{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VD32GFWZ6DNR2W4J7XIPHLANPM","short_pith_number":"pith:VD32GFWZ","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"},"canonical_sha256":"a8f7a316d9f0db1d5b89fdd0f3ac0d7b37885d9fadfe8533a59ceab9919827ae","source":{"kind":"arxiv","id":"1703.02455","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.02455","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"arxiv_version","alias_value":"1703.02455v5","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02455","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"pith_short_12","alias_value":"VD32GFWZ6DNR","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VD32GFWZ6DNR2W4J","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VD32GFWZ","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VD32GFWZ6DNR2W4J7XIPHLANPM","target":"record","payload":{"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"},"canonical_sha256":"a8f7a316d9f0db1d5b89fdd0f3ac0d7b37885d9fadfe8533a59ceab9919827ae","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"},"source_kind":"arxiv","source_id":"1703.02455","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DVdo8sp8uxvqemTfej27qZGzpkprnvC8mWm/Rcg1IriZUhvdAk20AelGOgzGSu9G5Lj2HyFflNsDSaWQLJEBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:50:24.349429Z"},"content_sha256":"846144c8a7f06817ab5dbc0258a429c247c19d0eb33a5c1b2a71ae6435bea0cc","schema_version":"1.0","event_id":"sha256:846144c8a7f06817ab5dbc0258a429c247c19d0eb33a5c1b2a71ae6435bea0cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VD32GFWZ6DNR2W4J7XIPHLANPM","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uyvkh2DbGtud6Sb1mYx/1eIiLVGOMSkYFEQmjnYg3a55j54yPaHRO7+LECWPh7KeT2uK2LoFfduE6Y10sS9zAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:50:24.349989Z"},"content_sha256":"ab9fa6d648d6dea4ab464ef7745430a8df58e4d1a7589e090d87c58fbd67f7a8","schema_version":"1.0","event_id":"sha256:ab9fa6d648d6dea4ab464ef7745430a8df58e4d1a7589e090d87c58fbd67f7a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VD32GFWZ6DNR2W4J7XIPHLANPM/bundle.json","state_url":"https://pith.science/pith/VD32GFWZ6DNR2W4J7XIPHLANPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VD32GFWZ6DNR2W4J7XIPHLANPM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T02:50:24Z","links":{"resolver":"https://pith.science/pith/VD32GFWZ6DNR2W4J7XIPHLANPM","bundle":"https://pith.science/pith/VD32GFWZ6DNR2W4J7XIPHLANPM/bundle.json","state":"https://pith.science/pith/VD32GFWZ6DNR2W4J7XIPHLANPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VD32GFWZ6DNR2W4J7XIPHLANPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VD32GFWZ6DNR2W4J7XIPHLANPM","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":"29f745e5f79a437e7eb71ecf2552048fd8b71dc8448b284ce8e99356e39448ee","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-07T16:24:28Z","title_canon_sha256":"cbf14507f6f73d2c2ba521a56cfb6cd767cc2b7e925d6b7ea2c431e9bf439235"},"schema_version":"1.0","source":{"id":"1703.02455","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.02455","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"arxiv_version","alias_value":"1703.02455v5","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02455","created_at":"2026-05-18T00:06:12Z"},{"alias_kind":"pith_short_12","alias_value":"VD32GFWZ6DNR","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VD32GFWZ6DNR2W4J","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VD32GFWZ","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:ab9fa6d648d6dea4ab464ef7745430a8df58e4d1a7589e090d87c58fbd67f7a8","target":"graph","created_at":"2026-05-18T00:06:12Z","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":"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","authors_text":"Alastair Fletcher, Doug Macclure","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-07T16:24:28Z","title":"Strongly automorphic mappings and Julia sets of uniformly quasiregular mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02455","kind":"arxiv","version":5},"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":"sha256:846144c8a7f06817ab5dbc0258a429c247c19d0eb33a5c1b2a71ae6435bea0cc","target":"record","created_at":"2026-05-18T00:06:12Z","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":"29f745e5f79a437e7eb71ecf2552048fd8b71dc8448b284ce8e99356e39448ee","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-07T16:24:28Z","title_canon_sha256":"cbf14507f6f73d2c2ba521a56cfb6cd767cc2b7e925d6b7ea2c431e9bf439235"},"schema_version":"1.0","source":{"id":"1703.02455","kind":"arxiv","version":5}},"canonical_sha256":"a8f7a316d9f0db1d5b89fdd0f3ac0d7b37885d9fadfe8533a59ceab9919827ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8f7a316d9f0db1d5b89fdd0f3ac0d7b37885d9fadfe8533a59ceab9919827ae","first_computed_at":"2026-05-18T00:06:12.475910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:12.475910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MUkpnTyGtSDSHxAGTUjelBijdBt4kHuwoFEra9fbLwUI/3VMRzeE+YwGwb5jE1gqy2ztcO7+U4xBG8xQ7HtuDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:12.476487Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.02455","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:846144c8a7f06817ab5dbc0258a429c247c19d0eb33a5c1b2a71ae6435bea0cc","sha256:ab9fa6d648d6dea4ab464ef7745430a8df58e4d1a7589e090d87c58fbd67f7a8"],"state_sha256":"688af0966919ad204bdfc211a625c762e8d5152183f86481dd38dbebaf123f79"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8tJvwBAoJdhrWHz4g/5xk2zv4SBO6rOVZtJZeeCwWoJ2/2+wKmq40TW3r0qNLeUDDHsq/r8gznSFEpOC3cv7CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T02:50:24.353352Z","bundle_sha256":"bc6165fc3c8cf93a308ccc79bb69c4a7d28a59c5e7a9b8273bfa36af57b9eb51"}}