{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JRTXNSPIGV3GWKQS4Y3WBRAQDZ","short_pith_number":"pith:JRTXNSPI","canonical_record":{"source":{"id":"1508.06778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-08-27T09:42:42Z","cross_cats_sorted":[],"title_canon_sha256":"623a5bbc255a059c23bd0d0655dd1666a718f1f4a7f6b968cb441e5e1ed24a51","abstract_canon_sha256":"ee35961129160eeb766681e5db81d2791eebae02e7a944f50a5ae0c446d17128"},"schema_version":"1.0"},"canonical_sha256":"4c6776c9e835766b2a12e63760c4101e459bc37047161fdd71e6aa95c3898442","source":{"kind":"arxiv","id":"1508.06778","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06778","created_at":"2026-05-17T23:42:59Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06778v1","created_at":"2026-05-17T23:42:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06778","created_at":"2026-05-17T23:42:59Z"},{"alias_kind":"pith_short_12","alias_value":"JRTXNSPIGV3G","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JRTXNSPIGV3GWKQS","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JRTXNSPI","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JRTXNSPIGV3GWKQS4Y3WBRAQDZ","target":"record","payload":{"canonical_record":{"source":{"id":"1508.06778","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-08-27T09:42:42Z","cross_cats_sorted":[],"title_canon_sha256":"623a5bbc255a059c23bd0d0655dd1666a718f1f4a7f6b968cb441e5e1ed24a51","abstract_canon_sha256":"ee35961129160eeb766681e5db81d2791eebae02e7a944f50a5ae0c446d17128"},"schema_version":"1.0"},"canonical_sha256":"4c6776c9e835766b2a12e63760c4101e459bc37047161fdd71e6aa95c3898442","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:59.359656Z","signature_b64":"dKRhDpYOFF+cTE15PNTmcAC9ux8rFCnryUwZcniNuh7avEAU4sX6a64tUwr8702dLIjBVBUHXRF4LS6I+7q+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4c6776c9e835766b2a12e63760c4101e459bc37047161fdd71e6aa95c3898442","last_reissued_at":"2026-05-17T23:42:59.359194Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:59.359194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.06778","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":"2026-05-17T23:42:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XJULUJcO6mQ/HInShjolMD+Q3Hj1ESl2xFQl0XA4uD80WFGWzeC7Yd1MbQEXBxu2wa1aY94sqT6ClypdV1KdAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:13:39.000472Z"},"content_sha256":"af403e88a6315cc6a6c3ba25dc609bdc9ee88d8819916f81100199cd0f2c732d","schema_version":"1.0","event_id":"sha256:af403e88a6315cc6a6c3ba25dc609bdc9ee88d8819916f81100199cd0f2c732d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JRTXNSPIGV3GWKQS4Y3WBRAQDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A graph interpretation of the least squares ranking method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"L\\'aszl\\'o Csat\\'o","submitted_at":"2015-08-27T09:42:42Z","abstract_excerpt":"The paper aims at analyzing the least squares ranking method for generalized tournaments with possible missing and multiple paired comparisons. The bilateral relationships may reflect the outcomes of a sport competition, product comparisons, or evaluation of political candidates and policies. It is shown that the rating vector can be obtained as a limit point of an iterative process based on the scores in almost all cases. The calculation is interpreted on an undirected graph with loops attached to some nodes, revealing that the procedure takes into account not only the given object's results "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06778","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":"2026-05-17T23:42:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/n8YX47uI0h6XatUinfv7e9MhHpHa3QSrx4G8G4SST5W2EJpcei3uTTpvs2GlynZ4SGhS4i1S0kLgoPeQZn5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:13:39.000826Z"},"content_sha256":"4afdb5cf64652a312c03536aefeb48b9c31e77e110c5c7f14aec3ed2fb5566b3","schema_version":"1.0","event_id":"sha256:4afdb5cf64652a312c03536aefeb48b9c31e77e110c5c7f14aec3ed2fb5566b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JRTXNSPIGV3GWKQS4Y3WBRAQDZ/bundle.json","state_url":"https://pith.science/pith