07 / Mathematics Verified construction
Every point, accounted for.
164 exact coordinates in an 11 × 11 × 11 grid.
The object in the opening study uses an actual 164-point witness, with all coordinates in the integer cube [0,10]³.
For this site, every one of the 721,764 triples was independently checked using exact integer cross products. The points are distinct and none of the triples is collinear.
Where the claim stops.
This certifies a lower bound of 164 at n = 11. It does not prove that 164 is optimal.
Source: a399138-witnesses / witnesses/n11_164_c26_ord12_strata.txt. Summary prepared from the local research record, 11 September 2026.
Research led by Aleksei Kudriashov (Alex Komang). Mathematical paper and witness text/data: CC BY 4.0 where stated in the source repository.