{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:V24Y6R6CNAW2E5Y4GNCOOEPCGI","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":"9276067a850069d85f19b6686e3eb8e91769abd1b58406a4b69d0cd525152d8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-08-12T19:53:13Z","title_canon_sha256":"8b05410421ce6a3d18c209315d1528b397ce441d4714ba3691a5ea9a15e178d9"},"schema_version":"1.0","source":{"id":"1308.2662","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2662","created_at":"2026-05-18T03:16:06Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2662v1","created_at":"2026-05-18T03:16:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2662","created_at":"2026-05-18T03:16:06Z"},{"alias_kind":"pith_short_12","alias_value":"V24Y6R6CNAW2","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"V24Y6R6CNAW2E5Y4","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"V24Y6R6C","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:34fa2e40ccddf1979218b76d871858bdfe3ed1c597e9f6724fa55db5ed9ff4c0","target":"graph","created_at":"2026-05-18T03:16:06Z","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 $\\{f_{\\lambda; j}\\}_{\\lambda\\in V; 1\\le j\\le k}$ be families of holomorphic functions in the open unit disk $\\Di\\subset\\Co$ depending holomorphically on a parameter $\\lambda\\in V\\subset \\Co^n$. We establish a Rolle type theorem for the generalized multiplicity (called {\\em cyclicity}) of zero of the family of univariate holomorphic functions ${\\sum_{j=1}^k f_{\\lambda;j}}_{\\lambda\\in V}$ at $0\\in\\Di$. As a corollary, we estimate the cyclicity of the family of generalized exponential polynomials, that is, the family of entire functions of the form $\\sum_{k=1}^m P_k(z)e^{Q_k(z)}$, $z\\in\\Co$, ","authors_text":"Alexander Brudnyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-08-12T19:53:13Z","title":"A Rolle type theorem for cyclicity of zeros of families of analytic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2662","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":"sha256:272b1348fcf132cb75be07827484786802a7526ce86aa3ba4e044f4258515876","target":"record","created_at":"2026-05-18T03:16:06Z","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":"9276067a850069d85f19b6686e3eb8e91769abd1b58406a4b69d0cd525152d8d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-08-12T19:53:13Z","title_canon_sha256":"8b05410421ce6a3d18c209315d1528b397ce441d4714ba3691a5ea9a15e178d9"},"schema_version":"1.0","source":{"id":"1308.2662","kind":"arxiv","version":1}},"canonical_sha256":"aeb98f47c2682da2771c3344e711e2322580c0dc4787876013d3622f8d8445ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aeb98f47c2682da2771c3344e711e2322580c0dc4787876013d3622f8d8445ee","first_computed_at":"2026-05-18T03:16:06.904113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:06.904113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QBbcGwIbja6VkpSAFvvNCEpn3geo2DneV9MbYJsdmZa7JyrEyF466QjDdqLVaMNP3FDL9AQFKA/yhsA/ZghwAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:06.904559Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2662","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:272b1348fcf132cb75be07827484786802a7526ce86aa3ba4e044f4258515876","sha256:34fa2e40ccddf1979218b76d871858bdfe3ed1c597e9f6724fa55db5ed9ff4c0"],"state_sha256":"75e75a06b6cda89fbb7e06565ff1fdd62ac73f84c71dc984c9f9b65e511d8189"}