{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:54DR6FEISIWWJAYZMXIED3BV5P","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":"b25f220ea1964042efe4873a07e7830dd7097596abcee41429290aff42f4cab7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2025-06-12T23:06:42Z","title_canon_sha256":"181045a2e97eb4958d67a6075f9bf7fa8d37e3b6b7242650bacc52648d216c01"},"schema_version":"1.0","source":{"id":"2506.11354","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.11354","created_at":"2026-07-05T11:35:35Z"},{"alias_kind":"arxiv_version","alias_value":"2506.11354v2","created_at":"2026-07-05T11:35:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.11354","created_at":"2026-07-05T11:35:35Z"},{"alias_kind":"pith_short_12","alias_value":"54DR6FEISIWW","created_at":"2026-07-05T11:35:35Z"},{"alias_kind":"pith_short_16","alias_value":"54DR6FEISIWWJAYZ","created_at":"2026-07-05T11:35:35Z"},{"alias_kind":"pith_short_8","alias_value":"54DR6FEI","created_at":"2026-07-05T11:35:35Z"}],"graph_snapshots":[{"event_id":"sha256:067bd8840298607b8c63b0c132e82a2ea7aa706a44bca9d49fb59f59515eb9e7","target":"graph","created_at":"2026-07-05T11:35:35Z","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/2506.11354/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Competitor rating systems for head-to-head games are typically used to measure playing strength from game outcomes. Ratings computed from these systems are often used to select top competitors for elite events, for pairing players of similar strength in online gaming, and for players to track their own strength over time. Most implemented rating systems assume only win/loss outcomes, and treat occurrences of ties as the equivalent to half a win and half a loss. However, in games such as chess, the probability of a tie (draw) is demonstrably higher for stronger players than for weaker players, ","authors_text":"Mark E. Glickman","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2025-06-12T23:06:42Z","title":"Rating competitors in games with strength-dependent tie probabilities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.11354","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":"sha256:9244dc66344623ae73ded215f8f7d501702c91933602a047e09a11d588e26da7","target":"record","created_at":"2026-07-05T11:35:35Z","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":"b25f220ea1964042efe4873a07e7830dd7097596abcee41429290aff42f4cab7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2025-06-12T23:06:42Z","title_canon_sha256":"181045a2e97eb4958d67a6075f9bf7fa8d37e3b6b7242650bacc52648d216c01"},"schema_version":"1.0","source":{"id":"2506.11354","kind":"arxiv","version":2}},"canonical_sha256":"ef071f1488922d64831965d041ec35ebeb09c7d64f68bf93ac6cba0bce5359a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef071f1488922d64831965d041ec35ebeb09c7d64f68bf93ac6cba0bce5359a1","first_computed_at":"2026-07-05T11:35:35.433712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:35:35.433712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HO0kgUqv9h9a7qFgD+wbLR6WVcbeevc+hSPOQ6uYgpR0YTCmwxY5bOpqs9dcqNqf3OJKcO/3o2ORaTSldYgFAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:35:35.434178Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.11354","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9244dc66344623ae73ded215f8f7d501702c91933602a047e09a11d588e26da7","sha256:067bd8840298607b8c63b0c132e82a2ea7aa706a44bca9d49fb59f59515eb9e7"],"state_sha256":"017e329dff172aa6e8d2f4f3da6a6a1230112ead0db17747556536319d27fd31"}