{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:47LFPLBIUVBF5EASXANNQRTELI","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":"8bd06752e3139eab22a9144eddb1c03b14c2562341aabffad600fb31d592c5d8","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-11-11T01:17:02Z","title_canon_sha256":"e7b3aeb360307c3eb282e5fa0e0cd2f0d1c767cdc31c83546196e30dadab70fa"},"schema_version":"1.0","source":{"id":"1611.03557","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03557","created_at":"2026-05-18T00:59:33Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03557v1","created_at":"2026-05-18T00:59:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03557","created_at":"2026-05-18T00:59:33Z"},{"alias_kind":"pith_short_12","alias_value":"47LFPLBIUVBF","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"47LFPLBIUVBF5EAS","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"47LFPLBI","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:ceee4fdf8d2dc853386d30e4510699ed9cc4f7037ecdbfc151845701090bc1f8","target":"graph","created_at":"2026-05-18T00:59:33Z","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":"V.I. Arnold (1971) constructed a simple normal form to which all complex matrices $B$ in a neighborhood $U$ of a given square matrix $A$ can be reduced by similarity transformations that smoothly depend on the entries of $B$. We calculate the radius of the neighborhood $U$. A.A. Mailybaev (1999, 2001) constructed a reducing similarity transformation in the form of Taylor series; we construct this transformation by another method. We extend Arnold's normal form to matrices over the field $\\mathbb Q_p$ of $p$-adic numbers and the field $\\mathbb F((T))$ of Laurent series over a field $\\mathbb F$.","authors_text":"Mohammed A. Salim, Victor A. Bovdi, Vladimir V. Sergeichuk","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-11-11T01:17:02Z","title":"Neighborhood radius estimation for Arnold's miniversal deformations of complex and $p$-adic matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03557","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":"sha256:6f3a3e83b57d41094470f87fd59d495933ce0e12d8d7c3a9f63bc9212041429a","target":"record","created_at":"2026-05-18T00:59:33Z","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":"8bd06752e3139eab22a9144eddb1c03b14c2562341aabffad600fb31d592c5d8","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-11-11T01:17:02Z","title_canon_sha256":"e7b3aeb360307c3eb282e5fa0e0cd2f0d1c767cdc31c83546196e30dadab70fa"},"schema_version":"1.0","source":{"id":"1611.03557","kind":"arxiv","version":1}},"canonical_sha256":"e7d657ac28a5425e9012b81ad846645a3c98ae5fc5762acdc253a04cc76eacac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7d657ac28a5425e9012b81ad846645a3c98ae5fc5762acdc253a04cc76eacac","first_computed_at":"2026-05-18T00:59:33.887355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:33.887355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nqq183xP9Ymjg7dzkr99O2GIBsfqpJ38PQ/mMAth4CCFoue4kKEL4RHypDiSuJBnCOX+tlm1bJJfG5nru1eEAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:33.888025Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03557","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f3a3e83b57d41094470f87fd59d495933ce0e12d8d7c3a9f63bc9212041429a","sha256:ceee4fdf8d2dc853386d30e4510699ed9cc4f7037ecdbfc151845701090bc1f8"],"state_sha256":"142554ed8923ba3935dd9bade0f7b6088e359abc71c30d009ca36e765de3777c"}