{"id":"openai-math/Full-support-of-the-zero-temperature-Sherrington-Kirkpatrick-order-parameter","pdf":"https://github.com/openai/math/blob/main/preprints/Full-support-of-the-zero-temperature-Sherrington-Kirkpatrick-order-parameter-September-27-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Full-support-of-the-zero-temperature-Sherrington-Kirkpatrick-order-parameter-September-27-2026","tags":["spin-glasses","probability","statistical-mechanics"],"score":0,"title":"Full support of the zero-temperature Sherrington-Kirkpatrick order parameter","domain":"Mathematical physics","family":"281","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"We prove that every admissible integrable minimizer of the zero-temperature Parisi functional for the pure, zero-field Sherrington–Kirkpatrick model has full relative Stieltjes support on $`[0,1)`$. Thus its support has no gaps at any overlap scale below one. We use the covariance normalization $`\\xi(t)=t^2/2`$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":false,"family_title":"QAOA attains the SK optimum in the thermodynamic-first limit"}