{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:MBT62JNDK7PXIN75L24ELE7BNP","short_pith_number":"pith:MBT62JND","canonical_record":{"source":{"id":"0811.1067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2008-11-07T01:23:09Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"53d4603b05427a5611581fb52bae4b9ec702a44c1ee248b4da7706f12f9dee61","abstract_canon_sha256":"5fc388bf72f0045e173afb1490da421a8099c861319bc2bcf99007b47fceb9a8"},"schema_version":"1.0"},"canonical_sha256":"6067ed25a357df7437fd5eb84593e16bcae7c00f06d6af97b8560898c861803c","source":{"kind":"arxiv","id":"0811.1067","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.1067","created_at":"2026-07-04T15:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"0811.1067v2","created_at":"2026-07-04T15:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.1067","created_at":"2026-07-04T15:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"MBT62JNDK7PX","created_at":"2026-07-04T15:47:32Z"},{"alias_kind":"pith_short_16","alias_value":"MBT62JNDK7PXIN75","created_at":"2026-07-04T15:47:32Z"},{"alias_kind":"pith_short_8","alias_value":"MBT62JND","created_at":"2026-07-04T15:47:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:MBT62JNDK7PXIN75L24ELE7BNP","target":"record","payload":{"canonical_record":{"source":{"id":"0811.1067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2008-11-07T01:23:09Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"53d4603b05427a5611581fb52bae4b9ec702a44c1ee248b4da7706f12f9dee61","abstract_canon_sha256":"5fc388bf72f0045e173afb1490da421a8099c861319bc2bcf99007b47fceb9a8"},"schema_version":"1.0"},"canonical_sha256":"6067ed25a357df7437fd5eb84593e16bcae7c00f06d6af97b8560898c861803c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:47:32.195332Z","signature_b64":"h10Jn7ota3y8/+5I8Q5mGjWtM/IFKEX55FqjTH/oAU1DoNJWorv/O0aF/jCIAiMb/CsoyJv3obrjasY7+nftDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6067ed25a357df7437fd5eb84593e16bcae7c00f06d6af97b8560898c861803c","last_reissued_at":"2026-07-04T15:47:32.194948Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:47:32.194948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0811.1067","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":"2026-07-04T15:47:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9mmG1k/ddob2jJczdBjB91hYJWjgu70Y6IbJiqMKTICKFrqS6pvZl6J/dc77XZyYwTc2ObdQTLksQnrrqQGxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T12:29:44.569522Z"},"content_sha256":"e3dd91eac153ed3b79e7fb9947589666f5e7cab03cf5ac6f3d2c92f5dff83c84","schema_version":"1.0","event_id":"sha256:e3dd91eac153ed3b79e7fb9947589666f5e7cab03cf5ac6f3d2c92f5dff83c84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:MBT62JNDK7PXIN75L24ELE7BNP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical ranking and combinatorial Hodge theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"stat.ML","authors_text":"Lek-Heng Lim, Xiaoye Jiang, Yinyu Ye, Yuan Yao","submitted_at":"2008-11-07T01:23:09Z","abstract_excerpt":"We propose a number of techniques for obtaining a global ranking from data that may be incomplete and imbalanced -- characteristics almost universal to modern datasets coming from e-commerce and internet applications. We are primarily interested in score or rating-based cardinal data. From raw ranking data, we construct pairwise rankings, represented as edge flows on an appropriate graph. Our statistical ranking method uses the graph Helmholtzian, the graph theoretic analogue of the Helmholtz operator or vector Laplacian, in much the same way the graph Laplacian is an analogue of the Laplace o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1067","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0811.1067/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:47:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VsGHyVWIbu1G22GTC3GDeku9P8SXfIt+RuGoPklJmh0C0F7+KSV7hGHoW8Nao5FwF1rASEuRVRa/uo1vFW4YDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T12:29:44.571694Z"},"content_sha256":"87f8b14fe515cf4880480b3fab7c767a6d5c9d5147c1ce07cd6b72bd57988684","schema_version":"1.0","event_id":"sha256:87f8b14fe515cf4880480b3fab7c767a6d5c9d5147c1ce07cd6b72bd57988684"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MBT62JNDK7PXIN75L24ELE7BNP/bundle.json","state_url":"https