{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:C4FZSCMGRUZ3DJE245IZFYRAEY","short_pith_number":"pith:C4FZSCMG","schema_version":"1.0","canonical_sha256":"170b9909868d33b1a49ae75192e22026291bb6a59341a726375ceacb7b040322","source":{"kind":"arxiv","id":"1505.08037","version":2},"attestation_state":"computed","paper":{"title":"$\\mathcal A$-compact mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pablo Turco","submitted_at":"2015-05-29T13:38:05Z","abstract_excerpt":"For a fixed Banach operator ideal $\\mathcal A$, we use the notion of $\\mathcal A$-compact sets of Carl and Stephani to study $\\mathcal A$-compact polynomials and $\\mathcal A$-compact holomorphic mappings. Namely, those mappings $g\\colon X\\rightarrow Y$ such that every $x \\in X$ has a neighborhood $V_x$ such that $g(V_x)$ is relatively $\\mathcal A$-compact. We show that the behavior of $\\mathcal A$-compact polynomials is determined by its behavior in any neighborhood of any point. We transfer some known properties of $\\mathcal A$-compact operators to $\\mathcal A$-compact polynomials. In order t"},"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":"1505.08037","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-05-29T13:38:05Z","cross_cats_sorted":[],"title_canon_sha256":"6d046c82869a8bfb2d32eabd694d5f8e87c0f7f82e1f9196e2b122eb63a62ca4","abstract_canon_sha256":"8b4b437c5423ec50be9c42c922936982e219c5214852139ae946ed32c4ee7e6b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:07.984540Z","signature_b64":"hEUrkwHqxj5QiYmaV6SCCv/cqWmiPEfZci3fXSpVMsFLGhLNTDrsySR5HNqWA/g62wLuDhdfJlkOKD6Nuv6UDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"170b9909868d33b1a49ae75192e22026291bb6a59341a726375ceacb7b040322","last_reissued_at":"2026-05-18T01:22:07.983820Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:07.983820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\mathcal A$-compact mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pablo Turco","submitted_at":"2015-05-29T13:38:05Z","abstract_excerpt":"For a fixed Banach operator ideal $\\mathcal A$, we use the notion of $\\mathcal A$-compact sets of Carl and Stephani to study $\\mathcal A$-compact polynomials and $\\mathcal A$-compact holomorphic mappings. Namely, those mappings $g\\colon X\\rightarrow Y$ such that every $x \\in X$ has a neighborhood $V_x$ such that $g(V_x)$ is relatively $\\mathcal A$-compact. We show that the behavior of $\\mathcal A$-compact polynomials is determined by its behavior in any neighborhood of any point. We transfer some known properties of $\\mathcal A$-compact operators to $\\mathcal A$-compact polynomials. In order t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.08037","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":"1505.08037","created_at":"2026-05-18T01:22:07.983944+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.08037v2","created_at":"2026-05-18T01:22:07.983944+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.08037","created_at":"2026-05-18T01:22:07.983944+00:00"},{"alias_kind":"pith_short_12","alias_value":"C4FZSCMGRUZ3","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"C4FZSCMGRUZ3DJE2","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"C4FZSCMG","created_at":"2026-05-18T12:29:14.074870+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/C4FZSCMGRUZ3DJE245IZFYRAEY","json":"https://pith.science/pith/C4FZSCMGRUZ3DJE245IZFYRAEY.json","graph_json":"https://pith.science/api/pith-number/C4FZSCMGRUZ3DJE245IZFYRAEY/graph.json","events_json":"https://pith.science/api/pith-number/C4FZSCMGRUZ3DJE245IZFYRAEY/events.json","paper":"https://pith.science/paper/C4FZSCMG"},"agent_actions":{"view_html":"https://pith.science/pith/C4FZSCMGRUZ3DJE245IZFYRAEY","download_json":"https://pith.science/pith/C4FZSCMGRUZ3DJE245IZFYRAEY.json","view_paper":"https://pith.science/paper/C4FZSCMG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.08037&json=true","fetch_graph":"https://pith.science/api/pith-number/C4FZSCMGRUZ3DJE245IZFYRAEY/graph.json","fetch_events":"https://pith.science/api/pith-number/C4FZSCMGRUZ3DJE245IZFYRAEY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C4FZSCMGRUZ3DJE245IZFYRAEY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C4FZSCMGRUZ3DJE245IZFYRAEY/action/storage_attestation","attest_author":"https://pith.science/pith/C4FZSCMGRUZ3DJE245IZFYRAEY/action/author_attestation","sign_citation":"https://pith.science/pith/C4FZSCMGRUZ3DJE245IZFYRAEY/action/citation_signature","submit_replication":"https://pith.science/pith/C4FZSCMGRUZ3DJE245IZFYRAEY/action/replication_record"}},"created_at":"2026-05-18T01:22:07.983944+00:00","updated_at":"2026-05-18T01:22:07.983944+00:00"}