{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:ONRK6GHRSZTLRQFUNF2JYLWTNX","short_pith_number":"pith:ONRK6GHR","canonical_record":{"source":{"id":"1211.1306","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-06T16:46:41Z","cross_cats_sorted":[],"title_canon_sha256":"5ff1f3ae677b47e4865703ccc2deabd5701f5046d925aeb0d87030b15a696817","abstract_canon_sha256":"333f34daf1fd114776d25c20598716141794220c224863c692d70cb9255a73f6"},"schema_version":"1.0"},"canonical_sha256":"7362af18f19666b8c0b469749c2ed36dd572531b063856d4806ef273028cc62e","source":{"kind":"arxiv","id":"1211.1306","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1306","created_at":"2026-05-18T03:14:50Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1306v2","created_at":"2026-05-18T03:14:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1306","created_at":"2026-05-18T03:14:50Z"},{"alias_kind":"pith_short_12","alias_value":"ONRK6GHRSZTL","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"ONRK6GHRSZTLRQFU","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"ONRK6GHR","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:ONRK6GHRSZTLRQFUNF2JYLWTNX","target":"record","payload":{"canonical_record":{"source":{"id":"1211.1306","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-06T16:46:41Z","cross_cats_sorted":[],"title_canon_sha256":"5ff1f3ae677b47e4865703ccc2deabd5701f5046d925aeb0d87030b15a696817","abstract_canon_sha256":"333f34daf1fd114776d25c20598716141794220c224863c692d70cb9255a73f6"},"schema_version":"1.0"},"canonical_sha256":"7362af18f19666b8c0b469749c2ed36dd572531b063856d4806ef273028cc62e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:50.172560Z","signature_b64":"1IkhXKz3cl+v5uSB9oKqjKV2r/eM8VwuVS9GYTP7c2d4oWhlI5vMvx5mYO9hNpDXVkuoMWsM5gzkLIbhRXMgCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7362af18f19666b8c0b469749c2ed36dd572531b063856d4806ef273028cc62e","last_reissued_at":"2026-05-18T03:14:50.171951Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:50.171951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.1306","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":"2026-05-18T03:14:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XyAoIoG2PWhjRYPUHsnc23ZW3lzj72242i9u4l1Ao96LXg+guMn7lfZ2GtifGD19bz7NYSG/nnpvIJ7UlmSxBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:43:51.818601Z"},"content_sha256":"9677b465f69762cb2f80540de715bdc730dfeda5d11b21f41a1528c4da0e896a","schema_version":"1.0","event_id":"sha256:9677b465f69762cb2f80540de715bdc730dfeda5d11b21f41a1528c4da0e896a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:ONRK6GHRSZTLRQFUNF2JYLWTNX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Delay colourings of cubic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Agelos Georgakopoulos","submitted_at":"2012-11-06T16:46:41Z","abstract_excerpt":"In this note we prove the conjecture of \\cite{HaWiWi} that every bipartite multigraph with integer edge delays admits an edge colouring with $d+1$ colours in the special case where $d=3$. A connection to the Brualdi-Ryser-Stein conjecture is discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1306","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":""},"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":"2026-05-18T03:14:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8pKdEjQqVA4AUH9rwe0VB0CBKWGH6WEj4uMrFHgzva9wZDZqsSdYoNZLZpuLcZIZFSd+WpnEC33IuLvG0jEEAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:43:51.818944Z"},"content_sha256":"691f33014a40619424beb4785e472a6ff75449e3eca24ef4a670ddc4cbc9c195","schema_version":"1.0","event_id":"sha256:691f33014a40619424beb4785e472a6ff75449e3eca24ef4a670ddc4cbc9c195"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ONRK6GHRSZTLRQFUNF2JYLWTNX/bundle.json","state_url":"https://pith.science/pith/ONRK6GHRSZTLRQFUNF2JYLWTNX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ONRK6GHRSZTLRQFUNF2JYLWTNX/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":"2026-07-04T23:43:51Z","links":{"resolver":"https://pith.science/pith/ONRK6GHRSZTLRQFUNF2JYLWTNX","bundle":"https://pith.science/pith/ONRK6GHRSZTLRQFUNF2JYLWTNX/bundle.json","state":"https://pith.science/pith/ONRK6GHRSZTLRQFUNF2JYLWTNX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ONRK6GHRSZTLRQFUNF2JYLWTNX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ONRK6GHRSZTLRQFUNF2JYLWTNX","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":"333f34daf1fd114776d25c20598716141794220c224863c692d70cb9255a73f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-06T16:46:41Z","title_canon_sha256":"5ff1f3ae677b47e4865703ccc2deabd5701f5046d925aeb0d87030b15a696817"},"schema_version":"1.0","source":{"id":"1211.1306","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1306","created_at":"2026-05-18T03:14:50Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1306v2","created_at":"2026-05-18T03:14:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1306","created_at":"2026-05-18T03:14:50Z"},{"alias_kind":"pith_short_12","alias_value":"ONRK6GHRSZTL","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"ONRK6GHRSZTLRQFU","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"ONRK6GHR","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:691f33014a40619424beb4785e472a6ff75449e3eca24ef4a670ddc4cbc9c195","target":"graph","created_at":"2026-05-18T03:14:50Z","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":"In this note we prove the conjecture of \\cite{HaWiWi} that every bipartite multigraph with integer edge delays admits an edge colouring with $d+1$ colours in the special case where $d=3$. A connection to the Brualdi-Ryser-Stein conjecture is discussed.","authors_text":"Agelos Georgakopoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-06T16:46:41Z","title":"Delay colourings of cubic graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1306","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":"sha256:9677b465f69762cb2f80540de715bdc730dfeda5d11b21f41a1528c4da0e896a","target":"record","created_at":"2026-05-18T03:14:50Z","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":"333f34daf1fd114776d25c20598716141794220c224863c692d70cb9255a73f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-06T16:46:41Z","title_canon_sha256":"5ff1f3ae677b47e4865703ccc2deabd5701f5046d925aeb0d87030b15a696817"},"schema_version":"1.0","source":{"id":"1211.1306","kind":"arxiv","version":2}},"canonical_sha256":"7362af18f19666b8c0b469749c2ed36dd572531b063856d4806ef273028cc62e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7362af18f19666b8c0b469749c2ed36dd572531b063856d4806ef273028cc62e","first_computed_at":"2026-05-18T03:14:50.171951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:50.171951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1IkhXKz3cl+v5uSB9oKqjKV2r/eM8VwuVS9GYTP7c2d4oWhlI5vMvx5mYO9hNpDXVkuoMWsM5gzkLIbhRXMgCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:50.172560Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1306","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9677b465f69762cb2f80540de715bdc730dfeda5d11b21f41a1528c4da0e896a","sha256:691f33014a40619424beb4785e472a6ff75449e3eca24ef4a670ddc4cbc9c195"],"state_sha256":"6c0ae9b9fdf473453f8037d64ab727000dbfbbf3af12559a6832613c38c0d47a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DGEBuZo6Jvdty5BmDm0Jt1nkaTC9AjaRFSp302yxAknbsV6+VSH7DfAxlIZDYJcMMTMQWOR+TmWhIHrwbvLJAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T23:43:51.821261Z","bundle_sha256":"5d41856a309dc3489402935d920e054abaee102fa85852bc82f47af62732b0fb"}}