{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:UT7NJHMKNRFIUZQOOGS7Q6GII7","short_pith_number":"pith:UT7NJHMK","schema_version":"1.0","canonical_sha256":"a4fed49d8a6c4a8a660e71a5f878c847f0b2381e3445e7be0ae8b649096bcc4b","source":{"kind":"arxiv","id":"1007.4081","version":1},"attestation_state":"computed","paper":{"title":"Extensions of witness mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.RA"],"primary_cat":"math-ph","authors_text":"Gejza Jen\\v{c}a","submitted_at":"2010-07-23T09:26:02Z","abstract_excerpt":"We deal with the problem of coexistence in interval effect algebras using the notion of a witness mapping. Suppose that we are given an interval effect algebra $E$, a coexistent subset $S$ of $E$, a witness mapping $\\beta$ for $S$, and an element $t\\in E\\setminus S$. We study the question whether there is a witness mapping $\\beta_t$ for $S\\cup\\{t\\}$ such that $\\beta_t$ is an extension of $\\beta$. In the main result, we prove that such an extension exists if and only if there is a mapping $e_t$ from finite subsets of $S$ to $E$ satisfying certain conditions. The main result is then applied seve"},"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":"1007.4081","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-23T09:26:02Z","cross_cats_sorted":["math.MP","math.RA"],"title_canon_sha256":"15efb05bd7c56760167df645fc7128e867305e5f5ccd1b15290e6ea0411b806e","abstract_canon_sha256":"06546862d559a2f773484e8defb6d6c916ef4d2813dce4ac9fc63c92de4e0677"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:51.804967Z","signature_b64":"W2OvuV/Uk/ayNyjewitvAYZPRqeIVlsHXGNcb84aUb+MVh80uIXdNvoi76TRb+CaMjIRYImEK3tEawZwa0MUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4fed49d8a6c4a8a660e71a5f878c847f0b2381e3445e7be0ae8b649096bcc4b","last_reissued_at":"2026-05-18T00:53:51.804275Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:51.804275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extensions of witness mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.RA"],"primary_cat":"math-ph","authors_text":"Gejza Jen\\v{c}a","submitted_at":"2010-07-23T09:26:02Z","abstract_excerpt":"We deal with the problem of coexistence in interval effect algebras using the notion of a witness mapping. Suppose that we are given an interval effect algebra $E$, a coexistent subset $S$ of $E$, a witness mapping $\\beta$ for $S$, and an element $t\\in E\\setminus S$. We study the question whether there is a witness mapping $\\beta_t$ for $S\\cup\\{t\\}$ such that $\\beta_t$ is an extension of $\\beta$. In the main result, we prove that such an extension exists if and only if there is a mapping $e_t$ from finite subsets of $S$ to $E$ satisfying certain conditions. The main result is then applied seve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4081","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1007.4081","created_at":"2026-05-18T00:53:51.804400+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.4081v1","created_at":"2026-05-18T00:53:51.804400+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4081","created_at":"2026-05-18T00:53:51.804400+00:00"},{"alias_kind":"pith_short_12","alias_value":"UT7NJHMKNRFI","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"UT7NJHMKNRFIUZQO","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"UT7NJHMK","created_at":"2026-05-18T12:26:15.391820+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/UT7NJHMKNRFIUZQOOGS7Q6GII7","json":"https://pith.science/pith/UT7NJHMKNRFIUZQOOGS7Q6GII7.json","graph_json":"https://pith.science/api/pith-number/UT7NJHMKNRFIUZQOOGS7Q6GII7/graph.json","events_json":"https://pith.science/api/pith-number/UT7NJHMKNRFIUZQOOGS7Q6GII7/events.json","paper":"https://pith.science/paper/UT7NJHMK"},"agent_actions":{"view_html":"https://pith.science/pith/UT7NJHMKNRFIUZQOOGS7Q6GII7","download_json":"https://pith.science/pith/UT7NJHMKNRFIUZQOOGS7Q6GII7.json","view_paper":"https://pith.science/paper/UT7NJHMK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.4081&json=true","fetch_graph":"https://pith.science/api/pith-number/UT7NJHMKNRFIUZQOOGS7Q6GII7/graph.json","fetch_events":"https://pith.science/api/pith-number/UT7NJHMKNRFIUZQOOGS7Q6GII7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UT7NJHMKNRFIUZQOOGS7Q6GII7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UT7NJHMKNRFIUZQOOGS7Q6GII7/action/storage_attestation","attest_author":"https://pith.science/pith/UT7NJHMKNRFIUZQOOGS7Q6GII7/action/author_attestation","sign_citation":"https://pith.science/pith/UT7NJHMKNRFIUZQOOGS7Q6GII7/action/citation_signature","submit_replication":"https://pith.science/pith/UT7NJHMKNRFIUZQOOGS7Q6GII7/action/replication_record"}},"created_at":"2026-05-18T00:53:51.804400+00:00","updated_at":"2026-05-18T00:53:51.804400+00:00"}