{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DGQ6GNGBHBEHVPXHESB52ZYMW7","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":"8f5227274b796060e78ec258795819f97ccc96247308bba5f18a34246dd2b29b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-01-08T03:22:56Z","title_canon_sha256":"9253a0cb72d3823e4399f31354ce4eb1b8fc8a4a4628c734476d7a291060c8d9"},"schema_version":"1.0","source":{"id":"1901.02142","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.02142","created_at":"2026-05-17T23:56:43Z"},{"alias_kind":"arxiv_version","alias_value":"1901.02142v1","created_at":"2026-05-17T23:56:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02142","created_at":"2026-05-17T23:56:43Z"},{"alias_kind":"pith_short_12","alias_value":"DGQ6GNGBHBEH","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DGQ6GNGBHBEHVPXH","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DGQ6GNGB","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:d4b30493b9e9bc1a1255fc414783b8371247e6d2fd4f868c01f2c3626416d77c","target":"graph","created_at":"2026-05-17T23:56:43Z","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 $f$ be the infinitesimal generator of a one-parameter semigroup $\\left\\{ F_{t}\\right\\} _{t\\ge0}$ of holomorphic self-mappings of the open unit disk $\\Delta$. In this paper we study properties of the family $R$ of resolvents $(I+rf)^{-1}:\\Delta\\to\\Delta~ (r\\ge0)$ in the spirit of geometric function theory. We discovered, in particular, that $R$ forms an inverse L\\\"owner chain of hyperbolically convex functions. Moreover, each element of $R$ satisfies the Noshiro-Warschawski condition and is a starlike function of order at least $\\frac12$,. This, in turn, implies that each element of $R$ is ","authors_text":"David Shoikhet, Mark Elin, Toshiyuki Sugawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-01-08T03:22:56Z","title":"Geometric properties of the nonlinear resolvent of holomorphic generators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02142","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":"sha256:0936e93361774edf6f0c829121a79abe077bb677075b9006308830761b260e70","target":"record","created_at":"2026-05-17T23:56:43Z","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":"8f5227274b796060e78ec258795819f97ccc96247308bba5f18a34246dd2b29b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2019-01-08T03:22:56Z","title_canon_sha256":"9253a0cb72d3823e4399f31354ce4eb1b8fc8a4a4628c734476d7a291060c8d9"},"schema_version":"1.0","source":{"id":"1901.02142","kind":"arxiv","version":1}},"canonical_sha256":"19a1e334c138487abee72483dd670cb7f60bd0cc849212d3d7a434616e2adde2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19a1e334c138487abee72483dd670cb7f60bd0cc849212d3d7a434616e2adde2","first_computed_at":"2026-05-17T23:56:43.924736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:43.924736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pOBOjDuasthOfKinoSN1t1bkY02nDnmYAY9MIr/ORFR7l7a8OqDwEy6IzQK1BNiR1IaZ/fEVsfdteUeXY0QpDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:43.925107Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.02142","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0936e93361774edf6f0c829121a79abe077bb677075b9006308830761b260e70","sha256:d4b30493b9e9bc1a1255fc414783b8371247e6d2fd4f868c01f2c3626416d77c"],"state_sha256":"abcca188a08ca103833f3aaa140d7b38bf7334cc9b74fd1ce7ec1d976078f8b8"}