{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:DKNQNYVYV3HZVK6D2Y37ZOSG5L","short_pith_number":"pith:DKNQNYVY","canonical_record":{"source":{"id":"1205.4044","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-17T21:13:08Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"5a5226dccfd4e36c81ad1de4b60dbdd22f184f0f2d566b156380fa3a6747925e","abstract_canon_sha256":"db3a05eb27c22f8268f33e1574296dc867041db2970cc7d0ab0c0848fc7eaaab"},"schema_version":"1.0"},"canonical_sha256":"1a9b06e2b8aecf9aabc3d637fcba46eaf395fe8f12a55d1f8622dccc55885947","source":{"kind":"arxiv","id":"1205.4044","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4044","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4044v1","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4044","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"pith_short_12","alias_value":"DKNQNYVYV3HZ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DKNQNYVYV3HZVK6D","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DKNQNYVY","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:DKNQNYVYV3HZVK6D2Y37ZOSG5L","target":"record","payload":{"canonical_record":{"source":{"id":"1205.4044","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-17T21:13:08Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"5a5226dccfd4e36c81ad1de4b60dbdd22f184f0f2d566b156380fa3a6747925e","abstract_canon_sha256":"db3a05eb27c22f8268f33e1574296dc867041db2970cc7d0ab0c0848fc7eaaab"},"schema_version":"1.0"},"canonical_sha256":"1a9b06e2b8aecf9aabc3d637fcba46eaf395fe8f12a55d1f8622dccc55885947","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:22.883741Z","signature_b64":"VoUx7OYny4I1aj6VUh2gsKy95sGvrYNE/GcH1IQC5Hl5OJs6jviygHozgjlV8rYpQXkcat6/EvYie4Q4x82EAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a9b06e2b8aecf9aabc3d637fcba46eaf395fe8f12a55d1f8622dccc55885947","last_reissued_at":"2026-05-18T03:55:22.883102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:22.883102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.4044","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zsDBfkpRUw+xfbUWTPmC/nityyAIRZAjq4dm7TvTGVFLPCuve/PIrT8GsLe6li2BJD6mKXpn4004c0anzlVdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:21:37.105774Z"},"content_sha256":"339876a3da7dbd339baa02e1df20f69b12e32cb67e8f675622c3d79829c0e1f6","schema_version":"1.0","event_id":"sha256:339876a3da7dbd339baa02e1df20f69b12e32cb67e8f675622c3d79829c0e1f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:DKNQNYVYV3HZVK6D2Y37ZOSG5L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamics of mappings with constant dilatation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CV","authors_text":"Alastair Fletcher, Robert Fryer","submitted_at":"2012-05-17T21:13:08Z","abstract_excerpt":"Let h:C \\to C be an R-linear map. In this article, we explore the dynamics of the quasiregular mapping H(z)=h(z)^2. Via the B\\\"{o}ttcher type coordinate constructed in \"On B\\\"{o}ttcher coordinates and quasiregular maps\" by Fletcher and Fryer, we are able to obtain results for any degree two mapping of the plane with constant complex dilatation. We show that any such mapping has either one, two or three fixed external rays, that all cases can occur, and exhibit how the dynamics changes in each case. We use results from complex dynamics to prove that these mappings are nowhere uniformly quasireg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4044","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:55:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WrJBCFPDEKppiAMjO+vxs/Iaqr4CW/t3u72i9/xTlwVHI/gtws0Pfi++aN/QsLGYbxFOKaTP6CqBTme5Gi8hCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T20:21:37.106156Z"},"content_sha256":"f91df5432d03bb3fff01098d7e7453ee7f751f92f57548768dbccbf834a38c9f","schema_version":"1.0","event_id":"sha256:f91df5432d03bb3fff01098d7e7453ee7f751f92f57548768dbccbf834a38c9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DKNQNYVYV3HZVK6D2Y37ZOSG5L/bundle.json","state_url":"https://pith.science/pith/DKNQNYVYV3HZVK6D2Y37ZOSG5L