{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:CASRRZISVPQGQSO3PVU2A4JPEV","short_pith_number":"pith:CASRRZIS","schema_version":"1.0","canonical_sha256":"102518e512abe06849db7d69a0712f255633be62af4dc3eb4d560199b7ac7534","source":{"kind":"arxiv","id":"2406.20049","version":2},"attestation_state":"computed","paper":{"title":"On cases where Litt's game is fair","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Anne-Laure Basdevant, Arvind Singh, Edouard Maurel-Segala, Olivier H\\'enard","submitted_at":"2024-06-28T17:02:49Z","abstract_excerpt":"A fair coin is flipped $n$ times, and two finite sequences of heads and tails (words) $A$ and $B$ of the same length are given. Each time the word $A$ appears in the sequence of coin flips, Alice gets a point, and each time the word $B$ appears, Bob gets a point. Who is more likely to win? This puzzle is a slight extension of Litt's game that recently set Twitter abuzz. We show that Litt's game is fair for any value of $n$ and any two words that have the same auto-correlation structure by building up a bijection that exchanges Bob and Alice scores; the fact that the inter-correlation does not "},"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":"2406.20049","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-06-28T17:02:49Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"d7e06fd324ba1f289b6a9bf6f4ed2495c022dddc90864bcf8ea086763d6293f9","abstract_canon_sha256":"a455ffb8332358eb8e6c13f07f93eb9019f5f062bc736a8249f69a0141510b43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:56:36.439237Z","signature_b64":"rbBJDUQYv10X6bZGL794AmQE8KjJh5nWK7A2W9pDVMOTuWgr2et88EIYB1W6X+O+AGwBuRAwFx2zRinQuUgYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"102518e512abe06849db7d69a0712f255633be62af4dc3eb4d560199b7ac7534","last_reissued_at":"2026-07-05T09:56:36.438676Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:56:36.438676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On cases where Litt's game is fair","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Anne-Laure Basdevant, Arvind Singh, Edouard Maurel-Segala, Olivier H\\'enard","submitted_at":"2024-06-28T17:02:49Z","abstract_excerpt":"A fair coin is flipped $n$ times, and two finite sequences of heads and tails (words) $A$ and $B$ of the same length are given. Each time the word $A$ appears in the sequence of coin flips, Alice gets a point, and each time the word $B$ appears, Bob gets a point. Who is more likely to win? This puzzle is a slight extension of Litt's game that recently set Twitter abuzz. We show that Litt's game is fair for any value of $n$ and any two words that have the same auto-correlation structure by building up a bijection that exchanges Bob and Alice scores; the fact that the inter-correlation does not "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.20049","kind":"arxiv","version":2},"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/2406.20049/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":"2406.20049","created_at":"2026-07-05T09:56:36.438742+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.20049v2","created_at":"2026-07-05T09:56:36.438742+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.20049","created_at":"2026-07-05T09:56:36.438742+00:00"},{"alias_kind":"pith_short_12","alias_value":"CASRRZISVPQG","created_at":"2026-07-05T09:56:36.438742+00:00"},{"alias_kind":"pith_short_16","alias_value":"CASRRZISVPQGQSO3","created_at":"2026-07-05T09:56:36.438742+00:00"},{"alias_kind":"pith_short_8","alias_value":"CASRRZIS","created_at":"2026-07-05T09:56:36.438742+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.07837","citing_title":"On Two Combinatorial Inequalities That Explain the Blimpy Shape of Heady-s and Taily-s Bit Strings","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CASRRZISVPQGQSO3PVU2A4JPEV","json":"https://pith.science/pith/CASRRZISVPQGQSO3PVU2A4JPEV.json","graph_json":"https://pith.science/api/pith-number/CASRRZISVPQGQSO3PVU2A4JPEV/graph.json","events_json":"https://pith.science/api/pith-number/CASRRZISVPQGQSO3PVU2A4JPEV/events.json","paper":"https://pith.science/paper/CASRRZIS"},"agent_actions":{"view_html":"https://pith.science/pith/CASRRZISVPQGQSO3PVU2A4JPEV","download_json":"https://pith.science/pith/CASRRZISVPQGQSO3PVU2A4JPEV.json","view_paper":"https://pith.science/paper/CASRRZIS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.20049&json=true","fetch_graph":"https://pith.science/api/pith-number/CASRRZISVPQGQSO3PVU2A4JPEV/graph.json","fetch_events":"https://pith.science/api/pith-number/CASRRZISVPQGQSO3PVU2A4JPEV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CASRRZISVPQGQSO3PVU2A4JPEV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CASRRZISVPQGQSO3PVU2A4JPEV/action/storage_attestation","attest_author":"https://pith.science/pith/CASRRZISVPQGQSO3PVU2A4JPEV/action/author_attestation","sign_citation":"https://pith.science/pith/CASRRZISVPQGQSO3PVU2A4JPEV/action/citation_signature","submit_replication":"https://pith.science/pith/CASRRZISVPQGQSO3PVU2A4JPEV/action/replication_record"}},"created_at":"2026-07-05T09:56:36.438742+00:00","updated_at":"2026-07-05T09:56:36.438742+00:00"}