{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QJHU46QDCUURTAP2B4IGTP2SOX","short_pith_number":"pith:QJHU46QD","canonical_record":{"source":{"id":"1201.3602","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.DS","submitted_at":"2012-01-17T19:57:11Z","cross_cats_sorted":[],"title_canon_sha256":"0a9a4ebb306269139838fddaa82c8d9b618ffb5c3804560127f7ccf3dc830cd0","abstract_canon_sha256":"67f4ae62afbac40d7a423eaf85f07266df0cf7d2dc1aea0a05f2715f7d1947de"},"schema_version":"1.0"},"canonical_sha256":"824f4e7a0315291981fa0f1069bf5275ffee080c135537696a3ab9fbbc26932d","source":{"kind":"arxiv","id":"1201.3602","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3602","created_at":"2026-05-18T04:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3602v1","created_at":"2026-05-18T04:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3602","created_at":"2026-05-18T04:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"QJHU46QDCUUR","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QJHU46QDCUURTAP2","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QJHU46QD","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QJHU46QDCUURTAP2B4IGTP2SOX","target":"record","payload":{"canonical_record":{"source":{"id":"1201.3602","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.DS","submitted_at":"2012-01-17T19:57:11Z","cross_cats_sorted":[],"title_canon_sha256":"0a9a4ebb306269139838fddaa82c8d9b618ffb5c3804560127f7ccf3dc830cd0","abstract_canon_sha256":"67f4ae62afbac40d7a423eaf85f07266df0cf7d2dc1aea0a05f2715f7d1947de"},"schema_version":"1.0"},"canonical_sha256":"824f4e7a0315291981fa0f1069bf5275ffee080c135537696a3ab9fbbc26932d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:28.819338Z","signature_b64":"N2LAzL3XPGjWo4bL9RpCi+ZBrcckrP0N5QZ4XXVJyeuzyJaG27egqgGW9YW9eyxHRr6Uc+A9K4xqAFT3h1paAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"824f4e7a0315291981fa0f1069bf5275ffee080c135537696a3ab9fbbc26932d","last_reissued_at":"2026-05-18T04:04:28.818597Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:28.818597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.3602","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":"2026-05-18T04:04:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YT60988cNVJbvUQ0VturjQ6cXVE0ncMGFoBrIZrn3v+nbOa2zyIdPWHEGcig3eu1sHibd6szJGRSp4bJ/GVaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:37:03.508348Z"},"content_sha256":"c17fb0204bb86358212b95a5c6469b8fe14816791218f4a2fd1eb66a8719e352","schema_version":"1.0","event_id":"sha256:c17fb0204bb86358212b95a5c6469b8fe14816791218f4a2fd1eb66a8719e352"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QJHU46QDCUURTAP2B4IGTP2SOX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compact Binary Relation Representations with Rich Functionality","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Francisco Claude, Gonzalo Navarro, J\\'er\\'emy Barbay","submitted_at":"2012-01-17T19:57:11Z","abstract_excerpt":"Binary relations are an important abstraction arising in many data representation problems. The data structures proposed so far to represent them support just a few basic operations required to fit one particular application. We identify many of those operations arising in applications and generalize them into a wide set of desirable queries for a binary relation representation. We also identify reductions among those operations. We then introduce several novel binary relation representations, some simple and some quite sophisticated, that not only are space-efficient but also efficiently supp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3602","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":"2026-05-18T04:04:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Lt/KpIZ2nosemH19CImAsgP2F8aPJiWtTFkvo1DwmFx6w1Mr8oF81GArvxvIz7N8Vw11UKSEs7u8+F8WOpeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T00:37:03.509209Z"},"content_sha256":"465b14a5a3a98cda1af55da6ea68f49d4ddcf19ccfd69902c3c5321e5d2515a4","schema_version":"1.0","event_id":"sha256:465b14a5a3a98cda1af55da6ea68f49d4ddcf19ccfd69902c3c5321e5d2515a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QJHU46QDCUURTAP2B4IGTP2SOX/bundle.json","state_url":"https://pith.science/pith/QJHU46QDCUURTAP2B4IGTP2SOX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QJHU46QDCUURTAP2B4IGTP2SOX/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":"2026-06-01T00:37:03Z","links":{"resolver":"https://pith.science/pith/QJHU46QDCUURTAP2B4IGTP2SOX","bundle":"https://pith.science/pith/QJHU46QDCUURTAP2B4IGTP2SOX/bundle.json","state":"https://pith.science/pith/QJHU46QDCUURTAP2B4IGTP2SOX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QJHU46QDCUURTAP2B4IGTP2SOX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QJHU46QDCUURTAP2B4IGTP2SOX","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":"67f4ae62afbac40d7a423eaf85f07266df0cf7d2dc1aea0a05f2715f7d1947de","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.DS","submitted_at":"2012-01-17T19:57:11Z","title_canon_sha256":"0a9a4ebb306269139838fddaa82c8d9b618ffb5c3804560127f7ccf3dc830cd0"},"schema_version":"1.0","source":{"id":"1201.3602","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3602","created_at":"2026-05-18T04:04:28Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3602v1","created_at":"2026-05-18T04:04:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3602","created_at":"2026-05-18T04:04:28Z"},{"alias_kind":"pith_short_12","alias_value":"QJHU46QDCUUR","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QJHU46QDCUURTAP2","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QJHU46QD","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:465b14a5a3a98cda1af55da6ea68f49d4ddcf19ccfd69902c3c5321e5d2515a4","target":"graph","created_at":"2026-05-18T04:04:28Z","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":"Binary relations are an important abstraction arising in many data representation problems. The data structures proposed so far to represent them support just a few basic operations required to fit one particular application. We identify many of those operations arising in applications and generalize them into a wide set of desirable queries for a binary relation representation. We also identify reductions among those operations. We then introduce several novel binary relation representations, some simple and some quite sophisticated, that not only are space-efficient but also efficiently supp","authors_text":"Francisco Claude, Gonzalo Navarro, J\\'er\\'emy Barbay","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.DS","submitted_at":"2012-01-17T19:57:11Z","title":"Compact Binary Relation Representations with Rich Functionality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3602","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:c17fb0204bb86358212b95a5c6469b8fe14816791218f4a2fd1eb66a8719e352","target":"record","created_at":"2026-05-18T04:04:28Z","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":"67f4ae62afbac40d7a423eaf85f07266df0cf7d2dc1aea0a05f2715f7d1947de","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"cs.DS","submitted_at":"2012-01-17T19:57:11Z","title_canon_sha256":"0a9a4ebb306269139838fddaa82c8d9b618ffb5c3804560127f7ccf3dc830cd0"},"schema_version":"1.0","source":{"id":"1201.3602","kind":"arxiv","version":1}},"canonical_sha256":"824f4e7a0315291981fa0f1069bf5275ffee080c135537696a3ab9fbbc26932d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"824f4e7a0315291981fa0f1069bf5275ffee080c135537696a3ab9fbbc26932d","first_computed_at":"2026-05-18T04:04:28.818597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:28.818597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N2LAzL3XPGjWo4bL9RpCi+ZBrcckrP0N5QZ4XXVJyeuzyJaG27egqgGW9YW9eyxHRr6Uc+A9K4xqAFT3h1paAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:28.819338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3602","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c17fb0204bb86358212b95a5c6469b8fe14816791218f4a2fd1eb66a8719e352","sha256:465b14a5a3a98cda1af55da6ea68f49d4ddcf19ccfd69902c3c5321e5d2515a4"],"state_sha256":"6e6404fc86407a067ddf35758fbdd39c0b5ab5462430f337b0d5dd65fd56e75b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bR9OvV8qm0mtx3wFP09mixU03YMyoNkbMnfzQ1j0YIPtdjKnt94BfrAIODWqbxakJrDwscRXzyYkCkTYAvE5DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T00:37:03.514792Z","bundle_sha256":"d3ac76bcec2f1441b451c09e0d79152a7747184adf752dd929ac5bec704e813d"}}