{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FWLACIIJGILCZDJSTECZSBXGS3","short_pith_number":"pith:FWLACIIJ","canonical_record":{"source":{"id":"1809.00142","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-01T09:31:55Z","cross_cats_sorted":[],"title_canon_sha256":"fb83091e273489602d71cf77e0672a2c7414cfb81322cad84deaed11fb5f7716","abstract_canon_sha256":"019813d8bdd7d6578cfdff1eb297c6167432c29254e1bcc4b8375ae09606f237"},"schema_version":"1.0"},"canonical_sha256":"2d9601210932162c8d3299059906e696f153dd372bc882d7d080e7875a263251","source":{"kind":"arxiv","id":"1809.00142","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00142","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00142v3","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00142","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"pith_short_12","alias_value":"FWLACIIJGILC","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FWLACIIJGILCZDJS","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FWLACIIJ","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FWLACIIJGILCZDJSTECZSBXGS3","target":"record","payload":{"canonical_record":{"source":{"id":"1809.00142","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-01T09:31:55Z","cross_cats_sorted":[],"title_canon_sha256":"fb83091e273489602d71cf77e0672a2c7414cfb81322cad84deaed11fb5f7716","abstract_canon_sha256":"019813d8bdd7d6578cfdff1eb297c6167432c29254e1bcc4b8375ae09606f237"},"schema_version":"1.0"},"canonical_sha256":"2d9601210932162c8d3299059906e696f153dd372bc882d7d080e7875a263251","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:39.829124Z","signature_b64":"0tsy2SDEH4xE4qZBa/+KxhKuTwW8UczmKB3sxTf0rTUv1Zm7r6HhUW1c2oZSEs+gsib8C3sybY2PKIQZnGEFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d9601210932162c8d3299059906e696f153dd372bc882d7d080e7875a263251","last_reissued_at":"2026-05-17T23:47:39.828702Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:39.828702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.00142","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r7HEnvoinuWQ6VG47lp5PK3B5F4RbvElmhbiuOtJiawt0r1bhjlkXemYZguyWGNFwpo8pdxQao2NUslGSVqtBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:21:41.206859Z"},"content_sha256":"0827a2247d9bcd5f11041bcc656a4448b28e4d1470d3b4a1a619e4507e4097c6","schema_version":"1.0","event_id":"sha256:0827a2247d9bcd5f11041bcc656a4448b28e4d1470d3b4a1a619e4507e4097c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FWLACIIJGILCZDJSTECZSBXGS3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Star Dichromatic Number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Raphael Steiner, Winfried Hochst\\\"attler","submitted_at":"2018-09-01T09:31:55Z","abstract_excerpt":"We introduce a new notion of circular colourings for digraphs. The idea of this quantity, called star dichromatic number $\\vec{\\chi}^\\ast(D)$ of a digraph $D$, is to allow a finer subdivision of digraphs with the same dichromatic number into such which are \"easier\" or \"harder\" to colour by allowing fractional values. This is related to a coherent notion for the vertex arboricity of graphs introduced by Wang et al. and resembles the concept of the star chromatic number of graphs introduced by Vince in the framework of digraph colouring. After presenting basic properties of the new quantity, inc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00142","kind":"arxiv","version":3},"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":"2026-05-17T23:47:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XNQSMd7o2Y0wltl0cpu/lSB2eVeoh/ZtrmGWejwmtUonc8AhRC4mv+PixG0uKDFWdxIRGspow02cZeLM8d6nCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:21:41.207569Z"},"content_sha256":"442b171b0e3278838eade192faed13126eaebfea0c1591ee53ccb8bf383124b9","schema_version":"1.0","event_id":"sha256:442b171b0e3278838eade192faed13126eaebfea0c1591ee53ccb8bf383124b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FWLACIIJGILCZDJSTECZSBXGS3/bundle.json","state_url":"https://pith.science/pith/FWLACIIJGILCZDJSTECZSBXGS3