{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ANFDCJ236RLLLJNUM6GHXCZXZZ","short_pith_number":"pith:ANFDCJ23","canonical_record":{"source":{"id":"1908.00639","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-01T21:46:59Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"01a3c15ea54a221c45917a89249dce5b0ead42cc5d18793046e2e6dc3585643f","abstract_canon_sha256":"0ac3b20252e38a5f3eb4120319b83d9ce6ae33ae85f5b850d6911d70ce8a047a"},"schema_version":"1.0"},"canonical_sha256":"034a31275bf456b5a5b4678c7b8b37ce7105ebb6b5f5fd41e724081aeacf939b","source":{"kind":"arxiv","id":"1908.00639","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00639","created_at":"2026-07-05T06:33:00Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00639v4","created_at":"2026-07-05T06:33:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00639","created_at":"2026-07-05T06:33:00Z"},{"alias_kind":"pith_short_12","alias_value":"ANFDCJ236RLL","created_at":"2026-07-05T06:33:00Z"},{"alias_kind":"pith_short_16","alias_value":"ANFDCJ236RLLLJNU","created_at":"2026-07-05T06:33:00Z"},{"alias_kind":"pith_short_8","alias_value":"ANFDCJ23","created_at":"2026-07-05T06:33:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ANFDCJ236RLLLJNUM6GHXCZXZZ","target":"record","payload":{"canonical_record":{"source":{"id":"1908.00639","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-01T21:46:59Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"01a3c15ea54a221c45917a89249dce5b0ead42cc5d18793046e2e6dc3585643f","abstract_canon_sha256":"0ac3b20252e38a5f3eb4120319b83d9ce6ae33ae85f5b850d6911d70ce8a047a"},"schema_version":"1.0"},"canonical_sha256":"034a31275bf456b5a5b4678c7b8b37ce7105ebb6b5f5fd41e724081aeacf939b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:33:00.531429Z","signature_b64":"vcP9XN6TkXtVtD201XYc1xCsIc1FiS/IquPoGpnqRBLiugfLXtbIU7G4g1hl1Sq7tVxXBPIOq5ua/qqQSOiaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"034a31275bf456b5a5b4678c7b8b37ce7105ebb6b5f5fd41e724081aeacf939b","last_reissued_at":"2026-07-05T06:33:00.530937Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:33:00.530937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.00639","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:33:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zvaik3R68s+T9laLjS+bTiuk2Z5EZ+iN8GRIaO7nYzhyPMqzgHLMXJKX3rmevXXyssz7ZuYTVLyCtoJZ6uGGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:37:38.025743Z"},"content_sha256":"11e6909067df5d634fbf0cece9349c09f9b4d0166238db4b48109a10bf22dfac","schema_version":"1.0","event_id":"sha256:11e6909067df5d634fbf0cece9349c09f9b4d0166238db4b48109a10bf22dfac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ANFDCJ236RLLLJNUM6GHXCZXZZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rayleigh Quotient Iteration, cubic convergence, and second covariant derivative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.OC","authors_text":"Du Nguyen","submitted_at":"2019-08-01T21:46:59Z","abstract_excerpt":"We generalize the Rayleigh Quotient Iteration (RQI) to the problem of solving a nonlinear equation where the variables are divided into two subsets, one satisfying additional equality constraints and the other could be considered as (generalized nonlinear Lagrange) multipliers. This framework covers several problems, including the (linear\\slash nonlinear) eigenvalue problems, the constrained optimization problem, and the tensor eigenpair problem. Often, the RQI increment could be computed in two equivalent forms. The classical Rayleigh quotient algorithm uses the {\\it Schur form}, while the pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00639","kind":"arxiv","version":4},"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/1908.00639/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":"2026-07-05T06:33:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kNIav6G1qTWnnPSoxf0GCV+XhhES5iuoOWI7ye6OCgjyjXT2powHAdMwFBLMnAuGA7EttaYBrSIDKa0NtKM9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:37:38.026399Z"},"content_sha256":"6d21b2eed886b61e89934a4a77c36bd2e963a5914b8280737d0a9d0ff21f0322","schema_version":"1.0","event_id":"sha256:6d21b2eed886b61e89934a4a77c36bd2e963a5914b8280737d0a9d0ff21f0322"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ANFDCJ236RLLLJNUM6GHXCZXZZ/bundle.json","state_url":"https://pith