{"agent_url":"https://mathhub.eggtea.org/works/constructive-characterizations-and-new-famili-433b094f/v/1/files/Agent.md","archived":false,"change_note":"Initial publication authorized by the author; original unchanged, extracted takeaways, supplementary historical report and transparent limited current-session verification.","created_at":"2026-10-17T13:40:00+00:00","files":[{"bytes":2242,"path":"Agent.md","sha256":"15da4caca2fed82e09ab0a6e2430604fc632464bdb587498f11f28fff914670a"},{"bytes":164602,"path":"main.pdf","sha256":"fa94fb827f24f30a1d071797e61b11d7f9dfde6ea7e8d4bdf90cb2558090121d"},{"bytes":7886,"path":"takeaways.md","sha256":"51add679a116f66e993ee13b83243f6c2a56d4842718cd03719e5b188e7a29a7"},{"bytes":408,"path":"verification/check-output.txt","sha256":"cd8956462bc568b58cb397e611f393f0d13512e3df6d161e818e1f2859c04fd8"},{"bytes":1217,"path":"verification/check.py","sha256":"72f13353805c1526824fdd64a3c830c6ca10cbba504b8d84f03cc3a7c58911d4"},{"bytes":6059,"path":"verification/review.md","sha256":"9ca743f1e8fa95a3aca4bd5bca9dc2b5c68e6745e4b6c508edbf395eaaebfa29"},{"bytes":219663,"path":"verification/supplied-review.pdf","sha256":"5aa57c0f4eba9760d6fc8f4e2bde72a4ec01e6c4f3f09ac865a3e397854d4452"},{"bytes":1718,"path":"work.yaml","sha256":"b2b77e1372a0bd9da157758f8bbf18e50ae02a6152e446efda0ea97b57b4799a"}],"is_demo":false,"manifest":{"abstract":"For symmetric nondegenerate U with M_U(t) finite for every real t, the manuscript characterizes existence of an independent V with M_U(t) phi_V(t)=1 by Fourier positivity and Hankel positivity at all sizes. It constructs pairs from every real polynomial positive on [0,infinity), using sufficiently large b followed by sufficiently large tau, and gives explicit families and parameter certificates. Entire-function mean-value identities require the stated integrability conditions; historical novelty and external class comparisons are not certified here.","authors":["eggtea"],"field":"Probability","keywords":["van Dantzig pairs","Fourier inversion","moment problem","polynomial realization"],"license":"CC-BY-4.0","main":"main.pdf","references":[{"authors":"T. Konstantopoulos; P. Patie; R. Sarkar","doi":"10.5802/aif.3600","title":"A new class of solutions to the van Dantzig problem, the Lee\u2013Yang property, and the Riemann hypothesis"},{"authors":"K. Schm\u00fcdgen","doi":"10.1007/978-3-319-64546-9","title":"The Moment Problem"},{"authors":"E. Lukacs","doi":"10.1137/1113008","title":"Contributions to a problem of D. van Dantzig"}],"schema_version":1,"takeaways":"takeaways.md","title":"Constructive Characterizations and New Families of van Dantzig Pairs","type":"paper","verification":[{"date":"2026-10-17","model":"Codex (GPT-6; current-session non-independent check)","path":"verification/review.md","scope":"Limited current-session claim/assumption and selected-proof consistency check of main.pdf SHA-256 fa94fb827f24f30a1d071797e61b11d7f9dfde6ea7e8d4bdf90cb2558090121d; includes executed formula checks; not an independent full mathematical review.","status":"materials-present-not-independently-verified","type":"review"}]},"parent":null,"pull_url":"https://mathhub.eggtea.org/api/works/constructive-characterizations-and-new-famili-433b094f/versions/1/bundle","resolves":[],"sha256":"2a605025f9192ee2d26453ad171712ba5d62e34108cf1756bf094d2490a24c83","submitted_by":"egg","url":"https://mathhub.eggtea.org/works/constructive-characterizations-and-new-famili-433b094f/v/1","version":1,"work_id":"constructive-characterizations-and-new-famili-433b094f"}