{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:Y5IBV6MNHMAZVMO57AULTF6EAO","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":"b6b2d21b830d6eb8da5a824a75926e7744d6429830e77efd9e3e0ddf24a37c6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-05-25T17:40:11Z","title_canon_sha256":"4ea89ecb5b83a9db3e8f0d7dc80771069c40778e531e72a53b6366695590ea55"},"schema_version":"1.0","source":{"id":"0905.4051","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.4051","created_at":"2026-05-18T04:34:55Z"},{"alias_kind":"arxiv_version","alias_value":"0905.4051v3","created_at":"2026-05-18T04:34:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.4051","created_at":"2026-05-18T04:34:55Z"},{"alias_kind":"pith_short_12","alias_value":"Y5IBV6MNHMAZ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"Y5IBV6MNHMAZVMO5","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"Y5IBV6MN","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:27817e2ea0b89a4517cd5e896054b5df61485588753871ecb6c89c3b530de39a","target":"graph","created_at":"2026-05-18T04:34:55Z","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":"Let A(z) be an analytic square matrix and $\\lambda_{0}$ an eigenvalue of A(0) of multiplicity m. Then under the generic condition, the characteristic polynomial of A(z) evaluated at $\\lambda_{0}$ has a simple zero at z=0, we prove that the Jordan normal form of A(0) corresponding to the eigenvalue $\\lambda_{0}$ consists of a single m-by-m Jordan block, the perturbed eigenvalues near $\\lambda_{0}$ and their eigenvectors can be represented by a single convergent Puiseux series containing only powers of z^{1/m}, and there are explicit recursive formulas to compute all the Puiseux series coefficie","authors_text":"Aaron Welters","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-05-25T17:40:11Z","title":"On Explicit Recursive Formulas in the Spectral Perturbation Analysis of a Jordan Block"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.4051","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:ae2a234c8a50599052bf49469d19790c9688a11a5d6b6228fd3ac80945a39fd3","target":"record","created_at":"2026-05-18T04:34:55Z","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":"b6b2d21b830d6eb8da5a824a75926e7744d6429830e77efd9e3e0ddf24a37c6b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2009-05-25T17:40:11Z","title_canon_sha256":"4ea89ecb5b83a9db3e8f0d7dc80771069c40778e531e72a53b6366695590ea55"},"schema_version":"1.0","source":{"id":"0905.4051","kind":"arxiv","version":3}},"canonical_sha256":"c7501af98d3b019ab1ddf828b997c403be1590bd69e0246bd6c7edc927a2355f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7501af98d3b019ab1ddf828b997c403be1590bd69e0246bd6c7edc927a2355f","first_computed_at":"2026-05-18T04:34:55.526556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:55.526556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+uIIT/2qSErq5fEPGaOHdROcbijW+dobWNmiK2mXs8v5gaE/rMKuWdD+6ALpOaOlP6dLkND6jwEcJ60+FPTeCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:55.527037Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.4051","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae2a234c8a50599052bf49469d19790c9688a11a5d6b6228fd3ac80945a39fd3","sha256:27817e2ea0b89a4517cd5e896054b5df61485588753871ecb6c89c3b530de39a"],"state_sha256":"3e594d926730588f6812d8bc404c1cdc2fbe06f96ac2120660ac3fe4870fd22d"}