{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:H5MXA6H7IIKJLPUPISXA2VBBBP","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":"7e0a908cee0c80abb531672dd722a393160544e83d9936f94c2b1224c3412264","cross_cats_sorted":["nlin.AO","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2009-11-12T15:05:05Z","title_canon_sha256":"f07a39292a97497121d1b6c4d148dd6b56aed9cff3fc1690f6168323c5d2f098"},"schema_version":"1.0","source":{"id":"0911.2406","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.2406","created_at":"2026-05-18T02:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"0911.2406v2","created_at":"2026-05-18T02:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.2406","created_at":"2026-05-18T02:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"H5MXA6H7IIKJ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"H5MXA6H7IIKJLPUP","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"H5MXA6H7","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:aa3cd31196ffb48ddb38f68eb301b40ed2c69fc122cc2b5900417969945b6213","target":"graph","created_at":"2026-05-18T02:10:48Z","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":"A continuous time model for multiagent systems governed by reinforcement learning with scale-free memory is developed. The agents are assumed to act independently of one another in optimizing their choice of possible actions via trial-and-error search. To gain awareness about the action value the agents accumulate in their memory the rewards obtained from taking a specific action at each moment of time. The contribution of the rewards in the past to the agent current perception of action value is described by an integral operator with a power-law kernel. Finally a fractional differential equat","authors_text":"Ihor Lubashevsky, Shigeru Kanemoto","cross_cats":["nlin.AO","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2009-11-12T15:05:05Z","title":"Scale-free memory model for multiagent reinforcement learning. Mean field approximation and rock-paper-scissors dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2406","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":"sha256:7b484a2dfcd05c6d520b59ce3d07f05842c1dd2a1380f34df104d3d7fd33531b","target":"record","created_at":"2026-05-18T02:10:48Z","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":"7e0a908cee0c80abb531672dd722a393160544e83d9936f94c2b1224c3412264","cross_cats_sorted":["nlin.AO","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2009-11-12T15:05:05Z","title_canon_sha256":"f07a39292a97497121d1b6c4d148dd6b56aed9cff3fc1690f6168323c5d2f098"},"schema_version":"1.0","source":{"id":"0911.2406","kind":"arxiv","version":2}},"canonical_sha256":"3f597078ff421495be8f44ae0d54210bdf0b6fee55a05facda5fb467dcf2d823","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f597078ff421495be8f44ae0d54210bdf0b6fee55a05facda5fb467dcf2d823","first_computed_at":"2026-05-18T02:10:48.257900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:48.257900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K0DrWwcpQcTcLSUjOrZATVq+VBns2EJZ3ohtKfj6HgIQIn3MsSMEDRkzj0eM4TvYGn+O+aqmbl7PJ+vDSO4RCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:48.258579Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.2406","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b484a2dfcd05c6d520b59ce3d07f05842c1dd2a1380f34df104d3d7fd33531b","sha256:aa3cd31196ffb48ddb38f68eb301b40ed2c69fc122cc2b5900417969945b6213"],"state_sha256":"6a3260ebdc2cb264b6c4aec0734a1fd8ecf5a8c46f268081a5e231da321aa7e6"}