter traces suffice for storage

Exact statement

Equality of completed storage-observation trace sets after contracting adjacent repeated labels is sufficient for exact peak storage in every downstream 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 R6.1; silent gadget steps commute with context steps because seam compatibility and Run 4 weight depend only on (R,μ,λ)(R,\mu,\lambda). Completion is retained by a terminal marker.

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.