/JRTXNSPIGV3GWKQS4Y3WBRAQDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JRTXNSPIGV3GWKQS4Y3WBRAQDZ/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":"2026-06-04T17:13:39Z","links":{"resolver":"https://pith.science/pith/JRTXNSPIGV3GWKQS4Y3WBRAQDZ","bundle":"https://pith.science/pith/JRTXNSPIGV3GWKQS4Y3WBRAQDZ/bundle.json","state":"https://pith.science/pith/JRTXNSPIGV3GWKQS4Y3WBRAQDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JRTXNSPIGV3GWKQS4Y3WBRAQDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JRTXNSPIGV3GWKQS4Y3WBRAQDZ","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":"ee35961129160eeb766681e5db81d2791eebae02e7a944f50a5ae0c446d17128","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-08-27T09:42:42Z","title_canon_sha256":"623a5bbc255a059c23bd0d0655dd1666a718f1f4a7f6b968cb441e5e1ed24a51"},"schema_version":"1.0","source":{"id":"1508.06778","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06778","created_at":"2026-05-17T23:42:59Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06778v1","created_at":"2026-05-17T23:42:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06778","created_at":"2026-05-17T23:42:59Z"},{"alias_kind":"pith_short_12","alias_value":"JRTXNSPIGV3G","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JRTXNSPIGV3GWKQS","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JRTXNSPI","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:4afdb5cf64652a312c03536aefeb48b9c31e77e110c5c7f14aec3ed2fb5566b3","target":"graph","created_at":"2026-05-17T23:42:59Z","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":"The paper aims at analyzing the least squares ranking method for generalized tournaments with possible missing and multiple paired comparisons. The bilateral relationships may reflect the outcomes of a sport competition, product comparisons, or evaluation of political candidates and policies. It is shown that the rating vector can be obtained as a limit point of an iterative process based on the scores in almost all cases. The calculation is interpreted on an undirected graph with loops attached to some nodes, revealing that the procedure takes into account not only the given object's results ","authors_text":"L\\'aszl\\'o Csat\\'o","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-08-27T09:42:42Z","title":"A graph interpretation of the least squares ranking method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06778","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:af403e88a6315cc6a6c3ba25dc609bdc9ee88d8819916f81100199cd0f2c732d","target":"record","created_at":"2026-05-17T23:42:59Z","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":"ee35961129160eeb766681e5db81d2791eebae02e7a944f50a5ae0c446d17128","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2015-08-27T09:42:42Z","title_canon_sha256":"623a5bbc255a059c23bd0d0655dd1666a718f1f4a7f6b968cb441e5e1ed24a51"},"schema_version":"1.0","source":{"id":"1508.06778","kind":"arxiv","version":1}},"canonical_sha256":"4c6776c9e835766b2a12e63760c4101e459bc37047161fdd71e6aa95c3898442","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c6776c9e835766b2a12e63760c4101e459bc37047161fdd71e6aa95c3898442","first_computed_at":"2026-05-17T23:42:59.359194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:59.359194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dKRhDpYOFF+cTE15PNTmcAC9ux8rFCnryUwZcniNuh7avEAU4sX6a64tUwr8702dLIjBVBUHXRF4LS6I+7q+AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:59.359656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06778","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af403e88a6315cc6a6c3ba25dc609bdc9ee88d8819916f81100199cd0f2c732d","sha256:4afdb5cf64652a312c03536aefeb48b9c31e77e110c5c7f14aec3ed2fb5566b3"],"state_sha256":"206f61b3aefbd43867f94eb5c021e311babadd6bef46b6fb3ccafca2924e5def"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FN/LwRUYE1s+iKDXp1YpYer8GlO15d7kc9zMdAlCW0rgDLS5q2A20p3H+NCeCDUkyEj9yXtBrhMMOSfv75tsBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:13:39.002818Z","bundle_sha256":"c55b8fc8a6fbcac785fe9dad827af96bbc6dbe1b560e781723f7fbc6a0392c0b"}}