{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:LZ3CXWLMF76YNS4LF2H7YZVBC3","short_pith_number":"pith:LZ3CXWLM","schema_version":"1.0","canonical_sha256":"5e762bd96c2ffd86cb8b2e8ffc66a116d6c67f5376e4d39120c88dc3aa4d67b9","source":{"kind":"arxiv","id":"2404.14939","version":1},"attestation_state":"computed","paper":{"title":"Approximative compactness in B\\\"ochner spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Guillaume Grelier, Jaime San Mart\\'in","submitted_at":"2024-04-23T11:31:35Z","abstract_excerpt":"For any $p\\in[1,\\infty)$, we prove that the set of simple functions taking at most $k$ different values is proximinal in B\\\"ochner spaces $L^p(X)$ whenever $X$ is a dual Banach space with $w^*$-sequentially compact unit ball. With additional properties on $X$ and its norm, we show these sets are approximatively $w^*$-compact for $p\\in(1,\\infty)$ and even approximatively norm-compact under stronger hypothesis."},"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":"2404.14939","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2024-04-23T11:31:35Z","cross_cats_sorted":[],"title_canon_sha256":"eb8f349f4c47f4d07fc7ebb6982165b164b30cf02fcbb336fabaa49f838c613c","abstract_canon_sha256":"f0dde931d6f87d71d05b604cf11346ac8cc0a80bf3c861935d1d85e3500e061c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:11:12.238289Z","signature_b64":"HP5rZwQkiiQ4AUrdpUzgfui0QcJ8A5PiSmrazj1WnkR237rHw6civijDZutiMm1bLxWT9+1GwwMH7WfqtLWtDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e762bd96c2ffd86cb8b2e8ffc66a116d6c67f5376e4d39120c88dc3aa4d67b9","last_reissued_at":"2026-07-05T08:11:12.237844Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:11:12.237844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximative compactness in B\\\"ochner spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Guillaume Grelier, Jaime San Mart\\'in","submitted_at":"2024-04-23T11:31:35Z","abstract_excerpt":"For any $p\\in[1,\\infty)$, we prove that the set of simple functions taking at most $k$ different values is proximinal in B\\\"ochner spaces $L^p(X)$ whenever $X$ is a dual Banach space with $w^*$-sequentially compact unit ball. With additional properties on $X$ and its norm, we show these sets are approximatively $w^*$-compact for $p\\in(1,\\infty)$ and even approximatively norm-compact under stronger hypothesis."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.14939","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.14939/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":"2404.14939","created_at":"2026-07-05T08:11:12.237903+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.14939v1","created_at":"2026-07-05T08:11:12.237903+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.14939","created_at":"2026-07-05T08:11:12.237903+00:00"},{"alias_kind":"pith_short_12","alias_value":"LZ3CXWLMF76Y","created_at":"2026-07-05T08:11:12.237903+00:00"},{"alias_kind":"pith_short_16","alias_value":"LZ3CXWLMF76YNS4L","created_at":"2026-07-05T08:11:12.237903+00:00"},{"alias_kind":"pith_short_8","alias_value":"LZ3CXWLM","created_at":"2026-07-05T08:11:12.237903+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/LZ3CXWLMF76YNS4LF2H7YZVBC3","json":"https://pith.science/pith/LZ3CXWLMF76YNS4LF2H7YZVBC3.json","graph_json":"https://pith.science/api/pith-number/LZ3CXWLMF76YNS4LF2H7YZVBC3/graph.json","events_json":"https://pith.science/api/pith-number/LZ3CXWLMF76YNS4LF2H7YZVBC3/events.json","paper":"https://pith.science/paper/LZ3CXWLM"},"agent_actions":{"view_html":"https://pith.science/pith/LZ3CXWLMF76YNS4LF2H7YZVBC3","download_json":"https://pith.science/pith/LZ3CXWLMF76YNS4LF2H7YZVBC3.json","view_paper":"https://pith.science/paper/LZ3CXWLM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.14939&json=true","fetch_graph":"https://pith.science/api/pith-number/LZ3CXWLMF76YNS4LF2H7YZVBC3/graph.json","fetch_events":"https://pith.science/api/pith-number/LZ3CXWLMF76YNS4LF2H7YZVBC3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LZ3CXWLMF76YNS4LF2H7YZVBC3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LZ3CXWLMF76YNS4LF2H7YZVBC3/action/storage_attestation","attest_author":"https://pith.science/pith/LZ3CXWLMF76YNS4LF2H7YZVBC3/action/author_attestation","sign_citation":"https://pith.science/pith/LZ3CXWLMF76YNS4LF2H7YZVBC3/action/citation_signature","submit_replication":"https://pith.science/pith/LZ3CXWLMF76YNS4LF2H7YZVBC3/action/replication_record"}},"created_at":"2026-07-05T08:11:12.237903+00:00","updated_at":"2026-07-05T08:11:12.237903+00:00"}