{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SPSLEPZVZ6MCNX7DZRLI227UQH","short_pith_number":"pith:SPSLEPZV","canonical_record":{"source":{"id":"1306.4287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-06-18T18:31:27Z","cross_cats_sorted":[],"title_canon_sha256":"71e7821f2ef07a45f5b0d6a4b88d808dde4a1554a3be54e480cb0c80e569216a","abstract_canon_sha256":"ade469a603ae84b5914651b8e3f27813b975b933e6aa2ac97aa1f36fd0701ae0"},"schema_version":"1.0"},"canonical_sha256":"93e4b23f35cf9826dfe3cc568d6bf481e748d3a5cf75cdcb32387f341713c412","source":{"kind":"arxiv","id":"1306.4287","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4287","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4287v1","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4287","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"pith_short_12","alias_value":"SPSLEPZVZ6MC","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SPSLEPZVZ6MCNX7D","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SPSLEPZV","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SPSLEPZVZ6MCNX7DZRLI227UQH","target":"record","payload":{"canonical_record":{"source":{"id":"1306.4287","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-06-18T18:31:27Z","cross_cats_sorted":[],"title_canon_sha256":"71e7821f2ef07a45f5b0d6a4b88d808dde4a1554a3be54e480cb0c80e569216a","abstract_canon_sha256":"ade469a603ae84b5914651b8e3f27813b975b933e6aa2ac97aa1f36fd0701ae0"},"schema_version":"1.0"},"canonical_sha256":"93e4b23f35cf9826dfe3cc568d6bf481e748d3a5cf75cdcb32387f341713c412","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:36.550337Z","signature_b64":"3B1+C9M0kVAYzKpwP4+vxB4Lt10NC2fp4pakxC7n9Hho6HXfFyPTM0a7+VJabQjLGVGUCejnq2NE21gpGmA7Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93e4b23f35cf9826dfe3cc568d6bf481e748d3a5cf75cdcb32387f341713c412","last_reissued_at":"2026-05-18T03:20:36.549533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:36.549533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.4287","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":"2026-05-18T03:20:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zkwCez0f71eV8NppmQJwx5CbSGgmAxokGk/QEyWkcaYUsAIVrUQqSDI5JJxDAq0j5UA8pFGcvKnjdiTjTvElCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T18:42:25.121043Z"},"content_sha256":"6acb9e38a2a5683f04a600ab2d371654c9399d97fab0f9a670e413e6b8f74a09","schema_version":"1.0","event_id":"sha256:6acb9e38a2a5683f04a600ab2d371654c9399d97fab0f9a670e413e6b8f74a09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SPSLEPZVZ6MCNX7DZRLI227UQH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Succinct data structures for representing equivalence classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"J. Ian Munro, Moshe Lewenstein, Venkatesh Raman","submitted_at":"2013-06-18T18:31:27Z","abstract_excerpt":"Given a partition of an n element set into equivalence classes, we consider time-space tradeoffs for representing it to support the query that asks whether two given elements are in the same equivalence class. This has various applications including for testing whether two vertices are in the same component in an undirected graph or in the same strongly connected component in a directed graph.\n  We consider the problem in several models.\n  -- Concerning labeling schemes where we assign labels to elements and the query is to be answered just by examining the labels of the queried elements (with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4287","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":"2026-05-18T03:20:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VgCOdL72lrIBDTy8MssobQ1YXP2V1SoSJEN6O6uCClrzFGixUl8UYZeztHyX+bLQyWMCBgCEC9djn2kmLc1oCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T18:42:25.121397Z"},"content_sha256":"c2c9f81783451b25db1585c90fc2af551a3bbbc53d77f16988b08ff29c70ac39","schema_version":"1.0","event_id":"sha256:c2c9f81783451b25db1585c90fc2af551a3bbbc53d77f16988b08ff29c70ac39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SPSLEPZVZ6MCNX7DZRLI227UQH/bundle.json","state_url":"https://pith.science/pith/SPSLEPZVZ6