{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UT7NJHMKNRFIUZQOOGS7Q6GII7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"06546862d559a2f773484e8defb6d6c916ef4d2813dce4ac9fc63c92de4e0677","cross_cats_sorted":["math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-23T09:26:02Z","title_canon_sha256":"15efb05bd7c56760167df645fc7128e867305e5f5ccd1b15290e6ea0411b806e"},"schema_version":"1.0","source":{"id":"1007.4081","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.4081","created_at":"2026-05-18T00:53:51Z"},{"alias_kind":"arxiv_version","alias_value":"1007.4081v1","created_at":"2026-05-18T00:53:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.4081","created_at":"2026-05-18T00:53:51Z"},{"alias_kind":"pith_short_12","alias_value":"UT7NJHMKNRFI","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UT7NJHMKNRFIUZQO","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UT7NJHMK","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:5e824f444ca5020b2062a50fd6bd2415b7a1c6ccbe1d2e0f606bc840682f37ed","target":"graph","created_at":"2026-05-18T00:53:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Gejza Jen\\v{c}a","cross_cats":["math.MP","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-23T09:26:02Z","title":"Extensions of witness mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.4081","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:47c5f935b4a449b2caa735b36c1de5cd3eac004a71f72fc5140065605499b045","target":"record","created_at":"2026-05-18T00:53:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"06546862d559a2f773484e8defb6d6c916ef4d2813dce4ac9fc63c92de4e0677","cross_cats_sorted":["math.MP","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-07-23T09:26:02Z","title_canon_sha256":"15efb05bd7c56760167df645fc7128e867305e5f5ccd1b15290e6ea0411b806e"},"schema_version":"1.0","source":{"id":"1007.4081","kind":"arxiv","version":1}},"canonical_sha256":"a4fed49d8a6c4a8a660e71a5f878c847f0b2381e3445e7be0ae8b649096bcc4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4fed49d8a6c4a8a660e71a5f878c847f0b2381e3445e7be0ae8b649096bcc4b","first_computed_at":"2026-05-18T00:53:51.804275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:51.804275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W2OvuV/Uk/ayNyjewitvAYZPRqeIVlsHXGNcb84aUb+MVh80uIXdNvoi76TRb+CaMjIRYImEK3tEawZwa0MUBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:51.804967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.4081","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47c5f935b4a449b2caa735b36c1de5cd3eac004a71f72fc5140065605499b045","sha256:5e824f444ca5020b2062a50fd6bd2415b7a1c6ccbe1d2e0f606bc840682f37ed"],"state_sha256":"48813b5640ecedca4a48de744cda0d9d1e6241e0988e59b884de198bdd16da56"}