{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YBGFVPFCF4BRA2YONXRWBDTD4I","short_pith_number":"pith:YBGFVPFC","schema_version":"1.0","canonical_sha256":"c04c5abca22f03106b0e6de3608e63e234924bab46b058b9b1851857a306f94e","source":{"kind":"arxiv","id":"1406.3797","version":6},"attestation_state":"computed","paper":{"title":"Abstract Separation Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Reinhard Diestel","submitted_at":"2014-06-15T07:05:37Z","abstract_excerpt":"Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree structure theorems in graphs, matroids or CW-complexes to, potentially, image segmentation and cluster analysis.\n  This paper is intended as a concise common reference for the basic definitions and facts about abstract separation systems in these and any future papers using this framework."},"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":"1406.3797","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-15T07:05:37Z","cross_cats_sorted":[],"title_canon_sha256":"bade54609bb4277fb4569d24c158b6adc21f9ce83ccf1f41c1e245d8e64db668","abstract_canon_sha256":"f31c844a70aa071665e01c2634bd1218a9c650de7149ad7d66a819d8c9b70437"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:17.032909Z","signature_b64":"31y25eSeg7V8o4YN7WOk1MDVVPhMGfWyaaorqkN8+20F4CVHhiY7KSGMwFXZ9WXlhCDS/rA/fAktbIUpcpLvAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c04c5abca22f03106b0e6de3608e63e234924bab46b058b9b1851857a306f94e","last_reissued_at":"2026-05-18T00:46:17.032462Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:17.032462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Abstract Separation Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Reinhard Diestel","submitted_at":"2014-06-15T07:05:37Z","abstract_excerpt":"Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree structure theorems in graphs, matroids or CW-complexes to, potentially, image segmentation and cluster analysis.\n  This paper is intended as a concise common reference for the basic definitions and facts about abstract separation systems in these and any future papers using this framework."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3797","kind":"arxiv","version":6},"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":"1406.3797","created_at":"2026-05-18T00:46:17.032548+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.3797v6","created_at":"2026-05-18T00:46:17.032548+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3797","created_at":"2026-05-18T00:46:17.032548+00:00"},{"alias_kind":"pith_short_12","alias_value":"YBGFVPFCF4BR","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YBGFVPFCF4BRA2YO","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YBGFVPFC","created_at":"2026-05-18T12:28:57.508820+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2304.12078","citing_title":"Optimal trees of tangles: refining the essential parts","ref_index":7,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YBGFVPFCF4BRA2YONXRWBDTD4I","json":"https://pith.science/pith/YBGFVPFCF4BRA2YONXRWBDTD4I.json","graph_json":"https://pith.science/api/pith-number/YBGFVPFCF4BRA2YONXRWBDTD4I/graph.json","events_json":"https://pith.science/api/pith-number/YBGFVPFCF4BRA2YONXRWBDTD4I/events.json","paper":"https://pith.science/paper/YBGFVPFC"},"agent_actions":{"view_html":"https://pith.science/pith/YBGFVPFCF4BRA2YONXRWBDTD4I","download_json":"https://pith.science/pith/YBGFVPFCF4BRA2YONXRWBDTD4I.json","view_paper":"https://pith.science/paper/YBGFVPFC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.3797&json=true","fetch_graph":"https://pith.science/api/pith-number/YBGFVPFCF4BRA2YONXRWBDTD4I/graph.json","fetch_events":"https://pith.science/api/pith-number/YBGFVPFCF4BRA2YONXRWBDTD4I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YBGFVPFCF4BRA2YONXRWBDTD4I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YBGFVPFCF4BRA2YONXRWBDTD4I/action/storage_attestation","attest_author":"https://pith.science/pith/YBGFVPFCF4BRA2YONXRWBDTD4I/action/author_attestation","sign_citation":"https://pith.science/pith/YBGFVPFCF4BRA2YONXRWBDTD4I/action/citation_signature","submit_replication":"https://pith.science/pith/YBGFVPFCF4BRA2YONXRWBDTD4I/action/replication_record"}},"created_at":"2026-05-18T00:46:17.032548+00:00","updated_at":"2026-05-18T00:46:17.032548+00:00"}