{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:GMI76EVHCZP3JGUMWLFIHEOJ3N","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":"413db63a4ad73795d72230b9dbb5882ee7c8caf4c9c922fd9a37080358a63a41","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-03-26T18:14:59Z","title_canon_sha256":"28c6e720ce780a93ae288a372a72bf53bdb7249e24617cd187640587e9bc9abb"},"schema_version":"1.0","source":{"id":"2103.14667","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2103.14667","created_at":"2026-07-05T04:47:38Z"},{"alias_kind":"arxiv_version","alias_value":"2103.14667v2","created_at":"2026-07-05T04:47:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.14667","created_at":"2026-07-05T04:47:38Z"},{"alias_kind":"pith_short_12","alias_value":"GMI76EVHCZP3","created_at":"2026-07-05T04:47:38Z"},{"alias_kind":"pith_short_16","alias_value":"GMI76EVHCZP3JGUM","created_at":"2026-07-05T04:47:38Z"},{"alias_kind":"pith_short_8","alias_value":"GMI76EVH","created_at":"2026-07-05T04:47:38Z"}],"graph_snapshots":[{"event_id":"sha256:a61807af6779868783f5423ecca86b1d601d02978134227a4f55882cc049be49","target":"graph","created_at":"2026-07-05T04:47:38Z","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/2103.14667/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Tree-cut width is a graph parameter introduced by Wollan that is an analogue of treewidth for the immersion order on graphs in the following sense: the tree-cut width of a graph is functionally equivalent to the largest size of a wall that can be found in it as an immersion. In this work we propose a variant of the definition of tree-cut width that is functionally equivalent to the original one, but for which we can state and prove a tight duality theorem relating it to naturally defined dual objects: appropriately defined brambles and tangles. Using this result we also propose a game characte","authors_text":"Karolina Okrasa, {\\L}ukasz Bo\\.zyk, Micha{\\l} Pilipczuk, Oscar Defrain","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-03-26T18:14:59Z","title":"On objects dual to tree-cut decompositions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.14667","kind":"arxiv","version":2},"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:c685fe00459c4b77d6f909b4e221781de70a59d2d79902595d913d13ee713ec7","target":"record","created_at":"2026-07-05T04:47:38Z","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":"413db63a4ad73795d72230b9dbb5882ee7c8caf4c9c922fd9a37080358a63a41","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-03-26T18:14:59Z","title_canon_sha256":"28c6e720ce780a93ae288a372a72bf53bdb7249e24617cd187640587e9bc9abb"},"schema_version":"1.0","source":{"id":"2103.14667","kind":"arxiv","version":2}},"canonical_sha256":"3311ff12a7165fb49a8cb2ca8391c9db727661a519b49b3226abcf6efc8ce411","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3311ff12a7165fb49a8cb2ca8391c9db727661a519b49b3226abcf6efc8ce411","first_computed_at":"2026-07-05T04:47:38.438531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:47:38.438531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0iq0hjMKALh5wsYoymS+ohs5AWEMwZBgzZUjWb6s3SU7c8m87w21sjd4n077BPp70kkNyxPyCQ7aZ3NhsyDwCw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:47:38.439002Z","signed_message":"canonical_sha256_bytes"},"source_id":"2103.14667","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c685fe00459c4b77d6f909b4e221781de70a59d2d79902595d913d13ee713ec7","sha256:a61807af6779868783f5423ecca86b1d601d02978134227a4f55882cc049be49"],"state_sha256":"ddb5cbf75722e49edc774173027f779639234d92323d3927a33065eb0cdc6229"}