{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:HRT7YKFCI2622XLBMSUO6G4VO7","short_pith_number":"pith:HRT7YKFC","schema_version":"1.0","canonical_sha256":"3c67fc28a246bdad5d6164a8ef1b9577e7f6d46c201d5d560385a413edf07a91","source":{"kind":"arxiv","id":"2501.07437","version":3},"attestation_state":"computed","paper":{"title":"Pairwise Comparisons without Stochastic Transitivity: Model, Theory and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Sze Ming Lee, Yunxiao Chen","submitted_at":"2025-01-13T16:05:41Z","abstract_excerpt":"Most statistical models for pairwise comparisons, including the Bradley-Terry (BT) and Thurstone models and many extensions, make a relatively strong assumption of stochastic transitivity. This assumption imposes the existence of an unobserved global ranking among all the players/teams/items and monotone constraints on the comparison probabilities implied by the global ranking. However, the stochastic transitivity assumption does not hold in many real-world scenarios of pairwise comparisons, especially games involving multiple skills or strategies. As a result, models relying on this assumptio"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2501.07437","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2025-01-13T16:05:41Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"7f05fb17a5b982aff32b33fb770dce80be2469a6b70c6d2aa738cb53f65c7ab0","abstract_canon_sha256":"08ee1878637c71b48eeca41d5148f8e825889341d72b5e4a806a3cbcd7dd5b33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:18:03.687024Z","signature_b64":"XnuHFhBtn2QuVOJEuW8/h/K9bMV6UKIEPhn+Gdqoi0DtU0GN4iFtstiK1J0jsB8TdhDGqDI+RH/mCelRo7FUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c67fc28a246bdad5d6164a8ef1b9577e7f6d46c201d5d560385a413edf07a91","last_reissued_at":"2026-06-30T02:18:03.686353Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:18:03.686353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pairwise Comparisons without Stochastic Transitivity: Model, Theory and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Sze Ming Lee, Yunxiao Chen","submitted_at":"2025-01-13T16:05:41Z","abstract_excerpt":"Most statistical models for pairwise comparisons, including the Bradley-Terry (BT) and Thurstone models and many extensions, make a relatively strong assumption of stochastic transitivity. This assumption imposes the existence of an unobserved global ranking among all the players/teams/items and monotone constraints on the comparison probabilities implied by the global ranking. However, the stochastic transitivity assumption does not hold in many real-world scenarios of pairwise comparisons, especially games involving multiple skills or strategies. As a result, models relying on this assumptio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.07437","kind":"arxiv","version":3},"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/2501.07437/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2501.07437","created_at":"2026-06-30T02:18:03.686442+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.07437v3","created_at":"2026-06-30T02:18:03.686442+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.07437","created_at":"2026-06-30T02:18:03.686442+00:00"},{"alias_kind":"pith_short_12","alias_value":"HRT7YKFCI262","created_at":"2026-06-30T02:18:03.686442+00:00"},{"alias_kind":"pith_short_16","alias_value":"HRT7YKFCI2622XLB","created_at":"2026-06-30T02:18:03.686442+00:00"},{"alias_kind":"pith_short_8","alias_value":"HRT7YKFC","created_at":"2026-06-30T02:18:03.686442+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.22148","citing_title":"Ordering Stochastic Block Models via prior transitivity","ref_index":93,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HRT7YKFCI2622XLBMSUO6G4VO7","json":"https://pith.science/pith/HRT7YKFCI2622XLBMSUO6G4VO7.json","graph_json":"https://pith.science/api/pith-number/HRT7YKFCI2622XLBMSUO6G4VO7/graph.json","events_json":"https://pith.science/api/pith-number/HRT7YKFCI2622XLBMSUO6G4VO7/events.json","paper":"https://pith.science/paper/HRT7YKFC"},"agent_actions":{"view_html":"https://pith.science/pith/HRT7YKFCI2622XLBMSUO6G4VO7","download_json":"https://pith.science/pith/HRT7YKFCI2622XLBMSUO6G4VO7.json","view_paper":"https://pith.science/paper/HRT7YKFC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.07437&json=true","fetch_graph":"https://pith.science/api/pith-number/HRT7YKFCI2622XLBMSUO6G4VO7/graph.json","fetch_events":"https://pith.science/api/pith-number/HRT7YKFCI2622XLBMSUO6G4VO7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HRT7YKFCI2622XLBMSUO6G4VO7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HRT7YKFCI2622XLBMSUO6G4VO7/action/storage_attestation","attest_author":"https://pith.science/pith/HRT7YKFCI2622XLBMSUO6G4VO7/action/author_attestation","sign_citation":"https://pith.science/pith/HRT7YKFCI2622XLBMSUO6G4VO7/action/citation_signature","submit_replication":"https://pith.science/pith/HRT7YKFCI2622XLBMSUO6G4VO7/action/replication_record"}},"created_at":"2026-06-30T02:18:03.686442+00:00","updated_at":"2026-06-30T02:18:03.686442+00:00"}