{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JSEACR44MKFA5YYSQIGGXRYAS3","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":"02461dcf4805f97c0e2e6897f831b66b7a155215d6027b2819fb95f3416f6f87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-09-12T20:36:29Z","title_canon_sha256":"9a321efcbc71602685f527170d7b3a19e4f45fc85c4580c5108b2be8f936d259"},"schema_version":"1.0","source":{"id":"1709.04050","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04050","created_at":"2026-05-18T00:15:47Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04050v3","created_at":"2026-05-18T00:15:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04050","created_at":"2026-05-18T00:15:47Z"},{"alias_kind":"pith_short_12","alias_value":"JSEACR44MKFA","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JSEACR44MKFA5YYS","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JSEACR44","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:84560818af87a1f5dea6328161cd8f023edbb5b599a558412c5a4a9e3c7b9e45","target":"graph","created_at":"2026-05-18T00:15:47Z","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":"Let $X$ be a compact subset of the complex plane. It is shown that if a point $x_0$ admits a bounded point derivation on $R^p(X)$, the closure of rational function with poles off $X$ in the $L^p(dA)$ norm, for $p >2$ and if $X$ contains an interior cone, then the bounded point derivation can be represented by the difference quotient if the limit is taken over a non-tangential ray to $x_0$. A similar result is proven for higher order bounded point derivations. These results extend a theorem of O'Farrell for $R(X)$, the closure of rational functions with poles off $X$ in the uniform norm.","authors_text":"Stephen Deterding","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-09-12T20:36:29Z","title":"A formula for a bounded point derivation on $R^p(X)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04050","kind":"arxiv","version":3},"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":"sha256:1b13ea4af5c8b1e60bee68e5ed8a121fcb4d99e25a331299fb4418d4dbcab217","target":"record","created_at":"2026-05-18T00:15:47Z","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":"02461dcf4805f97c0e2e6897f831b66b7a155215d6027b2819fb95f3416f6f87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-09-12T20:36:29Z","title_canon_sha256":"9a321efcbc71602685f527170d7b3a19e4f45fc85c4580c5108b2be8f936d259"},"schema_version":"1.0","source":{"id":"1709.04050","kind":"arxiv","version":3}},"canonical_sha256":"4c8801479c628a0ee312820c6bc70096e3190f00dcd8c6f37ef45b59626d9909","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4c8801479c628a0ee312820c6bc70096e3190f00dcd8c6f37ef45b59626d9909","first_computed_at":"2026-05-18T00:15:47.064918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:47.064918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Lq82F8k3Hz0/t0PCbxIeYaCoBnroHDpuznsNbPGAGipsDB6y5mhcme1lO/tRIhHFIurZJ8aVI5WmaMY0a7tBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:47.065533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04050","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b13ea4af5c8b1e60bee68e5ed8a121fcb4d99e25a331299fb4418d4dbcab217","sha256:84560818af87a1f5dea6328161cd8f023edbb5b599a558412c5a4a9e3c7b9e45"],"state_sha256":"4744d4fb6d2208fa0e2948dfecb45d7dc01dbe120da071ba7f841a4d0d7950d1"}