{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7BJONAEYY2CPPSA3A42MENDIC3","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":"15fed7bbc4d138d88cb47835d04fd76a6c150e0e8286e3478845c9f43c2720ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-11-05T14:00:32Z","title_canon_sha256":"93140a8aba3fd2a76273eebcee073392bb29b7936d8f97e1384b2c827a61f762"},"schema_version":"1.0","source":{"id":"1011.1399","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1399","created_at":"2026-05-18T04:33:26Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1399v2","created_at":"2026-05-18T04:33:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1399","created_at":"2026-05-18T04:33:26Z"},{"alias_kind":"pith_short_12","alias_value":"7BJONAEYY2CP","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7BJONAEYY2CPPSA3","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7BJONAEY","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:9c349bf1169e53b95c5041801be5c116c61310dc31d77c8d137d761de7cb46b7","target":"graph","created_at":"2026-05-18T04:33:26Z","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 give an elementary proof of a solvability criterion for the {\\em boundary Carath\\'{e}odory-Fej\\'{e}r problem}: given a point $x \\in \\R$ and, a finite set of target values, to construct a function $f$ in the Pick class such that the first few derivatives of $f$ take on the prescribed target values at $x$. We also derive a linear fractional parametrization of the set of solutions of the interpolation problem. The proofs are based on a reduction method due to Julia and Nevanlinna.","authors_text":"Jim Agler, N. J. Young, Zinaida A. Lykova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-11-05T14:00:32Z","title":"The boundary Carath\\'{e}odory-Fej\\'{e}r interpolation problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1399","kind":"arxiv","version":2},"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:e7bdb1b117714cd26288d3581d861f0e3dfeb8519cb9306a5af84f28028eb8c1","target":"record","created_at":"2026-05-18T04:33:26Z","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":"15fed7bbc4d138d88cb47835d04fd76a6c150e0e8286e3478845c9f43c2720ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2010-11-05T14:00:32Z","title_canon_sha256":"93140a8aba3fd2a76273eebcee073392bb29b7936d8f97e1384b2c827a61f762"},"schema_version":"1.0","source":{"id":"1011.1399","kind":"arxiv","version":2}},"canonical_sha256":"f852e68098c684f7c81b0734c2346816d6a02255145ddd8ce2d765ffcb903ed3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f852e68098c684f7c81b0734c2346816d6a02255145ddd8ce2d765ffcb903ed3","first_computed_at":"2026-05-18T04:33:26.690963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:26.690963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1VFk20Y+28V6o2RDgXZI4V9ZZymE+Xc5v+4xD8OlsH4hm6OfY7E9MlG4pQIMOfMSbfky+6NWuihIApZZrplwBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:26.691434Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.1399","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7bdb1b117714cd26288d3581d861f0e3dfeb8519cb9306a5af84f28028eb8c1","sha256:9c349bf1169e53b95c5041801be5c116c61310dc31d77c8d137d761de7cb46b7"],"state_sha256":"ff9af8dd0a413bf4c9561eae48fda73fff05e5f1009fbc75c62088f73a52400d"}