Abstract
How can a grid point set be modified without creating an isosceles triangle? This work introduces two local profiles: points that become individually admissible after deletions, and points that can actually be added together. It establishes exact profiles around two public AlphaEvolve configurations and lower bounds on the changes required to reach another configuration of equal or greater size.
Results
On the 64 × 64 grid: 5 compatible additions, compared with 6 individually admissible points.
Every addition-and-removal path to another equally large configuration must drop to 161 points or fewer.
Method
Vertex-cover reductions, antichains of minimal masks and exact searches. On the 100 × 100 grid, the bounds at radii 6 and 7 use independently regenerated SAT instances and verified DRAT certificates. The value at radius 8 uses a directly verified witness and a separately audited exhaustive search.
Limitations
The radius-8 upper bound has no portable DRAT/LRAT proof trace. Neither configuration is claimed to be globally optimal. The reconfiguration barrier is a lower bound, not an exact value.
AI disclosure
Generative language tools, including OpenAI Codex, assisted with computational exploration, code development, literature searches and writing. The human author is responsible for the manuscript, results, references and supporting artifacts.