{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:S3BFMVPHSP4POFST5T6KBTFAXH","short_pith_number":"pith:S3BFMVPH","canonical_record":{"source":{"id":"1807.08286","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-22T14:01:07Z","cross_cats_sorted":[],"title_canon_sha256":"064236b34eeaedc9627a5f375e7a99d4020aee5a5287cca4e0319a04e3052da2","abstract_canon_sha256":"a271a026ebd9f2600bfc239ac40d9434008625e6e28adaca32eaa9203515a236"},"schema_version":"1.0"},"canonical_sha256":"96c25655e793f8f71653ecfca0cca0b9e03dc12d642b8e0e882a6b3037e4185a","source":{"kind":"arxiv","id":"1807.08286","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08286","created_at":"2026-05-18T00:10:08Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08286v1","created_at":"2026-05-18T00:10:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08286","created_at":"2026-05-18T00:10:08Z"},{"alias_kind":"pith_short_12","alias_value":"S3BFMVPHSP4P","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S3BFMVPHSP4POFST","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S3BFMVPH","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:S3BFMVPHSP4POFST5T6KBTFAXH","target":"record","payload":{"canonical_record":{"source":{"id":"1807.08286","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-22T14:01:07Z","cross_cats_sorted":[],"title_canon_sha256":"064236b34eeaedc9627a5f375e7a99d4020aee5a5287cca4e0319a04e3052da2","abstract_canon_sha256":"a271a026ebd9f2600bfc239ac40d9434008625e6e28adaca32eaa9203515a236"},"schema_version":"1.0"},"canonical_sha256":"96c25655e793f8f71653ecfca0cca0b9e03dc12d642b8e0e882a6b3037e4185a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:08.580469Z","signature_b64":"R64r3/+08fv4KSk4XLMt6yZpD39eII+2JtqYt8gBoqvnndQcC0BahPEekjTIF4eAV16AzKsCAzfvFTsrSsCtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96c25655e793f8f71653ecfca0cca0b9e03dc12d642b8e0e882a6b3037e4185a","last_reissued_at":"2026-05-18T00:10:08.579778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:08.579778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.08286","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:10:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gktpqg2J9wQQm4BIxhTwD318krxYWMrnGZxZx/oiRWJtNZ5P1OF5j3fAVU1jhot2XwjSBqKM/8wOXxpuL2CSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:39:57.184819Z"},"content_sha256":"6a28f229d00cfa67ecc6342929b0093476571b33ccfd9b137dbaf03d9390a13a","schema_version":"1.0","event_id":"sha256:6a28f229d00cfa67ecc6342929b0093476571b33ccfd9b137dbaf03d9390a13a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:S3BFMVPHSP4POFST5T6KBTFAXH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On kernels by rainbow paths in arc-coloured digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ruijuan Li, Yanqin Cao","submitted_at":"2018-07-22T14:01:07Z","abstract_excerpt":"In 2018, Bai, Fujita and Zhang (\\emph{Discrete Math.} 2018, 341(6): 1523-1533) introduced the concept of a kernel by rainbow paths (for short, RP-kernel) of an arc-coloured digraph $D$, which is a subset $S$ of vertices of $D$ such that ($a$) there exists no rainbow path for any pair of distinct vertices of $S$, and ($b$) every vertex outside $S$ can reach $S$ by a rainbow path in $D$. They showed that it is NP-hard to recognize wether an arc-coloured digraph has a RP-kernel and it is NP-complete to decided wether an arc-coloured tournament has a RP-kernel. In this paper, we give the sufficien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08286","kind":"arxiv","version":1},"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":"2026-05-18T00:10:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hmY9J/bNxfz+plRLQ5kYFWCyD3c7twVDqAUJ0bHBG09PzLB/8DHgTVtjerwIzZfV4nGuJV1LP/D4ChGGHOUcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:39:57.185163Z"},"content_sha256":"552709e6e24feab74b9c7cfced022259c79ade42ff82fa80666c5263befb735a","schema_version":"1.0","event_id":"sha256:552709e6e24feab74b9c7cfced022259c79ade42ff82fa80666c5263befb735a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S3BFMVPHSP4POFST5T6KBTFAXH/bundle.json","state_url":"https://pith.science/pith