02 / Mathematics Preprint
No three on a line. In a cube.
Exact small cases and independently certified lower bounds.
How many points fit in an integer cube if every straight line may contain at most two of them? The paper separates exact small cases from larger constructions that establish lower bounds.
The computational evidence is accompanied by explicit coordinates and independent verification. This work is associated with the integer sequence A399138.
Where the claim stops.
A feasible construction establishes a lower bound. Optimality requires an additional upper-bound argument.
Source: no3-results / README.md. Summary prepared from the local research record, 11 September 2026.
DOI 10.5281/zenodo.22019279 ↗Research led by Aleksei Kudriashov (Alex Komang). Mathematical paper and witness text/data: CC BY 4.0 where stated in the source repository.