Early pruning during length-spectrum tiling

Construct a more efficient version of the verified length-spectrum algorithm that prunes candidate group elements during the tiling stage itself, thereby reducing the size of the pre-length spectrum before subsequent filtering and sorting.

Background

The length-spectrum algorithm first tiles the universal cover to produce a pre-length spectrum containing possible parabolic elements, nonprimitive elements, duplicates, and geodesics longer than necessary. These candidates are filtered only after the tiling stage.

The authors explicitly ask whether pruning can be moved earlier into the tiling process to improve efficiency. The question remains unresolved in the paper.

References

Is there a more efficient algorithm to compute the length spectrum algorithm that prunes early, that is during the tiling to obtain the pre-length spectrum?

— Verified Length Spectrum and Margulis number for Hyperbolic 3-Manifolds  (2609.26663 - Goerner et al., 22 Sep 2026) in Question 2.1, Section 2.1, “Steps of the length spectrum algorithm”