Acceleration from finite geometric triangulations

Determine whether switching from geometric spun-triangulations to geometric finite triangulations accelerates the new verified length-spectrum algorithm for closed hyperbolic 3-manifolds, particularly those with long systoles.

Background

The paper supports geometric spun-triangulations but does not support geometric finite triangulations in SnapPy version 3.3. Finite triangulations could avoid incompleteness loci and may be advantageous for closed manifolds.

The authors specifically identify closed manifolds with long systoles as likely beneficiaries, while noting that the expected acceleration has not been confirmed and may not occur for every manifold.

References

Since SnapPy does not support geometric finite triangulations, we expect but cannot confirm that we can accelerate the new length spectrum algorithm by switching to a finite triangulation for closed manifolds with long systole.

— Verified Length Spectrum and Margulis number for Hyperbolic 3-Manifolds  (2609.26663 - Goerner et al., 22 Sep 2026) in Section 14, “Future work,” and Section 13.1, “Performance dependence on spun-triangulation”