{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:PVQ5PP2HTIBSMTXCPFUP6TGHWQ","short_pith_number":"pith:PVQ5PP2H","schema_version":"1.0","canonical_sha256":"7d61d7bf479a03264ee27968ff4cc7b425927d23a5e885224cb213f11c3ef214","source":{"kind":"arxiv","id":"1105.6027","version":1},"attestation_state":"computed","paper":{"title":"Properties of semi-elementary imsets as sums of elementary imsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Akimichi Takemura, Kentaro Tanaka, Takuya Kashimura, Tomonari Sei","submitted_at":"2011-05-30T16:16:02Z","abstract_excerpt":"We study properties of semi-elementary imsets and elementary imsets introduced by Studeny (2005). The rules of the semi-graphoid axiom (decomposition, weak union and contraction) for conditional independence statements can be translated into a simple identity among three semi-elementary imsets. By recursively applying the identity, any semi-elementary imset can be written as a sum of elementary imsets, which we call a representation of the semi-elementary imset. A semi-elementary imset has many representations. We study properties of the set of possible representations of a semi-elementary ims"},"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":"1105.6027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-05-30T16:16:02Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"5cf5814a383ce1071665217b1093a353d07032e4d78ff0ce8cea8cd4e67a0281","abstract_canon_sha256":"9c761b5833d4533efdbad42bc4e43c7fdabd773006c5922d65d2785809c8c71b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:06.459426Z","signature_b64":"U2m7UKkp8VcwUx0oq2gFvIl2vOmCvK0X1V6RvjU/Hdbup8Cls9EYQy6Wz8IkqqMOezhRFUajRjXzcWRiY/6hAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d61d7bf479a03264ee27968ff4cc7b425927d23a5e885224cb213f11c3ef214","last_reissued_at":"2026-05-18T04:15:06.458913Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:06.458913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Properties of semi-elementary imsets as sums of elementary imsets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Akimichi Takemura, Kentaro Tanaka, Takuya Kashimura, Tomonari Sei","submitted_at":"2011-05-30T16:16:02Z","abstract_excerpt":"We study properties of semi-elementary imsets and elementary imsets introduced by Studeny (2005). The rules of the semi-graphoid axiom (decomposition, weak union and contraction) for conditional independence statements can be translated into a simple identity among three semi-elementary imsets. By recursively applying the identity, any semi-elementary imset can be written as a sum of elementary imsets, which we call a representation of the semi-elementary imset. A semi-elementary imset has many representations. We study properties of the set of possible representations of a semi-elementary ims"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6027","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":"1105.6027","created_at":"2026-05-18T04:15:06.458991+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.6027v1","created_at":"2026-05-18T04:15:06.458991+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.6027","created_at":"2026-05-18T04:15:06.458991+00:00"},{"alias_kind":"pith_short_12","alias_value":"PVQ5PP2HTIBS","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"PVQ5PP2HTIBSMTXC","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"PVQ5PP2H","created_at":"2026-05-18T12:26:39.201973+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/PVQ5PP2HTIBSMTXCPFUP6TGHWQ","json":"https://pith.science/pith/PVQ5PP2HTIBSMTXCPFUP6TGHWQ.json","graph_json":"https://pith.science/api/pith-number/PVQ5PP2HTIBSMTXCPFUP6TGHWQ/graph.json","events_json":"https://pith.science/api/pith-number/PVQ5PP2HTIBSMTXCPFUP6TGHWQ/events.json","paper":"https://pith.science/paper/PVQ5PP2H"},"agent_actions":{"view_html":"https://pith.science/pith/PVQ5PP2HTIBSMTXCPFUP6TGHWQ","download_json":"https://pith.science/pith/PVQ5PP2HTIBSMTXCPFUP6TGHWQ.json","view_paper":"https://pith.science/paper/PVQ5PP2H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.6027&json=true","fetch_graph":"https://pith.science/api/pith-number/PVQ5PP2HTIBSMTXCPFUP6TGHWQ/graph.json","fetch_events":"https://pith.science/api/pith-number/PVQ5PP2HTIBSMTXCPFUP6TGHWQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PVQ5PP2HTIBSMTXCPFUP6TGHWQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PVQ5PP2HTIBSMTXCPFUP6TGHWQ/action/storage_attestation","attest_author":"https://pith.science/pith/PVQ5PP2HTIBSMTXCPFUP6TGHWQ/action/author_attestation","sign_citation":"https://pith.science/pith/PVQ5PP2HTIBSMTXCPFUP6TGHWQ/action/citation_signature","submit_replication":"https://pith.science/pith/PVQ5PP2HTIBSMTXCPFUP6TGHWQ/action/replication_record"}},"created_at":"2026-05-18T04:15:06.458991+00:00","updated_at":"2026-05-18T04:15:06.458991+00:00"}