{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:WAZVDRYU57T2M36BTYFQEJNBNS","short_pith_number":"pith:WAZVDRYU","canonical_record":{"source":{"id":"2411.13234","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-20T11:55:18Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"0ac091c5459146188701ccfe0d1514f6e5d9425009a6313a6ba91e378b2e48ec","abstract_canon_sha256":"508f0af7ebd06de8e4c0bc14242737ce3be9b3a262e2c1a78a7da1eb204c9c6d"},"schema_version":"1.0"},"canonical_sha256":"b03351c714efe7a66fc19e0b0225a16c83d6cc3de9b6fb324bea58767fcbc8af","source":{"kind":"arxiv","id":"2411.13234","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.13234","created_at":"2026-07-05T09:38:07Z"},{"alias_kind":"arxiv_version","alias_value":"2411.13234v1","created_at":"2026-07-05T09:38:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13234","created_at":"2026-07-05T09:38:07Z"},{"alias_kind":"pith_short_12","alias_value":"WAZVDRYU57T2","created_at":"2026-07-05T09:38:07Z"},{"alias_kind":"pith_short_16","alias_value":"WAZVDRYU57T2M36B","created_at":"2026-07-05T09:38:07Z"},{"alias_kind":"pith_short_8","alias_value":"WAZVDRYU","created_at":"2026-07-05T09:38:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:WAZVDRYU57T2M36BTYFQEJNBNS","target":"record","payload":{"canonical_record":{"source":{"id":"2411.13234","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-20T11:55:18Z","cross_cats_sorted":["cs.SY","eess.SY"],"title_canon_sha256":"0ac091c5459146188701ccfe0d1514f6e5d9425009a6313a6ba91e378b2e48ec","abstract_canon_sha256":"508f0af7ebd06de8e4c0bc14242737ce3be9b3a262e2c1a78a7da1eb204c9c6d"},"schema_version":"1.0"},"canonical_sha256":"b03351c714efe7a66fc19e0b0225a16c83d6cc3de9b6fb324bea58767fcbc8af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:38:07.099557Z","signature_b64":"5Z8qD7CbrnmKsU2jatIFdMfUjEkrexIekKAyXalPmo6yQxwiGITUnhQHzIGk9WEet7+4uVces+dlZXHZF/+2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b03351c714efe7a66fc19e0b0225a16c83d6cc3de9b6fb324bea58767fcbc8af","last_reissued_at":"2026-07-05T09:38:07.099158Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:38:07.099158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.13234","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":"2026-07-05T09:38:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ByC/WSaqXEX4x51EcqPWUt6OUyNe640uHs2Shyl8Lv7pF9aalvsk2mBgDnH1E5oKIXxn+YD1wFtPToCrGZ7wBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:07:54.805084Z"},"content_sha256":"ca8ad75cc0d8dbc095671240488962804374ce4da1f458fb744ef7c35f342db8","schema_version":"1.0","event_id":"sha256:ca8ad75cc0d8dbc095671240488962804374ce4da1f458fb744ef7c35f342db8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:WAZVDRYU57T2M36BTYFQEJNBNS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extremum and Nash Equilibrium Seeking with Delays and PDEs: Designs & Applications","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","submitted_at":"2024-11-20T11:55:18Z","abstract_excerpt":"The development of extremum seeking (ES) has progressed, over the past hundred years, from static maps, to finite-dimensional dynamic systems, to networks of static and dynamic agents. Extensions from ODE dynamics to maps and agents that incorporate delays or even partial differential equations (PDEs) is the next natural step in that progression through ascending research challenges. This paper reviews results on algorithm design and theory of ES for such infinite-dimensional systems. Both hyperbolic and parabolic dynamics are presented: delays or transport equations, heat-dominated equation, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13234","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/2411.13234/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":"2026-07-05T09:38:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fomAAQgn2BVBVGb7iVWCo4gxZQJVzqiUfm3ZOH66ezAFqSyFK7DXivhnU2o2KUWwOa8kfgYykjOD+m1Tt82lBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:07:54.805493Z"},"content_sha256":"1bc66b6c4f03f75c3a891fb9ca9ea4bd6886e6238f511298211f7f433ab893bd","schema_version":"1.0","event_id":"sha256:1bc66b6c4f03f75c3a891fb9ca9ea4bd6886e6238f511298211f7f433ab893bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WAZVDRYU57T2M36BTYFQEJNBNS/bundle.json","state_url":"https://pith.science/pith/WAZVDRYU57T2M36BTYFQEJNBNS