{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JABIJHCYYX5ORW3ZLCN5ZENVSR","short_pith_number":"pith:JABIJHCY","canonical_record":{"source":{"id":"1610.01111","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-04T18:01:22Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"3c8781d4f1297685030dd917b6a49b7ea6ae6f6d510c12b0c3fd0c210d734374","abstract_canon_sha256":"f7a9da6b9c32274b09c6b94f230312d583d9440d620bc973e2a6db06999a148f"},"schema_version":"1.0"},"canonical_sha256":"4802849c58c5fae8db79589bdc91b5946bd1021576b0acf6f251fc7b5e11f36b","source":{"kind":"arxiv","id":"1610.01111","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01111","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01111v1","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01111","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"JABIJHCYYX5O","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"JABIJHCYYX5ORW3Z","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"JABIJHCY","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JABIJHCYYX5ORW3ZLCN5ZENVSR","target":"record","payload":{"canonical_record":{"source":{"id":"1610.01111","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-04T18:01:22Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"3c8781d4f1297685030dd917b6a49b7ea6ae6f6d510c12b0c3fd0c210d734374","abstract_canon_sha256":"f7a9da6b9c32274b09c6b94f230312d583d9440d620bc973e2a6db06999a148f"},"schema_version":"1.0"},"canonical_sha256":"4802849c58c5fae8db79589bdc91b5946bd1021576b0acf6f251fc7b5e11f36b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:12.419331Z","signature_b64":"SGSiqoG82KXG0B2ogjlw4+senw//IUL6Uc4IM8hXHfGOPH9BSkRM2n7nlHT71cXf3LgswsAb+EbWK+M8+fi/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4802849c58c5fae8db79589bdc91b5946bd1021576b0acf6f251fc7b5e11f36b","last_reissued_at":"2026-05-18T01:03:12.418847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:12.418847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.01111","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":"2026-05-18T01:03:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zN1vl8CrOFi9C9IEzOxHx1alfdZdDrwJnFxBfoW/WvKR7/WKPMc+ds3uXpmwdCmPpz5wVRftiKWx5QKvUA9mBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:53:47.032940Z"},"content_sha256":"a017da1ebd1555f1b06d27c2ccb39dd8f1ceac7397ce99043492b35350ad1983","schema_version":"1.0","event_id":"sha256:a017da1ebd1555f1b06d27c2ccb39dd8f1ceac7397ce99043492b35350ad1983"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JABIJHCYYX5ORW3ZLCN5ZENVSR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Chromatic Number of Ordered Graphs With Constrained Conflict Graphs","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":"2016-10-04T18:01:22Z","abstract_excerpt":"An ordered graph $G$ is a graph whose vertex set is a subset of integers. The edges are interpreted as tuples $(u,v)$ with $u < v$. For a positive integer $s$, a matrix $M \\in \\mathbb{Z}^{s \\times 4}$, and a vector $\\mathbf{p} = (p,\\ldots,p) \\in \\mathbb{Z}^s$ we build a conflict graph by saying that edges $(u,v)$ and $(x,y)$ are conflicting if $M(u,v,x,y)^\\top \\geq \\mathbf{p}$ or $M(x,y,u,v)^\\top \\geq \\mathbf{p}$, where the comparison is componentwise. This new framework generalizes many natural concepts of ordered and unordered graphs, such as the page-number, queue-number, band-width, interv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01111","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":"2026-05-18T01:03:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gs9ge2QpGjwTfPvSf43av4ZkkdoTfIgPNAb5tOaHHkEHh6XKMOQMQs573nRoFWLXTy2Hxh/5zk+TB5Vw4DF8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:53:47.033565Z"},"content_sha256":"67c72daf87fb6289b8139d895bf8a2b6973c33e3a907ebf7a53df1cf3934129d","schema_version":"1.0","event_id":"sha256:67c72daf87fb6289b8139d895bf8a2b6973c33e3a907ebf7a53df1cf3934129d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR/bundle.json","state_url":"https://pith.science/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR/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":"2026-05-29T17:53:47Z","links":{"resolver":"https://pith.science/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR","bundle":"https://pith.science/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR/bundle.json","state":"https://pith.science/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JABIJHCYYX5ORW3ZLCN5ZENVSR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JABIJHCYYX5ORW3ZLCN5ZENVSR","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":"f7a9da6b9c32274b09c6b94f230312d583d9440d620bc973e2a6db06999a148f","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-04T18:01:22Z","title_canon_sha256":"3c8781d4f1297685030dd917b6a49b7ea6ae6f6d510c12b0c3fd0c210d734374"},"schema_version":"1.0","source":{"id":"1610.01111","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01111","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01111v1","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01111","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"JABIJHCYYX5O","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"JABIJHCYYX5ORW3Z","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"JABIJHCY","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:67c72daf87fb6289b8139d895bf8a2b6973c33e3a907ebf7a53df1cf3934129d","target":"graph","created_at":"2026-05-18T01:03:12Z","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":"An ordered graph $G$ is a graph whose vertex set is a subset of integers. The edges are interpreted as tuples $(u,v)$ with $u < v$. For a positive integer $s$, a matrix $M \\in \\mathbb{Z}^{s \\times 4}$, and a vector $\\mathbf{p} = (p,\\ldots,p) \\in \\mathbb{Z}^s$ we build a conflict graph by saying that edges $(u,v)$ and $(x,y)$ are conflicting if $M(u,v,x,y)^\\top \\geq \\mathbf{p}$ or $M(x,y,u,v)^\\top \\geq \\mathbf{p}$, where the comparison is componentwise. This new framework generalizes many natural concepts of ordered and unordered graphs, such as the page-number, queue-number, band-width, interv","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":"2016-10-04T18:01:22Z","title":"The Chromatic Number of Ordered Graphs With Constrained Conflict Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01111","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:a017da1ebd1555f1b06d27c2ccb39dd8f1ceac7397ce99043492b35350ad1983","target":"record","created_at":"2026-05-18T01:03:12Z","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":"f7a9da6b9c32274b09c6b94f230312d583d9440d620bc973e2a6db06999a148f","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-04T18:01:22Z","title_canon_sha256":"3c8781d4f1297685030dd917b6a49b7ea6ae6f6d510c12b0c3fd0c210d734374"},"schema_version":"1.0","source":{"id":"1610.01111","kind":"arxiv","version":1}},"canonical_sha256":"4802849c58c5fae8db79589bdc91b5946bd1021576b0acf6f251fc7b5e11f36b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4802849c58c5fae8db79589bdc91b5946bd1021576b0acf6f251fc7b5e11f36b","first_computed_at":"2026-05-18T01:03:12.418847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:12.418847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SGSiqoG82KXG0B2ogjlw4+senw//IUL6Uc4IM8hXHfGOPH9BSkRM2n7nlHT71cXf3LgswsAb+EbWK+M8+fi/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:12.419331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01111","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a017da1ebd1555f1b06d27c2ccb39dd8f1ceac7397ce99043492b35350ad1983","sha256:67c72daf87fb6289b8139d895bf8a2b6973c33e3a907ebf7a53df1cf3934129d"],"state_sha256":"b80b1c81ca5747f0c662b1f91eec8411ae53881cb0ec3ccb5eb813ec5fc2cb1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ViCV2LE/5TeX746LgKxy9UoPhjNRC2Crx8EINt2GMPCUCxwk8mglD4TJMpO6y0M7t1Jvx7l7wkz60D8xUpVSCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:53:47.036961Z","bundle_sha256":"45326439feb3d9b2431e3c0bf9311975408c11b2e64aeb4ee65326500bb75491"}}