{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:S6CLJFZ6XSBU7OGB4M5O6YQKHQ","short_pith_number":"pith:S6CLJFZ6","schema_version":"1.0","canonical_sha256":"9784b4973ebc834fb8c1e33aef620a3c2094018e093d43e50217a4cc570aaf56","source":{"kind":"arxiv","id":"1808.06506","version":1},"attestation_state":"computed","paper":{"title":"Perturbation analysis of a matrix differential equation $\\dot x=ABx$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"M. Isabel Garc\\`ia-Planas, Tetiana Klymchuk","submitted_at":"2018-08-17T16:11:46Z","abstract_excerpt":"Two complex matrix pairs $(A,B)$ and $(A',B')$ are contragrediently equivalent if there are nonsingular $S$ and $R$ such that $(A',B')=(S^{-1}AR,R^{-1}BS)$. M.I. Garc\\'{\\i}a-Planas and V.V. Sergeichuk (1999) constructed a miniversal deformation of a canonical pair $(A,B)$ for contragredient equivalence; that is, a simple normal form to which all matrix pairs $(A + \\widetilde A, B+\\widetilde B)$ close to $(A,B)$ can be reduced by contragredient equivalence transformations that smoothly depend on the entries of $\\widetilde A$ and $ \\widetilde B$. Each perturbation $(\\widetilde A,\\widetilde B)$ o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1808.06506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-08-17T16:11:46Z","cross_cats_sorted":[],"title_canon_sha256":"6c3b89cacff1365bdf5fb8d571866487283d78a28fc3b9cae345ea259c0494b0","abstract_canon_sha256":"fed9a9039460c2a61a8ca407ad3888f1a04f9c71cf6fc595935446ad577b8b09"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:44.687579Z","signature_b64":"xgMU9cGnrvaGSTsgbU2HEZYOwpQeKDv425ZM33P4UgaCvBPizha/6hGRbbzgeQwHFBBDoKY2XMrBK2ZK3CibCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9784b4973ebc834fb8c1e33aef620a3c2094018e093d43e50217a4cc570aaf56","last_reissued_at":"2026-05-18T00:07:44.686812Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:44.686812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perturbation analysis of a matrix differential equation $\\dot x=ABx$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"M. Isabel Garc\\`ia-Planas, Tetiana Klymchuk","submitted_at":"2018-08-17T16:11:46Z","abstract_excerpt":"Two complex matrix pairs $(A,B)$ and $(A',B')$ are contragrediently equivalent if there are nonsingular $S$ and $R$ such that $(A',B')=(S^{-1}AR,R^{-1}BS)$. M.I. Garc\\'{\\i}a-Planas and V.V. Sergeichuk (1999) constructed a miniversal deformation of a canonical pair $(A,B)$ for contragredient equivalence; that is, a simple normal form to which all matrix pairs $(A + \\widetilde A, B+\\widetilde B)$ close to $(A,B)$ can be reduced by contragredient equivalence transformations that smoothly depend on the entries of $\\widetilde A$ and $ \\widetilde B$. Each perturbation $(\\widetilde A,\\widetilde B)$ o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.06506","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1808.06506","created_at":"2026-05-18T00:07:44.686937+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.06506v1","created_at":"2026-05-18T00:07:44.686937+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.06506","created_at":"2026-05-18T00:07:44.686937+00:00"},{"alias_kind":"pith_short_12","alias_value":"S6CLJFZ6XSBU","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"S6CLJFZ6XSBU7OGB","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"S6CLJFZ6","created_at":"2026-05-18T12:32:50.500415+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S6CLJFZ6XSBU7OGB4M5O6YQKHQ","json":"https://pith.science/pith/S6CLJFZ6XSBU7OGB4M5O6YQKHQ.json","graph_json":"https://pith.science/api/pith-number/S6CLJFZ6XSBU7OGB4M5O6YQKHQ/graph.json","events_json":"https://pith.science/api/pith-number/S6CLJFZ6XSBU7OGB4M5O6YQKHQ/events.json","paper":"https://pith.science/paper/S6CLJFZ6"},"agent_actions":{"view_html":"https://pith.science/pith/S6CLJFZ6XSBU7OGB4M5O6YQKHQ","download_json":"https://pith.science/pith/S6CLJFZ6XSBU7OGB4M5O6YQKHQ.json","view_paper":"https://pith.science/paper/S6CLJFZ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.06506&json=true","fetch_graph":"https://pith.science/api/pith-number/S6CLJFZ6XSBU7OGB4M5O6YQKHQ/graph.json","fetch_events":"https://pith.science/api/pith-number/S6CLJFZ6XSBU7OGB4M5O6YQKHQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S6CLJFZ6XSBU7OGB4M5O6YQKHQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S6CLJFZ6XSBU7OGB4M5O6YQKHQ/action/storage_attestation","attest_author":"https://pith.science/pith/S6CLJFZ6XSBU7OGB4M5O6YQKHQ/action/author_attestation","sign_citation":"https://pith.science/pith/S6CLJFZ6XSBU7OGB4M5O6YQKHQ/action/citation_signature","submit_replication":"https://pith.science/pith/S6CLJFZ6XSBU7OGB4M5O6YQKHQ/action/replication_record"}},"created_at":"2026-05-18T00:07:44.686937+00:00","updated_at":"2026-05-18T00:07:44.686937+00:00"}