{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:XSKKJKE7COP436L5DWHTAJDHVO","short_pith_number":"pith:XSKKJKE7","canonical_record":{"source":{"id":"2505.21386","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2025-05-27T16:13:14Z","cross_cats_sorted":["cs.GT","cs.SY","math.OC"],"title_canon_sha256":"b4225142c298e9734ed21bbfb99adacedf1ff753df321f2fb064ff8a24f68976","abstract_canon_sha256":"b71046830f7903d14e95c27b146e583fe7321c05d86e5607504f8aecbc25f250"},"schema_version":"1.0"},"canonical_sha256":"bc94a4a89f139fcdf97d1d8f302467ab8b2bf4534d5b8a9c16c0c0588b625847","source":{"kind":"arxiv","id":"2505.21386","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21386","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21386v1","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21386","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"pith_short_12","alias_value":"XSKKJKE7COP4","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"pith_short_16","alias_value":"XSKKJKE7COP436L5","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"pith_short_8","alias_value":"XSKKJKE7","created_at":"2026-07-05T11:10:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:XSKKJKE7COP436L5DWHTAJDHVO","target":"record","payload":{"canonical_record":{"source":{"id":"2505.21386","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2025-05-27T16:13:14Z","cross_cats_sorted":["cs.GT","cs.SY","math.OC"],"title_canon_sha256":"b4225142c298e9734ed21bbfb99adacedf1ff753df321f2fb064ff8a24f68976","abstract_canon_sha256":"b71046830f7903d14e95c27b146e583fe7321c05d86e5607504f8aecbc25f250"},"schema_version":"1.0"},"canonical_sha256":"bc94a4a89f139fcdf97d1d8f302467ab8b2bf4534d5b8a9c16c0c0588b625847","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:10:41.145022Z","signature_b64":"myLXL6jRlozDHpfIFdTeL2LSsvznu7zqHsOlyIrWXhapPMdbtcmH/UScHoGle7cSoVhdIxBTFFK+DJCKR9XuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc94a4a89f139fcdf97d1d8f302467ab8b2bf4534d5b8a9c16c0c0588b625847","last_reissued_at":"2026-07-05T11:10:41.144553Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:10:41.144553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.21386","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:10:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uQpsGkUgkUJk830Ty/ppdmMVxD6AIjq0cOwMHPMqzdEjFCEPShNaf54TX+QZ8qt8Kabomx7ABzgab0HeHDZIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:38:58.545604Z"},"content_sha256":"cbca36819d35d9885d3788541a53689e50c4b8df67dc3d96a6101debc4ee8308","schema_version":"1.0","event_id":"sha256:cbca36819d35d9885d3788541a53689e50c4b8df67dc3d96a6101debc4ee8308"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:XSKKJKE7COP436L5DWHTAJDHVO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distributed equilibrium seeking in aggregative games: linear convergence under singular perturbations lens","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT","cs.SY","math.OC"],"primary_cat":"eess.SY","authors_text":"Filiberto Fele, Filippo Fabiani, Giuseppe Notarstefano, Guido Carnevale, Kostas Margellos","submitted_at":"2025-05-27T16:13:14Z","abstract_excerpt":"We present a fully-distributed algorithm for Nash equilibrium seeking in aggregative games over networks. The proposed scheme endows each agent with a gradient-based scheme equipped with a tracking mechanism to locally reconstruct the aggregative variable, which is not available to the agents. We show that our method falls into the framework of singularly perturbed systems, as it involves the interconnection between a fast subsystem - the global information reconstruction dynamics - with a slow one concerning the optimization of the local strategies. This perspective plays a key role in analyz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21386","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.21386/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:10:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+sVYkScpQQDEndhSrI62fdH73rYeVxH5GPgULo0nuPJB9hCqktYOresQpJEO8sOz4L0QCU1W73aoerQ4C/oiBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T18:38:58.546128Z"},"content_sha256":"2fefbeedff3cae19c170bf055587329083f19e9c83ed45bd197523c995f05e17","schema_version":"1.0","event_id":"sha256:2fefbeedff3cae19c170bf055587329083f19e9c83ed45bd197523c995f05e17"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XSKKJKE7COP436L5DWHTAJDHVO/bundle.json","state_url":"https://pith.science/pith/XSKKJKE7COP436L5DWHTAJDHVO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XSKKJKE7COP436L5DWHTAJDHVO/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":"2026-08-08T18:38:58Z","links":{"resolver":"https://pith.science/pith/XSKKJKE7COP436L5DWHTAJDHVO","bundle":"https://pith.science/pith/XSKKJKE7COP436L5DWHTAJDHVO/bundle.json","state":"https://pith.science/pith/XSKKJKE7COP436L5DWHTAJDHVO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XSKKJKE7COP436L5DWHTAJDHVO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:XSKKJKE7COP436L5DWHTAJDHVO","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":"b71046830f7903d14e95c27b146e583fe7321c05d86e5607504f8aecbc25f250","cross_cats_sorted":["cs.GT","cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2025-05-27T16:13:14Z","title_canon_sha256":"b4225142c298e9734ed21bbfb99adacedf1ff753df321f2fb064ff8a24f68976"},"schema_version":"1.0","source":{"id":"2505.21386","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.21386","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"arxiv_version","alias_value":"2505.21386v1","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.21386","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"pith_short_12","alias_value":"XSKKJKE7COP4","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"pith_short_16","alias_value":"XSKKJKE7COP436L5","created_at":"2026-07-05T11:10:41Z"},{"alias_kind":"pith_short_8","alias_value":"XSKKJKE7","created_at":"2026-07-05T11:10:41Z"}],"graph_snapshots":[{"event_id":"sha256:2fefbeedff3cae19c170bf055587329083f19e9c83ed45bd197523c995f05e17","target":"graph","created_at":"2026-07-05T11:10:41Z","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/2505.21386/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a fully-distributed algorithm for Nash equilibrium seeking in aggregative games over networks. The proposed scheme endows each agent with a gradient-based scheme equipped with a tracking mechanism to locally reconstruct the aggregative variable, which is not available to the agents. We show that our method falls into the framework of singularly perturbed systems, as it involves the interconnection between a fast subsystem - the global information reconstruction dynamics - with a slow one concerning the optimization of the local strategies. This perspective plays a key role in analyz","authors_text":"Filiberto Fele, Filippo Fabiani, Giuseppe Notarstefano, Guido Carnevale, Kostas Margellos","cross_cats":["cs.GT","cs.SY","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2025-05-27T16:13:14Z","title":"Distributed equilibrium seeking in aggregative games: linear convergence under singular perturbations lens"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.21386","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:cbca36819d35d9885d3788541a53689e50c4b8df67dc3d96a6101debc4ee8308","target":"record","created_at":"2026-07-05T11:10:41Z","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":"b71046830f7903d14e95c27b146e583fe7321c05d86e5607504f8aecbc25f250","cross_cats_sorted":["cs.GT","cs.SY","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"eess.SY","submitted_at":"2025-05-27T16:13:14Z","title_canon_sha256":"b4225142c298e9734ed21bbfb99adacedf1ff753df321f2fb064ff8a24f68976"},"schema_version":"1.0","source":{"id":"2505.21386","kind":"arxiv","version":1}},"canonical_sha256":"bc94a4a89f139fcdf97d1d8f302467ab8b2bf4534d5b8a9c16c0c0588b625847","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc94a4a89f139fcdf97d1d8f302467ab8b2bf4534d5b8a9c16c0c0588b625847","first_computed_at":"2026-07-05T11:10:41.144553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:10:41.144553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"myLXL6jRlozDHpfIFdTeL2LSsvznu7zqHsOlyIrWXhapPMdbtcmH/UScHoGle7cSoVhdIxBTFFK+DJCKR9XuCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:10:41.145022Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.21386","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbca36819d35d9885d3788541a53689e50c4b8df67dc3d96a6101debc4ee8308","sha256:2fefbeedff3cae19c170bf055587329083f19e9c83ed45bd197523c995f05e17"],"state_sha256":"69b81e497d56438e65e8b7e45a5e68f895ba6c32675ee3227aa0519421e3621d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x5l6wAFUF5Et+b9k/EjzAE4yszpvRh1x+UXnK6N8/+1KMJUp8cXnoxTSsNoSKXj/wkzJwdteMGlImwdTVlmFCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T18:38:58.550306Z","bundle_sha256":"a7826396299b7f14cb28a0e706c4cac74514d846a85dddfc2027bd7f26966ba6"}}