Certificate for an equilateral set of 58 points in ℓ₅⁵⁶

Exact certificate data and independently rerunnable verifier supporting the paper “A counterexample to Kusner’s conjecture on equilateral sets.” The certificate proves the existence of 58 pairwise equidistant points in ℓ₅⁵⁶. The verifier checks the six certificate inequalities entirely in exact integer arithmetic. Requirements: any recent NumPy to load the data; python-flint is optional (verify.py falls back to regular Python, at the cost of hours instead of seconds). Tested on Python 3.9.6 with numpy 2.0.2 and python-flint 0.6.0 (the versions pinned in requirements.txt), and on Python 3.13 with numpy 2.5.2 and python-flint 0.9.0, with identical exact results.