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Open boundary

FPRD-LRS-B01

Deterministic indexed LRS zeroness remains open

Exact statement

The present reductions do not establish a deterministic polynomial-time zero test, EquSLP hardness, or equivalence with derandomizing general arithmetic-circuit identity testing.

StatusUnresolved under the explicit variable-order input model
External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

The structured powering circuit may be easier than a general arithmetic circuit, but the current work proves only a one-way reduction to EquSLP.

Proof or evidence

No reverse reduction or deterministic hitting set was constructed. A fixed polynomial list of primes is unsound because a nonzero term may be divisible by all of them.

Limits of the current reductions →

Verification notes

The boundary separates randomized decision, nondeterministic certificates, compact representation, and deterministic decision.

Limitations

  • A bounded literature search cannot certify universal novelty or open status.

Open work

Test fixed order, diagonalizable characteristic polynomials, nondegenerate recurrences, and restricted coefficient semigroups for deterministic algorithms.