Polynomial value density reference

Family 020: Squarefree quartics and power-free polynomial values. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Arithmetic sampling researchers can compare squarefree or power-free outputs of admissible irreducible polynomials to predicted Euler-product densities.

Applicability and commercial boundary

The local-divisor exclusion and degree ranges are essential. Positive limiting density supplies no finite sample rate or fast guaranteed generator.

Initial business decision

Research infrastructure or conditional engineering until a computable implementation, effective bounds and a recurring buyer need are demonstrated. No commercial novelty or profitability is established.

Next verification action

Extract effective error terms and a polynomial with computable local factors.

Evidence scope

The catalog statement was individually reviewed. Manuscript proof and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

Squarefree values of quartics and power-free values of polynomials.