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WAZVDRYU57T2M36BTYFQEJNBNS/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":"2026-07-07T11:07:54Z","links":{"resolver":"https://pith.science/pith/WAZVDRYU57T2M36BTYFQEJNBNS","bundle":"https://pith.science/pith/WAZVDRYU57T2M36BTYFQEJNBNS/bundle.json","state":"https://pith.science/pith/WAZVDRYU57T2M36BTYFQEJNBNS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WAZVDRYU57T2M36BTYFQEJNBNS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WAZVDRYU57T2M36BTYFQEJNBNS","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":"508f0af7ebd06de8e4c0bc14242737ce3be9b3a262e2c1a78a7da1eb204c9c6d","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-20T11:55:18Z","title_canon_sha256":"0ac091c5459146188701ccfe0d1514f6e5d9425009a6313a6ba91e378b2e48ec"},"schema_version":"1.0","source":{"id":"2411.13234","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.13234","created_at":"2026-07-05T09:38:07Z"},{"alias_kind":"arxiv_version","alias_value":"2411.13234v1","created_at":"2026-07-05T09:38:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13234","created_at":"2026-07-05T09:38:07Z"},{"alias_kind":"pith_short_12","alias_value":"WAZVDRYU57T2","created_at":"2026-07-05T09:38:07Z"},{"alias_kind":"pith_short_16","alias_value":"WAZVDRYU57T2M36B","created_at":"2026-07-05T09:38:07Z"},{"alias_kind":"pith_short_8","alias_value":"WAZVDRYU","created_at":"2026-07-05T09:38:07Z"}],"graph_snapshots":[{"event_id":"sha256:1bc66b6c4f03f75c3a891fb9ca9ea4bd6886e6238f511298211f7f433ab893bd","target":"graph","created_at":"2026-07-05T09:38:07Z","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/2411.13234/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The development of extremum seeking (ES) has progressed, over the past hundred years, from static maps, to finite-dimensional dynamic systems, to networks of static and dynamic agents. Extensions from ODE dynamics to maps and agents that incorporate delays or even partial differential equations (PDEs) is the next natural step in that progression through ascending research challenges. This paper reviews results on algorithm design and theory of ES for such infinite-dimensional systems. Both hyperbolic and parabolic dynamics are presented: delays or transport equations, heat-dominated equation, ","authors_text":"Miroslav Krsti\\'c, Tamer Ba\\c{s}ar, Tiago Roux Oliveira","cross_cats":["cs.SY","eess.SY"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-20T11:55:18Z","title":"Extremum and Nash Equilibrium Seeking with Delays and PDEs: Designs & Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13234","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:ca8ad75cc0d8dbc095671240488962804374ce4da1f458fb744ef7c35f342db8","target":"record","created_at":"2026-07-05T09:38:07Z","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":"508f0af7ebd06de8e4c0bc14242737ce3be9b3a262e2c1a78a7da1eb204c9c6d","cross_cats_sorted":["cs.SY","eess.SY"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2024-11-20T11:55:18Z","title_canon_sha256":"0ac091c5459146188701ccfe0d1514f6e5d9425009a6313a6ba91e378b2e48ec"},"schema_version":"1.0","source":{"id":"2411.13234","kind":"arxiv","version":1}},"canonical_sha256":"b03351c714efe7a66fc19e0b0225a16c83d6cc3de9b6fb324bea58767fcbc8af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b03351c714efe7a66fc19e0b0225a16c83d6cc3de9b6fb324bea58767fcbc8af","first_computed_at":"2026-07-05T09:38:07.099158Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:38:07.099158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5Z8qD7CbrnmKsU2jatIFdMfUjEkrexIekKAyXalPmo6yQxwiGITUnhQHzIGk9WEet7+4uVces+dlZXHZF/+2Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:38:07.099557Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.13234","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca8ad75cc0d8dbc095671240488962804374ce4da1f458fb744ef7c35f342db8","sha256:1bc66b6c4f03f75c3a891fb9ca9ea4bd6886e6238f511298211f7f433ab893bd"],"state_sha256":"1530aedbf5659c199ae9889a235c81221ae6284e6a785d30f1fee309f67d7e1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tha/BmTZbW4DgsvESSB+aVkW1E9QwSruJOzde6CLK1l89ZzkervJP/I2jZferlp5wKn1V/iaH5Nu24eD00onBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T11:07:54.807433Z","bundle_sha256":"316e2079ffd45d8e33734b49944bc752e330de45b234f109eb7c8d749e5ccda9"}}