{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6RUOTYQRSF7PIDDH6OQL2FV3GZ","short_pith_number":"pith:6RUOTYQR","schema_version":"1.0","canonical_sha256":"f468e9e211917ef40c67f3a0bd16bb3642dc7ffb60e6dd4abb7ba03c1b74cf26","source":{"kind":"arxiv","id":"1504.04665","version":1},"attestation_state":"computed","paper":{"title":"Nonuniform $(h,k,\\mu,\\nu)$-Dichotomy with Applications to Nonautonomous Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jimin Zhang, Liu Yang, Meng Fan","submitted_at":"2015-04-18T00:21:01Z","abstract_excerpt":"The paper develops and studies a very general notion of dichotomy, referred to as \"nonuniform $(h,k,\\mu,\\nu)$-dichotomy\". The new notion contains as special cases most versions of dichotomy existing in the literature. The paper then provides corresponding new versions of robustness, Hartman-Grobman theorem, and stable manifold theorem for nonautonomous dynamical systems in Banach spaces in term of the nonuniform $(h,k,\\mu,\\nu)$-dichotomy."},"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":"1504.04665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-04-18T00:21:01Z","cross_cats_sorted":[],"title_canon_sha256":"248a73db561a9a1747027d9f6419d9845b8ba3314b7d0e7fbf55f42b52e60489","abstract_canon_sha256":"3df0cf3df13b14056d6742f710e49b8ef642f031e7e79a14c1dbb0ac6298bbc7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:30.768022Z","signature_b64":"Qthu4eV1jEWeTCVPdx/LV+KFbjl0i9eEXe2OA41CmfifwJyLsfY1HKRq+Tg82LvVAc8mf2J8KSefJfnCQhp/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f468e9e211917ef40c67f3a0bd16bb3642dc7ffb60e6dd4abb7ba03c1b74cf26","last_reissued_at":"2026-05-18T02:18:30.767576Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:30.767576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonuniform $(h,k,\\mu,\\nu)$-Dichotomy with Applications to Nonautonomous Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jimin Zhang, Liu Yang, Meng Fan","submitted_at":"2015-04-18T00:21:01Z","abstract_excerpt":"The paper develops and studies a very general notion of dichotomy, referred to as \"nonuniform $(h,k,\\mu,\\nu)$-dichotomy\". The new notion contains as special cases most versions of dichotomy existing in the literature. The paper then provides corresponding new versions of robustness, Hartman-Grobman theorem, and stable manifold theorem for nonautonomous dynamical systems in Banach spaces in term of the nonuniform $(h,k,\\mu,\\nu)$-dichotomy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04665","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":"1504.04665","created_at":"2026-05-18T02:18:30.767646+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.04665v1","created_at":"2026-05-18T02:18:30.767646+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.04665","created_at":"2026-05-18T02:18:30.767646+00:00"},{"alias_kind":"pith_short_12","alias_value":"6RUOTYQRSF7P","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6RUOTYQRSF7PIDDH","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6RUOTYQR","created_at":"2026-05-18T12:29:07.941421+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/6RUOTYQRSF7PIDDH6OQL2FV3GZ","json":"https://pith.science/pith/6RUOTYQRSF7PIDDH6OQL2FV3GZ.json","graph_json":"https://pith.science/api/pith-number/6RUOTYQRSF7PIDDH6OQL2FV3GZ/graph.json","events_json":"https://pith.science/api/pith-number/6RUOTYQRSF7PIDDH6OQL2FV3GZ/events.json","paper":"https://pith.science/paper/6RUOTYQR"},"agent_actions":{"view_html":"https://pith.science/pith/6RUOTYQRSF7PIDDH6OQL2FV3GZ","download_json":"https://pith.science/pith/6RUOTYQRSF7PIDDH6OQL2FV3GZ.json","view_paper":"https://pith.science/paper/6RUOTYQR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.04665&json=true","fetch_graph":"https://pith.science/api/pith-number/6RUOTYQRSF7PIDDH6OQL2FV3GZ/graph.json","fetch_events":"https://pith.science/api/pith-number/6RUOTYQRSF7PIDDH6OQL2FV3GZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6RUOTYQRSF7PIDDH6OQL2FV3GZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6RUOTYQRSF7PIDDH6OQL2FV3GZ/action/storage_attestation","attest_author":"https://pith.science/pith/6RUOTYQRSF7PIDDH6OQL2FV3GZ/action/author_attestation","sign_citation":"https://pith.science/pith/6RUOTYQRSF7PIDDH6OQL2FV3GZ/action/citation_signature","submit_replication":"https://pith.science/pith/6RUOTYQRSF7PIDDH6OQL2FV3GZ/action/replication_record"}},"created_at":"2026-05-18T02:18:30.767646+00:00","updated_at":"2026-05-18T02:18:30.767646+00:00"}