{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YCF5GWWAGDPYLXPWTW3N4CA4RS","short_pith_number":"pith:YCF5GWWA","schema_version":"1.0","canonical_sha256":"c08bd35ac030df85ddf69db6de081c8cbad5728a0fd76b68458d3d6a3c8ff0c9","source":{"kind":"arxiv","id":"1305.4122","version":1},"attestation_state":"computed","paper":{"title":"Sharpness for $C^1$ linearization of planar hyperbolic diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Weinian Zhang, Wenmeng Zhang","submitted_at":"2013-05-17T16:06:32Z","abstract_excerpt":"Planar hyperbolic diffeomorphisms can be referred to two cases: Poincar\\'{e} domain (both eigenvalues lie inside the unit circle $S^1$) and Siegel domain (one eigenvalue inside $S^1$ but the other outside $S^1$). In Poincar\\'{e} domain it was proved that $C^{1,\\alpha}$ smoothness with $\\alpha_0:=1-\\log|\\lambda_2|/\\log|\\lambda_1|<\\alpha\\le 1$, where $\\lambda_1$ and $\\lambda_2$ are both eigenvalues such that $0<|\\lambda_1|<|\\lambda_2|<1$, admits $C^1$ linearization and the linearization is actually $C^{1,\\beta}$. While a sharp H\\\"older exponent $\\beta>0$ is given, an interesting problem is: Is t"},"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":"1305.4122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-05-17T16:06:32Z","cross_cats_sorted":[],"title_canon_sha256":"f7dd9effd13869a7508f2c295afcdd864d2724f8cc2c48c542151e097188e83b","abstract_canon_sha256":"30998b222e8aba720f1a636c14c58d8fa985a1116a6c3a96a47092f645a04902"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:26.200823Z","signature_b64":"fxcKOs5gAzPJMobU3I9Xv+nkoj4PxkwFndzPyrY2pMoGOxv994R9yzAe4HGY4yDEurIlOzBKdbeGp11R6mdCBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c08bd35ac030df85ddf69db6de081c8cbad5728a0fd76b68458d3d6a3c8ff0c9","last_reissued_at":"2026-05-18T03:25:26.200408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:26.200408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharpness for $C^1$ linearization of planar hyperbolic diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Weinian Zhang, Wenmeng Zhang","submitted_at":"2013-05-17T16:06:32Z","abstract_excerpt":"Planar hyperbolic diffeomorphisms can be referred to two cases: Poincar\\'{e} domain (both eigenvalues lie inside the unit circle $S^1$) and Siegel domain (one eigenvalue inside $S^1$ but the other outside $S^1$). In Poincar\\'{e} domain it was proved that $C^{1,\\alpha}$ smoothness with $\\alpha_0:=1-\\log|\\lambda_2|/\\log|\\lambda_1|<\\alpha\\le 1$, where $\\lambda_1$ and $\\lambda_2$ are both eigenvalues such that $0<|\\lambda_1|<|\\lambda_2|<1$, admits $C^1$ linearization and the linearization is actually $C^{1,\\beta}$. While a sharp H\\\"older exponent $\\beta>0$ is given, an interesting problem is: Is t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4122","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":"1305.4122","created_at":"2026-05-18T03:25:26.200466+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.4122v1","created_at":"2026-05-18T03:25:26.200466+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.4122","created_at":"2026-05-18T03:25:26.200466+00:00"},{"alias_kind":"pith_short_12","alias_value":"YCF5GWWAGDPY","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"YCF5GWWAGDPYLXPW","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"YCF5GWWA","created_at":"2026-05-18T12:28:06.772260+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/YCF5GWWAGDPYLXPWTW3N4CA4RS","json":"https://pith.science/pith/YCF5GWWAGDPYLXPWTW3N4CA4RS.json","graph_json":"https://pith.science/api/pith-number/YCF5GWWAGDPYLXPWTW3N4CA4RS/graph.json","events_json":"https://pith.science/api/pith-number/YCF5GWWAGDPYLXPWTW3N4CA4RS/events.json","paper":"https://pith.science/paper/YCF5GWWA"},"agent_actions":{"view_html":"https://pith.science/pith/YCF5GWWAGDPYLXPWTW3N4CA4RS","download_json":"https://pith.science/pith/YCF5GWWAGDPYLXPWTW3N4CA4RS.json","view_paper":"https://pith.science/paper/YCF5GWWA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.4122&json=true","fetch_graph":"https://pith.science/api/pith-number/YCF5GWWAGDPYLXPWTW3N4CA4RS/graph.json","fetch_events":"https://pith.science/api/pith-number/YCF5GWWAGDPYLXPWTW3N4CA4RS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YCF5GWWAGDPYLXPWTW3N4CA4RS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YCF5GWWAGDPYLXPWTW3N4CA4RS/action/storage_attestation","attest_author":"https://pith.science/pith/YCF5GWWAGDPYLXPWTW3N4CA4RS/action/author_attestation","sign_citation":"https://pith.science/pith/YCF5GWWAGDPYLXPWTW3N4CA4RS/action/citation_signature","submit_replication":"https://pith.science/pith/YCF5GWWAGDPYLXPWTW3N4CA4RS/action/replication_record"}},"created_at":"2026-05-18T03:25:26.200466+00:00","updated_at":"2026-05-18T03:25:26.200466+00:00"}