{"id":"palomar/PALOMAR-2026-10-15-000001","url":"https://github.com/JD-Jones-ASES/support-criterion/tree/f6185744e26f5862fd704ef637ebef3fd068cef5","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-15-000001-v1.json","repo":"https://github.com/JD-Jones-ASES/support-criterion","tags":["math.PR","msc:60E15","msc:60E05","probability","sub-gaussian","concentration-inequalities"],"score":0,"title":"Sharp universal support criterion for sub-Gaussian laws","trust":"high","domain":"math.PR","source":"palomar","authors":["JD Jones"],"reviews":0,"subject":"math.PR","summary":"For every Borel probability law on the real line that is symmetric about zero and satisfies 0 < a <= |X| <= b almost surely, the support ratio b/a <= sqrt(3) + sqrt(2) guarantees E exp(t X) <= exp(t^2 E X^2 / 2) for every real t. The inequality is strict for nonzero t, and the actual variance is the optimal quadratic proxy. An explicit symmetric law on {-R,-1,1,R} violates the bound near zero for each larger ratio R. In the normalization 3-sqrt(6) <= X^2 <= 3+sqrt(6), the development also establishes the sharp eighth-order MGF gap with its optimal interiority coefficient, identifies the…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-15","reactions":{},"formalized":true}