{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OGMLEUPI3DE65KKFE2PQ3LC3N5","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":"90ce19ddc25a8b7c0f74b70bf91c14d4144a4adad5d09cf2a99f79e9ab9768f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-10T10:37:36Z","title_canon_sha256":"16a9b033e82e740c20c2a6aa9cddd3e217ed888724d484b109b62f2809492404"},"schema_version":"1.0","source":{"id":"1701.02509","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02509","created_at":"2026-07-05T02:07:24Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02509v4","created_at":"2026-07-05T02:07:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02509","created_at":"2026-07-05T02:07:24Z"},{"alias_kind":"pith_short_12","alias_value":"OGMLEUPI3DE6","created_at":"2026-07-05T02:07:24Z"},{"alias_kind":"pith_short_16","alias_value":"OGMLEUPI3DE65KKF","created_at":"2026-07-05T02:07:24Z"},{"alias_kind":"pith_short_8","alias_value":"OGMLEUPI","created_at":"2026-07-05T02:07:24Z"}],"graph_snapshots":[{"event_id":"sha256:9f0bd41099006bb44888a4c690e20066fb9c3d7bab0be7a6709f9289ec661240","target":"graph","created_at":"2026-07-05T02:07:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1701.02509/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a general width duality theorem for combinatorial structures with well-defined notions of cohesion and separation. These might be graphs and matroids, but can be much more general or quite different. The theorem asserts a duality between the existence of high cohesiveness somewhere local and a global overall tree structure.\n  We describe cohesive substructures in a unified way in the format of tangles: as orientations of low-order separations satisfying certain consistency axioms. These axioms can be expressed without reference to the underlying structure, such as a graph or matroid, ","authors_text":"Reinhard Diestel, Sang-il Oum","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-10T10:37:36Z","title":"Tangle-tree duality in abstract separation systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02509","kind":"arxiv","version":4},"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:f94fdb896f8e762731ee318e7bc300932c9beb699867b808c25161317768ead8","target":"record","created_at":"2026-07-05T02:07:24Z","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":"90ce19ddc25a8b7c0f74b70bf91c14d4144a4adad5d09cf2a99f79e9ab9768f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-10T10:37:36Z","title_canon_sha256":"16a9b033e82e740c20c2a6aa9cddd3e217ed888724d484b109b62f2809492404"},"schema_version":"1.0","source":{"id":"1701.02509","kind":"arxiv","version":4}},"canonical_sha256":"7198b251e8d8c9eea945269f0dac5b6f660412360c19a54558ec764853d8eea0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7198b251e8d8c9eea945269f0dac5b6f660412360c19a54558ec764853d8eea0","first_computed_at":"2026-07-05T02:07:24.275532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:07:24.275532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yG/zHL4cOdRzJCeiwkuO8ERPNiC3OkQdC7FxkxWMgLeA1Sm87iwPHcSGYlpin9jINp6sBkPIBBHeRqMCYMfjBg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:07:24.275982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02509","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f94fdb896f8e762731ee318e7bc300932c9beb699867b808c25161317768ead8","sha256:9f0bd41099006bb44888a4c690e20066fb9c3d7bab0be7a6709f9289ec661240"],"state_sha256":"e13e7797eac58afe28aa499fd6448f66893a1f738736b068606c5265a9b61150"}