{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:A5WMW6S2MNYDZ27K2LKGHWVJTW","short_pith_number":"pith:A5WMW6S2","canonical_record":{"source":{"id":"2208.14250","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2022-08-30T13:24:28Z","cross_cats_sorted":[],"title_canon_sha256":"0e3d326eea2c2ef44334b8c58ce33413eb4d78f2237accd1f2af6098138d637b","abstract_canon_sha256":"e22998129658bd2ee5f6e187da3b791066b4caeb0def9b044e5767b975c0c0de"},"schema_version":"1.0"},"canonical_sha256":"076ccb7a5a63703cebead2d463daa99d809ccdf995253d2513fcec6d80ccb0d0","source":{"kind":"arxiv","id":"2208.14250","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.14250","created_at":"2026-07-05T08:53:13Z"},{"alias_kind":"arxiv_version","alias_value":"2208.14250v2","created_at":"2026-07-05T08:53:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.14250","created_at":"2026-07-05T08:53:13Z"},{"alias_kind":"pith_short_12","alias_value":"A5WMW6S2MNYD","created_at":"2026-07-05T08:53:13Z"},{"alias_kind":"pith_short_16","alias_value":"A5WMW6S2MNYDZ27K","created_at":"2026-07-05T08:53:13Z"},{"alias_kind":"pith_short_8","alias_value":"A5WMW6S2","created_at":"2026-07-05T08:53:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:A5WMW6S2MNYDZ27K2LKGHWVJTW","target":"record","payload":{"canonical_record":{"source":{"id":"2208.14250","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2022-08-30T13:24:28Z","cross_cats_sorted":[],"title_canon_sha256":"0e3d326eea2c2ef44334b8c58ce33413eb4d78f2237accd1f2af6098138d637b","abstract_canon_sha256":"e22998129658bd2ee5f6e187da3b791066b4caeb0def9b044e5767b975c0c0de"},"schema_version":"1.0"},"canonical_sha256":"076ccb7a5a63703cebead2d463daa99d809ccdf995253d2513fcec6d80ccb0d0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:53:13.982844Z","signature_b64":"o4GDKoDDHuIzjBDIwKLfU9pQZsBAyeSuNW1BhDYjTOO/9H4h+8BAXYGnzvfQNc/HRtBYrUgkWXsgGQf6UwXkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"076ccb7a5a63703cebead2d463daa99d809ccdf995253d2513fcec6d80ccb0d0","last_reissued_at":"2026-07-05T08:53:13.982428Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:53:13.982428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.14250","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":"2026-07-05T08:53:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Djl10wpHghASkJFc9/xltpaf344h6oQ7anuRfWUIw49v6I3GRdXC7TciN7zq1FCnibUznFUG9dOWplt7Y8aoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T22:24:47.974868Z"},"content_sha256":"760f47aed6ada4bfdb2ae09713c2d4a552e9cf929cc67138d9fed864d1406418","schema_version":"1.0","event_id":"sha256:760f47aed6ada4bfdb2ae09713c2d4a552e9cf929cc67138d9fed864d1406418"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:A5WMW6S2MNYDZ27K2LKGHWVJTW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coloring Mixed and Directional Interval Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Alexander Wolff, Florian Mittelst\\\"adt, Grzegorz Gutowski, Ignaz Rutter, Joachim Spoerhase, Johannes Zink","submitted_at":"2022-08-30T13:24:28Z","abstract_excerpt":"A mixed graph has a set of vertices, a set of undirected egdes, and a set of directed arcs. A proper coloring of a mixed graph $G$ is a function $c$ that assigns to each vertex in $G$ a positive integer such that, for each edge $uv$ in $G$, $c(u) \\ne c(v)$ and, for each arc $uv$ in $G$, $c(u) < c(v)$. For a mixed graph $G$, the chromatic number $\\chi(G)$ is the smallest number of colors in any proper coloring of $G$. A directional interval graph is a mixed graph whose vertices correspond to intervals on the real line. Such a graph has an edge between every two intervals where one is contained "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.14250","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.14250/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:53:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fRGjIEK887pZa/D699c0nv3xw4wiqXL9TyDJGgYLwyPAIUKKHfmuE/txnbTcMinVs0dmggkKQCWbVLII3FNMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T22:24:47.975643Z"},"content_sha256":"47d782cc6efeb4ced58a9e78f01a58b8847c22fa3da3d8abeb77c8b1285f37e1","schema_version":"1.0","event_id":"sha256:47d782cc6efeb4ced58a9e78f01a58b8847c22fa3da3d8abeb77c8b1285f37e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A5WMW6S2MNYDZ27K2LKGHWVJTW/bundle.json","state_url":"https://pith.science/pith/A5