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Nestoridis conjectured that if $\\Omega$ is a simply connected subset of $\\mathbb{C}$ that does not contain $0$ and $S(\\Omega)$ is the set of all functions $f\\in \\mathcal{H}(\\Omega)$ with the property that the set $\\left\\{T_N(f)(z)\\coloneqq\\sum_{n=0}^N\\dfrac{f^{(n)}(z)}{n!} (-z)^n : N = 0,1,2,\\dots \\right\\}$ is dense in $\\mathcal{H}(\\Omega)$, then $S(\\Omega)$ is a dense $G_\\delta$ set in $\\mathcal{H}(\\Omega)$. We answer the conjecture in the affirmative in the special case where $\\Omega$ is an open disc $D(z_0,r)$ that does not contain $0$."},"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":"1710.03114","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-10-09T14:20:47Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"e377b5e467ef9d7b52fd3940738ff3d23ea358a2949c1f872b05aa75d38fa505","abstract_canon_sha256":"f101dea29d262732fb1651a5ab4240249ff1ccf74849a5cf9d3ae423ad877448"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:27.030560Z","signature_b64":"8O8+iPV9/q5NZgolhpEXitT8rKWds+HIjpd5xlX/WqH7JleQg298Wa4M1MU0QdPnBQ1CxBwlxi7kZdflAoVoDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea4eccd21c90a3fce2294182371d6ce855d8cf2ce686521e28c4a5f0115b2520","last_reissued_at":"2026-05-18T00:33:27.029801Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:27.029801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universal partial sums of Taylor series as functions of the centre of expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.CV","authors_text":"Christoforos Panagiotis","submitted_at":"2017-10-09T14:20:47Z","abstract_excerpt":"V. Nestoridis conjectured that if $\\Omega$ is a simply connected subset of $\\mathbb{C}$ that does not contain $0$ and $S(\\Omega)$ is the set of all functions $f\\in \\mathcal{H}(\\Omega)$ with the property that the set $\\left\\{T_N(f)(z)\\coloneqq\\sum_{n=0}^N\\dfrac{f^{(n)}(z)}{n!} (-z)^n : N = 0,1,2,\\dots \\right\\}$ is dense in $\\mathcal{H}(\\Omega)$, then $S(\\Omega)$ is a dense $G_\\delta$ set in $\\mathcal{H}(\\Omega)$. We answer the conjecture in the affirmative in the special case where $\\Omega$ is an open disc $D(z_0,r)$ that does not contain $0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03114","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":"1710.03114","created_at":"2026-05-18T00:33:27.029929+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.03114v1","created_at":"2026-05-18T00:33:27.029929+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03114","created_at":"2026-05-18T00:33:27.029929+00:00"},{"alias_kind":"pith_short_12","alias_value":"5JHMZUQ4SCR7","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"5JHMZUQ4SCR7ZYRJ","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"5JHMZUQ4","created_at":"2026-05-18T12:31:00.734936+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/5JHMZUQ4SCR7ZYRJIGBDOHLM5B","json":"https://pith.science/pith/5JHMZUQ4SCR7ZYRJIGBDOHLM5B.json","graph_json":"https://pith.science/api/pith-number/5JHMZUQ4SCR7ZYRJIGBDOHLM5B/graph.json","events_json":"https://pith.science/api/pith-number/5JHMZUQ4SCR7ZYRJIGBDOHLM5B/events.json","paper":"https://pith.science/paper/5JHMZUQ4"},"agent_actions":{"view_html":"https://pith.science/pith/5JHMZUQ4SCR7ZYRJIGBDOHLM5B","download_json":"https://pith.science/pith/5JHMZUQ4SCR7ZYRJIGBDOHLM5B.json","view_paper":"https://pith.science/paper/5JHMZUQ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.03114&json=true","fetch_graph":"https://pith.science/api/pith-number/5JHMZUQ4SCR7ZYRJIGBDOHLM5B/graph.json","fetch_events":"https://pith.science/api/pith-number/5JHMZUQ4SCR7ZYRJIGBDOHLM5B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5JHMZUQ4SCR7ZYRJIGBDOHLM5B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5JHMZUQ4SCR7ZYRJIGBDOHLM5B/action/storage_attestation","attest_author":"https://pith.science/pith/5JHMZUQ4SCR7ZYRJIGBDOHLM5B/action/author_attestation","sign_citation":"https://pith.science/pith/5JHMZUQ4SCR7ZYRJIGBDOHLM5B/action/citation_signature","submit_replication":"https://pith.science/pith/5JHMZUQ4SCR7ZYRJIGBDOHLM5B/action/replication_record"}},"created_at":"2026-05-18T00:33:27.029929+00:00","updated_at":"2026-05-18T00:33:27.029929+00:00"}