{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2IWJN4EBX43SWB4QO3ZIUP5WOV","short_pith_number":"pith:2IWJN4EB","canonical_record":{"source":{"id":"1509.03016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-09-10T05:31:46Z","cross_cats_sorted":["cs.DB"],"title_canon_sha256":"c10379063782824cac4fb52790c47598978e4a3bc9d67fed7770ab26033ee487","abstract_canon_sha256":"27d030a63fb8fcb4daedca7d74e940bb8a652c9bde3dbfa5e594ec2272a086f1"},"schema_version":"1.0"},"canonical_sha256":"d22c96f081bf372b079076f28a3fb6757b0324c88ece9fc08afb2e20eec99a46","source":{"kind":"arxiv","id":"1509.03016","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03016","created_at":"2026-05-18T01:33:25Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03016v1","created_at":"2026-05-18T01:33:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03016","created_at":"2026-05-18T01:33:25Z"},{"alias_kind":"pith_short_12","alias_value":"2IWJN4EBX43S","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2IWJN4EBX43SWB4Q","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2IWJN4EB","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2IWJN4EBX43SWB4QO3ZIUP5WOV","target":"record","payload":{"canonical_record":{"source":{"id":"1509.03016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-09-10T05:31:46Z","cross_cats_sorted":["cs.DB"],"title_canon_sha256":"c10379063782824cac4fb52790c47598978e4a3bc9d67fed7770ab26033ee487","abstract_canon_sha256":"27d030a63fb8fcb4daedca7d74e940bb8a652c9bde3dbfa5e594ec2272a086f1"},"schema_version":"1.0"},"canonical_sha256":"d22c96f081bf372b079076f28a3fb6757b0324c88ece9fc08afb2e20eec99a46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:25.777158Z","signature_b64":"Fg8qGp9L1v9CUGWn9UBC90Y2RFlxhHCe1n5EDN4e5GloJiXJhvVPsCwC4Ubc0XRuV6+pf+hDlO/p8cq0eyycDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d22c96f081bf372b079076f28a3fb6757b0324c88ece9fc08afb2e20eec99a46","last_reissued_at":"2026-05-18T01:33:25.776390Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:25.776390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.03016","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":"2026-05-18T01:33:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xSrmelGPZvIuXJlUtSGHEW7fh/zR3rkcuVsgkqVDKJrBORj1P0gJ2LTVfAHLMc3GlEc+4ZDKoLwr6BeO6OCvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T13:01:32.007965Z"},"content_sha256":"e2733546d885ee865f5567d200588decca0ed5366b4b03ece7c8f61b3b520fc8","schema_version":"1.0","event_id":"sha256:e2733546d885ee865f5567d200588decca0ed5366b4b03ece7c8f61b3b520fc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2IWJN4EBX43SWB4QO3ZIUP5WOV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-Correlation and Maximum Independence in Finite Relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DB"],"primary_cat":"cs.DM","authors_text":"Bulgaria), Dilian Gurov (KTH Royal Institute of Technology, Minko Markov (St. Kliment Ohridski University of Sofia, Sofia, Stockholm, Sweden)","submitted_at":"2015-09-10T05:31:46Z","abstract_excerpt":"We consider relations with no order on their attributes as in Database Theory.  An independent partition of the set of attributes S of a finite relation R is any partition X of S such that the join of the projections of R over the elements of X yields R. Identifying independent partitions has many applications and corresponds conceptually to revealing orthogonality between sets of dimensions in multidimensional point spaces. A subset of S is termed self-correlated if there is a value of each of its attributes such that no tuple of R contains all those values.  This paper uncovers a connection "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03016","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":"2026-05-18T01:33:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OsGLq1hf7phzMDp6mx308A0bQg7T4qz/6HYkc0Hh5KzebGjXoRXQeaVy3dbCoYSD6bWcLberHYyR+IB5DsllBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T13:01:32.008351Z"},"content_sha256":"3a76d1656deb5806b965dffd62e52cfc1486fe85e1398f4f6838089783d6e890","schema_version":"1.0","event_id":"sha256:3a76d1656deb5806b965dffd62e52cfc1486fe85e1398f4f6838089783d6e890"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2IWJN4EBX43SWB4QO3ZIUP5WOV/bundle.json","state_url":"https://pith.science/pith/2IWJN4EBX43SWB4QO3ZIUP5WOV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2IWJN4EBX43SWB4QO3ZIUP5WOV/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":"2026-05-19T13:01:32Z","links":{"resolver":"https://pith.science/pith/2IWJN4EBX43SWB4QO3ZIUP5WOV","bundle":"https://pith.science/pith/2IWJN4EBX43SWB4QO3ZIUP5WOV/bundle.json","state":"https://pith.science/pith/2IWJN4EBX43SWB4QO3ZIUP5WOV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2IWJN4EBX43SWB4QO3ZIUP5WOV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2IWJN4EBX43SWB4QO3ZIUP5WOV","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":"27d030a63fb8fcb4daedca7d74e940bb8a652c9bde3dbfa5e594ec2272a086f1","cross_cats_sorted":["cs.DB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-09-10T05:31:46Z","title_canon_sha256":"c10379063782824cac4fb52790c47598978e4a3bc9d67fed7770ab26033ee487"},"schema_version":"1.0","source":{"id":"1509.03016","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03016","created_at":"2026-05-18T01:33:25Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03016v1","created_at":"2026-05-18T01:33:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03016","created_at":"2026-05-18T01:33:25Z"},{"alias_kind":"pith_short_12","alias_value":"2IWJN4EBX43S","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"2IWJN4EBX43SWB4Q","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"2IWJN4EB","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:3a76d1656deb5806b965dffd62e52cfc1486fe85e1398f4f6838089783d6e890","target":"graph","created_at":"2026-05-18T01:33:25Z","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":"We consider relations with no order on their attributes as in Database Theory.  An independent partition of the set of attributes S of a finite relation R is any partition X of S such that the join of the projections of R over the elements of X yields R. Identifying independent partitions has many applications and corresponds conceptually to revealing orthogonality between sets of dimensions in multidimensional point spaces. A subset of S is termed self-correlated if there is a value of each of its attributes such that no tuple of R contains all those values.  This paper uncovers a connection ","authors_text":"Bulgaria), Dilian Gurov (KTH Royal Institute of Technology, Minko Markov (St. Kliment Ohridski University of Sofia, Sofia, Stockholm, Sweden)","cross_cats":["cs.DB"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-09-10T05:31:46Z","title":"Self-Correlation and Maximum Independence in Finite Relations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03016","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:e2733546d885ee865f5567d200588decca0ed5366b4b03ece7c8f61b3b520fc8","target":"record","created_at":"2026-05-18T01:33:25Z","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":"27d030a63fb8fcb4daedca7d74e940bb8a652c9bde3dbfa5e594ec2272a086f1","cross_cats_sorted":["cs.DB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-09-10T05:31:46Z","title_canon_sha256":"c10379063782824cac4fb52790c47598978e4a3bc9d67fed7770ab26033ee487"},"schema_version":"1.0","source":{"id":"1509.03016","kind":"arxiv","version":1}},"canonical_sha256":"d22c96f081bf372b079076f28a3fb6757b0324c88ece9fc08afb2e20eec99a46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d22c96f081bf372b079076f28a3fb6757b0324c88ece9fc08afb2e20eec99a46","first_computed_at":"2026-05-18T01:33:25.776390Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:25.776390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fg8qGp9L1v9CUGWn9UBC90Y2RFlxhHCe1n5EDN4e5GloJiXJhvVPsCwC4Ubc0XRuV6+pf+hDlO/p8cq0eyycDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:25.777158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03016","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2733546d885ee865f5567d200588decca0ed5366b4b03ece7c8f61b3b520fc8","sha256:3a76d1656deb5806b965dffd62e52cfc1486fe85e1398f4f6838089783d6e890"],"state_sha256":"96770c93df64d0e5ab6927b92f92db61a957d060ea95ee6c2d4da8973f21c1da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D1Df6qG/5zRZ+mpHzB4LfSqSNLFEAwjT3m+8M8A3sSRXXfxkkQUDlSY/jGAzIpdoNeLLtS673Cqa+Z46lsyZBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T13:01:32.010785Z","bundle_sha256":"a98d21a04d719375a281dbf297d15c9164e41c93152fb1b2d3d105e072c0de15"}}