{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:ND433ETVD5Q4KXRA2PO26TDE3E","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":"4cfa7b205cd9435419675cc07dd53abffb0c999ff4e026e5d96abfcaddedcb98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2008-08-20T19:12:40Z","title_canon_sha256":"d496dcdab8048aa1803afeed2b156161cbfed0807c75f9a2579f54f5428ff306"},"schema_version":"1.0","source":{"id":"0808.2801","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.2801","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"arxiv_version","alias_value":"0808.2801v1","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.2801","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"pith_short_12","alias_value":"ND433ETVD5Q4","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"ND433ETVD5Q4KXRA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"ND433ETV","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:26393889cac58d27cccf3fb857cda641f8dd8537f9505a2ce651f7916596b977","target":"graph","created_at":"2026-05-18T00:59:11Z","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":"We show that there is a polynomial-time approximation scheme for computing Nash equilibria in anonymous games with any fixed number of strategies (a very broad and important class of games), extending the two-strategy result of Daskalakis and Papadimitriou 2007. The approximation guarantee follows from a probabilistic result of more general interest: The distribution of the sum of n independent unit vectors with values ranging over {e1, e2, ...,ek}, where ei is the unit vector along dimension i of the k-dimensional Euclidean space, can be approximated by the distribution of the sum of another ","authors_text":"Christos H. Papadimitriou, Constantinos Daskalakis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2008-08-20T19:12:40Z","title":"Discretized Multinomial Distributions and Nash Equilibria in Anonymous Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.2801","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":"sha256:9c182fdbb2d380177ef9cfd55abe08580198d40d73cda91a2ab7af95b2608e57","target":"record","created_at":"2026-05-18T00:59:11Z","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":"4cfa7b205cd9435419675cc07dd53abffb0c999ff4e026e5d96abfcaddedcb98","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GT","submitted_at":"2008-08-20T19:12:40Z","title_canon_sha256":"d496dcdab8048aa1803afeed2b156161cbfed0807c75f9a2579f54f5428ff306"},"schema_version":"1.0","source":{"id":"0808.2801","kind":"arxiv","version":1}},"canonical_sha256":"68f9bd92751f61c55e20d3ddaf4c64d904249c2baa377cd3941d10b0c761a726","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68f9bd92751f61c55e20d3ddaf4c64d904249c2baa377cd3941d10b0c761a726","first_computed_at":"2026-05-18T00:59:11.657524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:11.657524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wvJiRdKI/LgS/UaXjXL2i41Jj6KZ8MrrtuXjVL7Y8yr5E6zuXzPMx+VmcgtAnmk67WlgjwS3566oXRxVAaBTCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:11.658199Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.2801","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c182fdbb2d380177ef9cfd55abe08580198d40d73cda91a2ab7af95b2608e57","sha256:26393889cac58d27cccf3fb857cda641f8dd8537f9505a2ce651f7916596b977"],"state_sha256":"e4655e48ec1175566045cfc4a7dd6ce598c655643354ee823b99d1ede57e7881"}