{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:B6DLQPNFTW34X4KM5TTKVKORUX","short_pith_number":"pith:B6DLQPNF","schema_version":"1.0","canonical_sha256":"0f86b83da59db7cbf14cece6aaa9d1a5ff0ad67c9825d2b75042e7f198bdae7b","source":{"kind":"arxiv","id":"1409.0726","version":1},"attestation_state":"computed","paper":{"title":"On the zeros of asymptotically extremal polynomial sequences in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Edward B. Saff, Nikos Stylianopoulos","submitted_at":"2014-09-02T14:33:06Z","abstract_excerpt":"Let $E$ be a compact set of positive logarithmic capacity in the complex plane and let $\\{P_n(z)\\}_{1}^{\\infty}$ be a sequence of asymptotically extremal monic polynomials for $E$ in the sense that \\begin{equation*}%\\label{} \\limsup_{n\\to\\infty}\\|P_n\\|_E^{1/n}\\le\\mathrm{cap}(E). \\end{equation*} The purpose of this note is to provide sufficient geometric conditions on $E$ under which the (full) sequence of normalized counting measures of the zeros of $\\{P_n\\}$ converges in the weak-star topology to the equilibrium measure on $E$, as $n\\to\\infty.$ Utilizing an argument of Gardiner and Pommerenk"},"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":"1409.0726","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-09-02T14:33:06Z","cross_cats_sorted":[],"title_canon_sha256":"f490b300d00a670fd905e752a5c8d966fb310a15ad2ff446f42250f9f830cb5f","abstract_canon_sha256":"8e6763f0b7a81fb6e7e4db8011c639743c33484b82f5adde81470ed6c986a43e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:46.254590Z","signature_b64":"bdZ0lGLWl8uQS4es4nJxyovLe52JLFhhVuDvH0N4FVJRzVsNdmVVOg3GguQsGE0+eGngLAojDnjXkASG+WexCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f86b83da59db7cbf14cece6aaa9d1a5ff0ad67c9825d2b75042e7f198bdae7b","last_reissued_at":"2026-05-18T02:43:46.254094Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:46.254094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the zeros of asymptotically extremal polynomial sequences in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Edward B. Saff, Nikos Stylianopoulos","submitted_at":"2014-09-02T14:33:06Z","abstract_excerpt":"Let $E$ be a compact set of positive logarithmic capacity in the complex plane and let $\\{P_n(z)\\}_{1}^{\\infty}$ be a sequence of asymptotically extremal monic polynomials for $E$ in the sense that \\begin{equation*}%\\label{} \\limsup_{n\\to\\infty}\\|P_n\\|_E^{1/n}\\le\\mathrm{cap}(E). \\end{equation*} The purpose of this note is to provide sufficient geometric conditions on $E$ under which the (full) sequence of normalized counting measures of the zeros of $\\{P_n\\}$ converges in the weak-star topology to the equilibrium measure on $E$, as $n\\to\\infty.$ Utilizing an argument of Gardiner and Pommerenk"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0726","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":"1409.0726","created_at":"2026-05-18T02:43:46.254178+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.0726v1","created_at":"2026-05-18T02:43:46.254178+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0726","created_at":"2026-05-18T02:43:46.254178+00:00"},{"alias_kind":"pith_short_12","alias_value":"B6DLQPNFTW34","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_16","alias_value":"B6DLQPNFTW34X4KM","created_at":"2026-05-18T12:28:22.404517+00:00"},{"alias_kind":"pith_short_8","alias_value":"B6DLQPNF","created_at":"2026-05-18T12:28:22.404517+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/B6DLQPNFTW34X4KM5TTKVKORUX","json":"https://pith.science/pith/B6DLQPNFTW34X4KM5TTKVKORUX.json","graph_json":"https://pith.science/api/pith-number/B6DLQPNFTW34X4KM5TTKVKORUX/graph.json","events_json":"https://pith.science/api/pith-number/B6DLQPNFTW34X4KM5TTKVKORUX/events.json","paper":"https://pith.science/paper/B6DLQPNF"},"agent_actions":{"view_html":"https://pith.science/pith/B6DLQPNFTW34X4KM5TTKVKORUX","download_json":"https://pith.science/pith/B6DLQPNFTW34X4KM5TTKVKORUX.json","view_paper":"https://pith.science/paper/B6DLQPNF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.0726&json=true","fetch_graph":"https://pith.science/api/pith-number/B6DLQPNFTW34X4KM5TTKVKORUX/graph.json","fetch_events":"https://pith.science/api/pith-number/B6DLQPNFTW34X4KM5TTKVKORUX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B6DLQPNFTW34X4KM5TTKVKORUX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B6DLQPNFTW34X4KM5TTKVKORUX/action/storage_attestation","attest_author":"https://pith.science/pith/B6DLQPNFTW34X4KM5TTKVKORUX/action/author_attestation","sign_citation":"https://pith.science/pith/B6DLQPNFTW34X4KM5TTKVKORUX/action/citation_signature","submit_replication":"https://pith.science/pith/B6DLQPNFTW34X4KM5TTKVKORUX/action/replication_record"}},"created_at":"2026-05-18T02:43:46.254178+00:00","updated_at":"2026-05-18T02:43:46.254178+00:00"}