{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HAYQ6V5JDI4Q5BJIUJ2WVH2SLB","short_pith_number":"pith:HAYQ6V5J","schema_version":"1.0","canonical_sha256":"38310f57a91a390e8528a2756a9f525875546cdaffaf3c06b42cd4f7706f1673","source":{"kind":"arxiv","id":"1801.06804","version":1},"attestation_state":"computed","paper":{"title":"On Taylor coefficients of smooth functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Avner Kiro","submitted_at":"2018-01-21T10:36:17Z","abstract_excerpt":"We study the Borel map, which maps infinitely differentiable functions on an interval to the jets of their Taylor coefficients at a given point in the interval. Our main results include a complete description of the image of the Borel map for Beurling classes of smooth functions and a moment-type summation method which allows one to recover a function from its Taylor jet. A surprising feature of this description is an unexpected threshold at the logarithmic class. Another interesting finding is a \"duality\" between non-quasianalytic and quasianalytic classes, which reduces the description of th"},"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":"1801.06804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-21T10:36:17Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"3e211a147f91a383ae9816ffc43eb679f997408fea8c76607c35840aa7fb77cd","abstract_canon_sha256":"f13622a5e44da22b6ec23c89a0b85cc67afb26944cdcdd187f978256f304aa5c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:27.664737Z","signature_b64":"VyPPdIAvCsOJGIQaOcN6kNv5RV/Ai6pA4kn6nZg5Hvuq2Wvj/waIHG/nW+3p913uBS5K79udbh7CEeY+VK/0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38310f57a91a390e8528a2756a9f525875546cdaffaf3c06b42cd4f7706f1673","last_reissued_at":"2026-05-18T00:25:27.664022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:27.664022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Taylor coefficients of smooth functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Avner Kiro","submitted_at":"2018-01-21T10:36:17Z","abstract_excerpt":"We study the Borel map, which maps infinitely differentiable functions on an interval to the jets of their Taylor coefficients at a given point in the interval. Our main results include a complete description of the image of the Borel map for Beurling classes of smooth functions and a moment-type summation method which allows one to recover a function from its Taylor jet. A surprising feature of this description is an unexpected threshold at the logarithmic class. Another interesting finding is a \"duality\" between non-quasianalytic and quasianalytic classes, which reduces the description of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06804","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":"1801.06804","created_at":"2026-05-18T00:25:27.664136+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.06804v1","created_at":"2026-05-18T00:25:27.664136+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.06804","created_at":"2026-05-18T00:25:27.664136+00:00"},{"alias_kind":"pith_short_12","alias_value":"HAYQ6V5JDI4Q","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HAYQ6V5JDI4Q5BJI","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HAYQ6V5J","created_at":"2026-05-18T12:32:28.185984+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/HAYQ6V5JDI4Q5BJIUJ2WVH2SLB","json":"https://pith.science/pith/HAYQ6V5JDI4Q5BJIUJ2WVH2SLB.json","graph_json":"https://pith.science/api/pith-number/HAYQ6V5JDI4Q5BJIUJ2WVH2SLB/graph.json","events_json":"https://pith.science/api/pith-number/HAYQ6V5JDI4Q5BJIUJ2WVH2SLB/events.json","paper":"https://pith.science/paper/HAYQ6V5J"},"agent_actions":{"view_html":"https://pith.science/pith/HAYQ6V5JDI4Q5BJIUJ2WVH2SLB","download_json":"https://pith.science/pith/HAYQ6V5JDI4Q5BJIUJ2WVH2SLB.json","view_paper":"https://pith.science/paper/HAYQ6V5J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.06804&json=true","fetch_graph":"https://pith.science/api/pith-number/HAYQ6V5JDI4Q5BJIUJ2WVH2SLB/graph.json","fetch_events":"https://pith.science/api/pith-number/HAYQ6V5JDI4Q5BJIUJ2WVH2SLB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HAYQ6V5JDI4Q5BJIUJ2WVH2SLB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HAYQ6V5JDI4Q5BJIUJ2WVH2SLB/action/storage_attestation","attest_author":"https://pith.science/pith/HAYQ6V5JDI4Q5BJIUJ2WVH2SLB/action/author_attestation","sign_citation":"https://pith.science/pith/HAYQ6V5JDI4Q5BJIUJ2WVH2SLB/action/citation_signature","submit_replication":"https://pith.science/pith/HAYQ6V5JDI4Q5BJIUJ2WVH2SLB/action/replication_record"}},"created_at":"2026-05-18T00:25:27.664136+00:00","updated_at":"2026-05-18T00:25:27.664136+00:00"}