{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HHANL365V2OFFYCXXGEC3P7JJ5","short_pith_number":"pith:HHANL365","schema_version":"1.0","canonical_sha256":"39c0d5efddae9c52e057b9882dbfe94f5a90912a6ab4c43da37959cb93351317","source":{"kind":"arxiv","id":"1806.07838","version":1},"attestation_state":"computed","paper":{"title":"Minimax functions on Galton-Watson trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"James B. Martin, Roman Stasi\\'nski","submitted_at":"2018-06-20T16:41:19Z","abstract_excerpt":"We consider the behaviour of minimax recursions defined on random trees. Such recursions give the value of a general class of two-player combinatorial games. We examine in particular the case where the tree is given by a Galton-Watson branching process, truncated at some depth $2n$, and the terminal values of the level-$2n$ nodes are drawn independently from some common distribution. The case of a regular tree was previously considered by Pearl, who showed that as $n\\to\\infty$ the value of the game converges to a constant, and by Ali Khan, Devroye and Neininger, who obtained a distributional l"},"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":"1806.07838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-20T16:41:19Z","cross_cats_sorted":[],"title_canon_sha256":"23e8123bf3039b3b0496f36e497a01eb8e3ecf7f5f11fc971ef1c026be2794ca","abstract_canon_sha256":"6a9eee49b8b776e5b80594242d33f838b621d972a605dbf895eeb6c76a6149e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:46.493349Z","signature_b64":"CkJJHIwr7Z4MSH+nDwYvYubhJvQ44eoffKntklqEYAnHZigSINfda4jhn1ToV1PJpL4lqKb8TrSXoQKavXf1Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39c0d5efddae9c52e057b9882dbfe94f5a90912a6ab4c43da37959cb93351317","last_reissued_at":"2026-05-18T00:12:46.492773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:46.492773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimax functions on Galton-Watson trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"James B. Martin, Roman Stasi\\'nski","submitted_at":"2018-06-20T16:41:19Z","abstract_excerpt":"We consider the behaviour of minimax recursions defined on random trees. Such recursions give the value of a general class of two-player combinatorial games. We examine in particular the case where the tree is given by a Galton-Watson branching process, truncated at some depth $2n$, and the terminal values of the level-$2n$ nodes are drawn independently from some common distribution. The case of a regular tree was previously considered by Pearl, who showed that as $n\\to\\infty$ the value of the game converges to a constant, and by Ali Khan, Devroye and Neininger, who obtained a distributional l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07838","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1806.07838","created_at":"2026-05-18T00:12:46.492877+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.07838v1","created_at":"2026-05-18T00:12:46.492877+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07838","created_at":"2026-05-18T00:12:46.492877+00:00"},{"alias_kind":"pith_short_12","alias_value":"HHANL365V2OF","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HHANL365V2OFFYCX","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HHANL365","created_at":"2026-05-18T12:32:28.185984+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HHANL365V2OFFYCXXGEC3P7JJ5","json":"https://pith.science/pith/HHANL365V2OFFYCXXGEC3P7JJ5.json","graph_json":"https://pith.science/api/pith-number/HHANL365V2OFFYCXXGEC3P7JJ5/graph.json","events_json":"https://pith.science/api/pith-number/HHANL365V2OFFYCXXGEC3P7JJ5/events.json","paper":"https://pith.science/paper/HHANL365"},"agent_actions":{"view_html":"https://pith.science/pith/HHANL365V2OFFYCXXGEC3P7JJ5","download_json":"https://pith.science/pith/HHANL365V2OFFYCXXGEC3P7JJ5.json","view_paper":"https://pith.science/paper/HHANL365","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.07838&json=true","fetch_graph":"https://pith.science/api/pith-number/HHANL365V2OFFYCXXGEC3P7JJ5/graph.json","fetch_events":"https://pith.science/api/pith-number/HHANL365V2OFFYCXXGEC3P7JJ5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HHANL365V2OFFYCXXGEC3P7JJ5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HHANL365V2OFFYCXXGEC3P7JJ5/action/storage_attestation","attest_author":"https://pith.science/pith/HHANL365V2OFFYCXXGEC3P7JJ5/action/author_attestation","sign_citation":"https://pith.science/pith/HHANL365V2OFFYCXXGEC3P7JJ5/action/citation_signature","submit_replication":"https://pith.science/pith/HHANL365V2OFFYCXXGEC3P7JJ5/action/replication_record"}},"created_at":"2026-05-18T00:12:46.492877+00:00","updated_at":"2026-05-18T00:12:46.492877+00:00"}