{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:CMBHNDGKSMJFXJ3J6ANJMD7NVO","short_pith_number":"pith:CMBHNDGK","schema_version":"1.0","canonical_sha256":"1302768cca93125ba769f01a960fedabbec78f9fddce3e65b556bd11ab7868d2","source":{"kind":"arxiv","id":"1607.06649","version":2},"attestation_state":"computed","paper":{"title":"The dynamics of quasiregular maps of punctured space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Daniel A. Nicks, David J. Sixsmith","submitted_at":"2016-07-22T12:25:34Z","abstract_excerpt":"The Fatou-Julia iteration theory of rational and transcendental entire functions has recently been extended to quasiregular maps in more than two real dimensions. Our goal in this paper is similar; we extend the iteration theory of analytic self-maps of the punctured plane to quasiregular self-maps of punctured space.\n  We define the Julia set as the set of points for which the complement of the forward orbit of any neighbourhood of the point is a finite set. We show that the Julia set is non-empty, and shares many properties with the classical Julia set of an analytic function. These properti"},"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":"1607.06649","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-07-22T12:25:34Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"98e50e84cde254af14485bc07b8ce28da5874d04ab2ed181c1ef04761b028bc7","abstract_canon_sha256":"5e334c3159c361d63af47f314e2f11af0e997df5e97153f4e497ad03dac3e7a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:53.275354Z","signature_b64":"t+GReoloyLp55yKy9kRZPr/6r7DMjJJ2qvoFhaM9J4PWPpRR2IQDtPAc4SeC9zKlyv1iiLq8i8EfqvqFRzEKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1302768cca93125ba769f01a960fedabbec78f9fddce3e65b556bd11ab7868d2","last_reissued_at":"2026-05-17T23:48:53.274711Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:53.274711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The dynamics of quasiregular maps of punctured space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Daniel A. Nicks, David J. Sixsmith","submitted_at":"2016-07-22T12:25:34Z","abstract_excerpt":"The Fatou-Julia iteration theory of rational and transcendental entire functions has recently been extended to quasiregular maps in more than two real dimensions. Our goal in this paper is similar; we extend the iteration theory of analytic self-maps of the punctured plane to quasiregular self-maps of punctured space.\n  We define the Julia set as the set of points for which the complement of the forward orbit of any neighbourhood of the point is a finite set. We show that the Julia set is non-empty, and shares many properties with the classical Julia set of an analytic function. These properti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06649","kind":"arxiv","version":2},"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":"1607.06649","created_at":"2026-05-17T23:48:53.274795+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.06649v2","created_at":"2026-05-17T23:48:53.274795+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06649","created_at":"2026-05-17T23:48:53.274795+00:00"},{"alias_kind":"pith_short_12","alias_value":"CMBHNDGKSMJF","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_16","alias_value":"CMBHNDGKSMJFXJ3J","created_at":"2026-05-18T12:30:09.641336+00:00"},{"alias_kind":"pith_short_8","alias_value":"CMBHNDGK","created_at":"2026-05-18T12:30:09.641336+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/CMBHNDGKSMJFXJ3J6ANJMD7NVO","json":"https://pith.science/pith/CMBHNDGKSMJFXJ3J6ANJMD7NVO.json","graph_json":"https://pith.science/api/pith-number/CMBHNDGKSMJFXJ3J6ANJMD7NVO/graph.json","events_json":"https://pith.science/api/pith-number/CMBHNDGKSMJFXJ3J6ANJMD7NVO/events.json","paper":"https://pith.science/paper/CMBHNDGK"},"agent_actions":{"view_html":"https://pith.science/pith/CMBHNDGKSMJFXJ3J6ANJMD7NVO","download_json":"https://pith.science/pith/CMBHNDGKSMJFXJ3J6ANJMD7NVO.json","view_paper":"https://pith.science/paper/CMBHNDGK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.06649&json=true","fetch_graph":"https://pith.science/api/pith-number/CMBHNDGKSMJFXJ3J6ANJMD7NVO/graph.json","fetch_events":"https://pith.science/api/pith-number/CMBHNDGKSMJFXJ3J6ANJMD7NVO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CMBHNDGKSMJFXJ3J6ANJMD7NVO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CMBHNDGKSMJFXJ3J6ANJMD7NVO/action/storage_attestation","attest_author":"https://pith.science/pith/CMBHNDGKSMJFXJ3J6ANJMD7NVO/action/author_attestation","sign_citation":"https://pith.science/pith/CMBHNDGKSMJFXJ3J6ANJMD7NVO/action/citation_signature","submit_replication":"https://pith.science/pith/CMBHNDGKSMJFXJ3J6ANJMD7NVO/action/replication_record"}},"created_at":"2026-05-17T23:48:53.274795+00:00","updated_at":"2026-05-17T23:48:53.274795+00:00"}