MCNX7DZRLI227UQH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SPSLEPZVZ6MCNX7DZRLI227UQH/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":"2026-05-22T18:42:25Z","links":{"resolver":"https://pith.science/pith/SPSLEPZVZ6MCNX7DZRLI227UQH","bundle":"https://pith.science/pith/SPSLEPZVZ6MCNX7DZRLI227UQH/bundle.json","state":"https://pith.science/pith/SPSLEPZVZ6MCNX7DZRLI227UQH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SPSLEPZVZ6MCNX7DZRLI227UQH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SPSLEPZVZ6MCNX7DZRLI227UQH","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":"ade469a603ae84b5914651b8e3f27813b975b933e6aa2ac97aa1f36fd0701ae0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-06-18T18:31:27Z","title_canon_sha256":"71e7821f2ef07a45f5b0d6a4b88d808dde4a1554a3be54e480cb0c80e569216a"},"schema_version":"1.0","source":{"id":"1306.4287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.4287","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"arxiv_version","alias_value":"1306.4287v1","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.4287","created_at":"2026-05-18T03:20:36Z"},{"alias_kind":"pith_short_12","alias_value":"SPSLEPZVZ6MC","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SPSLEPZVZ6MCNX7D","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SPSLEPZV","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:c2c9f81783451b25db1585c90fc2af551a3bbbc53d77f16988b08ff29c70ac39","target":"graph","created_at":"2026-05-18T03:20:36Z","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":"Given a partition of an n element set into equivalence classes, we consider time-space tradeoffs for representing it to support the query that asks whether two given elements are in the same equivalence class. This has various applications including for testing whether two vertices are in the same component in an undirected graph or in the same strongly connected component in a directed graph.\n  We consider the problem in several models.\n  -- Concerning labeling schemes where we assign labels to elements and the query is to be answered just by examining the labels of the queried elements (with","authors_text":"J. Ian Munro, Moshe Lewenstein, Venkatesh Raman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-06-18T18:31:27Z","title":"Succinct data structures for representing equivalence classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.4287","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":"sha256:6acb9e38a2a5683f04a600ab2d371654c9399d97fab0f9a670e413e6b8f74a09","target":"record","created_at":"2026-05-18T03:20:36Z","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":"ade469a603ae84b5914651b8e3f27813b975b933e6aa2ac97aa1f36fd0701ae0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-06-18T18:31:27Z","title_canon_sha256":"71e7821f2ef07a45f5b0d6a4b88d808dde4a1554a3be54e480cb0c80e569216a"},"schema_version":"1.0","source":{"id":"1306.4287","kind":"arxiv","version":1}},"canonical_sha256":"93e4b23f35cf9826dfe3cc568d6bf481e748d3a5cf75cdcb32387f341713c412","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93e4b23f35cf9826dfe3cc568d6bf481e748d3a5cf75cdcb32387f341713c412","first_computed_at":"2026-05-18T03:20:36.549533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:36.549533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3B1+C9M0kVAYzKpwP4+vxB4Lt10NC2fp4pakxC7n9Hho6HXfFyPTM0a7+VJabQjLGVGUCejnq2NE21gpGmA7Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:36.550337Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.4287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6acb9e38a2a5683f04a600ab2d371654c9399d97fab0f9a670e413e6b8f74a09","sha256:c2c9f81783451b25db1585c90fc2af551a3bbbc53d77f16988b08ff29c70ac39"],"state_sha256":"ef19140232ad21251220c15acd9ad962983ed5787d1859b10a39f40b27a2d567"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uLrZdLaPqNxIz7MQVFZDVDQFNIELCghEwjne5IJxww7t4DxVZAYHMj0iGGrAVCJXBm6AzswESUxrZPPCzim/Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T18:42:25.123428Z","bundle_sha256":"049737a197f6117eb3e4d6afaaf6062186027f5d800a0a1d176c770afa1b97f3"}}