{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7IZKGGTRXWFH7L2DFQV6V5RXCB","short_pith_number":"pith:7IZKGGTR","canonical_record":{"source":{"id":"1406.4694","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-18T12:35:32Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a393c32ccbca08930c9766c9243981b9ad0dbc868374000b2a394dc7576026ad","abstract_canon_sha256":"ad7d46638e2481c018fa5ccb812090aa1831a8e602dfc6bc9a699868fa214640"},"schema_version":"1.0"},"canonical_sha256":"fa32a31a71bd8a7faf432c2beaf637104c6c09881b37dbc83758fa7211a61655","source":{"kind":"arxiv","id":"1406.4694","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4694","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4694v3","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4694","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"7IZKGGTRXWFH","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7IZKGGTRXWFH7L2D","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7IZKGGTR","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7IZKGGTRXWFH7L2DFQV6V5RXCB","target":"record","payload":{"canonical_record":{"source":{"id":"1406.4694","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-18T12:35:32Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"a393c32ccbca08930c9766c9243981b9ad0dbc868374000b2a394dc7576026ad","abstract_canon_sha256":"ad7d46638e2481c018fa5ccb812090aa1831a8e602dfc6bc9a699868fa214640"},"schema_version":"1.0"},"canonical_sha256":"fa32a31a71bd8a7faf432c2beaf637104c6c09881b37dbc83758fa7211a61655","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:15.536675Z","signature_b64":"2htObwYOeeIithiqdVaY4CbbMLsZn6sI/DJO8CS0owsHShhApu5im5tEYL91LPCDHdtAuxBS35n3iIEXNzftBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa32a31a71bd8a7faf432c2beaf637104c6c09881b37dbc83758fa7211a61655","last_reissued_at":"2026-05-18T02:30:15.536170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:15.536170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.4694","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wfeJP+h3VDbdMC3xsXQQ6vQCqA9d/vEZuI3loWt4hKvoiU4XKQx1hROhPTd4gh1TOFYallGbOAFgNwqSiiZXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T02:13:52.640819Z"},"content_sha256":"7d2d529780040050f6ddf2c85fd0fb2f6b3f442adffa7a603485676f7fe37902","schema_version":"1.0","event_id":"sha256:7d2d529780040050f6ddf2c85fd0fb2f6b3f442adffa7a603485676f7fe37902"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7IZKGGTRXWFH7L2DFQV6V5RXCB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hopf bifurcation analysis of the generalized Lorenz system with time delayed feedback control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Marco Sammartino, Maria Carmela Lombardo, Rachele Barresi","submitted_at":"2014-06-18T12:35:32Z","abstract_excerpt":"In this work we propose a feedback approach to regulate the chaotic behavior of the whole family of the generalized Lorenz system, by designing a nonlinear delayed feedback control. We first study the effect of the delay on the dynamics of the system and we investigate the existence of Hopf bifurcations. Then, by using the center manifold reduction technique and the normal form theory, we derive the explicit formulas for the direction, stability and period of the periodic solutions bifurcating from the steady state at certain critical values of the delay."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4694","kind":"arxiv","version":3},"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":"2026-05-18T02:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YbS8qHjnp+66guLOmaEY3gX7gtf/g1jgkHnCka+BVjYtEF5jfINI9EnhLUclNMeoZ9YfQAWOj/r7UxmvSMnODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T02:13:52.641152Z"},"content_sha256":"49f12869b02f13095e94480092bff5544bf18da1ebbdce751a9882c93e5323fa","schema_version":"1.0","event_id":"sha256:49f12869b02f13095e94480092bff5544bf18da1ebbdce751a9882c93e5323fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7IZKGGTRXWFH7L2DFQV6V5RXCB/bundle.json","state_url":"https://pith.science/pith/7IZKGGTRXWFH7L2DFQV6V5RXCB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7IZKGGTRXWFH7L2DFQV6V5RXCB/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":"2026-07-01T02:13:52Z","links":{"resolver":"https://pith.science/pith/7IZKGGTRXWFH7L2DFQV6V5RXCB","bundle":"https://pith.science/pith/7IZKGGTRXWFH7L2DFQV6V5RXCB/bundle.json","state":"https://pith.science/pith/7IZKGGTRXWFH7L2DFQV6V5RXCB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7IZKGGTRXWFH7L2DFQV6V5RXCB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7IZKGGTRXWFH7L2DFQV6V5RXCB","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":"ad7d46638e2481c018fa5ccb812090aa1831a8e602dfc6bc9a699868fa214640","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-18T12:35:32Z","title_canon_sha256":"a393c32ccbca08930c9766c9243981b9ad0dbc868374000b2a394dc7576026ad"},"schema_version":"1.0","source":{"id":"1406.4694","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4694","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4694v3","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4694","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"7IZKGGTRXWFH","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7IZKGGTRXWFH7L2D","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7IZKGGTR","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:49f12869b02f13095e94480092bff5544bf18da1ebbdce751a9882c93e5323fa","target":"graph","created_at":"2026-05-18T02:30:15Z","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 work we propose a feedback approach to regulate the chaotic behavior of the whole family of the generalized Lorenz system, by designing a nonlinear delayed feedback control. We first study the effect of the delay on the dynamics of the system and we investigate the existence of Hopf bifurcations. Then, by using the center manifold reduction technique and the normal form theory, we derive the explicit formulas for the direction, stability and period of the periodic solutions bifurcating from the steady state at certain critical values of the delay.","authors_text":"Marco Sammartino, Maria Carmela Lombardo, Rachele Barresi","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-18T12:35:32Z","title":"Hopf bifurcation analysis of the generalized Lorenz system with time delayed feedback control"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4694","kind":"arxiv","version":3},"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":"sha256:7d2d529780040050f6ddf2c85fd0fb2f6b3f442adffa7a603485676f7fe37902","target":"record","created_at":"2026-05-18T02:30:15Z","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":"ad7d46638e2481c018fa5ccb812090aa1831a8e602dfc6bc9a699868fa214640","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-06-18T12:35:32Z","title_canon_sha256":"a393c32ccbca08930c9766c9243981b9ad0dbc868374000b2a394dc7576026ad"},"schema_version":"1.0","source":{"id":"1406.4694","kind":"arxiv","version":3}},"canonical_sha256":"fa32a31a71bd8a7faf432c2beaf637104c6c09881b37dbc83758fa7211a61655","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa32a31a71bd8a7faf432c2beaf637104c6c09881b37dbc83758fa7211a61655","first_computed_at":"2026-05-18T02:30:15.536170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:15.536170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2htObwYOeeIithiqdVaY4CbbMLsZn6sI/DJO8CS0owsHShhApu5im5tEYL91LPCDHdtAuxBS35n3iIEXNzftBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:15.536675Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4694","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d2d529780040050f6ddf2c85fd0fb2f6b3f442adffa7a603485676f7fe37902","sha256:49f12869b02f13095e94480092bff5544bf18da1ebbdce751a9882c93e5323fa"],"state_sha256":"9f9ff52eaba105584b707bc679116d7376f6d309017d3f40253685a09252de93"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NwtvzmbWKe4uW7AgY5FHQudLtDRjL8JA730hvaVA2cuWljM2R4vtuVE7WIoL9qQcirepmUWSl8StjKVqXAp7Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T02:13:52.643085Z","bundle_sha256":"fc83d4c16fe1d4053c4488dbe94f487d1218da5be6c77ea3a880081f8efb3e4e"}}