Claims

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1966_01_01_elbert: The supremum of the measure of {|f| < 1} over monic real polynomials with all roots in [-1, 1] is 2 sqrt 2, as Erdős, Herzog and Piranian conjectured; proved in two refereed papers of 1966 and 1968, cited by the later claimants.

2025_12_21_tao: For a probability measure on an interval of length two, the set where the logarithmic potential is nonnegative has measure at most 2 sqrt 2, so the supremum of the measure of {|f| < 1} over the class is 2 sqrt 2.

2026_07_14_wang: Claims the infimum of the measure of {|f| < 1} over monic real polynomials with roots in [-1, 1] is L = 1.834430475762661..., not attained, and the supremum 2 sqrt 2; author-run Lean.

2026_07_15_darvas_peng_tao: Claims that the infimum of the measure of {|f| < 1}, over monic polynomials with roots in [-1, 1] and over probability measures on [-1, 1] alike, is D = 1.834430475762661711..., by a dual measure completing Terence Tao's reduction.

2026_08_24_budala: Claims the infimum D = 1.834430475762661711..., never attained, with explicit degree-n polynomials within O(log n / sqrt n) of D, and the supremum 2 sqrt 2 attained exactly by (x^2 - 1)^m.

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