{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:VD32GFWZ6DNR2W4J7XIPHLANPM","short_pith_number":"pith:VD32GFWZ","schema_version":"1.0","canonical_sha256":"a8f7a316d9f0db1d5b89fdd0f3ac0d7b37885d9fadfe8533a59ceab9919827ae","source":{"kind":"arxiv","id":"1703.02455","version":5},"attestation_state":"computed","paper":{"title":"Strongly automorphic mappings and Julia sets of uniformly quasiregular mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Alastair Fletcher, Doug Macclure","submitted_at":"2017-03-07T16:24:28Z","abstract_excerpt":"A theorem of Ritt states the a linearizer of a holomorphic function at a repelling fixed point is periodic only if the holomorphic map is conjugate to a power of $z$, a Chebyshev polynomial or a Latt\\`es map. The converse, except for some exceptions, is also true. In this paper, we prove the analogous statement in the setting of strongly automorphic quasiregular mappings and uniformly quasiregular mappings in $\\mathbb{R}^n$. Along the way, we characterize the possible automorphy groups that can arise via crystallographic orbifolds and a use of the Poincar\\'e conjecture. We further give a class"},"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":"1703.02455","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-07T16:24:28Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"cbf14507f6f73d2c2ba521a56cfb6cd767cc2b7e925d6b7ea2c431e9bf439235","abstract_canon_sha256":"29f745e5f79a437e7eb71ecf2552048fd8b71dc8448b284ce8e99356e39448ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:12.476487Z","signature_b64":"MUkpnTyGtSDSHxAGTUjelBijdBt4kHuwoFEra9fbLwUI/3VMRzeE+YwGwb5jE1gqy2ztcO7+U4xBG8xQ7HtuDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8f7a316d9f0db1d5b89fdd0f3ac0d7b37885d9fadfe8533a59ceab9919827ae","last_reissued_at":"2026-05-18T00:06:12.475910Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:12.475910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strongly automorphic mappings and Julia sets of uniformly quasiregular mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Alastair Fletcher, Doug Macclure","submitted_at":"2017-03-07T16:24:28Z","abstract_excerpt":"A theorem of Ritt states the a linearizer of a holomorphic function at a repelling fixed point is periodic only if the holomorphic map is conjugate to a power of $z$, a Chebyshev polynomial or a Latt\\`es map. The converse, except for some exceptions, is also true. In this paper, we prove the analogous statement in the setting of strongly automorphic quasiregular mappings and uniformly quasiregular mappings in $\\mathbb{R}^n$. Along the way, we characterize the possible automorphy groups that can arise via crystallographic orbifolds and a use of the Poincar\\'e conjecture. We further give a class"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02455","kind":"arxiv","version":5},"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":"1703.02455","created_at":"2026-05-18T00:06:12.475995+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.02455v5","created_at":"2026-05-18T00:06:12.475995+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02455","created_at":"2026-05-18T00:06:12.475995+00:00"},{"alias_kind":"pith_short_12","alias_value":"VD32GFWZ6DNR","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"VD32GFWZ6DNR2W4J","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"VD32GFWZ","created_at":"2026-05-18T12:31:49.984773+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/VD32GFWZ6DNR2W4J7XIPHLANPM","json":"https://pith.science/pith/VD32GFWZ6DNR2W4J7XIPHLANPM.json","graph_json":"https://pith.science/api/pith-number/VD32GFWZ6DNR2W4J7XIPHLANPM/graph.json","events_json":"https://pith.science/api/pith-number/VD32GFWZ6DNR2W4J7XIPHLANPM/events.json","paper":"https://pith.science/paper/VD32GFWZ"},"agent_actions":{"view_html":"https://pith.science/pith/VD32GFWZ6DNR2W4J7XIPHLANPM","download_json":"https://pith.science/pith/VD32GFWZ6DNR2W4J7XIPHLANPM.json","view_paper":"https://pith.science/paper/VD32GFWZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.02455&json=true","fetch_graph":"https://pith.science/api/pith-number/VD32GFWZ6DNR2W4J7XIPHLANPM/graph.json","fetch_events":"https://pith.science/api/pith-number/VD32GFWZ6DNR2W4J7XIPHLANPM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VD32GFWZ6DNR2W4J7XIPHLANPM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VD32GFWZ6DNR2W4J7XIPHLANPM/action/storage_attestation","attest_author":"https://pith.science/pith/VD32GFWZ6DNR2W4J7XIPHLANPM/action/author_attestation","sign_citation":"https://pith.science/pith/VD32GFWZ6DNR2W4J7XIPHLANPM/action/citation_signature","submit_replication":"https://pith.science/pith/VD32GFWZ6DNR2W4J7XIPHLANPM/action/replication_record"}},"created_at":"2026-05-18T00:06:12.475995+00:00","updated_at":"2026-05-18T00:06:12.475995+00:00"}