{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HRDMWGRL47XWTLLPJWVLSEHARN","short_pith_number":"pith:HRDMWGRL","canonical_record":{"source":{"id":"2605.26317","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-05-25T20:17:07Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"c10cead30c1d2af081153ca3898ecaf46910709c1113d80e779bd7cacca84ba1","abstract_canon_sha256":"6dabadb6d81c25125bd3633a8bb7e7e97877c201373cfddf9eaa46a05b8140b5"},"schema_version":"1.0"},"canonical_sha256":"3c46cb1a2be7ef69ad6f4daab910e08b4a6e9d92ba4d5baaafff82e4d90a803b","source":{"kind":"arxiv","id":"2605.26317","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26317","created_at":"2026-05-27T01:05:11Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26317v1","created_at":"2026-05-27T01:05:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26317","created_at":"2026-05-27T01:05:11Z"},{"alias_kind":"pith_short_12","alias_value":"HRDMWGRL47XW","created_at":"2026-05-27T01:05:11Z"},{"alias_kind":"pith_short_16","alias_value":"HRDMWGRL47XWTLLP","created_at":"2026-05-27T01:05:11Z"},{"alias_kind":"pith_short_8","alias_value":"HRDMWGRL","created_at":"2026-05-27T01:05:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HRDMWGRL47XWTLLPJWVLSEHARN","target":"record","payload":{"canonical_record":{"source":{"id":"2605.26317","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-05-25T20:17:07Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"c10cead30c1d2af081153ca3898ecaf46910709c1113d80e779bd7cacca84ba1","abstract_canon_sha256":"6dabadb6d81c25125bd3633a8bb7e7e97877c201373cfddf9eaa46a05b8140b5"},"schema_version":"1.0"},"canonical_sha256":"3c46cb1a2be7ef69ad6f4daab910e08b4a6e9d92ba4d5baaafff82e4d90a803b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T01:05:11.704809Z","signature_b64":"1HWOslxACvCxEurALyNn717Psurgfg3xj9DUyMTq0sAacPBGmdloMvO+P0yCjrdad5sZ16+RDi5WMFLWL2bVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c46cb1a2be7ef69ad6f4daab910e08b4a6e9d92ba4d5baaafff82e4d90a803b","last_reissued_at":"2026-05-27T01:05:11.704036Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T01:05:11.704036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.26317","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":"2026-05-27T01:05:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZsaxCQF9Jv3X4v5k8IxalvNzmS76mL71qG9aQbPAIvMv/RJu81f83zWQ1NQ4GPjBHPB0vBDTsOXf/GV5KZLiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:17:32.088993Z"},"content_sha256":"4fa4eddd9312697450a99a6d06c25ef833650b2f53d5f8c6c664c847da788c69","schema_version":"1.0","event_id":"sha256:4fa4eddd9312697450a99a6d06c25ef833650b2f53d5f8c6c664c847da788c69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HRDMWGRL47XWTLLPJWVLSEHARN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Jacobi-like algorithm for normal matrices by the skew-symmetric part","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"P.-A. Absil, Simon Mataigne","submitted_at":"2026-05-25T20:17:07Z","abstract_excerpt":"We present a fast Jacobi-like algorithm for computing the eigenvalues, and optionally the eigenvectors, of a real normal matrix. The method gains a computational advantage by using Paardekooper's method for skew-symmetric matrices The method is most efficient for matrices where most eigenvalues are complex, such as random orthogonal matrices arising in the context of statistics on manifolds. In this case, the method is faster than the other Jacobi-like algorithms. In the last section of this paper, we also give explicit formulas for the nearest symmetric skew-Hamiltonian and the nearest ortho-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26317","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/2605.26317/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":"2026-05-27T01:05:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DeHK9u3DKxAFHtd5WPw9I0flkH8lqS7N6V9cKGO7MK7TqtCUcchjD6jeieQKFaQRWjfk3NAYcBkv4oURl8ckCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:17:32.089867Z"},"content_sha256":"7494e74a5e2db41f181723a9a8f34fe4d878cbe452762db2652f74ee0c3c2db1","schema_version":"1.0","event_id":"sha256:7494e74a5e2db41f181723a9a8f34fe4d878cbe452762db2652f74ee0c3c2db1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HRDMWGRL47XWTLLPJWVLSEHARN/bundle.json","state_url":"https://pith.science