{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:3XJJ6YTB4FWK2ENX6ANPCEFQ5P","short_pith_number":"pith:3XJJ6YTB","schema_version":"1.0","canonical_sha256":"ddd29f6261e16cad11b7f01af110b0ebeb48fb43839ae14b3116336b15a82e8e","source":{"kind":"arxiv","id":"0706.2169","version":2},"attestation_state":"computed","paper":{"title":"Nonarchimedean Green functions and dynamics on projective space","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Joseph H. Silverman, Shu Kawaguchi","submitted_at":"2007-06-14T17:54:02Z","abstract_excerpt":"Let F: P^N_K --> P^N_K be a morphism of degree d > 1 defined over a field K that is algebraically closed and complete with respect to a nonarchimedean absolute value. We prove that a modified Green function G_F associated to F is Holder continuous on P^N(K) and that the Fatou set F is equal to the set of points at which G_F is locally constant. Further, G_F vanishes precisely on the set of points P such that F has good reduction at every point in the forward orbit of P. We also prove that the iterates of F are locally uniformly Lipschitz on the Fatou set of F."},"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":"0706.2169","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.NT","submitted_at":"2007-06-14T17:54:02Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"84de4ff4f8d37578a2671c4c9c2160e2d8be0fb02e25291b4c5f35977a68db04","abstract_canon_sha256":"239b8c496e119935031ace56b16f237343f22c7f290b5656d0152b132f55840f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:12.542286Z","signature_b64":"qKQ5e7wkKaZb0nUA8GGKvlqsXN+EWN44x2dKYZ3XlBvZGF8QwTyPilk7Q0Ci8aUDTfCp1J2wbgO5TZZxHRxNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddd29f6261e16cad11b7f01af110b0ebeb48fb43839ae14b3116336b15a82e8e","last_reissued_at":"2026-05-18T04:21:12.541641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:12.541641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonarchimedean Green functions and dynamics on projective space","license":"","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Joseph H. Silverman, Shu Kawaguchi","submitted_at":"2007-06-14T17:54:02Z","abstract_excerpt":"Let F: P^N_K --> P^N_K be a morphism of degree d > 1 defined over a field K that is algebraically closed and complete with respect to a nonarchimedean absolute value. We prove that a modified Green function G_F associated to F is Holder continuous on P^N(K) and that the Fatou set F is equal to the set of points at which G_F is locally constant. Further, G_F vanishes precisely on the set of points P such that F has good reduction at every point in the forward orbit of P. We also prove that the iterates of F are locally uniformly Lipschitz on the Fatou set of F."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.2169","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":"0706.2169","created_at":"2026-05-18T04:21:12.541755+00:00"},{"alias_kind":"arxiv_version","alias_value":"0706.2169v2","created_at":"2026-05-18T04:21:12.541755+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.2169","created_at":"2026-05-18T04:21:12.541755+00:00"},{"alias_kind":"pith_short_12","alias_value":"3XJJ6YTB4FWK","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"3XJJ6YTB4FWK2ENX","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"3XJJ6YTB","created_at":"2026-05-18T12:25:54.717736+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/3XJJ6YTB4FWK2ENX6ANPCEFQ5P","json":"https://pith.science/pith/3XJJ6YTB4FWK2ENX6ANPCEFQ5P.json","graph_json":"https://pith.science/api/pith-number/3XJJ6YTB4FWK2ENX6ANPCEFQ5P/graph.json","events_json":"https://pith.science/api/pith-number/3XJJ6YTB4FWK2ENX6ANPCEFQ5P/events.json","paper":"https://pith.science/paper/3XJJ6YTB"},"agent_actions":{"view_html":"https://pith.science/pith/3XJJ6YTB4FWK2ENX6ANPCEFQ5P","download_json":"https://pith.science/pith/3XJJ6YTB4FWK2ENX6ANPCEFQ5P.json","view_paper":"https://pith.science/paper/3XJJ6YTB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0706.2169&json=true","fetch_graph":"https://pith.science/api/pith-number/3XJJ6YTB4FWK2ENX6ANPCEFQ5P/graph.json","fetch_events":"https://pith.science/api/pith-number/3XJJ6YTB4FWK2ENX6ANPCEFQ5P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3XJJ6YTB4FWK2ENX6ANPCEFQ5P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3XJJ6YTB4FWK2ENX6ANPCEFQ5P/action/storage_attestation","attest_author":"https://pith.science/pith/3XJJ6YTB4FWK2ENX6ANPCEFQ5P/action/author_attestation","sign_citation":"https://pith.science/pith/3XJJ6YTB4FWK2ENX6ANPCEFQ5P/action/citation_signature","submit_replication":"https://pith.science/pith/3XJJ6YTB4FWK2ENX6ANPCEFQ5P/action/replication_record"}},"created_at":"2026-05-18T04:21:12.541755+00:00","updated_at":"2026-05-18T04:21:12.541755+00:00"}