{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CXX2V5KDRJSAX3DLX47AZBUH74","short_pith_number":"pith:CXX2V5KD","canonical_record":{"source":{"id":"1603.00312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-01T15:14:20Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"c4e270aa525bad03818e04a521f7eda76569da6ec674df6ea3370fbf0b66b851","abstract_canon_sha256":"4ec2ef961de5aba3a7a6f7576a521dbb9a64c717f37b9b6668a157d18f21f789"},"schema_version":"1.0"},"canonical_sha256":"15efaaf5438a640bec6bbf3e0c8687ff08d006be6b04c09a143524e05068aad2","source":{"kind":"arxiv","id":"1603.00312","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00312","created_at":"2026-05-18T01:19:45Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00312v1","created_at":"2026-05-18T01:19:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00312","created_at":"2026-05-18T01:19:45Z"},{"alias_kind":"pith_short_12","alias_value":"CXX2V5KDRJSA","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CXX2V5KDRJSAX3DL","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CXX2V5KD","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CXX2V5KDRJSAX3DLX47AZBUH74","target":"record","payload":{"canonical_record":{"source":{"id":"1603.00312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-01T15:14:20Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"c4e270aa525bad03818e04a521f7eda76569da6ec674df6ea3370fbf0b66b851","abstract_canon_sha256":"4ec2ef961de5aba3a7a6f7576a521dbb9a64c717f37b9b6668a157d18f21f789"},"schema_version":"1.0"},"canonical_sha256":"15efaaf5438a640bec6bbf3e0c8687ff08d006be6b04c09a143524e05068aad2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:45.364894Z","signature_b64":"ls02IN5GDWSCTMljahUScqZa3PqxMKfK94e4HYqPOQ42eOcNh+lIHV63t2+0BvvjNjapak6lUZZzyMsXIngDBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15efaaf5438a640bec6bbf3e0c8687ff08d006be6b04c09a143524e05068aad2","last_reissued_at":"2026-05-18T01:19:45.364211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:45.364211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.00312","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":"2026-05-18T01:19:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zul1oDbxcod+/ex43WRF1fmXHKrvlmoHlKkTAVMwUjODXMW1N8gp0wZE7CZmT8gHqQTPBcho9ROCzYFYEqqjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:03:45.597188Z"},"content_sha256":"61af3096e9bb4d06b079760502a92944833d4dbd5715d94081ff53d92dcf67d6","schema_version":"1.0","event_id":"sha256:61af3096e9bb4d06b079760502a92944833d4dbd5715d94081ff53d92dcf67d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CXX2V5KDRJSAX3DLX47AZBUH74","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chromatic number of ordered graphs with forbidden ordered subgraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Jonathan Rollin, Maria Axenovich, Torsten Ueckerdt","submitted_at":"2016-03-01T15:14:20Z","abstract_excerpt":"It is well-known that the graphs not containing a given graph H as a subgraph have bounded chromatic number if and only if H is acyclic. Here we consider ordered graphs, i.e., graphs with a linear ordering on their vertex set, and the function f(H) = sup{chi(G) | G in Forb(H)} where Forb(H) denotes the set of all ordered graphs that do not contain a copy of H. If H contains a cycle, then as in the case of unordered graphs, f(H) is infinity. However, in contrast to the unordered graphs, we describe an infinite family of ordered forests H with infinite f(H). An ordered graph is crossing if there"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00312","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":"2026-05-18T01:19:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t9UeuYiRyRotGbehIBeIexkIOBKetZwoUcgGQgZnZVR4rhmgYu+/Obtx5A78WTKPEkDUHJkYTWVEKPUN9dWBBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:03:45.597558Z"},"content_sha256":"3554cf060e8560fc7578459c75745aed333cb24bff6925bf41cfd87eccbf71c5","schema_version":"1.0","event_id":"sha256:3554cf060e8560fc7578459c75745aed333cb24bff6925bf41cfd87eccbf71c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CXX2V5KDRJSAX3DLX47AZBUH74/bundle.json","state_url":"https://pith.science/pith/CXX2V5KDRJSAX3DLX47AZBUH74/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CXX2V5KDRJSAX3DLX47AZBUH74/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":"2026-05-28T15:03:45Z","links":{"resolver":"https://pith.science/pith/CXX2V5KDRJSAX3DLX47AZBUH74","bundle":"https://pith.science/pith/CXX2V5KDRJSAX3DLX47AZBUH74/bundle.json","state":"https://pith.science/pith/CXX2V5KDRJSAX3DLX47AZBUH74/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CXX2V5KDRJSAX3DLX47AZBUH74/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CXX2V5KDRJSAX3DLX47AZBUH74","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":"4ec2ef961de5aba3a7a6f7576a521dbb9a64c717f37b9b6668a157d18f21f789","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-01T15:14:20Z","title_canon_sha256":"c4e270aa525bad03818e04a521f7eda76569da6ec674df6ea3370fbf0b66b851"},"schema_version":"1.0","source":{"id":"1603.00312","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00312","created_at":"2026-05-18T01:19:45Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00312v1","created_at":"2026-05-18T01:19:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00312","created_at":"2026-05-18T01:19:45Z"},{"alias_kind":"pith_short_12","alias_value":"CXX2V5KDRJSA","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CXX2V5KDRJSAX3DL","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CXX2V5KD","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:3554cf060e8560fc7578459c75745aed333cb24bff6925bf41cfd87eccbf71c5","target":"graph","created_at":"2026-05-18T01:19:45Z","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":"It is well-known that the graphs not containing a given graph H as a subgraph have bounded chromatic number if and only if H is acyclic. Here we consider ordered graphs, i.e., graphs with a linear ordering on their vertex set, and the function f(H) = sup{chi(G) | G in Forb(H)} where Forb(H) denotes the set of all ordered graphs that do not contain a copy of H. If H contains a cycle, then as in the case of unordered graphs, f(H) is infinity. However, in contrast to the unordered graphs, we describe an infinite family of ordered forests H with infinite f(H). An ordered graph is crossing if there","authors_text":"Jonathan Rollin, Maria Axenovich, Torsten Ueckerdt","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-01T15:14:20Z","title":"Chromatic number of ordered graphs with forbidden ordered subgraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00312","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":"sha256:61af3096e9bb4d06b079760502a92944833d4dbd5715d94081ff53d92dcf67d6","target":"record","created_at":"2026-05-18T01:19:45Z","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":"4ec2ef961de5aba3a7a6f7576a521dbb9a64c717f37b9b6668a157d18f21f789","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-01T15:14:20Z","title_canon_sha256":"c4e270aa525bad03818e04a521f7eda76569da6ec674df6ea3370fbf0b66b851"},"schema_version":"1.0","source":{"id":"1603.00312","kind":"arxiv","version":1}},"canonical_sha256":"15efaaf5438a640bec6bbf3e0c8687ff08d006be6b04c09a143524e05068aad2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15efaaf5438a640bec6bbf3e0c8687ff08d006be6b04c09a143524e05068aad2","first_computed_at":"2026-05-18T01:19:45.364211Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:45.364211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ls02IN5GDWSCTMljahUScqZa3PqxMKfK94e4HYqPOQ42eOcNh+lIHV63t2+0BvvjNjapak6lUZZzyMsXIngDBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:45.364894Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.00312","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61af3096e9bb4d06b079760502a92944833d4dbd5715d94081ff53d92dcf67d6","sha256:3554cf060e8560fc7578459c75745aed333cb24bff6925bf41cfd87eccbf71c5"],"state_sha256":"4e9c470b0ffd10c6bfcdd1560e1a73f5dd7cce3effe62ea96d6960bf1f05e783"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mn1jSXebo7eWmbwZPrPqzH9RWS+pDhOap2AYqMG696vaylx3q9OOFGvnEmIo94KoDHrktWDJvFWHL8hSzhHVBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:03:45.599525Z","bundle_sha256":"864aa3bceabf788fda4176f859fd951f2c4fecafcf8365e0b0b71b69e79c2ec2"}}