{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JTJ6A7SZ2ABLJPHEDUOMTH3WDL","short_pith_number":"pith:JTJ6A7SZ","canonical_record":{"source":{"id":"1304.4577","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-16T19:51:39Z","cross_cats_sorted":["cs.GT","cs.SY"],"title_canon_sha256":"c2f6969caa4b0d6ecf89d1583541c1e16534020fbdab6b72009be63272df90e3","abstract_canon_sha256":"ba53c85acae6ed34d829e7acc2990ff4c26271c098ca0d11683bb7d92ec8d1b8"},"schema_version":"1.0"},"canonical_sha256":"4cd3e07e59d002b4bce41d1cc99f761adf6c536a23f549bd817f003cd446031a","source":{"kind":"arxiv","id":"1304.4577","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4577","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4577v2","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4577","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"JTJ6A7SZ2ABL","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JTJ6A7SZ2ABLJPHE","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JTJ6A7SZ","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JTJ6A7SZ2ABLJPHEDUOMTH3WDL","target":"record","payload":{"canonical_record":{"source":{"id":"1304.4577","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-16T19:51:39Z","cross_cats_sorted":["cs.GT","cs.SY"],"title_canon_sha256":"c2f6969caa4b0d6ecf89d1583541c1e16534020fbdab6b72009be63272df90e3","abstract_canon_sha256":"ba53c85acae6ed34d829e7acc2990ff4c26271c098ca0d11683bb7d92ec8d1b8"},"schema_version":"1.0"},"canonical_sha256":"4cd3e07e59d002b4bce41d1cc99f761adf6c536a23f549bd817f003cd446031a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:42.476967Z","signature_b64":"09dbVIzgYd9dgDKYGOSq9ltB48Torxe28EpZYIF/gy9vTDYoGnKVNuBWFlFy3rwNWiGgnr3nM/BU0NG478NmDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cd3e07e59d002b4bce41d1cc99f761adf6c536a23f549bd817f003cd446031a","last_reissued_at":"2026-05-18T00:58:42.476494Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:42.476494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.4577","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/a82+7EhUSX8G2aIQwQ99Epo9cWscISbGvEq5dmrlS8hYXK3uEXq1NJZl79gLByQwZ++yDCwInYXOnKWfkGFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:44:22.450599Z"},"content_sha256":"6c66a3ca8a151500f21add129109d24484ce3c2307f33a2bb860cd0a7367ed1f","schema_version":"1.0","event_id":"sha256:6c66a3ca8a151500f21add129109d24484ce3c2307f33a2bb860cd0a7367ed1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JTJ6A7SZ2ABLJPHEDUOMTH3WDL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Empirical Centroid Fictitious Play: An Approach For Distributed Learning In Multi-Agent Games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT","cs.SY"],"primary_cat":"math.OC","authors_text":"Brian Swenson, Joao Xavier, Soummya Kar","submitted_at":"2013-04-16T19:51:39Z","abstract_excerpt":"The paper is concerned with distributed learning in large-scale games. The well-known fictitious play (FP) algorithm is addressed, which, despite theoretical convergence results, might be impractical to implement in large-scale settings due to intense computation and communication requirements. An adaptation of the FP algorithm, designated as the empirical centroid fictitious play (ECFP), is presented. In ECFP players respond to the centroid of all players' actions rather than track and respond to the individual actions of every player. Convergence of the ECFP algorithm in terms of average emp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4577","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k78lw6NL07FzgW/7qX86Pn46BRdWvlAqPApXrBO6YmxwBws/y8cGot2ZccGfRomUdUgeFTMtW9Gm2UtVMp52AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:44:22.451066Z"},"content_sha256":"e99c609757bb54a02510ed318c413f16a5c1af3186e0f603f9ebe303165c0586","schema_version":"1.0","event_id":"sha256:e99c609757bb54a02510ed318c413f16a5c1af3186e0f603f9ebe303165c0586"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JTJ6A7SZ2ABLJPHEDUOMTH3WDL/bundle.json","state_url":"https://pith.science/pith/JTJ6A7SZ2ABLJPHEDUOMTH3WDL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