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DKNQNYVYV3HZVK6D2Y37ZOSG5L/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":"2026-05-27T20:21:37Z","links":{"resolver":"https://pith.science/pith/DKNQNYVYV3HZVK6D2Y37ZOSG5L","bundle":"https://pith.science/pith/DKNQNYVYV3HZVK6D2Y37ZOSG5L/bundle.json","state":"https://pith.science/pith/DKNQNYVYV3HZVK6D2Y37ZOSG5L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DKNQNYVYV3HZVK6D2Y37ZOSG5L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DKNQNYVYV3HZVK6D2Y37ZOSG5L","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":"db3a05eb27c22f8268f33e1574296dc867041db2970cc7d0ab0c0848fc7eaaab","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-17T21:13:08Z","title_canon_sha256":"5a5226dccfd4e36c81ad1de4b60dbdd22f184f0f2d566b156380fa3a6747925e"},"schema_version":"1.0","source":{"id":"1205.4044","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4044","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4044v1","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4044","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"pith_short_12","alias_value":"DKNQNYVYV3HZ","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"DKNQNYVYV3HZVK6D","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"DKNQNYVY","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:f91df5432d03bb3fff01098d7e7453ee7f751f92f57548768dbccbf834a38c9f","target":"graph","created_at":"2026-05-18T03:55:22Z","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":"Let h:C \\to C be an R-linear map. In this article, we explore the dynamics of the quasiregular mapping H(z)=h(z)^2. Via the B\\\"{o}ttcher type coordinate constructed in \"On B\\\"{o}ttcher coordinates and quasiregular maps\" by Fletcher and Fryer, we are able to obtain results for any degree two mapping of the plane with constant complex dilatation. We show that any such mapping has either one, two or three fixed external rays, that all cases can occur, and exhibit how the dynamics changes in each case. We use results from complex dynamics to prove that these mappings are nowhere uniformly quasireg","authors_text":"Alastair Fletcher, Robert Fryer","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-17T21:13:08Z","title":"Dynamics of mappings with constant dilatation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4044","kind":"arxiv","version":1},"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":"sha256:339876a3da7dbd339baa02e1df20f69b12e32cb67e8f675622c3d79829c0e1f6","target":"record","created_at":"2026-05-18T03:55:22Z","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":"db3a05eb27c22f8268f33e1574296dc867041db2970cc7d0ab0c0848fc7eaaab","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-05-17T21:13:08Z","title_canon_sha256":"5a5226dccfd4e36c81ad1de4b60dbdd22f184f0f2d566b156380fa3a6747925e"},"schema_version":"1.0","source":{"id":"1205.4044","kind":"arxiv","version":1}},"canonical_sha256":"1a9b06e2b8aecf9aabc3d637fcba46eaf395fe8f12a55d1f8622dccc55885947","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a9b06e2b8aecf9aabc3d637fcba46eaf395fe8f12a55d1f8622dccc55885947","first_computed_at":"2026-05-18T03:55:22.883102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:22.883102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VoUx7OYny4I1aj6VUh2gsKy95sGvrYNE/GcH1IQC5Hl5OJs6jviygHozgjlV8rYpQXkcat6/EvYie4Q4x82EAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:22.883741Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4044","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:339876a3da7dbd339baa02e1df20f69b12e32cb67e8f675622c3d79829c0e1f6","sha256:f91df5432d03bb3fff01098d7e7453ee7f751f92f57548768dbccbf834a38c9f"],"state_sha256":"f07169b110843ab504cf7e337792fbfdbc26d25b2ecaf3d114bf2ecace1cf25e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VfEEukLAPPJxsFI0GyG5jtY1CmSNC9xD31qdTQumm417ii72732mEc02gnga8gry2oqT7WWS43i18FiZSAmTCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T20:21:37.109045Z","bundle_sha256":"07d8c84ed8155c0d92e083e6f6a4c90e4e00e6da6b7a04b6c24d49097cd8b715"}}