{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:BZOQ543TDQRI2NJUYQTULNHVWB","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":"00f24aaa0827c371c2e3c9532c331cfc3a71d6b4970824372860cec78bb2eaab","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2022-04-01T17:34:59Z","title_canon_sha256":"f09e0c0f44dc18889b217167caf50ed81484f248ba2eaa2270501be6fcb51dcc"},"schema_version":"1.0","source":{"id":"2204.00593","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.00593","created_at":"2026-07-05T04:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"2204.00593v1","created_at":"2026-07-05T04:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.00593","created_at":"2026-07-05T04:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"BZOQ543TDQRI","created_at":"2026-07-05T04:10:48Z"},{"alias_kind":"pith_short_16","alias_value":"BZOQ543TDQRI2NJU","created_at":"2026-07-05T04:10:48Z"},{"alias_kind":"pith_short_8","alias_value":"BZOQ543T","created_at":"2026-07-05T04:10:48Z"}],"graph_snapshots":[{"event_id":"sha256:c0ae27d39f19c6bd5043627705d24b2831381c622c1f3080724ef79a71264868","target":"graph","created_at":"2026-07-05T04:10:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2204.00593/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The prevailing methodology for analyzing population games and evolutionary dynamics in the large population limit assumes that a Poisson process (or clock) inherent to each agent determines when the agent can revise its strategy. Hence, such an approach presupposes exponentially distributed inter-revision intervals, and is inadequate for cases where each strategy entails a sequence of sub-tasks (sub-strategies) that must be completed before a new revision time occurs. This article proposes a methodology for such cases under the premise that a sub-strategy's duration is exponentially-distribute","authors_text":"Murat Arcak, Nuno C. Martins, Semih Kara","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2022-04-01T17:34:59Z","title":"Population Games With Erlang Clocks: Convergence to Nash Equilibria For Pairwise Comparison Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.00593","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":"sha256:7c5449cfe2a557c088dc94ce78a3064b4e3d715d606a8d953c0d06c70e1ecb29","target":"record","created_at":"2026-07-05T04:10:48Z","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":"00f24aaa0827c371c2e3c9532c331cfc3a71d6b4970824372860cec78bb2eaab","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2022-04-01T17:34:59Z","title_canon_sha256":"f09e0c0f44dc18889b217167caf50ed81484f248ba2eaa2270501be6fcb51dcc"},"schema_version":"1.0","source":{"id":"2204.00593","kind":"arxiv","version":1}},"canonical_sha256":"0e5d0ef3731c228d3534c42745b4f5b058b581576b66356b91c36734ff0cbf32","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e5d0ef3731c228d3534c42745b4f5b058b581576b66356b91c36734ff0cbf32","first_computed_at":"2026-07-05T04:10:48.974467Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:10:48.974467Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Dz10oThoaHcj47CXGp1ruKAj5qjHOtdk1SV5siAH38nT4SyJ6fHG9PwPrwuDikcU21vq1aAhZfyybn2aOcUSBg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:10:48.974869Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.00593","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c5449cfe2a557c088dc94ce78a3064b4e3d715d606a8d953c0d06c70e1ecb29","sha256:c0ae27d39f19c6bd5043627705d24b2831381c622c1f3080724ef79a71264868"],"state_sha256":"3532ea4c5c4522a87a046d781a7ee305140824440d5010db922ebc43da9eb66d"}