04 / Mathematics Preprint
When symmetry leaves a gap.
Balanced orbit defects in half-turn-symmetric configurations.
Symmetry can organize a search, but the missing pieces matter too. This study examines balanced orbit defects in half-turn-symmetric, planar no-three-in-line configurations.
The paper connects the orbit description to explicit 2n-point constructions. The underlying programme preserves the witness configurations alongside their verification.
Where the claim stops.
This is a result about specified symmetry classes and constructions, not a universal existence theorem for every grid size.
Source: no3-results / README.md. Summary prepared from the local research record, 11 September 2026.
DOI 10.5281/zenodo.22063287 ↗Research led by Aleksei Kudriashov (Alex Komang). Mathematical paper and witness text/data: CC BY 4.0 where stated in the source repository.