{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TW5PQYU3DRKS7LVPABLHCTYRJD","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":"37f994ba99e712cdcc7d5a1b8bc30b8f6dc217adde66c5d86e2c9f7563ea2c14","cross_cats_sorted":["cs.GT","cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-28T08:03:28Z","title_canon_sha256":"cd9dac1992ac52f4e296e0d81f8565fbcf17acb06fd0263a02f25c4669e14ede"},"schema_version":"1.0","source":{"id":"1803.10448","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.10448","created_at":"2026-05-18T00:19:55Z"},{"alias_kind":"arxiv_version","alias_value":"1803.10448v1","created_at":"2026-05-18T00:19:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.10448","created_at":"2026-05-18T00:19:55Z"},{"alias_kind":"pith_short_12","alias_value":"TW5PQYU3DRKS","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TW5PQYU3DRKS7LVP","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TW5PQYU3","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:eb76612594c0da2329a8497c51f1ac7401b66a22c0ee295c9121e9c0b12e10cb","target":"graph","created_at":"2026-05-18T00:19:55Z","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":"In this paper, we consider continuous-time semi-decentralized dynamics for the equilibrium computation in a class of aggregative games. Specifically, we propose a scheme where decentralized projected-gradient dynamics are driven by an integral control law. To prove global exponential convergence of the proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov function argument. We derive a sufficient condition for global convergence that we position within the recent literature on aggregative games, and in particular we show that it improves on established results.","authors_text":"Claudio De Persis, Sergio Grammatico","cross_cats":["cs.GT","cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-28T08:03:28Z","title":"Continuous-time integral dynamics for Aggregative Game equilibrium seeking"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.10448","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:f92a739c97c7d22e4d999bcf4e10035712b2307e78e2cfeedd3977b2f648bf5e","target":"record","created_at":"2026-05-18T00:19:55Z","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":"37f994ba99e712cdcc7d5a1b8bc30b8f6dc217adde66c5d86e2c9f7563ea2c14","cross_cats_sorted":["cs.GT","cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-03-28T08:03:28Z","title_canon_sha256":"cd9dac1992ac52f4e296e0d81f8565fbcf17acb06fd0263a02f25c4669e14ede"},"schema_version":"1.0","source":{"id":"1803.10448","kind":"arxiv","version":1}},"canonical_sha256":"9dbaf8629b1c552faeaf0056714f1148cc3198b7e4f3b797cc859135bf545bd0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9dbaf8629b1c552faeaf0056714f1148cc3198b7e4f3b797cc859135bf545bd0","first_computed_at":"2026-05-18T00:19:55.376193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:55.376193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ffb1qW5jwub8rZwrfD31A3zI7wJNg8wfBX1jyNAqd2wg5JfdI0BAUKs4yQQiCvebMj3AZsC9DcAEdgoEwXfECw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:55.377024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.10448","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f92a739c97c7d22e4d999bcf4e10035712b2307e78e2cfeedd3977b2f648bf5e","sha256:eb76612594c0da2329a8497c51f1ac7401b66a22c0ee295c9121e9c0b12e10cb"],"state_sha256":"e5dde25f5d582ab918b505312ce1c9df3f3abe90f0b685e888ea82038a38f73e"}