{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:I7ECAPDM3GFMNZCLMUDMHAEBTE","short_pith_number":"pith:I7ECAPDM","schema_version":"1.0","canonical_sha256":"47c8203c6cd98ac6e44b6506c3808199247f053ce712a9d4e54f069c630e85c4","source":{"kind":"arxiv","id":"1607.01725","version":2},"attestation_state":"computed","paper":{"title":"Smooth surjections and surjective restrictions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Enrico Le Donne, Jes\\'us A. Jaramillo, Richard M. Aron","submitted_at":"2016-07-06T17:56:49Z","abstract_excerpt":"Given a surjective mapping $f : E \\to F$ between Banach spaces, we investigate the existence of a subspace $G$ of $E$, with the same density character as $F$, such that the restriction of $f$ to $G$ remains surjective. We obtain a positive answer whenever $f$ is continuous and uniformly open. In the smooth case, we deduce a positive answer when $f$ is a $C^1$-smooth surjection whose set of critical values is countable. Finally we show that, when $f$ takes values in the Euclidean space $\\mathbb R^n$, in order to obtain this result it is not sufficient to assume that the set of critical values o"},"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":"1607.01725","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-07-06T17:56:49Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"b8e481aaa736aeb44cbd9aeef0a0b609ade8aed8ec8abd4da19dcf20c3b3cb76","abstract_canon_sha256":"f68ddbad28e52ac51839a9a4a632e4e3663f194f7fab18f5d8f3cb2bf7865093"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:14.465684Z","signature_b64":"XNbV6KOfxzA2axVk9f/5mW9BPSYYniXb3+OYHMaR8vq4LcflxvcvLkkftg8h72KmvFainy1M3dLx4Yn0YYBiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47c8203c6cd98ac6e44b6506c3808199247f053ce712a9d4e54f069c630e85c4","last_reissued_at":"2026-05-18T00:12:14.465033Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:14.465033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Smooth surjections and surjective restrictions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Enrico Le Donne, Jes\\'us A. Jaramillo, Richard M. Aron","submitted_at":"2016-07-06T17:56:49Z","abstract_excerpt":"Given a surjective mapping $f : E \\to F$ between Banach spaces, we investigate the existence of a subspace $G$ of $E$, with the same density character as $F$, such that the restriction of $f$ to $G$ remains surjective. We obtain a positive answer whenever $f$ is continuous and uniformly open. In the smooth case, we deduce a positive answer when $f$ is a $C^1$-smooth surjection whose set of critical values is countable. Finally we show that, when $f$ takes values in the Euclidean space $\\mathbb R^n$, in order to obtain this result it is not sufficient to assume that the set of critical values o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.01725","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":"1607.01725","created_at":"2026-05-18T00:12:14.465114+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.01725v2","created_at":"2026-05-18T00:12:14.465114+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.01725","created_at":"2026-05-18T00:12:14.465114+00:00"},{"alias_kind":"pith_short_12","alias_value":"I7ECAPDM3GFM","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"I7ECAPDM3GFMNZCL","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"I7ECAPDM","created_at":"2026-05-18T12:30:22.444734+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/I7ECAPDM3GFMNZCLMUDMHAEBTE","json":"https://pith.science/pith/I7ECAPDM3GFMNZCLMUDMHAEBTE.json","graph_json":"https://pith.science/api/pith-number/I7ECAPDM3GFMNZCLMUDMHAEBTE/graph.json","events_json":"https://pith.science/api/pith-number/I7ECAPDM3GFMNZCLMUDMHAEBTE/events.json","paper":"https://pith.science/paper/I7ECAPDM"},"agent_actions":{"view_html":"https://pith.science/pith/I7ECAPDM3GFMNZCLMUDMHAEBTE","download_json":"https://pith.science/pith/I7ECAPDM3GFMNZCLMUDMHAEBTE.json","view_paper":"https://pith.science/paper/I7ECAPDM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.01725&json=true","fetch_graph":"https://pith.science/api/pith-number/I7ECAPDM3GFMNZCLMUDMHAEBTE/graph.json","fetch_events":"https://pith.science/api/pith-number/I7ECAPDM3GFMNZCLMUDMHAEBTE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I7ECAPDM3GFMNZCLMUDMHAEBTE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I7ECAPDM3GFMNZCLMUDMHAEBTE/action/storage_attestation","attest_author":"https://pith.science/pith/I7ECAPDM3GFMNZCLMUDMHAEBTE/action/author_attestation","sign_citation":"https://pith.science/pith/I7ECAPDM3GFMNZCLMUDMHAEBTE/action/citation_signature","submit_replication":"https://pith.science/pith/I7ECAPDM3GFMNZCLMUDMHAEBTE/action/replication_record"}},"created_at":"2026-05-18T00:12:14.465114+00:00","updated_at":"2026-05-18T00:12:14.465114+00:00"}