{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZOC7466GVWNSGHN4QULWEURCRW","short_pith_number":"pith:ZOC7466G","canonical_record":{"source":{"id":"1609.05194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-16T19:45:27Z","cross_cats_sorted":[],"title_canon_sha256":"8452ffaaa641067b3671c1163b61de9ecc36806b23fe691ce4fbce03a15472fa","abstract_canon_sha256":"83e1be9706aad337a04e355728486de66e8a82549e7da360452e4141f8ffc137"},"schema_version":"1.0"},"canonical_sha256":"cb85fe7bc6ad9b231dbc85176252228d942d5b09b91ef0f9d1ac34745e630b79","source":{"kind":"arxiv","id":"1609.05194","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05194","created_at":"2026-05-18T01:04:31Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05194v1","created_at":"2026-05-18T01:04:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05194","created_at":"2026-05-18T01:04:31Z"},{"alias_kind":"pith_short_12","alias_value":"ZOC7466GVWNS","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZOC7466GVWNSGHN4","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZOC7466G","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZOC7466GVWNSGHN4QULWEURCRW","target":"record","payload":{"canonical_record":{"source":{"id":"1609.05194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-16T19:45:27Z","cross_cats_sorted":[],"title_canon_sha256":"8452ffaaa641067b3671c1163b61de9ecc36806b23fe691ce4fbce03a15472fa","abstract_canon_sha256":"83e1be9706aad337a04e355728486de66e8a82549e7da360452e4141f8ffc137"},"schema_version":"1.0"},"canonical_sha256":"cb85fe7bc6ad9b231dbc85176252228d942d5b09b91ef0f9d1ac34745e630b79","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:31.147110Z","signature_b64":"WGdxRyooDJRn1KK5m9q3WmJ43RiVVa6oNelshcyMh8xM9yfE0dPIFgkTOTdd4UWma+FV2uD7gS6g6iQH4mQqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb85fe7bc6ad9b231dbc85176252228d942d5b09b91ef0f9d1ac34745e630b79","last_reissued_at":"2026-05-18T01:04:31.146421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:31.146421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.05194","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":"2026-05-18T01:04:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vS1082FKwFVputKQf+WY1m7HvL4onXQJ0GLz+1p8SuNJyqRlhZm6b69zvo4d5q4xb4EZhW+WnnaqRWmxsYpdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T21:13:52.977785Z"},"content_sha256":"eb445af9c000111a6c965917ab6982c8c71e5ae14c9303d681f925b80cdfe78f","schema_version":"1.0","event_id":"sha256:eb445af9c000111a6c965917ab6982c8c71e5ae14c9303d681f925b80cdfe78f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZOC7466GVWNSGHN4QULWEURCRW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Bradley--Terry condition is $L_1$--testable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Agelos Georgakopoulos, Konstantinos Tyros","submitted_at":"2016-09-16T19:45:27Z","abstract_excerpt":"We provide an algorithm with constant running time that given a weighted tournament $T$, distinguishes with high probability of success between the cases that $T$ can be represented by a Bradley--Terry model, or cannot even be approximated by one. The same algorithm tests whether the corresponding Markov chain is reversible."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05194","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":"2026-05-18T01:04:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bm3mR1F5mIHIssHv5h0WyVxkIlixnXw+FOwBTZFJ24VoIatXpWA8OpIUBbD9QMQTzlQCGuBW9rgwmNSrCdhcCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T21:13:52.978120Z"},"content_sha256":"8bac743eda1d933cfb50c844017081f3907d8dd20aef8a252f8032d15858acad","schema_version":"1.0","event_id":"sha256:8bac743eda1d933cfb50c844017081f3907d8dd20aef8a252f8032d15858acad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZOC7466GVWNSGHN4QULWEURCRW/bundle.json","state_url":"https://pith.science/pith/ZOC7466GVWNSGHN4QULWEURCRW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZOC7466GVWNSGHN4QULWEURCRW/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":"2026-07-04T21:13:52Z","links":{"resolver":"https://pith.science/pith/ZOC7466GVWNSGHN4QULWEURCRW","bundle":"https://pith.science/pith/ZOC7466GVWNSGHN4QULWEURCRW/bundle.json","state":"https://pith.science/pith/ZOC7466GVWNSGHN4QULWEURCRW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZOC7466GVWNSGHN4QULWEURCRW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZOC7466GVWNSGHN4QULWEURCRW","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":"83e1be9706aad337a04e355728486de66e8a82549e7da360452e4141f8ffc137","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-16T19:45:27Z","title_canon_sha256":"8452ffaaa641067b3671c1163b61de9ecc36806b23fe691ce4fbce03a15472fa"},"schema_version":"1.0","source":{"id":"1609.05194","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05194","created_at":"2026-05-18T01:04:31Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05194v1","created_at":"2026-05-18T01:04:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05194","created_at":"2026-05-18T01:04:31Z"},{"alias_kind":"pith_short_12","alias_value":"ZOC7466GVWNS","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZOC7466GVWNSGHN4","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZOC7466G","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:8bac743eda1d933cfb50c844017081f3907d8dd20aef8a252f8032d15858acad","target":"graph","created_at":"2026-05-18T01:04:31Z","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 provide an algorithm with constant running time that given a weighted tournament $T$, distinguishes with high probability of success between the cases that $T$ can be represented by a Bradley--Terry model, or cannot even be approximated by one. The same algorithm tests whether the corresponding Markov chain is reversible.","authors_text":"Agelos Georgakopoulos, Konstantinos Tyros","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-16T19:45:27Z","title":"The Bradley--Terry condition is $L_1$--testable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05194","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:eb445af9c000111a6c965917ab6982c8c71e5ae14c9303d681f925b80cdfe78f","target":"record","created_at":"2026-05-18T01:04:31Z","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":"83e1be9706aad337a04e355728486de66e8a82549e7da360452e4141f8ffc137","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-16T19:45:27Z","title_canon_sha256":"8452ffaaa641067b3671c1163b61de9ecc36806b23fe691ce4fbce03a15472fa"},"schema_version":"1.0","source":{"id":"1609.05194","kind":"arxiv","version":1}},"canonical_sha256":"cb85fe7bc6ad9b231dbc85176252228d942d5b09b91ef0f9d1ac34745e630b79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb85fe7bc6ad9b231dbc85176252228d942d5b09b91ef0f9d1ac34745e630b79","first_computed_at":"2026-05-18T01:04:31.146421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:31.146421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WGdxRyooDJRn1KK5m9q3WmJ43RiVVa6oNelshcyMh8xM9yfE0dPIFgkTOTdd4UWma+FV2uD7gS6g6iQH4mQqBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:31.147110Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.05194","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb445af9c000111a6c965917ab6982c8c71e5ae14c9303d681f925b80cdfe78f","sha256:8bac743eda1d933cfb50c844017081f3907d8dd20aef8a252f8032d15858acad"],"state_sha256":"0987731c3be53e5f99b20201f4121418d09a46c44fdd345625484285d898dbd5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nDMHtLH3pX2kxV3XkAOKUlg8J3Xkp4c0D1bZ0q8uof9oymZIaMLaDvwo1Mbpn6KdCF7fXnD+SZSSLHJN8ZZ4DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T21:13:52.979931Z","bundle_sha256":"3a3e3520f04478a51ca1ff6c127fd6ef0d198a47f569584bed5c5f9550939dee"}}