{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TYKFDCRKHC475TJ2ARET3WCYIJ","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":"719ee214175ac9eadd79fa1a314ed00692f32176edade3b53736d588cd2148a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-23T14:39:40Z","title_canon_sha256":"896812359ff8b2d60449b350a43e7d4cee6b6a2884cb1ba5117e3d6a78b65e18"},"schema_version":"1.0","source":{"id":"1510.06947","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06947","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06947v1","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06947","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"TYKFDCRKHC47","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"TYKFDCRKHC475TJ2","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"TYKFDCRK","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:4cdeeffe61e17d94df25d4212806edb37c3c9eaf6a956146982b780643f1e311","target":"graph","created_at":"2026-05-18T01:29:22Z","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":"Parrondo games with one-dimensional spatial dependence were introduced by Toral and extended to the two-dimensional setting by Mihailovi\\'c and Rajkovi\\'c. $MN$ players are arranged in an $M\\times N$ array. There are three games, the fair, spatially independent game $A$, the spatially dependent game $B$, and game $C$, which is a random mixture or nonrandom pattern of games $A$ and $B$. Of interest is $\\mu_B$ (or $\\mu_C$), the mean profit per turn at equilibrium to the set of $MN$ players playing game $B$ (or game $C$). Game $A$ is fair, so if $\\mu_B\\le0$ and $\\mu_C>0$, then we say the Parrondo","authors_text":"Jiyeon Lee, S. N. Ethier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-23T14:39:40Z","title":"Parrondo games with two-dimensional spatial dependence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06947","kind":"arxiv","version":1},"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:ed24bde8acac8574060c38d741fbaf78e0ff87e18bde9e16d674fbf6c2579e56","target":"record","created_at":"2026-05-18T01:29:22Z","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":"719ee214175ac9eadd79fa1a314ed00692f32176edade3b53736d588cd2148a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-10-23T14:39:40Z","title_canon_sha256":"896812359ff8b2d60449b350a43e7d4cee6b6a2884cb1ba5117e3d6a78b65e18"},"schema_version":"1.0","source":{"id":"1510.06947","kind":"arxiv","version":1}},"canonical_sha256":"9e14518a2a38b9fecd3a04493dd858424b32b3efe6b6ed39e515b0e3319c2be3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e14518a2a38b9fecd3a04493dd858424b32b3efe6b6ed39e515b0e3319c2be3","first_computed_at":"2026-05-18T01:29:22.616605Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:22.616605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zk/kz7v29s4gJzZgxna2mz2ztScP57oSzJKAe9pztq2UKLlQ2kxLvsY55mJzAeObfpdKswwMSZDzXpihgSmBDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:22.617218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.06947","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed24bde8acac8574060c38d741fbaf78e0ff87e18bde9e16d674fbf6c2579e56","sha256:4cdeeffe61e17d94df25d4212806edb37c3c9eaf6a956146982b780643f1e311"],"state_sha256":"579a08a91c3267b4fca0dc6d4f00b5529cc2d6c0809d16e544a0fa2e071140c8"}