{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5TPTPM7EER7YAQ2VSCFJ3Z7SZC","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":"36759a957acaa94084f9e77c679b0c0ad2f6e7bfc8d531cb8e2d1c5fc024fddf","cross_cats_sorted":["cs.GT","physics.soc-ph"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2010-09-06T11:30:24Z","title_canon_sha256":"968116ed961fb2c87b397836ea7fd3eeff02d2dea314a43d6db84291cb31f9dc"},"schema_version":"1.0","source":{"id":"1009.1031","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1031","created_at":"2026-05-18T03:31:18Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1031v3","created_at":"2026-05-18T03:31:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1031","created_at":"2026-05-18T03:31:18Z"},{"alias_kind":"pith_short_12","alias_value":"5TPTPM7EER7Y","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5TPTPM7EER7YAQ2V","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5TPTPM7E","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:879a465a67728f3e3585375b3982a364ed84bab57c213f8b3cf16571d11a4e30","target":"graph","created_at":"2026-05-18T03:31:18Z","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":"Mafia (also called Werewolf) is a party game. The participants are divided into two competing groups: citizens and a mafia. The objective is to eliminate the opponent group. The game consists of two consecutive phases (day and night) and a certain set of actions (e.g. lynching during day). The mafia members have additional powers (knowing each other, killing during night) whereas the citizens are more numerous.\n  We propose a simple mathematical model of the game, which is essentially a pure death process with discrete time. We find the closed-form solutions for the mafia winning-chance, w(n,m","authors_text":"Piotr Migda{\\l}","cross_cats":["cs.GT","physics.soc-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2010-09-06T11:30:24Z","title":"A mathematical model of the Mafia game"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1031","kind":"arxiv","version":3},"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:cdd63d33c2e9a55ac8323618d4181803803547b9d1633b497ed9bc54bf84efa5","target":"record","created_at":"2026-05-18T03:31:18Z","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":"36759a957acaa94084f9e77c679b0c0ad2f6e7bfc8d531cb8e2d1c5fc024fddf","cross_cats_sorted":["cs.GT","physics.soc-ph"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2010-09-06T11:30:24Z","title_canon_sha256":"968116ed961fb2c87b397836ea7fd3eeff02d2dea314a43d6db84291cb31f9dc"},"schema_version":"1.0","source":{"id":"1009.1031","kind":"arxiv","version":3}},"canonical_sha256":"ecdf37b3e4247f804355908a9de7f2c8a0254dfac6afb310286ced506ffccb4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecdf37b3e4247f804355908a9de7f2c8a0254dfac6afb310286ced506ffccb4e","first_computed_at":"2026-05-18T03:31:18.157496Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:18.157496Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z/Mhd6SMKr/6F6r2SYYcmSoAwAs1D4aolxrA1+j/39X0JzEQ9X4rirvd5QRUuJV/LJXsgZvt2qwx6gDHqbd9BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:18.157984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1031","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdd63d33c2e9a55ac8323618d4181803803547b9d1633b497ed9bc54bf84efa5","sha256:879a465a67728f3e3585375b3982a364ed84bab57c213f8b3cf16571d11a4e30"],"state_sha256":"3cb77a7d19557be8855f52d11e51a72daf74f6196b24abfa2f417efaf6ce3680"}