/S3BFMVPHSP4POFST5T6KBTFAXH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S3BFMVPHSP4POFST5T6KBTFAXH/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":"2026-06-01T18:39:57Z","links":{"resolver":"https://pith.science/pith/S3BFMVPHSP4POFST5T6KBTFAXH","bundle":"https://pith.science/pith/S3BFMVPHSP4POFST5T6KBTFAXH/bundle.json","state":"https://pith.science/pith/S3BFMVPHSP4POFST5T6KBTFAXH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S3BFMVPHSP4POFST5T6KBTFAXH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:S3BFMVPHSP4POFST5T6KBTFAXH","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":"a271a026ebd9f2600bfc239ac40d9434008625e6e28adaca32eaa9203515a236","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-22T14:01:07Z","title_canon_sha256":"064236b34eeaedc9627a5f375e7a99d4020aee5a5287cca4e0319a04e3052da2"},"schema_version":"1.0","source":{"id":"1807.08286","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08286","created_at":"2026-05-18T00:10:08Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08286v1","created_at":"2026-05-18T00:10:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08286","created_at":"2026-05-18T00:10:08Z"},{"alias_kind":"pith_short_12","alias_value":"S3BFMVPHSP4P","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S3BFMVPHSP4POFST","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S3BFMVPH","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:552709e6e24feab74b9c7cfced022259c79ade42ff82fa80666c5263befb735a","target":"graph","created_at":"2026-05-18T00:10:08Z","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 2018, Bai, Fujita and Zhang (\\emph{Discrete Math.} 2018, 341(6): 1523-1533) introduced the concept of a kernel by rainbow paths (for short, RP-kernel) of an arc-coloured digraph $D$, which is a subset $S$ of vertices of $D$ such that ($a$) there exists no rainbow path for any pair of distinct vertices of $S$, and ($b$) every vertex outside $S$ can reach $S$ by a rainbow path in $D$. They showed that it is NP-hard to recognize wether an arc-coloured digraph has a RP-kernel and it is NP-complete to decided wether an arc-coloured tournament has a RP-kernel. In this paper, we give the sufficien","authors_text":"Ruijuan Li, Yanqin Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-22T14:01:07Z","title":"On kernels by rainbow paths in arc-coloured digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08286","kind":"arxiv","version":1},"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":"sha256:6a28f229d00cfa67ecc6342929b0093476571b33ccfd9b137dbaf03d9390a13a","target":"record","created_at":"2026-05-18T00:10:08Z","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":"a271a026ebd9f2600bfc239ac40d9434008625e6e28adaca32eaa9203515a236","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-22T14:01:07Z","title_canon_sha256":"064236b34eeaedc9627a5f375e7a99d4020aee5a5287cca4e0319a04e3052da2"},"schema_version":"1.0","source":{"id":"1807.08286","kind":"arxiv","version":1}},"canonical_sha256":"96c25655e793f8f71653ecfca0cca0b9e03dc12d642b8e0e882a6b3037e4185a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96c25655e793f8f71653ecfca0cca0b9e03dc12d642b8e0e882a6b3037e4185a","first_computed_at":"2026-05-18T00:10:08.579778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:08.579778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R64r3/+08fv4KSk4XLMt6yZpD39eII+2JtqYt8gBoqvnndQcC0BahPEekjTIF4eAV16AzKsCAzfvFTsrSsCtAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:08.580469Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.08286","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a28f229d00cfa67ecc6342929b0093476571b33ccfd9b137dbaf03d9390a13a","sha256:552709e6e24feab74b9c7cfced022259c79ade42ff82fa80666c5263befb735a"],"state_sha256":"38239fff5f056989a6fb27c946f63a2795d695e643d1a2641d97f240fb465c08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gBq7ryDTHgSK7d5seGfcjY+cOXNvOAHjvOZVFg201gnZTeuB9qXCJ8L7SRgihbbwPRV5Qyz5fNgxkkkV04NIBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:39:57.187091Z","bundle_sha256":"90ce2a4e38de14508388c88a7b2b1708c79b6205139c0352d8ae39545049319c"}}