{"paper":{"title":"The average value inequality in sequential effect algebras","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.LO","math.MP","math.QA","quant-ph"],"primary_cat":"math-ph","authors_text":"Shen Jun, Wu Junde","submitted_at":"2009-03-30T02:46:40Z","abstract_excerpt":"A sequential effect algebra $(E,0,1, \\oplus, \\circ)$ is an effect algebra on which a sequential product $\\circ$ with certain physics properties is defined, in particular, sequential effect algebra is an important model for studying quantum measurement theory. In 2005, Gudder asked the following problem: If $a, b\\in (E,0,1,\\oplus, \\circ)$ and $a\\bot b$ and $a\\circ b\\bot a\\circ b$, is it the case that $2(a\\circ b)\\leq a^2\\oplus b^2$ ? In this paper, we construct an example to answer the problem negatively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.5115","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}