{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:X7R7FQ5KHJVFRCU7CZRWUR3TKM","short_pith_number":"pith:X7R7FQ5K","schema_version":"1.0","canonical_sha256":"bfe3f2c3aa3a6a588a9f16636a4773533082d905b6fb56dcc8e09909103dc5ed","source":{"kind":"arxiv","id":"2310.17628","version":2},"attestation_state":"computed","paper":{"title":"Skew Products on the Berkovich Projective Line","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.DS","authors_text":"Richard A. P. Birkett","submitted_at":"2023-10-26T17:47:14Z","abstract_excerpt":"In this article, we develop a dynamical theory for what shall be called a skew product on the Berkovich projective line, $\\phi_*: \\mathbb{P}^1_{\\text{an}}(K) \\to \\mathbb{P}^1_{\\text{an}}(K)$ over a non-Archimedean field $K$. These functions are defined algebraically yet strictly generalise the notion of a rational map on $\\mathbb{P}^1_{\\text{an}}$. We describe the analytical, algebraic, and dynamical properties of skew products, including a study of periodic points, and a Fatou/Julia dichotomy. The article culminates with the classification of the connected components of the Fatou set."},"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":"2310.17628","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-10-26T17:47:14Z","cross_cats_sorted":["math.AG","math.NT"],"title_canon_sha256":"2c2b2feb4dfcf3f4b3b1583e10469b566f18ee4a52af9195699b3525798efca3","abstract_canon_sha256":"80b3d97068cad329326f51541e422fb6fe98779db9e962cff15ab511bb39a5fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:07:18.563234Z","signature_b64":"M50U1RtWAvEZn7HVBr2LgznfxwpVNDbIUZUXZGdHIm52iJK7HCOJe8jgKyEMZsE9iTUzkBU3Dy97G54l6I6ZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfe3f2c3aa3a6a588a9f16636a4773533082d905b6fb56dcc8e09909103dc5ed","last_reissued_at":"2026-07-05T07:07:18.562810Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:07:18.562810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Skew Products on the Berkovich Projective Line","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.DS","authors_text":"Richard A. P. Birkett","submitted_at":"2023-10-26T17:47:14Z","abstract_excerpt":"In this article, we develop a dynamical theory for what shall be called a skew product on the Berkovich projective line, $\\phi_*: \\mathbb{P}^1_{\\text{an}}(K) \\to \\mathbb{P}^1_{\\text{an}}(K)$ over a non-Archimedean field $K$. These functions are defined algebraically yet strictly generalise the notion of a rational map on $\\mathbb{P}^1_{\\text{an}}$. We describe the analytical, algebraic, and dynamical properties of skew products, including a study of periodic points, and a Fatou/Julia dichotomy. The article culminates with the classification of the connected components of the Fatou set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.17628","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.17628/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2310.17628","created_at":"2026-07-05T07:07:18.562875+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.17628v2","created_at":"2026-07-05T07:07:18.562875+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.17628","created_at":"2026-07-05T07:07:18.562875+00:00"},{"alias_kind":"pith_short_12","alias_value":"X7R7FQ5KHJVF","created_at":"2026-07-05T07:07:18.562875+00:00"},{"alias_kind":"pith_short_16","alias_value":"X7R7FQ5KHJVFRCU7","created_at":"2026-07-05T07:07:18.562875+00:00"},{"alias_kind":"pith_short_8","alias_value":"X7R7FQ5K","created_at":"2026-07-05T07:07:18.562875+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.26598","citing_title":"The Calculus of Blowups on a Ruled Surface","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/X7R7FQ5KHJVFRCU7CZRWUR3TKM","json":"https://pith.science/pith/X7R7FQ5KHJVFRCU7CZRWUR3TKM.json","graph_json":"https://pith.science/api/pith-number/X7R7FQ5KHJVFRCU7CZRWUR3TKM/graph.json","events_json":"https://pith.science/api/pith-number/X7R7FQ5KHJVFRCU7CZRWUR3TKM/events.json","paper":"https://pith.science/paper/X7R7FQ5K"},"agent_actions":{"view_html":"https://pith.science/pith/X7R7FQ5KHJVFRCU7CZRWUR3TKM","download_json":"https://pith.science/pith/X7R7FQ5KHJVFRCU7CZRWUR3TKM.json","view_paper":"https://pith.science/paper/X7R7FQ5K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.17628&json=true","fetch_graph":"https://pith.science/api/pith-number/X7R7FQ5KHJVFRCU7CZRWUR3TKM/graph.json","fetch_events":"https://pith.science/api/pith-number/X7R7FQ5KHJVFRCU7CZRWUR3TKM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X7R7FQ5KHJVFRCU7CZRWUR3TKM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X7R7FQ5KHJVFRCU7CZRWUR3TKM/action/storage_attestation","attest_author":"https://pith.science/pith/X7R7FQ5KHJVFRCU7CZRWUR3TKM/action/author_attestation","sign_citation":"https://pith.science/pith/X7R7FQ5KHJVFRCU7CZRWUR3TKM/action/citation_signature","submit_replication":"https://pith.science/pith/X7R7FQ5KHJVFRCU7CZRWUR3TKM/action/replication_record"}},"created_at":"2026-07-05T07:07:18.562875+00:00","updated_at":"2026-07-05T07:07:18.562875+00:00"}