{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LGNXSAOYBQBVE5TXOMSQNMOARN","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":"5ce0aa166f402f16055bb2ac170414dbc36631bda2b1093eac94bb29f3d0fa32","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-06-20T19:20:22Z","title_canon_sha256":"c11b51b8d4d82b0f935062770b5d04723f7f93fd51ce74dde289f71156fa2c6c"},"schema_version":"1.0","source":{"id":"1406.5492","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5492","created_at":"2026-05-18T01:25:18Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5492v2","created_at":"2026-05-18T01:25:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5492","created_at":"2026-05-18T01:25:18Z"},{"alias_kind":"pith_short_12","alias_value":"LGNXSAOYBQBV","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LGNXSAOYBQBVE5TX","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LGNXSAOY","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:c5531c1685507fbc0a1895821e329c37a76f6f71537ce64e01697c90f44bee84","target":"graph","created_at":"2026-05-18T01:25:18Z","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":"We study differentiability properties in a particular case of the Palmer's linearization Theorem, which states the existence of an homeomorphism $H$ between the solutions of a linear ODE system having exponential dichotomy and a quasilinear system. Indeed, if the linear system is uniformly asymptotically stable, sufficient conditions ensuring that $H$ is a $C^{2}$ preserving orientation diffeomorphism are given. As an application, we generalize a converse result of density functions for a nonlinear system in the nonautonomous case.","authors_text":"Alvaro Casta\\~neda, Gonzalo Robledo","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-06-20T19:20:22Z","title":"Differentiability of Palmer's linearization Theorem and converse result for density functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5492","kind":"arxiv","version":2},"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":"sha256:5d0c2bbc8bef8b92923d98754e71014bdbfd1d5b533b371f0197e9fdd743ee12","target":"record","created_at":"2026-05-18T01:25:18Z","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":"5ce0aa166f402f16055bb2ac170414dbc36631bda2b1093eac94bb29f3d0fa32","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-06-20T19:20:22Z","title_canon_sha256":"c11b51b8d4d82b0f935062770b5d04723f7f93fd51ce74dde289f71156fa2c6c"},"schema_version":"1.0","source":{"id":"1406.5492","kind":"arxiv","version":2}},"canonical_sha256":"599b7901d80c03527677732506b1c08b7fbed130ea710dfd48b7c9967a9073f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"599b7901d80c03527677732506b1c08b7fbed130ea710dfd48b7c9967a9073f7","first_computed_at":"2026-05-18T01:25:18.489921Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:18.489921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A6UXntDEzG9aFSJTRWoTQRcB2Po0Z9ArrQ4yXP7THXho4ub2RsVTiIWk2yIWFRMrhnJh4w1RJWIG8PMqXs6YAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:18.490427Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5492","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d0c2bbc8bef8b92923d98754e71014bdbfd1d5b533b371f0197e9fdd743ee12","sha256:c5531c1685507fbc0a1895821e329c37a76f6f71537ce64e01697c90f44bee84"],"state_sha256":"fd990b992040d5ba31e7b7a86ef64fc6deaf9293179d0eb9cb98903b4c9a4722"}