/pith/HRDMWGRL47XWTLLPJWVLSEHARN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HRDMWGRL47XWTLLPJWVLSEHARN/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":"2026-05-30T18:17:32Z","links":{"resolver":"https://pith.science/pith/HRDMWGRL47XWTLLPJWVLSEHARN","bundle":"https://pith.science/pith/HRDMWGRL47XWTLLPJWVLSEHARN/bundle.json","state":"https://pith.science/pith/HRDMWGRL47XWTLLPJWVLSEHARN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HRDMWGRL47XWTLLPJWVLSEHARN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HRDMWGRL47XWTLLPJWVLSEHARN","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":"6dabadb6d81c25125bd3633a8bb7e7e97877c201373cfddf9eaa46a05b8140b5","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-05-25T20:17:07Z","title_canon_sha256":"c10cead30c1d2af081153ca3898ecaf46910709c1113d80e779bd7cacca84ba1"},"schema_version":"1.0","source":{"id":"2605.26317","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.26317","created_at":"2026-05-27T01:05:11Z"},{"alias_kind":"arxiv_version","alias_value":"2605.26317v1","created_at":"2026-05-27T01:05:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.26317","created_at":"2026-05-27T01:05:11Z"},{"alias_kind":"pith_short_12","alias_value":"HRDMWGRL47XW","created_at":"2026-05-27T01:05:11Z"},{"alias_kind":"pith_short_16","alias_value":"HRDMWGRL47XWTLLP","created_at":"2026-05-27T01:05:11Z"},{"alias_kind":"pith_short_8","alias_value":"HRDMWGRL","created_at":"2026-05-27T01:05:11Z"}],"graph_snapshots":[{"event_id":"sha256:7494e74a5e2db41f181723a9a8f34fe4d878cbe452762db2652f74ee0c3c2db1","target":"graph","created_at":"2026-05-27T01:05:11Z","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/2605.26317/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a fast Jacobi-like algorithm for computing the eigenvalues, and optionally the eigenvectors, of a real normal matrix. The method gains a computational advantage by using Paardekooper's method for skew-symmetric matrices The method is most efficient for matrices where most eigenvalues are complex, such as random orthogonal matrices arising in the context of statistics on manifolds. In this case, the method is faster than the other Jacobi-like algorithms. In the last section of this paper, we also give explicit formulas for the nearest symmetric skew-Hamiltonian and the nearest ortho-","authors_text":"P.-A. Absil, Simon Mataigne","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-05-25T20:17:07Z","title":"A Jacobi-like algorithm for normal matrices by the skew-symmetric part"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26317","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":"sha256:4fa4eddd9312697450a99a6d06c25ef833650b2f53d5f8c6c664c847da788c69","target":"record","created_at":"2026-05-27T01:05:11Z","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":"6dabadb6d81c25125bd3633a8bb7e7e97877c201373cfddf9eaa46a05b8140b5","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-05-25T20:17:07Z","title_canon_sha256":"c10cead30c1d2af081153ca3898ecaf46910709c1113d80e779bd7cacca84ba1"},"schema_version":"1.0","source":{"id":"2605.26317","kind":"arxiv","version":1}},"canonical_sha256":"3c46cb1a2be7ef69ad6f4daab910e08b4a6e9d92ba4d5baaafff82e4d90a803b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c46cb1a2be7ef69ad6f4daab910e08b4a6e9d92ba4d5baaafff82e4d90a803b","first_computed_at":"2026-05-27T01:05:11.704036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T01:05:11.704036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1HWOslxACvCxEurALyNn717Psurgfg3xj9DUyMTq0sAacPBGmdloMvO+P0yCjrdad5sZ16+RDi5WMFLWL2bVDw==","signature_status":"signed_v1","signed_at":"2026-05-27T01:05:11.704809Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.26317","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4fa4eddd9312697450a99a6d06c25ef833650b2f53d5f8c6c664c847da788c69","sha256:7494e74a5e2db41f181723a9a8f34fe4d878cbe452762db2652f74ee0c3c2db1"],"state_sha256":"8a104743f9615f80d25ba7953c4a33f1b352c754abaf2c381f6941a6a00758cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"US106ZVolaupXnlWe3W5lsD0qbg+SRaMo52Vr+0k0bGfCnayWy19l4se6fCqr83ug4u05jfrq1RJDJ036AIDDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T18:17:32.094208Z","bundle_sha256":"a40bfc16d250ba9b3d6d8f76fc53fbb40a1cef6387889cfa547801c1287c0d69"}}