Quadratic twist rank distribution reference

Family 006: Goldfeld’s conjecture: densities and mean analytic rank. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Arithmetic database researchers can compare twist samples to the rank-zero/rank-one densities and mean-rank limit.

Applicability and commercial boundary

Signed squarefree twists are ordered by absolute value; limiting density gives no finite-twist classification or a convergence rate.

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 finite error estimates and compare a public curve family.

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.

Goldfeld's analytic density conjecture and the 2-converse for elliptic curves.