{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:DVAPVZJN3WNMBPBZBO652HN75D","short_pith_number":"pith:DVAPVZJN","schema_version":"1.0","canonical_sha256":"1d40fae52ddd9ac0bc390bbddd1dbfe8e7dd20bf17cdfc1c8a2e253bff42e3cd","source":{"kind":"arxiv","id":"1105.4890","version":1},"attestation_state":"computed","paper":{"title":"On global linearization of planar involutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Benito Pires, Marco Antonio Teixeira","submitted_at":"2011-05-24T20:55:49Z","abstract_excerpt":"Let $\\phi:\\R^2\\to\\R^2$ be an orientation--preserving $C^1$ involution such that $\\phi(0)=0$ and let ${\\rm Spc}\\,(\\phi)=\\{{\\rm Eigenvalues\\,\\,of}\\,\\, D\\phi(p)\\mid p\\in\\R^2\\}$. We prove that if ${\\rm Spc}\\,{(\\phi)}\\subset\\R$ or ${\\rm Spc}\\,(\\phi)\\cap [1,1+\\epsilon)=\\emptyset$ for some $\\epsilon>0$ then $\\phi$ is globally $C^1$ conjugate to the linear involution $D\\phi(0)$ via the conjugacy $h=(I+D\\phi(0)\\phi)/2$, where $I:\\R^2\\to\\R^2$ is the identity map. Similarly, if $\\phi$ is an orientation-reversing $C^1$ involution such that $\\phi(0)=0$ and ${\\rm Trace}\\,\\big(D\\phi(0)D\\phi(p)\\big)>-1 $ for "},"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":"1105.4890","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-24T20:55:49Z","cross_cats_sorted":[],"title_canon_sha256":"15240b2426caad85182b2cc59aa90c0b8fb8a9b7bd21eba90aabbe9697f954d5","abstract_canon_sha256":"93d53754f46c9e3c300556f251b959cec895aca8730e051272071bb7d95725fc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:21.117558Z","signature_b64":"SuKklIBC0t788jJzrZtcajYEdS4BJWBAcgn/KIzfFxvjshU4uQmqqd3cRW7Tnr9TG5qr91uAEdplpElmgERuCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d40fae52ddd9ac0bc390bbddd1dbfe8e7dd20bf17cdfc1c8a2e253bff42e3cd","last_reissued_at":"2026-05-18T04:21:21.116965Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:21.116965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On global linearization of planar involutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Benito Pires, Marco Antonio Teixeira","submitted_at":"2011-05-24T20:55:49Z","abstract_excerpt":"Let $\\phi:\\R^2\\to\\R^2$ be an orientation--preserving $C^1$ involution such that $\\phi(0)=0$ and let ${\\rm Spc}\\,(\\phi)=\\{{\\rm Eigenvalues\\,\\,of}\\,\\, D\\phi(p)\\mid p\\in\\R^2\\}$. We prove that if ${\\rm Spc}\\,{(\\phi)}\\subset\\R$ or ${\\rm Spc}\\,(\\phi)\\cap [1,1+\\epsilon)=\\emptyset$ for some $\\epsilon>0$ then $\\phi$ is globally $C^1$ conjugate to the linear involution $D\\phi(0)$ via the conjugacy $h=(I+D\\phi(0)\\phi)/2$, where $I:\\R^2\\to\\R^2$ is the identity map. Similarly, if $\\phi$ is an orientation-reversing $C^1$ involution such that $\\phi(0)=0$ and ${\\rm Trace}\\,\\big(D\\phi(0)D\\phi(p)\\big)>-1 $ for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4890","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":"1105.4890","created_at":"2026-05-18T04:21:21.117044+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.4890v1","created_at":"2026-05-18T04:21:21.117044+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4890","created_at":"2026-05-18T04:21:21.117044+00:00"},{"alias_kind":"pith_short_12","alias_value":"DVAPVZJN3WNM","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"DVAPVZJN3WNMBPBZ","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"DVAPVZJN","created_at":"2026-05-18T12:26:26.731475+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/DVAPVZJN3WNMBPBZBO652HN75D","json":"https://pith.science/pith/DVAPVZJN3WNMBPBZBO652HN75D.json","graph_json":"https://pith.science/api/pith-number/DVAPVZJN3WNMBPBZBO652HN75D/graph.json","events_json":"https://pith.science/api/pith-number/DVAPVZJN3WNMBPBZBO652HN75D/events.json","paper":"https://pith.science/paper/DVAPVZJN"},"agent_actions":{"view_html":"https://pith.science/pith/DVAPVZJN3WNMBPBZBO652HN75D","download_json":"https://pith.science/pith/DVAPVZJN3WNMBPBZBO652HN75D.json","view_paper":"https://pith.science/paper/DVAPVZJN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.4890&json=true","fetch_graph":"https://pith.science/api/pith-number/DVAPVZJN3WNMBPBZBO652HN75D/graph.json","fetch_events":"https://pith.science/api/pith-number/DVAPVZJN3WNMBPBZBO652HN75D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DVAPVZJN3WNMBPBZBO652HN75D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DVAPVZJN3WNMBPBZBO652HN75D/action/storage_attestation","attest_author":"https://pith.science/pith/DVAPVZJN3WNMBPBZBO652HN75D/action/author_attestation","sign_citation":"https://pith.science/pith/DVAPVZJN3WNMBPBZBO652HN75D/action/citation_signature","submit_replication":"https://pith.science/pith/DVAPVZJN3WNMBPBZBO652HN75D/action/replication_record"}},"created_at":"2026-05-18T04:21:21.117044+00:00","updated_at":"2026-05-18T04:21:21.117044+00:00"}