{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6EYBSB2BZCQZ3RKCQYHCIFFVOR","short_pith_number":"pith:6EYBSB2B","canonical_record":{"source":{"id":"1307.0079","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-29T09:02:28Z","cross_cats_sorted":[],"title_canon_sha256":"d1929bbf8222267a16787efe2dc4bec3c9e42c0ec3400c454414e30a021e3940","abstract_canon_sha256":"67701123bfc5022a5002ceaa52c4a91ccb36e63d82c5e77fde839f80e3038c89"},"schema_version":"1.0"},"canonical_sha256":"f130190741c8a19dc542860e2414b5747f550c5b438a2a739f94acfcf96baf28","source":{"kind":"arxiv","id":"1307.0079","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0079","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0079v3","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0079","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"pith_short_12","alias_value":"6EYBSB2BZCQZ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6EYBSB2BZCQZ3RKC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6EYBSB2B","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6EYBSB2BZCQZ3RKCQYHCIFFVOR","target":"record","payload":{"canonical_record":{"source":{"id":"1307.0079","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-29T09:02:28Z","cross_cats_sorted":[],"title_canon_sha256":"d1929bbf8222267a16787efe2dc4bec3c9e42c0ec3400c454414e30a021e3940","abstract_canon_sha256":"67701123bfc5022a5002ceaa52c4a91ccb36e63d82c5e77fde839f80e3038c89"},"schema_version":"1.0"},"canonical_sha256":"f130190741c8a19dc542860e2414b5747f550c5b438a2a739f94acfcf96baf28","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:24.008772Z","signature_b64":"kc5qcFK/oEFAQEYfc4MOdDqsH8PMk5UPExXFL7JsvEp476fWWaA0jDnWDCIg41dqQurV4KKlC8YmWb/d0l86Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f130190741c8a19dc542860e2414b5747f550c5b438a2a739f94acfcf96baf28","last_reissued_at":"2026-05-18T03:19:24.007754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:24.007754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.0079","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":"2026-05-18T03:19:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iQaFppH6yYabJSRqju1zMyL6KB56ENDiVmyfQITiWo8Tgqik5U6wdd5t4O8HU3wSr8Wy7e5mhuSR32mvlDsqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:39:23.946494Z"},"content_sha256":"1c18804313c35bcffe22a5d44ef0328bfb86d638f5bb8f011652d5cec9933273","schema_version":"1.0","event_id":"sha256:1c18804313c35bcffe22a5d44ef0328bfb86d638f5bb8f011652d5cec9933273"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6EYBSB2BZCQZ3RKCQYHCIFFVOR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The 3-rainbow index of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kang Yang, Lily Chen, Xueliang Li, Yan Zhao","submitted_at":"2013-06-29T09:02:28Z","abstract_excerpt":"Let $G$ be a nontrivial connected graph with an edge-coloring $c: E(G)\\rightarrow \\{1,2,...,q\\},$ $q \\in \\mathbb{N}$, where adjacent edges may be colored the same. A tree $T$ in $G$ is a $rainbow tree$ if no two edges of $T$ receive the same color. For a vertex subset $S\\subseteq V(G)$, a tree that connects $S$ in $G$ is called an $S$-tree. The minimum number of colors that are needed in an edge-coloring of $G$ such that there is a rainbow $S$-tree for each $k$-subset $S$ of $V(G)$ is called $k$-rainbow index, denoted by $rx_k(G)$. In this paper, we first determine the graphs whose 3-rainbow i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0079","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":"2026-05-18T03:19:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qXfEt8UIAyD8zHasAwTZh0nsFMvGf7vhiRH6yw5ZhcUwxE1iezdQ9y9+O+Su/ko0VMFNtK82fT4jX5Di4KKPBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:39:23.946885Z"},"content_sha256":"303b25ef8a73901a462ac2b4e2912d01ad5e36319ccb0bd93e70352e090623d6","schema_version":"1.0","event_id":"sha256:303b25ef8a73901a462ac2b4e2912d01ad5e36319ccb0bd93e70352e090623d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6EYBSB2BZCQZ3RKCQYHCIFFVOR/bundle.json","state_url":"https://pith.science