{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:UM4ZQ3UGX3R3D3FZPEMM72FJQ7","short_pith_number":"pith:UM4ZQ3UG","canonical_record":{"source":{"id":"2404.07287","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-10T18:32:17Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"821c3cd56c09bfec663ec1af8f99107827fb76042a279034ae42717c1e64eb74","abstract_canon_sha256":"824d39023c3f5c40c374c4e8919cc9f63325f45cb050f2cf404ce802342d5f59"},"schema_version":"1.0"},"canonical_sha256":"a339986e86bee3b1ecb97918cfe8a987dd143171d0e061e72243889cc448d9c9","source":{"kind":"arxiv","id":"2404.07287","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.07287","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"arxiv_version","alias_value":"2404.07287v1","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.07287","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"pith_short_12","alias_value":"UM4ZQ3UGX3R3","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"pith_short_16","alias_value":"UM4ZQ3UGX3R3D3FZ","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"pith_short_8","alias_value":"UM4ZQ3UG","created_at":"2026-07-05T08:06:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:UM4ZQ3UGX3R3D3FZPEMM72FJQ7","target":"record","payload":{"canonical_record":{"source":{"id":"2404.07287","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-10T18:32:17Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"821c3cd56c09bfec663ec1af8f99107827fb76042a279034ae42717c1e64eb74","abstract_canon_sha256":"824d39023c3f5c40c374c4e8919cc9f63325f45cb050f2cf404ce802342d5f59"},"schema_version":"1.0"},"canonical_sha256":"a339986e86bee3b1ecb97918cfe8a987dd143171d0e061e72243889cc448d9c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:06:50.319531Z","signature_b64":"hZuu9TeEmJBN4Lzy3J5fEBt0oCEDcSUfMjnYmR7RMu4esNDsICRaVtdsE1O3jtwN/KMT55DjOd3HHQ9atuIuBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a339986e86bee3b1ecb97918cfe8a987dd143171d0e061e72243889cc448d9c9","last_reissued_at":"2026-07-05T08:06:50.318940Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:06:50.318940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.07287","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":"2026-07-05T08:06:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gjmYJlf3HXUfVWh9f006y8GxIY3JQuqoof5k59oPtLS1AqvJ4Gqh2JQANcxGSFr5U8Rljqt8+CkrNqmkM1ApBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:23:23.383438Z"},"content_sha256":"d55956b4a6720d83ca7fd3168e8602d0c2c70aafc79bcc396909749d4c26280d","schema_version":"1.0","event_id":"sha256:d55956b4a6720d83ca7fd3168e8602d0c2c70aafc79bcc396909749d4c26280d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:UM4ZQ3UGX3R3D3FZPEMM72FJQ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nash Equilibrium Seeking for Noncooperative Duopoly Games via Event-Triggered Control","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.SY","eess.SY"],"primary_cat":"math.OC","authors_text":"Miroslav Krsti\\'c, Tamer Ba\\c{s}ar, Tiago Roux Oliveira, Victor Hugo Pereira Rodrigues","submitted_at":"2024-04-10T18:32:17Z","abstract_excerpt":"This paper proposes a novel approach for locally stable convergence to Nash equilibrium in duopoly noncooperative games based on a distributed event-triggered control scheme. The proposed approach employs extremum seeking, with sinusoidal perturbation signals applied to estimate the Gradient (first derivative) of unknown quadratic payoff functions. This is the first instance of noncooperative games being tackled in a model-free fashion integrated with the event-triggered methodology. Each player evaluates independently the deviation between the corresponding current state variable and its last"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.07287","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/2404.07287/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":"2026-07-05T08:06:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V+YmaprTKk47zJAJUK9K10kyztbT0ZUhMHi3nfLcIfvfI5mFDM0BaGbBeZKSTQYakfSgaT4chSkeRnyjsGYkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:23:23.383819Z"},"content_sha256":"5fa371d1558199839271bebfc11c6bbc41028b966f71a20a5b4f1e258e104d27","schema_version":"1.0","event_id":"sha256:5fa371d1558199839271bebfc11c6bbc41028b966f71a20a5b4f1e258e104d27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UM4ZQ3UGX3R3D3FZPEMM72FJQ7/bundle.json","state_url":"https://pith.science/pith/UM4ZQ3UGX3R3D3FZPEMM72FJQ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UM4ZQ3UGX3R3D3FZPEMM72FJQ7/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":"2026-07-06T19:23:23Z","links":{"resolver":"https://pith.science/pith/UM4ZQ3UGX3R3D3FZPEMM72FJQ7","bundle":"https://pith.science/pith/UM4ZQ3UGX3R3D3FZPEMM72FJQ7/bundle.json","state":"https://pith.science/pith/UM4ZQ3UGX3R3D3FZPEMM72FJQ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UM4ZQ3UGX3R3D3FZPEMM72FJQ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UM4ZQ3UGX3R3D3FZPEMM72FJQ7","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":"824d39023c3f5c40c374c4e8919cc9f63325f45cb050f2cf404ce802342d5f59","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-10T18:32:17Z","title_canon_sha256":"821c3cd56c09bfec663ec1af8f99107827fb76042a279034ae42717c1e64eb74"},"schema_version":"1.0","source":{"id":"2404.07287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.07287","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"arxiv_version","alias_value":"2404.07287v1","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.07287","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"pith_short_12","alias_value":"UM4ZQ3UGX3R3","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"pith_short_16","alias_value":"UM4ZQ3UGX3R3D3FZ","created_at":"2026-07-05T08:06:50Z"},{"alias_kind":"pith_short_8","alias_value":"UM4ZQ3UG","created_at":"2026-07-05T08:06:50Z"}],"graph_snapshots":[{"event_id":"sha256:5fa371d1558199839271bebfc11c6bbc41028b966f71a20a5b4f1e258e104d27","target":"graph","created_at":"2026-07-05T08:06:50Z","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/2404.07287/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper proposes a novel approach for locally stable convergence to Nash equilibrium in duopoly noncooperative games based on a distributed event-triggered control scheme. The proposed approach employs extremum seeking, with sinusoidal perturbation signals applied to estimate the Gradient (first derivative) of unknown quadratic payoff functions. This is the first instance of noncooperative games being tackled in a model-free fashion integrated with the event-triggered methodology. Each player evaluates independently the deviation between the corresponding current state variable and its last","authors_text":"Miroslav Krsti\\'c, Tamer Ba\\c{s}ar, Tiago Roux Oliveira, Victor Hugo Pereira Rodrigues","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-10T18:32:17Z","title":"Nash Equilibrium Seeking for Noncooperative Duopoly Games via Event-Triggered Control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.07287","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:d55956b4a6720d83ca7fd3168e8602d0c2c70aafc79bcc396909749d4c26280d","target":"record","created_at":"2026-07-05T08:06:50Z","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":"824d39023c3f5c40c374c4e8919cc9f63325f45cb050f2cf404ce802342d5f59","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-04-10T18:32:17Z","title_canon_sha256":"821c3cd56c09bfec663ec1af8f99107827fb76042a279034ae42717c1e64eb74"},"schema_version":"1.0","source":{"id":"2404.07287","kind":"arxiv","version":1}},"canonical_sha256":"a339986e86bee3b1ecb97918cfe8a987dd143171d0e061e72243889cc448d9c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a339986e86bee3b1ecb97918cfe8a987dd143171d0e061e72243889cc448d9c9","first_computed_at":"2026-07-05T08:06:50.318940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:06:50.318940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hZuu9TeEmJBN4Lzy3J5fEBt0oCEDcSUfMjnYmR7RMu4esNDsICRaVtdsE1O3jtwN/KMT55DjOd3HHQ9atuIuBA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:06:50.319531Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.07287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d55956b4a6720d83ca7fd3168e8602d0c2c70aafc79bcc396909749d4c26280d","sha256:5fa371d1558199839271bebfc11c6bbc41028b966f71a20a5b4f1e258e104d27"],"state_sha256":"5550f310de7d161faadafc4f82e0960207d651ac2b22cacbe5a2d0a64c7a5c35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JJdE+baMKLOCqq/xoG91/sxeim7ZoulcDMAsZ+RrJNft8ZvtUqXREBhDyM8cnEHvkStkS8sm65lyPhAdnVFGCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T19:23:23.386329Z","bundle_sha256":"91ad71a47195f04d5dc7e012c4665ce7abb636fc2efe839712f031fbc0f927ab"}}