{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:YERGJSI554FQADYQ4RNPKRJV72","short_pith_number":"pith:YERGJSI5","schema_version":"1.0","canonical_sha256":"c12264c91def0b000f10e45af54535fe91c871a08808e2d6f411127c07c238e4","source":{"kind":"arxiv","id":"2502.07448","version":1},"attestation_state":"computed","paper":{"title":"Polynomial Approximation in $ L^2 $ of the Double Exponential via Complex Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Boaz Klartag, Pierre Bizeul","submitted_at":"2025-02-11T10:50:36Z","abstract_excerpt":"We study the polynomial approximation problem in $L^2(\\mu_1)$ where $\\mu_1(dx) = e^{-|x|}/2 dx$. We show that for any absolutely continuous function $f$, $$ \\sum_{k=1}^{\\infty} \\log^2(e+k) \\langle f, P_k \\rangle^2 \\ \\leq C \\left( \\int_{\\mathbb{R}} \\log^2(e+\\lvert x \\rvert) f^2 \\, d\\mu_1 \\ + \\ \\int_{\\mathbb{R}} (f')^2 \\, d\\mu_1 \\right) $$\n  for some universal constant $C>0$, where $(P_k)_{k \\in N}$ are the orthonormal polynomials associated with $\\mu_1$. This inequality is tight in the sense that $\\log^2(e +k)$ on the left hand-side cannot be replaced by $a_k \\log^2(e +k)$ with a sequence $a_k "},"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":"2502.07448","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2025-02-11T10:50:36Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"31911c6570e22173395c66615ba8c634830479753798a6c10b0640369cdf2373","abstract_canon_sha256":"36e7c08c65b76dd889e9e9fd072c7d77bb8d3b38de970d096209fe837f0c3c9d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:12:37.566130Z","signature_b64":"LKiS1CZo/V6Hkpxce6PBAYrMoCyOa3+J9kxZgoykzvk9FGqJNCunP1+Oyp8lw/Tzb4OE0+FJequdnw/RtC7ICg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c12264c91def0b000f10e45af54535fe91c871a08808e2d6f411127c07c238e4","last_reissued_at":"2026-07-05T10:12:37.565649Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:12:37.565649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polynomial Approximation in $ L^2 $ of the Double Exponential via Complex Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Boaz Klartag, Pierre Bizeul","submitted_at":"2025-02-11T10:50:36Z","abstract_excerpt":"We study the polynomial approximation problem in $L^2(\\mu_1)$ where $\\mu_1(dx) = e^{-|x|}/2 dx$. We show that for any absolutely continuous function $f$, $$ \\sum_{k=1}^{\\infty} \\log^2(e+k) \\langle f, P_k \\rangle^2 \\ \\leq C \\left( \\int_{\\mathbb{R}} \\log^2(e+\\lvert x \\rvert) f^2 \\, d\\mu_1 \\ + \\ \\int_{\\mathbb{R}} (f')^2 \\, d\\mu_1 \\right) $$\n  for some universal constant $C>0$, where $(P_k)_{k \\in N}$ are the orthonormal polynomials associated with $\\mu_1$. This inequality is tight in the sense that $\\log^2(e +k)$ on the left hand-side cannot be replaced by $a_k \\log^2(e +k)$ with a sequence $a_k "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07448","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/2502.07448/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":"2502.07448","created_at":"2026-07-05T10:12:37.565706+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.07448v1","created_at":"2026-07-05T10:12:37.565706+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07448","created_at":"2026-07-05T10:12:37.565706+00:00"},{"alias_kind":"pith_short_12","alias_value":"YERGJSI554FQ","created_at":"2026-07-05T10:12:37.565706+00:00"},{"alias_kind":"pith_short_16","alias_value":"YERGJSI554FQADYQ","created_at":"2026-07-05T10:12:37.565706+00:00"},{"alias_kind":"pith_short_8","alias_value":"YERGJSI5","created_at":"2026-07-05T10:12:37.565706+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.10355","citing_title":"Entropy and Learning of Lipschitz Functions under Log-Concave Measures","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YERGJSI554FQADYQ4RNPKRJV72","json":"https://pith.science/pith/YERGJSI554FQADYQ4RNPKRJV72.json","graph_json":"https://pith.science/api/pith-number/YERGJSI554FQADYQ4RNPKRJV72/graph.json","events_json":"https://pith.science/api/pith-number/YERGJSI554FQADYQ4RNPKRJV72/events.json","paper":"https://pith.science/paper/YERGJSI5"},"agent_actions":{"view_html":"https://pith.science/pith/YERGJSI554FQADYQ4RNPKRJV72","download_json":"https://pith.science/pith/YERGJSI554FQADYQ4RNPKRJV72.json","view_paper":"https://pith.science/paper/YERGJSI5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.07448&json=true","fetch_graph":"https://pith.science/api/pith-number/YERGJSI554FQADYQ4RNPKRJV72/graph.json","fetch_events":"https://pith.science/api/pith-number/YERGJSI554FQADYQ4RNPKRJV72/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YERGJSI554FQADYQ4RNPKRJV72/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YERGJSI554FQADYQ4RNPKRJV72/action/storage_attestation","attest_author":"https://pith.science/pith/YERGJSI554FQADYQ4RNPKRJV72/action/author_attestation","sign_citation":"https://pith.science/pith/YERGJSI554FQADYQ4RNPKRJV72/action/citation_signature","submit_replication":"https://pith.science/pith/YERGJSI554FQADYQ4RNPKRJV72/action/replication_record"}},"created_at":"2026-07-05T10:12:37.565706+00:00","updated_at":"2026-07-05T10:12:37.565706+00:00"}