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Open problem · exact residual obligation

FPRD-CPA-C06

The remaining commutative-control normalization problem

Exact statement

It remains unresolved whether every commutative polynomial-automaton series belongs to a finite derivative-stable Hadamard algebra consisting entirely of commutative series.

StatusOpen; no general yes/no answer claimed
External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

The exact reformulation survives the factorial counterexample, but finite generation of the visible derivative algebra does not.

Hypotheses and scope

  • Polynomial/Hadamard automata over the rationals.

Proof or evidence

The exact reformulation and the failed derivative-algebra route isolate existence of a finite commutative over-algebra as the remaining obligation.

Unresolved proof obligations →

Verification notes

The public page explicitly separates proved partial results from this unresolved universal claim.

Limitations

  • No counterexample to the originating question is established here.
  • No claim is made that the problem is open in the published literature beyond the bounded source search.

Open work

Search for finite commutative over-algebras or an invariant violated by a commutative output with chronology-sensitive controls.