.science/pith/ANFDCJ236RLLLJNUM6GHXCZXZZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ANFDCJ236RLLLJNUM6GHXCZXZZ/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":"2026-08-16T07:37:38Z","links":{"resolver":"https://pith.science/pith/ANFDCJ236RLLLJNUM6GHXCZXZZ","bundle":"https://pith.science/pith/ANFDCJ236RLLLJNUM6GHXCZXZZ/bundle.json","state":"https://pith.science/pith/ANFDCJ236RLLLJNUM6GHXCZXZZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ANFDCJ236RLLLJNUM6GHXCZXZZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ANFDCJ236RLLLJNUM6GHXCZXZZ","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":"0ac3b20252e38a5f3eb4120319b83d9ce6ae33ae85f5b850d6911d70ce8a047a","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-01T21:46:59Z","title_canon_sha256":"01a3c15ea54a221c45917a89249dce5b0ead42cc5d18793046e2e6dc3585643f"},"schema_version":"1.0","source":{"id":"1908.00639","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.00639","created_at":"2026-07-05T06:33:00Z"},{"alias_kind":"arxiv_version","alias_value":"1908.00639v4","created_at":"2026-07-05T06:33:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.00639","created_at":"2026-07-05T06:33:00Z"},{"alias_kind":"pith_short_12","alias_value":"ANFDCJ236RLL","created_at":"2026-07-05T06:33:00Z"},{"alias_kind":"pith_short_16","alias_value":"ANFDCJ236RLLLJNU","created_at":"2026-07-05T06:33:00Z"},{"alias_kind":"pith_short_8","alias_value":"ANFDCJ23","created_at":"2026-07-05T06:33:00Z"}],"graph_snapshots":[{"event_id":"sha256:6d21b2eed886b61e89934a4a77c36bd2e963a5914b8280737d0a9d0ff21f0322","target":"graph","created_at":"2026-07-05T06:33:00Z","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/1908.00639/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalize the Rayleigh Quotient Iteration (RQI) to the problem of solving a nonlinear equation where the variables are divided into two subsets, one satisfying additional equality constraints and the other could be considered as (generalized nonlinear Lagrange) multipliers. This framework covers several problems, including the (linear\\slash nonlinear) eigenvalue problems, the constrained optimization problem, and the tensor eigenpair problem. Often, the RQI increment could be computed in two equivalent forms. The classical Rayleigh quotient algorithm uses the {\\it Schur form}, while the pr","authors_text":"Du Nguyen","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-01T21:46:59Z","title":"Rayleigh Quotient Iteration, cubic convergence, and second covariant derivative"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.00639","kind":"arxiv","version":4},"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":"sha256:11e6909067df5d634fbf0cece9349c09f9b4d0166238db4b48109a10bf22dfac","target":"record","created_at":"2026-07-05T06:33:00Z","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":"0ac3b20252e38a5f3eb4120319b83d9ce6ae33ae85f5b850d6911d70ce8a047a","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-08-01T21:46:59Z","title_canon_sha256":"01a3c15ea54a221c45917a89249dce5b0ead42cc5d18793046e2e6dc3585643f"},"schema_version":"1.0","source":{"id":"1908.00639","kind":"arxiv","version":4}},"canonical_sha256":"034a31275bf456b5a5b4678c7b8b37ce7105ebb6b5f5fd41e724081aeacf939b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"034a31275bf456b5a5b4678c7b8b37ce7105ebb6b5f5fd41e724081aeacf939b","first_computed_at":"2026-07-05T06:33:00.530937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:33:00.530937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vcP9XN6TkXtVtD201XYc1xCsIc1FiS/IquPoGpnqRBLiugfLXtbIU7G4g1hl1Sq7tVxXBPIOq5ua/qqQSOiaCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:33:00.531429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.00639","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11e6909067df5d634fbf0cece9349c09f9b4d0166238db4b48109a10bf22dfac","sha256:6d21b2eed886b61e89934a4a77c36bd2e963a5914b8280737d0a9d0ff21f0322"],"state_sha256":"6b48e516582f7e47f41b7b61d098313098fd64467a9c6d6328fe87e373283ad1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CLA0OFT60twYlzKEGkh4zdDJzls5H+8p2neve57SZrwjJ71KP7llBJ3uMIB7mqlcxs87a0aeXCDA3k1DttluAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T07:37:38.030818Z","bundle_sha256":"c6a2a31004cfb005eea146e7cd188b103021bc9e7a169bff421d2dbeb6707617"}}