{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:JWCHL373TFU5OI5XFYTN5IV3AK","short_pith_number":"pith:JWCHL373","canonical_record":{"source":{"id":"1104.4190","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-21T07:08:03Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"1b789447c6e725d1dd61a1bba6a0ee964b84984b5086b60aab5934a3222a0f64","abstract_canon_sha256":"2f664b4f9c7d6a8a4974e20b24aecd5a13b9c011c10b55bc87b8a18af777c51c"},"schema_version":"1.0"},"canonical_sha256":"4d8475effb9969d723b72e26dea2bb02900e14561c0580c143365821b3b4344d","source":{"kind":"arxiv","id":"1104.4190","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4190","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4190v2","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4190","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"pith_short_12","alias_value":"JWCHL373TFU5","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JWCHL373TFU5OI5X","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JWCHL373","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:JWCHL373TFU5OI5XFYTN5IV3AK","target":"record","payload":{"canonical_record":{"source":{"id":"1104.4190","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-21T07:08:03Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"1b789447c6e725d1dd61a1bba6a0ee964b84984b5086b60aab5934a3222a0f64","abstract_canon_sha256":"2f664b4f9c7d6a8a4974e20b24aecd5a13b9c011c10b55bc87b8a18af777c51c"},"schema_version":"1.0"},"canonical_sha256":"4d8475effb9969d723b72e26dea2bb02900e14561c0580c143365821b3b4344d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:17:04.255010Z","signature_b64":"4Pv6OTQ9MA+dvvFxFPklTF66q4+vmwwDLCDd/4PCiYyF44DtkNarbPO+68YOt6Aym7Mpe8r8WB7JqbDKtUKyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d8475effb9969d723b72e26dea2bb02900e14561c0580c143365821b3b4344d","last_reissued_at":"2026-05-18T04:17:04.254422Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:17:04.254422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.4190","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":"2026-05-18T04:17:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M/0uUf/ObvHNlc4MJtyoH1s0GWNUlb0jD01SpZUU2CGNT+7mev5ypcq529M+pXyNaZQgRgkJHaNDj6Iu6I/rBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T00:39:12.331708Z"},"content_sha256":"724f0f2e6fb0dd62770aa9c89b322f146df821051eba16472d2ba5eefaa5c13c","schema_version":"1.0","event_id":"sha256:724f0f2e6fb0dd62770aa9c89b322f146df821051eba16472d2ba5eefaa5c13c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:JWCHL373TFU5OI5XFYTN5IV3AK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rainbow Connection Number of Graph Power and Graph Products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Arunselvan Ramaswamy, Deepak Rajendraprasad, L. Sunil Chandran, Manu Basavaraju","submitted_at":"2011-04-21T07:08:03Z","abstract_excerpt":"Rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges so that every pair of vertices is connected by at least one path in which no two edges are colored the same (Note that the coloring need not be proper). In this paper we study the rainbow connection number with respect to three important graph product operations (namely cartesian product, lexicographic product and strong product) and the operation of taking the power of a graph. In this direction, we show that if G is a graph obtained by applying any of the operations mentioned ab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4190","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":"2026-05-18T04:17:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EtJ91BnKaVWIzdrQLLmDQAV8Yzan0z0sCDXAm7bED555MMMe15i7GbDT9xxICqSOztqS+wZ07Y1iRZAsh1O+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T00:39:12.332052Z"},"content_sha256":"42cae8465001a6085a82c63df8ce9312d232ec34688eb76e2a73106d711cecff","schema_version":"1.0","event_id":"sha256:42cae8465001a6085a82c63df8ce9312d232ec34688eb76e2a73106d711cecff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JWCHL373TFU5OI5XFYTN5IV3AK/bundle.json","state_url":"https://pith.science/pith/JWCHL373TFU5OI5XFYTN5IV3AK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JWCHL373TFU5OI5XFYTN5IV3AK/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":"2026-06-04T00:39:12Z","links":{"resolver":"https://pith.science/pith/JWCHL373TFU5OI5XFYTN5IV3AK","bundle":"https://pith.science/pith/JWCHL373TFU5OI5XFYTN5IV3AK/bundle.json","state":"https://pith.science/pith/JWCHL373TFU5OI5XFYTN5IV3AK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JWCHL373TFU5OI5XFYTN5IV3AK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:JWCHL373TFU5OI5XFYTN5IV3AK","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":"2f664b4f9c7d6a8a4974e20b24aecd5a13b9c011c10b55bc87b8a18af777c51c","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-21T07:08:03Z","title_canon_sha256":"1b789447c6e725d1dd61a1bba6a0ee964b84984b5086b60aab5934a3222a0f64"},"schema_version":"1.0","source":{"id":"1104.4190","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4190","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4190v2","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4190","created_at":"2026-05-18T04:17:04Z"},{"alias_kind":"pith_short_12","alias_value":"JWCHL373TFU5","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"JWCHL373TFU5OI5X","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"JWCHL373","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:42cae8465001a6085a82c63df8ce9312d232ec34688eb76e2a73106d711cecff","target":"graph","created_at":"2026-05-18T04:17:04Z","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":"Rainbow connection number, rc(G), of a connected graph G is the minimum number of colors needed to color its edges so that every pair of vertices is connected by at least one path in which no two edges are colored the same (Note that the coloring need not be proper). In this paper we study the rainbow connection number with respect to three important graph product operations (namely cartesian product, lexicographic product and strong product) and the operation of taking the power of a graph. In this direction, we show that if G is a graph obtained by applying any of the operations mentioned ab","authors_text":"Arunselvan Ramaswamy, Deepak Rajendraprasad, L. Sunil Chandran, Manu Basavaraju","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-21T07:08:03Z","title":"Rainbow Connection Number of Graph Power and Graph Products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4190","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":"sha256:724f0f2e6fb0dd62770aa9c89b322f146df821051eba16472d2ba5eefaa5c13c","target":"record","created_at":"2026-05-18T04:17:04Z","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":"2f664b4f9c7d6a8a4974e20b24aecd5a13b9c011c10b55bc87b8a18af777c51c","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-04-21T07:08:03Z","title_canon_sha256":"1b789447c6e725d1dd61a1bba6a0ee964b84984b5086b60aab5934a3222a0f64"},"schema_version":"1.0","source":{"id":"1104.4190","kind":"arxiv","version":2}},"canonical_sha256":"4d8475effb9969d723b72e26dea2bb02900e14561c0580c143365821b3b4344d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d8475effb9969d723b72e26dea2bb02900e14561c0580c143365821b3b4344d","first_computed_at":"2026-05-18T04:17:04.254422Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:04.254422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4Pv6OTQ9MA+dvvFxFPklTF66q4+vmwwDLCDd/4PCiYyF44DtkNarbPO+68YOt6Aym7Mpe8r8WB7JqbDKtUKyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:04.255010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.4190","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:724f0f2e6fb0dd62770aa9c89b322f146df821051eba16472d2ba5eefaa5c13c","sha256:42cae8465001a6085a82c63df8ce9312d232ec34688eb76e2a73106d711cecff"],"state_sha256":"72096b8718621959cd21819315a9a13fbfbf36d1a21a3054a93d705dbf808d4a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AGqWqMRTOm/PVKi4SN/o+TUOqm5NFu4prZbgwKcaV+pRFBvph00I/nKQv2YURuEtaQxnkmrpCR2MnU9FUR+rDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T00:39:12.333987Z","bundle_sha256":"1567d7b1c12d387147ff207228bb2fc03bed842936baf07b9dbb03a265c0df08"}}