{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HAYQ6V5JDI4Q5BJIUJ2WVH2SLB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f13622a5e44da22b6ec23c89a0b85cc67afb26944cdcdd187f978256f304aa5c","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-21T10:36:17Z","title_canon_sha256":"3e211a147f91a383ae9816ffc43eb679f997408fea8c76607c35840aa7fb77cd"},"schema_version":"1.0","source":{"id":"1801.06804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.06804","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1801.06804v1","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.06804","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"HAYQ6V5JDI4Q","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HAYQ6V5JDI4Q5BJI","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HAYQ6V5J","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:1a0bd04dc6f903feadf5cf4e0de6d1255895f436e2262af2204afde2a51657b8","target":"graph","created_at":"2026-05-18T00:25:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Avner Kiro","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-21T10:36:17Z","title":"On Taylor coefficients of smooth functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06804","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8213ebc6f1fa44970baa3a665d84f01642762b8eb09409acaa46c739a3affa4b","target":"record","created_at":"2026-05-18T00:25:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f13622a5e44da22b6ec23c89a0b85cc67afb26944cdcdd187f978256f304aa5c","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-01-21T10:36:17Z","title_canon_sha256":"3e211a147f91a383ae9816ffc43eb679f997408fea8c76607c35840aa7fb77cd"},"schema_version":"1.0","source":{"id":"1801.06804","kind":"arxiv","version":1}},"canonical_sha256":"38310f57a91a390e8528a2756a9f525875546cdaffaf3c06b42cd4f7706f1673","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38310f57a91a390e8528a2756a9f525875546cdaffaf3c06b42cd4f7706f1673","first_computed_at":"2026-05-18T00:25:27.664022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:27.664022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VyPPdIAvCsOJGIQaOcN6kNv5RV/Ai6pA4kn6nZg5Hvuq2Wvj/waIHG/nW+3p913uBS5K79udbh7CEeY+VK/0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:27.664737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.06804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8213ebc6f1fa44970baa3a665d84f01642762b8eb09409acaa46c739a3affa4b","sha256:1a0bd04dc6f903feadf5cf4e0de6d1255895f436e2262af2204afde2a51657b8"],"state_sha256":"e63eec6e090c2517c38c5fe5e5e5f3b0ff0ae5d9399ebc9ed425d4492ebf112b"}