://pith.science/pith/MBT62JNDK7PXIN75L24ELE7BNP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MBT62JNDK7PXIN75L24ELE7BNP/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":"2026-08-17T12:29:44Z","links":{"resolver":"https://pith.science/pith/MBT62JNDK7PXIN75L24ELE7BNP","bundle":"https://pith.science/pith/MBT62JNDK7PXIN75L24ELE7BNP/bundle.json","state":"https://pith.science/pith/MBT62JNDK7PXIN75L24ELE7BNP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MBT62JNDK7PXIN75L24ELE7BNP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:MBT62JNDK7PXIN75L24ELE7BNP","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":"5fc388bf72f0045e173afb1490da421a8099c861319bc2bcf99007b47fceb9a8","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2008-11-07T01:23:09Z","title_canon_sha256":"53d4603b05427a5611581fb52bae4b9ec702a44c1ee248b4da7706f12f9dee61"},"schema_version":"1.0","source":{"id":"0811.1067","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.1067","created_at":"2026-07-04T15:47:32Z"},{"alias_kind":"arxiv_version","alias_value":"0811.1067v2","created_at":"2026-07-04T15:47:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.1067","created_at":"2026-07-04T15:47:32Z"},{"alias_kind":"pith_short_12","alias_value":"MBT62JNDK7PX","created_at":"2026-07-04T15:47:32Z"},{"alias_kind":"pith_short_16","alias_value":"MBT62JNDK7PXIN75","created_at":"2026-07-04T15:47:32Z"},{"alias_kind":"pith_short_8","alias_value":"MBT62JND","created_at":"2026-07-04T15:47:32Z"}],"graph_snapshots":[{"event_id":"sha256:87f8b14fe515cf4880480b3fab7c767a6d5c9d5147c1ce07cd6b72bd57988684","target":"graph","created_at":"2026-07-04T15:47:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0811.1067/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a number of techniques for obtaining a global ranking from data that may be incomplete and imbalanced -- characteristics almost universal to modern datasets coming from e-commerce and internet applications. We are primarily interested in score or rating-based cardinal data. From raw ranking data, we construct pairwise rankings, represented as edge flows on an appropriate graph. Our statistical ranking method uses the graph Helmholtzian, the graph theoretic analogue of the Helmholtz operator or vector Laplacian, in much the same way the graph Laplacian is an analogue of the Laplace o","authors_text":"Lek-Heng Lim, Xiaoye Jiang, Yinyu Ye, Yuan Yao","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2008-11-07T01:23:09Z","title":"Statistical ranking and combinatorial Hodge theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1067","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:e3dd91eac153ed3b79e7fb9947589666f5e7cab03cf5ac6f3d2c92f5dff83c84","target":"record","created_at":"2026-07-04T15:47:32Z","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":"5fc388bf72f0045e173afb1490da421a8099c861319bc2bcf99007b47fceb9a8","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2008-11-07T01:23:09Z","title_canon_sha256":"53d4603b05427a5611581fb52bae4b9ec702a44c1ee248b4da7706f12f9dee61"},"schema_version":"1.0","source":{"id":"0811.1067","kind":"arxiv","version":2}},"canonical_sha256":"6067ed25a357df7437fd5eb84593e16bcae7c00f06d6af97b8560898c861803c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6067ed25a357df7437fd5eb84593e16bcae7c00f06d6af97b8560898c861803c","first_computed_at":"2026-07-04T15:47:32.194948Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:47:32.194948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h10Jn7ota3y8/+5I8Q5mGjWtM/IFKEX55FqjTH/oAU1DoNJWorv/O0aF/jCIAiMb/CsoyJv3obrjasY7+nftDA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:47:32.195332Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.1067","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3dd91eac153ed3b79e7fb9947589666f5e7cab03cf5ac6f3d2c92f5dff83c84","sha256:87f8b14fe515cf4880480b3fab7c767a6d5c9d5147c1ce07cd6b72bd57988684"],"state_sha256":"334bfd05accb2b17e42969be2739434b51ec0c1659990379595a7c57cb9a3dfa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SZnxno3+3WIFP81alG17oi0WgqZt78IhykSCFwgmXl+mYHYzP5DBPht7HKadN5/qZDWFtAmVsTwc6lXQYmdSBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T12:29:44.585157Z","bundle_sha256":"3bc86d76b4d3b4673519c077f150ac5e7187d2469cca5a7414b0a9426958331f"}}