{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:UEGNZLF3PHWWLARVSEJKDUUPIH","short_pith_number":"pith:UEGNZLF3","schema_version":"1.0","canonical_sha256":"a10cdcacbb79ed6582359112a1d28f41fdd16797df6528e40207b392ced2405e","source":{"kind":"arxiv","id":"0812.2502","version":2},"attestation_state":"computed","paper":{"title":"Not each sequential effect algebra is sharply dominating","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.MP","math.QA","quant-ph"],"primary_cat":"math-ph","authors_text":"Shen Jun, Wu Junde","submitted_at":"2008-12-12T23:09:02Z","abstract_excerpt":"Let $E$ be an effect algebra and $E_S$ be the set of all sharp elements of $E$. $E$ is said to be sharply dominating if for each $a\\in E$ there exists a smallest element $\\widehat{a}\\in E_s$ such that $a\\leq \\widehat{a}$. In 2002, Professors Gudder and Greechie proved that each $\\sigma$-sequential effect algebra is sharply dominating. In 2005, Professor Gudder presented 25 open problems in International Journal of Theoretical Physics, Vol. 44, 2199-2205, the 3th problem asked: Is each sequential effect algebra sharply dominating? Now, we construct an example to answer the problem negatively."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0812.2502","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math-ph","submitted_at":"2008-12-12T23:09:02Z","cross_cats_sorted":["math.MP","math.QA","quant-ph"],"title_canon_sha256":"6b8c9e994427d93efdbf9d599391dc7cb8974d3f8b6f649d7a88d3a3dc9ef5bf","abstract_canon_sha256":"2d8af4f9443fe08d7564cffa43624788e221956fc83bf0ffd40c00154ef76d98"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:05.894546Z","signature_b64":"NTTh6U0UdTGmNaFWHwy8OEK/IDDJXdcAphJEYq231Z0g2UGK1BYhzNQBx8ZEFmlyEd03WmqQ4Di9fK5GQXJ7CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a10cdcacbb79ed6582359112a1d28f41fdd16797df6528e40207b392ced2405e","last_reissued_at":"2026-05-18T00:31:05.893959Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:05.893959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Not each sequential effect algebra is sharply dominating","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.MP","math.QA","quant-ph"],"primary_cat":"math-ph","authors_text":"Shen Jun, Wu Junde","submitted_at":"2008-12-12T23:09:02Z","abstract_excerpt":"Let $E$ be an effect algebra and $E_S$ be the set of all sharp elements of $E$. $E$ is said to be sharply dominating if for each $a\\in E$ there exists a smallest element $\\widehat{a}\\in E_s$ such that $a\\leq \\widehat{a}$. In 2002, Professors Gudder and Greechie proved that each $\\sigma$-sequential effect algebra is sharply dominating. In 2005, Professor Gudder presented 25 open problems in International Journal of Theoretical Physics, Vol. 44, 2199-2205, the 3th problem asked: Is each sequential effect algebra sharply dominating? Now, we construct an example to answer the problem negatively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.2502","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0812.2502","created_at":"2026-05-18T00:31:05.894040+00:00"},{"alias_kind":"arxiv_version","alias_value":"0812.2502v2","created_at":"2026-05-18T00:31:05.894040+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.2502","created_at":"2026-05-18T00:31:05.894040+00:00"},{"alias_kind":"pith_short_12","alias_value":"UEGNZLF3PHWW","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"UEGNZLF3PHWWLARV","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"UEGNZLF3","created_at":"2026-05-18T12:25:58.018023+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UEGNZLF3PHWWLARVSEJKDUUPIH","json":"https://pith.science/pith/UEGNZLF3PHWWLARVSEJKDUUPIH.json","graph_json":"https://pith.science/api/pith-number/UEGNZLF3PHWWLARVSEJKDUUPIH/graph.json","events_json":"https://pith.science/api/pith-number/UEGNZLF3PHWWLARVSEJKDUUPIH/events.json","paper":"https://pith.science/paper/UEGNZLF3"},"agent_actions":{"view_html":"https://pith.science/pith/UEGNZLF3PHWWLARVSEJKDUUPIH","download_json":"https://pith.science/pith/UEGNZLF3PHWWLARVSEJKDUUPIH.json","view_paper":"https://pith.science/paper/UEGNZLF3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0812.2502&json=true","fetch_graph":"https://pith.science/api/pith-number/UEGNZLF3PHWWLARVSEJKDUUPIH/graph.json","fetch_events":"https://pith.science/api/pith-number/UEGNZLF3PHWWLARVSEJKDUUPIH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UEGNZLF3PHWWLARVSEJKDUUPIH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UEGNZLF3PHWWLARVSEJKDUUPIH/action/storage_attestation","attest_author":"https://pith.science/pith/UEGNZLF3PHWWLARVSEJKDUUPIH/action/author_attestation","sign_citation":"https://pith.science/pith/UEGNZLF3PHWWLARVSEJKDUUPIH/action/citation_signature","submit_replication":"https://pith.science/pith/UEGNZLF3PHWWLARVSEJKDUUPIH/action/replication_record"}},"created_at":"2026-05-18T00:31:05.894040+00:00","updated_at":"2026-05-18T00:31:05.894040+00:00"}