{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:HQ5GG2ML57T7HZB4XIG4U2ZUWW","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":"11b08af592b3e9a2c5a9863bc9e3c9b2c424578fd5e1602fd1f23a9e0866b5e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-15T03:28:08Z","title_canon_sha256":"d384c0e04456f8beccd00622e645a568860339bae6e023b150a00c33384cb245"},"schema_version":"1.0","source":{"id":"2106.07859","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.07859","created_at":"2026-07-05T02:49:34Z"},{"alias_kind":"arxiv_version","alias_value":"2106.07859v1","created_at":"2026-07-05T02:49:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.07859","created_at":"2026-07-05T02:49:34Z"},{"alias_kind":"pith_short_12","alias_value":"HQ5GG2ML57T7","created_at":"2026-07-05T02:49:34Z"},{"alias_kind":"pith_short_16","alias_value":"HQ5GG2ML57T7HZB4","created_at":"2026-07-05T02:49:34Z"},{"alias_kind":"pith_short_8","alias_value":"HQ5GG2ML","created_at":"2026-07-05T02:49:34Z"}],"graph_snapshots":[{"event_id":"sha256:ab05458ebcbfcd650d920abadeb1355ceccc58f349212666abb79049a1a49e07","target":"graph","created_at":"2026-07-05T02:49:34Z","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/2106.07859/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a game for a continuum of non-identical players evolving on a finite state space. Their heterogeneous interactions are represented by a graphon, which can be viewed as the limit of a dense random graph. The player's transition rates between the states depend on their own control and the interaction strengths with the other players. We develop a rigorous mathematical framework for this game and analyze Nash equilibria. We provide a sufficient condition for a Nash equilibrium and prove existence of solutions to a continuum of fully coupled forward-backward ordinary differential equat","authors_text":"Alexander Aurell, Gokce Dayanikli, Mathieu Lauriere, Rene Carmona","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-15T03:28:08Z","title":"Finite State Graphon Games with Applications to Epidemics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.07859","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:a9efe804bb1c423f134913c942847900901219ebf8f809e88eda910b67430630","target":"record","created_at":"2026-07-05T02:49:34Z","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":"11b08af592b3e9a2c5a9863bc9e3c9b2c424578fd5e1602fd1f23a9e0866b5e8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-15T03:28:08Z","title_canon_sha256":"d384c0e04456f8beccd00622e645a568860339bae6e023b150a00c33384cb245"},"schema_version":"1.0","source":{"id":"2106.07859","kind":"arxiv","version":1}},"canonical_sha256":"3c3a63698befe7f3e43cba0dca6b34b5ad1a93f46c8522daee2c0f99f856b93e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c3a63698befe7f3e43cba0dca6b34b5ad1a93f46c8522daee2c0f99f856b93e","first_computed_at":"2026-07-05T02:49:34.724217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:49:34.724217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yOd590HPJoLG2gVDN3gJ2nfHf2D2VM3RpjJDEW0/GDSC9IUOce7nusJpHE9uLxtQSDb+IHcE6ZQYEG71KttYAg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:49:34.724615Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.07859","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9efe804bb1c423f134913c942847900901219ebf8f809e88eda910b67430630","sha256:ab05458ebcbfcd650d920abadeb1355ceccc58f349212666abb79049a1a49e07"],"state_sha256":"c842f0ec0a0e094d4c16705a2d38e866263f5c5f8ccff3775c46e14be0eb5c24"}