JTJ6A7SZ2ABLJPHEDUOMTH3WDL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T15:44:22Z","links":{"resolver":"https://pith.science/pith/JTJ6A7SZ2ABLJPHEDUOMTH3WDL","bundle":"https://pith.science/pith/JTJ6A7SZ2ABLJPHEDUOMTH3WDL/bundle.json","state":"https://pith.science/pith/JTJ6A7SZ2ABLJPHEDUOMTH3WDL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JTJ6A7SZ2ABLJPHEDUOMTH3WDL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JTJ6A7SZ2ABLJPHEDUOMTH3WDL","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":"ba53c85acae6ed34d829e7acc2990ff4c26271c098ca0d11683bb7d92ec8d1b8","cross_cats_sorted":["cs.GT","cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-16T19:51:39Z","title_canon_sha256":"c2f6969caa4b0d6ecf89d1583541c1e16534020fbdab6b72009be63272df90e3"},"schema_version":"1.0","source":{"id":"1304.4577","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4577","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4577v2","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4577","created_at":"2026-05-18T00:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"JTJ6A7SZ2ABL","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JTJ6A7SZ2ABLJPHE","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JTJ6A7SZ","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:e99c609757bb54a02510ed318c413f16a5c1af3186e0f603f9ebe303165c0586","target":"graph","created_at":"2026-05-18T00:58:42Z","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":"The paper is concerned with distributed learning in large-scale games. The well-known fictitious play (FP) algorithm is addressed, which, despite theoretical convergence results, might be impractical to implement in large-scale settings due to intense computation and communication requirements. An adaptation of the FP algorithm, designated as the empirical centroid fictitious play (ECFP), is presented. In ECFP players respond to the centroid of all players' actions rather than track and respond to the individual actions of every player. Convergence of the ECFP algorithm in terms of average emp","authors_text":"Brian Swenson, Joao Xavier, Soummya Kar","cross_cats":["cs.GT","cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-16T19:51:39Z","title":"Empirical Centroid Fictitious Play: An Approach For Distributed Learning In Multi-Agent Games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4577","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":"sha256:6c66a3ca8a151500f21add129109d24484ce3c2307f33a2bb860cd0a7367ed1f","target":"record","created_at":"2026-05-18T00:58:42Z","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":"ba53c85acae6ed34d829e7acc2990ff4c26271c098ca0d11683bb7d92ec8d1b8","cross_cats_sorted":["cs.GT","cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-04-16T19:51:39Z","title_canon_sha256":"c2f6969caa4b0d6ecf89d1583541c1e16534020fbdab6b72009be63272df90e3"},"schema_version":"1.0","source":{"id":"1304.4577","kind":"arxiv","version":2}},"canonical_sha256":"4cd3e07e59d002b4bce41d1cc99f761adf6c536a23f549bd817f003cd446031a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4cd3e07e59d002b4bce41d1cc99f761adf6c536a23f549bd817f003cd446031a","first_computed_at":"2026-05-18T00:58:42.476494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:42.476494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"09dbVIzgYd9dgDKYGOSq9ltB48Torxe28EpZYIF/gy9vTDYoGnKVNuBWFlFy3rwNWiGgnr3nM/BU0NG478NmDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:42.476967Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4577","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c66a3ca8a151500f21add129109d24484ce3c2307f33a2bb860cd0a7367ed1f","sha256:e99c609757bb54a02510ed318c413f16a5c1af3186e0f603f9ebe303165c0586"],"state_sha256":"714af64ff2f0b9c70d49d4a31ef042bf263cdd4f289835c88d1e782d11d6c1c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yz27VhMhm0pjU4POuuUzDW6ECLg4B0z9v8pmO8AZBKOaX2lfbKIqcqsXdjAqKf6eZKqls8WXuBeIKqflBSt9Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:44:22.453954Z","bundle_sha256":"e4fbfad8414f27ac968e7509754c65f3958b80c2ccc5faefda3bb6e856830212"}}