{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CKM3IDWXTWWBVDEPM7UC6UAPVL","short_pith_number":"pith:CKM3IDWX","canonical_record":{"source":{"id":"1608.06981","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-24T22:49:03Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"2a3d09bb45b0165deee4881366591cc378e8c520225fcf15b3aad8cdd73adb38","abstract_canon_sha256":"bdd43bf4805b651c15f5b23a38b35b7bd2b1339e935735d7dbe5a34868e9f88d"},"schema_version":"1.0"},"canonical_sha256":"1299b40ed79dac1a8c8f67e82f500faadcbf6365d29d969c672c4f9c61ec4ddc","source":{"kind":"arxiv","id":"1608.06981","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06981","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06981v3","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06981","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"pith_short_12","alias_value":"CKM3IDWXTWWB","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CKM3IDWXTWWBVDEP","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CKM3IDWX","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CKM3IDWXTWWBVDEPM7UC6UAPVL","target":"record","payload":{"canonical_record":{"source":{"id":"1608.06981","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-24T22:49:03Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"2a3d09bb45b0165deee4881366591cc378e8c520225fcf15b3aad8cdd73adb38","abstract_canon_sha256":"bdd43bf4805b651c15f5b23a38b35b7bd2b1339e935735d7dbe5a34868e9f88d"},"schema_version":"1.0"},"canonical_sha256":"1299b40ed79dac1a8c8f67e82f500faadcbf6365d29d969c672c4f9c61ec4ddc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:00.410139Z","signature_b64":"JzYeJk6h7MmH48zVg6XWExiMGkZp1DJbUbyxxznRRBIa4K7ve+J3wPcQIAYhOor4b3mslyMKLsEkVBMrwLeEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1299b40ed79dac1a8c8f67e82f500faadcbf6365d29d969c672c4f9c61ec4ddc","last_reissued_at":"2026-05-18T00:31:00.409440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:00.409440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.06981","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":"2026-05-18T00:31:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KQFcf95VmvZs+SaC1eu57eLiVpIVEsXpPCL8YHVvc/Bcpkbv8zh81+UOlz0SaiJuttbiekt41fl0+nfzZvvCAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T21:20:02.957567Z"},"content_sha256":"932c006ed578f266ac236e31847054c0f0161d157dcb8bfbbf055ccafa023d91","schema_version":"1.0","event_id":"sha256:932c006ed578f266ac236e31847054c0f0161d157dcb8bfbbf055ccafa023d91"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CKM3IDWXTWWBVDEPM7UC6UAPVL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orientations of graphs with uncountable chromatic number","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"D\\'aniel T. Soukup","submitted_at":"2016-08-24T22:49:03Z","abstract_excerpt":"Motivated by an old conjecture of P. Erd\\H{o}s and V. Neumann-Lara, our aim is to investigate digraphs with uncountable dichromatic number and orientations of undirected graphs with uncountable chromatic number. A graph has uncountable chromatic number if its vertices cannot be covered by countably many independent sets, and a digraph has uncountable dichromatic number if its vertices cannot be covered by countably many acyclic sets. We prove that consistently there are digraphs with uncountable dichromatic number and arbitrarily large digirth; this is in surprising contrast with the undirecte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06981","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":"2026-05-18T00:31:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GaDEc4HYR3ePlljSDa8AdqFQxZGR09QThK0n+oHtNSXOxUMYLHn+MCnh4xLoB/GGK/OAEPwLE7JtTDPtGqCoDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T21:20:02.958191Z"},"content_sha256":"51939f74c3d402d37c6c751a077fd19acfbc1ba61fa78dbe9566a8a8ed550763","schema_version":"1.0","event_id":"sha256:51939f74c3d402d37c6c751a077fd19acfbc1ba61fa78dbe9566a8a8ed550763"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKM3IDWXTWWBVDEPM7UC6UAPVL/bundle.json","state_url":"https://pith