{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:DNLPF7D3PHS3BC47PRTWKYEQZG","short_pith_number":"pith:DNLPF7D3","canonical_record":{"source":{"id":"1006.3167","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-06-16T09:00:16Z","cross_cats_sorted":[],"title_canon_sha256":"469ccfa6672db8aa14563f3bf429505c226aafe60d6262ce0615d898a4820a7c","abstract_canon_sha256":"db3a799432bd28e1b3204331caf4e921f3d6d6781a116a4c507fa4fd833dfa7e"},"schema_version":"1.0"},"canonical_sha256":"1b56f2fc7b79e5b08b9f7c67656090c98bb412b7f8c6de641965778cf29156d6","source":{"kind":"arxiv","id":"1006.3167","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.3167","created_at":"2026-05-18T04:07:17Z"},{"alias_kind":"arxiv_version","alias_value":"1006.3167v2","created_at":"2026-05-18T04:07:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3167","created_at":"2026-05-18T04:07:17Z"},{"alias_kind":"pith_short_12","alias_value":"DNLPF7D3PHS3","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DNLPF7D3PHS3BC47","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DNLPF7D3","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:DNLPF7D3PHS3BC47PRTWKYEQZG","target":"record","payload":{"canonical_record":{"source":{"id":"1006.3167","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-06-16T09:00:16Z","cross_cats_sorted":[],"title_canon_sha256":"469ccfa6672db8aa14563f3bf429505c226aafe60d6262ce0615d898a4820a7c","abstract_canon_sha256":"db3a799432bd28e1b3204331caf4e921f3d6d6781a116a4c507fa4fd833dfa7e"},"schema_version":"1.0"},"canonical_sha256":"1b56f2fc7b79e5b08b9f7c67656090c98bb412b7f8c6de641965778cf29156d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:17.900460Z","signature_b64":"4zvZCPZq3qIjLSdEz02ih9b7CMU0TRNv32Mf6aPyCCSyEqdCNUUvU+hehtCXMg2NqOx6PZi8xBOHXIRQfiXVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b56f2fc7b79e5b08b9f7c67656090c98bb412b7f8c6de641965778cf29156d6","last_reissued_at":"2026-05-18T04:07:17.899694Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:17.899694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.3167","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nUJ+fmqFZXH57a/HZ1CzGnj8e6A9VtJumrS5QJNIB/h1AT+vqEPyajXqcffEmN2Lj5uOSgWRE/ltNtpepFNECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:38:10.602517Z"},"content_sha256":"54d75796d9dbe4f9fab6a8caaeb193c6d80a4bcb8238aa734fee19066ac74a87","schema_version":"1.0","event_id":"sha256:54d75796d9dbe4f9fab6a8caaeb193c6d80a4bcb8238aa734fee19066ac74a87"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:DNLPF7D3PHS3BC47PRTWKYEQZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tree-width of hypergraphs and surface duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Fr\\'ed\\'eric Mazoit (LaBRI)","submitted_at":"2010-06-16T09:00:16Z","abstract_excerpt":"In Graph Minors III, Robertson and Seymour write: \"It seems that the tree-width of a planar graph and the tree-width of its geometric dual are approximately equal - indeed, we have convinced ourselves that they differ by at most one\". They never gave a proof of this. In this paper, we prove a generalisation of this statement to embedding of hypergraphs on general surfaces, and we prove that our bound is tight."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3167","kind":"arxiv","version":2},"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":"2026-05-18T04:07:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"erkcbmrogCM0mMMZGplk4PLpvMRj16EpUaqimVj1yd/ybd3u10nLy9LjBBOzRLbHq4U7gSmO3/lVR8urP6c1Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:38:10.602884Z"},"content_sha256":"a17fca4f7329053f3e4f585c8f2f7ec5caffb0f3e7cac67b538bcad3ce06dacd","schema_version":"1.0","event_id":"sha256:a17fca4f7329053f3e4f585c8f2f7ec5caffb0f3e7cac67b538bcad3ce06dacd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DNLPF7D3PHS3BC47PRTWKYEQZG/bundle.json","state_url":"https://pith.science/pith/DNLPF7D3PHS3BC47PRTWKYEQZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DNLPF7D3PHS3BC47PRTWKYEQZG/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":"2026-05-26T15:38:10Z","links":{"resolver":"https://pith.science/pith/DNLPF7D3PHS3BC47PRTWKYEQZG","bundle":"https://pith.science/pith/DNLPF7D3PHS3BC47PRTWKYEQZG/bundle.json","state":"https://pith.science/pith/DNLPF7D3PHS3BC47PRTWKYEQZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DNLPF7D3PHS3BC47PRTWKYEQZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DNLPF7D3PHS3BC47PRTWKYEQZG","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":"db3a799432bd28e1b3204331caf4e921f3d6d6781a116a4c507fa4fd833dfa7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-06-16T09:00:16Z","title_canon_sha256":"469ccfa6672db8aa14563f3bf429505c226aafe60d6262ce0615d898a4820a7c"},"schema_version":"1.0","source":{"id":"1006.3167","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.3167","created_at":"2026-05-18T04:07:17Z"},{"alias_kind":"arxiv_version","alias_value":"1006.3167v2","created_at":"2026-05-18T04:07:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3167","created_at":"2026-05-18T04:07:17Z"},{"alias_kind":"pith_short_12","alias_value":"DNLPF7D3PHS3","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DNLPF7D3PHS3BC47","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DNLPF7D3","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:a17fca4f7329053f3e4f585c8f2f7ec5caffb0f3e7cac67b538bcad3ce06dacd","target":"graph","created_at":"2026-05-18T04:07:17Z","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":"In Graph Minors III, Robertson and Seymour write: \"It seems that the tree-width of a planar graph and the tree-width of its geometric dual are approximately equal - indeed, we have convinced ourselves that they differ by at most one\". They never gave a proof of this. In this paper, we prove a generalisation of this statement to embedding of hypergraphs on general surfaces, and we prove that our bound is tight.","authors_text":"Fr\\'ed\\'eric Mazoit (LaBRI)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-06-16T09:00:16Z","title":"Tree-width of hypergraphs and surface duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3167","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":"sha256:54d75796d9dbe4f9fab6a8caaeb193c6d80a4bcb8238aa734fee19066ac74a87","target":"record","created_at":"2026-05-18T04:07:17Z","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":"db3a799432bd28e1b3204331caf4e921f3d6d6781a116a4c507fa4fd833dfa7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2010-06-16T09:00:16Z","title_canon_sha256":"469ccfa6672db8aa14563f3bf429505c226aafe60d6262ce0615d898a4820a7c"},"schema_version":"1.0","source":{"id":"1006.3167","kind":"arxiv","version":2}},"canonical_sha256":"1b56f2fc7b79e5b08b9f7c67656090c98bb412b7f8c6de641965778cf29156d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b56f2fc7b79e5b08b9f7c67656090c98bb412b7f8c6de641965778cf29156d6","first_computed_at":"2026-05-18T04:07:17.899694Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:17.899694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4zvZCPZq3qIjLSdEz02ih9b7CMU0TRNv32Mf6aPyCCSyEqdCNUUvU+hehtCXMg2NqOx6PZi8xBOHXIRQfiXVDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:17.900460Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.3167","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54d75796d9dbe4f9fab6a8caaeb193c6d80a4bcb8238aa734fee19066ac74a87","sha256:a17fca4f7329053f3e4f585c8f2f7ec5caffb0f3e7cac67b538bcad3ce06dacd"],"state_sha256":"5dcfedcee74043b9c27766aab0db51b19ed56a0aaa8519d863cff8783db0875d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ktahuCbvOjg2HTATP0cJR//s9j8TdTqZ1ZkZQSdCjk6tNhp+yw3pPs/LarDd+FfJIbHZewZUEnxUtlTXgcjRDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:38:10.605697Z","bundle_sha256":"0b737cd56e9740bbb2a49b4559069bbc852cd8ed4943e57982ed6a565547c133"}}