WMW6S2MNYDZ27K2LKGHWVJTW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A5WMW6S2MNYDZ27K2LKGHWVJTW/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":"2026-08-21T22:24:47Z","links":{"resolver":"https://pith.science/pith/A5WMW6S2MNYDZ27K2LKGHWVJTW","bundle":"https://pith.science/pith/A5WMW6S2MNYDZ27K2LKGHWVJTW/bundle.json","state":"https://pith.science/pith/A5WMW6S2MNYDZ27K2LKGHWVJTW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A5WMW6S2MNYDZ27K2LKGHWVJTW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:A5WMW6S2MNYDZ27K2LKGHWVJTW","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":"e22998129658bd2ee5f6e187da3b791066b4caeb0def9b044e5767b975c0c0de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2022-08-30T13:24:28Z","title_canon_sha256":"0e3d326eea2c2ef44334b8c58ce33413eb4d78f2237accd1f2af6098138d637b"},"schema_version":"1.0","source":{"id":"2208.14250","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.14250","created_at":"2026-07-05T08:53:13Z"},{"alias_kind":"arxiv_version","alias_value":"2208.14250v2","created_at":"2026-07-05T08:53:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.14250","created_at":"2026-07-05T08:53:13Z"},{"alias_kind":"pith_short_12","alias_value":"A5WMW6S2MNYD","created_at":"2026-07-05T08:53:13Z"},{"alias_kind":"pith_short_16","alias_value":"A5WMW6S2MNYDZ27K","created_at":"2026-07-05T08:53:13Z"},{"alias_kind":"pith_short_8","alias_value":"A5WMW6S2","created_at":"2026-07-05T08:53:13Z"}],"graph_snapshots":[{"event_id":"sha256:47d782cc6efeb4ced58a9e78f01a58b8847c22fa3da3d8abeb77c8b1285f37e1","target":"graph","created_at":"2026-07-05T08:53:13Z","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/2208.14250/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A mixed graph has a set of vertices, a set of undirected egdes, and a set of directed arcs. A proper coloring of a mixed graph $G$ is a function $c$ that assigns to each vertex in $G$ a positive integer such that, for each edge $uv$ in $G$, $c(u) \\ne c(v)$ and, for each arc $uv$ in $G$, $c(u) < c(v)$. For a mixed graph $G$, the chromatic number $\\chi(G)$ is the smallest number of colors in any proper coloring of $G$. A directional interval graph is a mixed graph whose vertices correspond to intervals on the real line. Such a graph has an edge between every two intervals where one is contained ","authors_text":"Alexander Wolff, Florian Mittelst\\\"adt, Grzegorz Gutowski, Ignaz Rutter, Joachim Spoerhase, Johannes Zink","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2022-08-30T13:24:28Z","title":"Coloring Mixed and Directional Interval Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.14250","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":"sha256:760f47aed6ada4bfdb2ae09713c2d4a552e9cf929cc67138d9fed864d1406418","target":"record","created_at":"2026-07-05T08:53:13Z","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":"e22998129658bd2ee5f6e187da3b791066b4caeb0def9b044e5767b975c0c0de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2022-08-30T13:24:28Z","title_canon_sha256":"0e3d326eea2c2ef44334b8c58ce33413eb4d78f2237accd1f2af6098138d637b"},"schema_version":"1.0","source":{"id":"2208.14250","kind":"arxiv","version":2}},"canonical_sha256":"076ccb7a5a63703cebead2d463daa99d809ccdf995253d2513fcec6d80ccb0d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"076ccb7a5a63703cebead2d463daa99d809ccdf995253d2513fcec6d80ccb0d0","first_computed_at":"2026-07-05T08:53:13.982428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:53:13.982428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o4GDKoDDHuIzjBDIwKLfU9pQZsBAyeSuNW1BhDYjTOO/9H4h+8BAXYGnzvfQNc/HRtBYrUgkWXsgGQf6UwXkCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:53:13.982844Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.14250","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:760f47aed6ada4bfdb2ae09713c2d4a552e9cf929cc67138d9fed864d1406418","sha256:47d782cc6efeb4ced58a9e78f01a58b8847c22fa3da3d8abeb77c8b1285f37e1"],"state_sha256":"1f65d09231ba91192d74ea9602db94a0a160439aa64168683bd0ff28b1b74288"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hHYRo9wS80c7OUa271WEh5glQLr9wJW9npP7guFX3/Uwwx6F8BfPFtw4Nh27AuZHxoLjq0UHE3khm4zQ4acYDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T22:24:47.982208Z","bundle_sha256":"d5665cea3c75251784d63f38e64ffb6e0e961a45828a62339b969eb483dfee27"}}