{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:JAFT4XNU4LTNTRJQRXNN34HWQF","short_pith_number":"pith:JAFT4XNU","schema_version":"1.0","canonical_sha256":"480b3e5db4e2e6d9c5308ddaddf0f6816038924b3cc0e9580a158c537ef11243","source":{"kind":"arxiv","id":"1003.5677","version":1},"attestation_state":"computed","paper":{"title":"Maps on ultrametric spaces, Hensel's Lemma, and differential equations over valued fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Franz-Viktor Kuhlmann","submitted_at":"2010-03-29T20:58:43Z","abstract_excerpt":"We give a criterion for maps on ultrametric spaces to be surjective and to preserve spherical completeness. We show how Hensel's Lemma and the multi-dimensional Hensel's Lemma follow from our result. We give an easy proof that the latter holds in every henselian field. We also prove a basic infinite-dimensional Implicit Function Theorem. Further, we apply the criterion to deduce various versions of Hensel's Lemma for polynomials in several additive operators, and to give a criterion for the existence of integration and solutions of certain differential equations on spherically complete valued "},"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":"1003.5677","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-03-29T20:58:43Z","cross_cats_sorted":[],"title_canon_sha256":"e557f9f3dcb03a6dd44bdcc78286e591befacd662d009ac493e80294ae619597","abstract_canon_sha256":"b6d1abd2b4133a1110b7c2a35a1bacbe229f36a052bc05174ade8c64248fd347"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:28.071148Z","signature_b64":"PRcKwKk03sCQPuHfDIZRQ5clMgpj28ECL7DVRtUR1pPUY2mPdwXMJmUkULgTCK9iBD9B3AepqP4DXfEfiIz8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"480b3e5db4e2e6d9c5308ddaddf0f6816038924b3cc0e9580a158c537ef11243","last_reissued_at":"2026-05-18T03:29:28.070428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:28.070428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maps on ultrametric spaces, Hensel's Lemma, and differential equations over valued fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Franz-Viktor Kuhlmann","submitted_at":"2010-03-29T20:58:43Z","abstract_excerpt":"We give a criterion for maps on ultrametric spaces to be surjective and to preserve spherical completeness. We show how Hensel's Lemma and the multi-dimensional Hensel's Lemma follow from our result. We give an easy proof that the latter holds in every henselian field. We also prove a basic infinite-dimensional Implicit Function Theorem. Further, we apply the criterion to deduce various versions of Hensel's Lemma for polynomials in several additive operators, and to give a criterion for the existence of integration and solutions of certain differential equations on spherically complete valued "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5677","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1003.5677","created_at":"2026-05-18T03:29:28.070543+00:00"},{"alias_kind":"arxiv_version","alias_value":"1003.5677v1","created_at":"2026-05-18T03:29:28.070543+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5677","created_at":"2026-05-18T03:29:28.070543+00:00"},{"alias_kind":"pith_short_12","alias_value":"JAFT4XNU4LTN","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"JAFT4XNU4LTNTRJQ","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"JAFT4XNU","created_at":"2026-05-18T12:26:09.077623+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/JAFT4XNU4LTNTRJQRXNN34HWQF","json":"https://pith.science/pith/JAFT4XNU4LTNTRJQRXNN34HWQF.json","graph_json":"https://pith.science/api/pith-number/JAFT4XNU4LTNTRJQRXNN34HWQF/graph.json","events_json":"https://pith.science/api/pith-number/JAFT4XNU4LTNTRJQRXNN34HWQF/events.json","paper":"https://pith.science/paper/JAFT4XNU"},"agent_actions":{"view_html":"https://pith.science/pith/JAFT4XNU4LTNTRJQRXNN34HWQF","download_json":"https://pith.science/pith/JAFT4XNU4LTNTRJQRXNN34HWQF.json","view_paper":"https://pith.science/paper/JAFT4XNU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1003.5677&json=true","fetch_graph":"https://pith.science/api/pith-number/JAFT4XNU4LTNTRJQRXNN34HWQF/graph.json","fetch_events":"https://pith.science/api/pith-number/JAFT4XNU4LTNTRJQRXNN34HWQF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JAFT4XNU4LTNTRJQRXNN34HWQF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JAFT4XNU4LTNTRJQRXNN34HWQF/action/storage_attestation","attest_author":"https://pith.science/pith/JAFT4XNU4LTNTRJQRXNN34HWQF/action/author_attestation","sign_citation":"https://pith.science/pith/JAFT4XNU4LTNTRJQRXNN34HWQF/action/citation_signature","submit_replication":"https://pith.science/pith/JAFT4XNU4LTNTRJQRXNN34HWQF/action/replication_record"}},"created_at":"2026-05-18T03:29:28.070543+00:00","updated_at":"2026-05-18T03:29:28.070543+00:00"}