/pith/6EYBSB2BZCQZ3RKCQYHCIFFVOR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6EYBSB2BZCQZ3RKCQYHCIFFVOR/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":"2026-06-01T18:39:23Z","links":{"resolver":"https://pith.science/pith/6EYBSB2BZCQZ3RKCQYHCIFFVOR","bundle":"https://pith.science/pith/6EYBSB2BZCQZ3RKCQYHCIFFVOR/bundle.json","state":"https://pith.science/pith/6EYBSB2BZCQZ3RKCQYHCIFFVOR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6EYBSB2BZCQZ3RKCQYHCIFFVOR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6EYBSB2BZCQZ3RKCQYHCIFFVOR","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":"67701123bfc5022a5002ceaa52c4a91ccb36e63d82c5e77fde839f80e3038c89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-29T09:02:28Z","title_canon_sha256":"d1929bbf8222267a16787efe2dc4bec3c9e42c0ec3400c454414e30a021e3940"},"schema_version":"1.0","source":{"id":"1307.0079","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0079","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0079v3","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0079","created_at":"2026-05-18T03:19:24Z"},{"alias_kind":"pith_short_12","alias_value":"6EYBSB2BZCQZ","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6EYBSB2BZCQZ3RKC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6EYBSB2B","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:303b25ef8a73901a462ac2b4e2912d01ad5e36319ccb0bd93e70352e090623d6","target":"graph","created_at":"2026-05-18T03:19:24Z","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":"Let $G$ be a nontrivial connected graph with an edge-coloring $c: E(G)\\rightarrow \\{1,2,...,q\\},$ $q \\in \\mathbb{N}$, where adjacent edges may be colored the same. A tree $T$ in $G$ is a $rainbow tree$ if no two edges of $T$ receive the same color. For a vertex subset $S\\subseteq V(G)$, a tree that connects $S$ in $G$ is called an $S$-tree. The minimum number of colors that are needed in an edge-coloring of $G$ such that there is a rainbow $S$-tree for each $k$-subset $S$ of $V(G)$ is called $k$-rainbow index, denoted by $rx_k(G)$. In this paper, we first determine the graphs whose 3-rainbow i","authors_text":"Kang Yang, Lily Chen, Xueliang Li, Yan Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-29T09:02:28Z","title":"The 3-rainbow index of a graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0079","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":"sha256:1c18804313c35bcffe22a5d44ef0328bfb86d638f5bb8f011652d5cec9933273","target":"record","created_at":"2026-05-18T03:19:24Z","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":"67701123bfc5022a5002ceaa52c4a91ccb36e63d82c5e77fde839f80e3038c89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-29T09:02:28Z","title_canon_sha256":"d1929bbf8222267a16787efe2dc4bec3c9e42c0ec3400c454414e30a021e3940"},"schema_version":"1.0","source":{"id":"1307.0079","kind":"arxiv","version":3}},"canonical_sha256":"f130190741c8a19dc542860e2414b5747f550c5b438a2a739f94acfcf96baf28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f130190741c8a19dc542860e2414b5747f550c5b438a2a739f94acfcf96baf28","first_computed_at":"2026-05-18T03:19:24.007754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:24.007754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kc5qcFK/oEFAQEYfc4MOdDqsH8PMk5UPExXFL7JsvEp476fWWaA0jDnWDCIg41dqQurV4KKlC8YmWb/d0l86Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:24.008772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0079","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c18804313c35bcffe22a5d44ef0328bfb86d638f5bb8f011652d5cec9933273","sha256:303b25ef8a73901a462ac2b4e2912d01ad5e36319ccb0bd93e70352e090623d6"],"state_sha256":"207088900f5059148e5a0df3e4a4c7b9dd296d755466a6ae70ff71075d1f482c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/sZosjYnIQkielcqioT9j+BHNe1TQEvXJEHCq84qeu8A6/zvkvkclfMHUlOTopJobUqgA7tBHctOEnjl9DOwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:39:23.948828Z","bundle_sha256":"1c5beff6dbb4c5875d4ff01ef56b3976cebb9ff7d0ec81c4c468fb65bcdcb9b9"}}