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FWLACIIJGILCZDJSTECZSBXGS3/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":"2026-05-31T23:21:41Z","links":{"resolver":"https://pith.science/pith/FWLACIIJGILCZDJSTECZSBXGS3","bundle":"https://pith.science/pith/FWLACIIJGILCZDJSTECZSBXGS3/bundle.json","state":"https://pith.science/pith/FWLACIIJGILCZDJSTECZSBXGS3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FWLACIIJGILCZDJSTECZSBXGS3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FWLACIIJGILCZDJSTECZSBXGS3","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":"019813d8bdd7d6578cfdff1eb297c6167432c29254e1bcc4b8375ae09606f237","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-01T09:31:55Z","title_canon_sha256":"fb83091e273489602d71cf77e0672a2c7414cfb81322cad84deaed11fb5f7716"},"schema_version":"1.0","source":{"id":"1809.00142","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.00142","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"arxiv_version","alias_value":"1809.00142v3","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.00142","created_at":"2026-05-17T23:47:39Z"},{"alias_kind":"pith_short_12","alias_value":"FWLACIIJGILC","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FWLACIIJGILCZDJS","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FWLACIIJ","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:442b171b0e3278838eade192faed13126eaebfea0c1591ee53ccb8bf383124b9","target":"graph","created_at":"2026-05-17T23:47:39Z","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 introduce a new notion of circular colourings for digraphs. The idea of this quantity, called star dichromatic number $\\vec{\\chi}^\\ast(D)$ of a digraph $D$, is to allow a finer subdivision of digraphs with the same dichromatic number into such which are \"easier\" or \"harder\" to colour by allowing fractional values. This is related to a coherent notion for the vertex arboricity of graphs introduced by Wang et al. and resembles the concept of the star chromatic number of graphs introduced by Vince in the framework of digraph colouring. After presenting basic properties of the new quantity, inc","authors_text":"Raphael Steiner, Winfried Hochst\\\"attler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-01T09:31:55Z","title":"The Star Dichromatic Number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.00142","kind":"arxiv","version":3},"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":"sha256:0827a2247d9bcd5f11041bcc656a4448b28e4d1470d3b4a1a619e4507e4097c6","target":"record","created_at":"2026-05-17T23:47:39Z","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":"019813d8bdd7d6578cfdff1eb297c6167432c29254e1bcc4b8375ae09606f237","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-01T09:31:55Z","title_canon_sha256":"fb83091e273489602d71cf77e0672a2c7414cfb81322cad84deaed11fb5f7716"},"schema_version":"1.0","source":{"id":"1809.00142","kind":"arxiv","version":3}},"canonical_sha256":"2d9601210932162c8d3299059906e696f153dd372bc882d7d080e7875a263251","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d9601210932162c8d3299059906e696f153dd372bc882d7d080e7875a263251","first_computed_at":"2026-05-17T23:47:39.828702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:39.828702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0tsy2SDEH4xE4qZBa/+KxhKuTwW8UczmKB3sxTf0rTUv1Zm7r6HhUW1c2oZSEs+gsib8C3sybY2PKIQZnGEFBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:39.829124Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.00142","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0827a2247d9bcd5f11041bcc656a4448b28e4d1470d3b4a1a619e4507e4097c6","sha256:442b171b0e3278838eade192faed13126eaebfea0c1591ee53ccb8bf383124b9"],"state_sha256":"d54437db7028395aa9690be70bf760f396791c30a888f4d0f8c517d1bf1ec742"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NTIA5WR/VlRmpykJnpivOcwNIAUTq78/10BJtTVXE8GDGUaQU82ZYk8u0n2s7ieQzRQ+RmWthOI4yo0JG2w+BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:21:41.211245Z","bundle_sha256":"eb67bd90e6718fef14d61346f72f4372dc1631aad71ac8acb8f57c7ee5f837f3"}}