Claims

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1989_01_01_margulis: Margulis's theorem on indefinite irrational ternary forms gives, for every positive irrational alpha, positive integers x, y, z with x^2 + y^2 - z^2 alpha arbitrarily small; the site's curator records the problem as proved.

2026_08_21_alexeev: Answers the site's wording (every irrational alpha), not the corrected Statement (alpha > 0), so it does not count toward the problem's standing. A Lean theorem in Alexeev's repository, by Codex and GPT-5.6 Sol, refutes that wording at alpha = -sqrt 2 and epsilon = 1.

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