{"id":"palomar/PALOMAR-2026-10-08-000007","url":"https://github.com/JD-Jones-ASES/four-row/tree/861abe5342847d3f32985d55403547e1832ffac4","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-08-000007-v1.json","repo":"https://github.com/JD-Jones-ASES/four-row","tags":["math.CO","math.PR","msc:15A15","msc:60E15","msc:26D15","permanent-inequality","combinatorics","lean-formalization"],"score":0,"title":"Sharp robustness and stability of the four-row permanent inequality","trust":"high","domain":"math.CO","source":"palomar","authors":["JD Jones"],"reviews":0,"subject":"math.CO","summary":"A formalization of sharp balanced-law robustness and stability refinements of the classical four-row permanent inequalities of Carlen-Lieb-Loss and Bristiel-Caputo. It proves the exact total-variation radius 1/24, optimal variance-deficit coefficient (1-24r)/9, complete nonnegative equality cases, sharp endpoint entropy constants, and adaptive tensorization. The explicit interior exponent is sufficient rather than optimal; at radius zero it is weaker than the classical optimal uniform exponent. Lean checks exhaustive support coverage and exact rational Gram identities.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-08","reactions":{},"formalized":true,"formalizes":[{"title":"Sharp four-row permanent robustness, stability, and entropy","identifier":"","relationship":"formalizes"},{"title":"A strict four-row permanent inequality and permutation moments","identifier":"https://github.com/openai/math/tree/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/A-strict-four-row-permanent-inequality-and-permutation-moments-September-26-2026","relationship":"adapts"}]}