{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:Q4OMQ4VCGVA4JOGNKHD6DV7NIB","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":"2eea4f1c8e0a46df185c4e8c770cf41dd9eaccaceee30205fa11856baeed8852","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-11-19T19:02:58Z","title_canon_sha256":"7ff8a64a9ebd34cbbdcc364fef629daba1d283b4b58fa9fc547c02ab3a0ac8de"},"schema_version":"1.0","source":{"id":"2011.10067","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.10067","created_at":"2026-07-05T09:32:01Z"},{"alias_kind":"arxiv_version","alias_value":"2011.10067v2","created_at":"2026-07-05T09:32:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.10067","created_at":"2026-07-05T09:32:01Z"},{"alias_kind":"pith_short_12","alias_value":"Q4OMQ4VCGVA4","created_at":"2026-07-05T09:32:01Z"},{"alias_kind":"pith_short_16","alias_value":"Q4OMQ4VCGVA4JOGN","created_at":"2026-07-05T09:32:01Z"},{"alias_kind":"pith_short_8","alias_value":"Q4OMQ4VC","created_at":"2026-07-05T09:32:01Z"}],"graph_snapshots":[{"event_id":"sha256:46bb294912ef28604ce0988884076cd1f449117b54ada55f03038e4a4aaa5b0b","target":"graph","created_at":"2026-07-05T09:32:01Z","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/2011.10067/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We settle a version of the conjecture about intransitive dice posed by Conrey, Gabbard, Grant, Liu and Morrison in 2016 and Polymath in 2017. We consider generalized dice with $n$ faces and we say that a die $A$ beats $B$ if a random face of $A$ is more likely to show a higher number than a random face of $B$. We study random dice with faces drawn iid from the uniform distribution on $[0,1]$ and conditioned on the sum of the faces equal to $n/2$. Considering the \"beats\" relation for three such random dice, Polymath showed that each of eight possible tournaments between them is asymptotically e","authors_text":"Elisabetta Cornacchia, Jan H\\k{a}z{\\l}a","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-11-19T19:02:58Z","title":"Intransitive dice tournament is not quasirandom"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.10067","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":"sha256:0038aa112f418211bd031df97d9e973bfae184d318dd87a954a1a996ec7c1f4c","target":"record","created_at":"2026-07-05T09:32:01Z","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":"2eea4f1c8e0a46df185c4e8c770cf41dd9eaccaceee30205fa11856baeed8852","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-11-19T19:02:58Z","title_canon_sha256":"7ff8a64a9ebd34cbbdcc364fef629daba1d283b4b58fa9fc547c02ab3a0ac8de"},"schema_version":"1.0","source":{"id":"2011.10067","kind":"arxiv","version":2}},"canonical_sha256":"871cc872a23541c4b8cd51c7e1d7ed407f1591d64b5f222ef7fec5b5578a1fb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"871cc872a23541c4b8cd51c7e1d7ed407f1591d64b5f222ef7fec5b5578a1fb2","first_computed_at":"2026-07-05T09:32:01.665364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:32:01.665364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JPJTW2jksDmhHSNlZvtQIYBdNSQ9AOBLFIJlJ+QHZTP0CnmlnBAxCL/M4pBZR8qYagpMRXs+6xUPN85r0l4uBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:32:01.665765Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.10067","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0038aa112f418211bd031df97d9e973bfae184d318dd87a954a1a996ec7c1f4c","sha256:46bb294912ef28604ce0988884076cd1f449117b54ada55f03038e4a4aaa5b0b"],"state_sha256":"d2736b5d7755b1b628603c9e17318845036fe33cbca526d9f140f55768ff97b5"}