{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YWJ6MSQBAQZNVFIFJAYEGAWMSD","short_pith_number":"pith:YWJ6MSQB","canonical_record":{"source":{"id":"1406.3798","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-15T07:06:49Z","cross_cats_sorted":[],"title_canon_sha256":"5114fc21b644a5041e015ee2fd27c8193157d4842467332641fa5ebd4cfcd27a","abstract_canon_sha256":"6010fea595b43e893e07e7fc12a0604329f7846ad11ae5483836e3908b0b7b41"},"schema_version":"1.0"},"canonical_sha256":"c593e64a010432da950548304302cc90c736b8e6248ec6977dcb78a03c125a1e","source":{"kind":"arxiv","id":"1406.3798","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3798","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3798v1","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3798","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"pith_short_12","alias_value":"YWJ6MSQBAQZN","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YWJ6MSQBAQZNVFIF","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YWJ6MSQB","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YWJ6MSQBAQZNVFIFJAYEGAWMSD","target":"record","payload":{"canonical_record":{"source":{"id":"1406.3798","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-15T07:06:49Z","cross_cats_sorted":[],"title_canon_sha256":"5114fc21b644a5041e015ee2fd27c8193157d4842467332641fa5ebd4cfcd27a","abstract_canon_sha256":"6010fea595b43e893e07e7fc12a0604329f7846ad11ae5483836e3908b0b7b41"},"schema_version":"1.0"},"canonical_sha256":"c593e64a010432da950548304302cc90c736b8e6248ec6977dcb78a03c125a1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:39.703416Z","signature_b64":"20sCzR9kBplAxgOImQjrUBNHluiMMPceB8PhYGdK1Fy49+AwI/4kIAQU+SMnq0LFuJpTDai7mD2ChSXv4L8lDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c593e64a010432da950548304302cc90c736b8e6248ec6977dcb78a03c125a1e","last_reissued_at":"2026-05-18T02:49:39.703094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:39.703094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.3798","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xaK9o164AENwV0Zrq1cMr7LwaEh/TuS5+Gc68jKPw0LKXVepBmfyDvq+j+yVbkaD8IcPZmAQko2I+ChZUV/yBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:50:05.434282Z"},"content_sha256":"1759f18fbc559ff9b6ae52fbdbd5d409d6416708f3ba4ffe07d450c8042ee26c","schema_version":"1.0","event_id":"sha256:1759f18fbc559ff9b6ae52fbdbd5d409d6416708f3ba4ffe07d450c8042ee26c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YWJ6MSQBAQZNVFIFJAYEGAWMSD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unifying duality theorems for width parameters in graphs and matroids. II. General duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Reinhard Diestel, Sang-il Oum","submitted_at":"2014-06-15T07:06:49Z","abstract_excerpt":"We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3798","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:49:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/plnCq+OrVNbd3AYA37DlZgwyHqtie0IVT8HHzeiFxo/737WvPildNnbuaqz6EObCs6ajGbQKYLRRQ4zyi+JBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:50:05.434969Z"},"content_sha256":"182dc3d6e81cce16ba7a9cac58db837c5e730425ec2f0cfc4c21fd0c22aaf08a","schema_version":"1.0","event_id":"sha256:182dc3d6e81cce16ba7a9cac58db837c5e730425ec2f0cfc4c21fd0c22aaf08a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YWJ6MSQBAQZNVFIFJAYEGAWMSD/bundle.json","state_url":"https://pith.science/pith/YWJ6MSQBAQZNVFIFJAYEGAWMSD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YWJ6MSQBAQZNVFIFJAYEGAWMSD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T00:50:05Z","links":{"resolver":"https://pith.science/pith/YWJ6MSQBAQZNVFIFJAYEGAWMSD","bundle":"https://pith.science/pith/YWJ6MSQBAQZNVFIFJAYEGAWMSD/bundle.json","state":"https://pith.science/pith/YWJ6MSQBAQZNVFIFJAYEGAWMSD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YWJ6MSQBAQZNVFIFJAYEGAWMSD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YWJ6MSQBAQZNVFIFJAYEGAWMSD","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":"6010fea595b43e893e07e7fc12a0604329f7846ad11ae5483836e3908b0b7b41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-15T07:06:49Z","title_canon_sha256":"5114fc21b644a5041e015ee2fd27c8193157d4842467332641fa5ebd4cfcd27a"},"schema_version":"1.0","source":{"id":"1406.3798","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3798","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3798v1","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3798","created_at":"2026-05-18T02:49:39Z"},{"alias_kind":"pith_short_12","alias_value":"YWJ6MSQBAQZN","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YWJ6MSQBAQZNVFIF","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YWJ6MSQB","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:182dc3d6e81cce16ba7a9cac58db837c5e730425ec2f0cfc4c21fd0c22aaf08a","target":"graph","created_at":"2026-05-18T02:49:39Z","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 prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]","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":"2014-06-15T07:06:49Z","title":"Unifying duality theorems for width parameters in graphs and matroids. II. General duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3798","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":"sha256:1759f18fbc559ff9b6ae52fbdbd5d409d6416708f3ba4ffe07d450c8042ee26c","target":"record","created_at":"2026-05-18T02:49:39Z","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":"6010fea595b43e893e07e7fc12a0604329f7846ad11ae5483836e3908b0b7b41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-06-15T07:06:49Z","title_canon_sha256":"5114fc21b644a5041e015ee2fd27c8193157d4842467332641fa5ebd4cfcd27a"},"schema_version":"1.0","source":{"id":"1406.3798","kind":"arxiv","version":1}},"canonical_sha256":"c593e64a010432da950548304302cc90c736b8e6248ec6977dcb78a03c125a1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c593e64a010432da950548304302cc90c736b8e6248ec6977dcb78a03c125a1e","first_computed_at":"2026-05-18T02:49:39.703094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:39.703094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"20sCzR9kBplAxgOImQjrUBNHluiMMPceB8PhYGdK1Fy49+AwI/4kIAQU+SMnq0LFuJpTDai7mD2ChSXv4L8lDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:39.703416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3798","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1759f18fbc559ff9b6ae52fbdbd5d409d6416708f3ba4ffe07d450c8042ee26c","sha256:182dc3d6e81cce16ba7a9cac58db837c5e730425ec2f0cfc4c21fd0c22aaf08a"],"state_sha256":"f616e2cd845624e3977cfc0ddf1870252fadfd7ced8de60d1d0a02c7800fc5b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zCcGK5ww3n3qjF1XfzEb22+QwvZQBiyZ96SMycLgb4Rkep++ndk1kHWnFMnX1BNXYJWyIKdd0xk2t4XROUh/Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:50:05.439032Z","bundle_sha256":"b1f4cdfe0167639d84b9883df575a14cc6847cfc05b3e6e41928e0cf4fc6df99"}}