.science/pith/CKM3IDWXTWWBVDEPM7UC6UAPVL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKM3IDWXTWWBVDEPM7UC6UAPVL/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":"2026-05-18T21:20:02Z","links":{"resolver":"https://pith.science/pith/CKM3IDWXTWWBVDEPM7UC6UAPVL","bundle":"https://pith.science/pith/CKM3IDWXTWWBVDEPM7UC6UAPVL/bundle.json","state":"https://pith.science/pith/CKM3IDWXTWWBVDEPM7UC6UAPVL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKM3IDWXTWWBVDEPM7UC6UAPVL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CKM3IDWXTWWBVDEPM7UC6UAPVL","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":"bdd43bf4805b651c15f5b23a38b35b7bd2b1339e935735d7dbe5a34868e9f88d","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-24T22:49:03Z","title_canon_sha256":"2a3d09bb45b0165deee4881366591cc378e8c520225fcf15b3aad8cdd73adb38"},"schema_version":"1.0","source":{"id":"1608.06981","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06981","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06981v3","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06981","created_at":"2026-05-18T00:31:00Z"},{"alias_kind":"pith_short_12","alias_value":"CKM3IDWXTWWB","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CKM3IDWXTWWBVDEP","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CKM3IDWX","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:51939f74c3d402d37c6c751a077fd19acfbc1ba61fa78dbe9566a8a8ed550763","target":"graph","created_at":"2026-05-18T00:31:00Z","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":"Motivated by an old conjecture of P. Erd\\H{o}s and V. Neumann-Lara, our aim is to investigate digraphs with uncountable dichromatic number and orientations of undirected graphs with uncountable chromatic number. A graph has uncountable chromatic number if its vertices cannot be covered by countably many independent sets, and a digraph has uncountable dichromatic number if its vertices cannot be covered by countably many acyclic sets. We prove that consistently there are digraphs with uncountable dichromatic number and arbitrarily large digirth; this is in surprising contrast with the undirecte","authors_text":"D\\'aniel T. Soukup","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-24T22:49:03Z","title":"Orientations of graphs with uncountable chromatic number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06981","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":"sha256:932c006ed578f266ac236e31847054c0f0161d157dcb8bfbbf055ccafa023d91","target":"record","created_at":"2026-05-18T00:31:00Z","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":"bdd43bf4805b651c15f5b23a38b35b7bd2b1339e935735d7dbe5a34868e9f88d","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-24T22:49:03Z","title_canon_sha256":"2a3d09bb45b0165deee4881366591cc378e8c520225fcf15b3aad8cdd73adb38"},"schema_version":"1.0","source":{"id":"1608.06981","kind":"arxiv","version":3}},"canonical_sha256":"1299b40ed79dac1a8c8f67e82f500faadcbf6365d29d969c672c4f9c61ec4ddc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1299b40ed79dac1a8c8f67e82f500faadcbf6365d29d969c672c4f9c61ec4ddc","first_computed_at":"2026-05-18T00:31:00.409440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:00.409440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JzYeJk6h7MmH48zVg6XWExiMGkZp1DJbUbyxxznRRBIa4K7ve+J3wPcQIAYhOor4b3mslyMKLsEkVBMrwLeEAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:00.410139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06981","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:932c006ed578f266ac236e31847054c0f0161d157dcb8bfbbf055ccafa023d91","sha256:51939f74c3d402d37c6c751a077fd19acfbc1ba61fa78dbe9566a8a8ed550763"],"state_sha256":"caaab79a045f10b04cbbeda4696a046618ef4a62b3e60492fb32d9c89e0d87ad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oeEwBEE0esVJBZtUmcspcKFxLvriZgUvmnrgYWCivNAZla8+GPDcR1nYT6Cp7dLO+MFfq1ZtcGGXlHADmUCwAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T21:20:02.960173Z","bundle_sha256":"de26864352b78c63277e34418a7bb1f1c3f40dccfd193d699eff4b19a8e6d1f7"}}