{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:42P2IFIXQFPAZO6NDDXOGQSRXH","short_pith_number":"pith:42P2IFIX","canonical_record":{"source":{"id":"1711.02916","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-08T12:26:36Z","cross_cats_sorted":[],"title_canon_sha256":"ebcb574f579eedfcd3e249c2a25552c867d9262b44b85ac2dcc1c5eb9b8e84b4","abstract_canon_sha256":"1b37526190b385e6f6698adb07bd8499aadc4ebb0e4eb97a06b5605988d5acda"},"schema_version":"1.0"},"canonical_sha256":"e69fa41517815e0cbbcd18eee34251b9ebed08b2811c19e167022cd20ea3106a","source":{"kind":"arxiv","id":"1711.02916","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02916","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02916v2","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02916","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"pith_short_12","alias_value":"42P2IFIXQFPA","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"42P2IFIXQFPAZO6N","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"42P2IFIX","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:42P2IFIXQFPAZO6NDDXOGQSRXH","target":"record","payload":{"canonical_record":{"source":{"id":"1711.02916","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-08T12:26:36Z","cross_cats_sorted":[],"title_canon_sha256":"ebcb574f579eedfcd3e249c2a25552c867d9262b44b85ac2dcc1c5eb9b8e84b4","abstract_canon_sha256":"1b37526190b385e6f6698adb07bd8499aadc4ebb0e4eb97a06b5605988d5acda"},"schema_version":"1.0"},"canonical_sha256":"e69fa41517815e0cbbcd18eee34251b9ebed08b2811c19e167022cd20ea3106a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:01.748228Z","signature_b64":"htmx2H5BHL6XmkfeflL18NmMV7hut8wqIXCrqiTt/H5hr/F0SVEiJBqqqKTbtvEemZwhjtb6iYykAPCTpDy7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e69fa41517815e0cbbcd18eee34251b9ebed08b2811c19e167022cd20ea3106a","last_reissued_at":"2026-05-18T00:28:01.747543Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:01.747543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.02916","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":"2026-05-18T00:28:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jxH0T6FYbEcyUk3bZ9W6gOQhOOcTXKUvQFwTrCn3vBJpO4tclT3+ZD76DMqBDYq4gz/+GZXz6Twr8i/xloOADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T11:06:41.046209Z"},"content_sha256":"f3d604bbd4eeb38c9015c16db5bd8c6c3ae8856d3f5990999c2ceb2ffad0db72","schema_version":"1.0","event_id":"sha256:f3d604bbd4eeb38c9015c16db5bd8c6c3ae8856d3f5990999c2ceb2ffad0db72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:42P2IFIXQFPAZO6NDDXOGQSRXH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rainbow matchings in Dirac bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guillem Perarnau, Matthew Coulson","submitted_at":"2017-11-08T12:26:36Z","abstract_excerpt":"We show the existence of rainbow perfect matchings in $\\mu n$-bounded edge colourings of Dirac bipartite graphs, for a sufficiently small $\\mu>0$. As an application of our results, we obtain several results on the existence of rainbow $k$-factors in Dirac graphs and rainbow spanning subgraphs of bounded maximum degree on graphs with large minimum degree."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02916","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":"2026-05-18T00:28:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6SQT2R+HE8MP+mVBpCA5N28wD09euKNjxgF9fY5oXwJCy+h4I1WVFNS4SO2ot7n/VWxPMF7ZV2ffVCPC2om4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T11:06:41.046909Z"},"content_sha256":"2f4751aa48657537d758d71cb1e954b2d368edb4c483a705d1be13ef33442439","schema_version":"1.0","event_id":"sha256:2f4751aa48657537d758d71cb1e954b2d368edb4c483a705d1be13ef33442439"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/42P2IFIXQFPAZO6NDDXOGQSRXH/bundle.json","state_url":"https://pith.science/pith/42P2IFIXQFPAZO6NDDXOGQSRXH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/42P2IFIXQFPAZO6NDDXOGQSRXH/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":"2026-06-06T11:06:41Z","links":{"resolver":"https://pith.science/pith/42P2IFIXQFPAZO6NDDXOGQSRXH","bundle":"https://pith.science/pith/42P2IFIXQFPAZO6NDDXOGQSRXH/bundle.json","state":"https://pith.science/pith/42P2IFIXQFPAZO6NDDXOGQSRXH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/42P2IFIXQFPAZO6NDDXOGQSRXH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:42P2IFIXQFPAZO6NDDXOGQSRXH","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":"1b37526190b385e6f6698adb07bd8499aadc4ebb0e4eb97a06b5605988d5acda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-08T12:26:36Z","title_canon_sha256":"ebcb574f579eedfcd3e249c2a25552c867d9262b44b85ac2dcc1c5eb9b8e84b4"},"schema_version":"1.0","source":{"id":"1711.02916","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.02916","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"arxiv_version","alias_value":"1711.02916v2","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.02916","created_at":"2026-05-18T00:28:01Z"},{"alias_kind":"pith_short_12","alias_value":"42P2IFIXQFPA","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"42P2IFIXQFPAZO6N","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"42P2IFIX","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:2f4751aa48657537d758d71cb1e954b2d368edb4c483a705d1be13ef33442439","target":"graph","created_at":"2026-05-18T00:28:01Z","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 show the existence of rainbow perfect matchings in $\\mu n$-bounded edge colourings of Dirac bipartite graphs, for a sufficiently small $\\mu>0$. As an application of our results, we obtain several results on the existence of rainbow $k$-factors in Dirac graphs and rainbow spanning subgraphs of bounded maximum degree on graphs with large minimum degree.","authors_text":"Guillem Perarnau, Matthew Coulson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-08T12:26:36Z","title":"Rainbow matchings in Dirac bipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02916","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:f3d604bbd4eeb38c9015c16db5bd8c6c3ae8856d3f5990999c2ceb2ffad0db72","target":"record","created_at":"2026-05-18T00:28:01Z","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":"1b37526190b385e6f6698adb07bd8499aadc4ebb0e4eb97a06b5605988d5acda","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-08T12:26:36Z","title_canon_sha256":"ebcb574f579eedfcd3e249c2a25552c867d9262b44b85ac2dcc1c5eb9b8e84b4"},"schema_version":"1.0","source":{"id":"1711.02916","kind":"arxiv","version":2}},"canonical_sha256":"e69fa41517815e0cbbcd18eee34251b9ebed08b2811c19e167022cd20ea3106a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e69fa41517815e0cbbcd18eee34251b9ebed08b2811c19e167022cd20ea3106a","first_computed_at":"2026-05-18T00:28:01.747543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:01.747543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"htmx2H5BHL6XmkfeflL18NmMV7hut8wqIXCrqiTt/H5hr/F0SVEiJBqqqKTbtvEemZwhjtb6iYykAPCTpDy7DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:01.748228Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.02916","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3d604bbd4eeb38c9015c16db5bd8c6c3ae8856d3f5990999c2ceb2ffad0db72","sha256:2f4751aa48657537d758d71cb1e954b2d368edb4c483a705d1be13ef33442439"],"state_sha256":"89441eef4be380f6055a2488327c4b12c6245b3d0864ceef00a0325f0c3c92ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q5zkhOsIEFNJW9xkl4yowdIBLqO6Yzr2m8xgPQXyKPZQQbJJTdzgc09mIJdtRBWDQLwmcT+qCbExy4LdiE2fDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T11:06:41.051086Z","bundle_sha256":"35c7ecca9415dafb800dac6c599be81cf41512fbe0c5733e5042d630957e034b"}}