Closed geodesic research benchmark library

Family 345: Infinitely many closed geodesics on Riemannian spheres and closed three-manifolds. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Researchers can organize infinite distinct prime geodesic existence across spherical-cover and closed three-manifold cases.

Applicability and commercial boundary

Existence of infinitely many paths supplies no efficient path enumerator, finite length budget or navigation improvement.

Initial business decision

Research or conditional engineering only. A practical implementation, recurring buyer problem and willingness to pay have not been established. Mathematical usefulness alone is insufficient evidence for a standalone lucrative product.

Next verification action

Extract a concrete computable metric and a limited geodesic-search reference.

Evidence scope

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

Infinitely many closed geodesic images on every Riemannian sphere.