{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:47BHEJPKD2DHTSDSSMYUZLWVJV","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":"4b6bae51777023009512d48217d81c0d12cca3868d290ae663159a985dbc2bd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-06T07:30:38Z","title_canon_sha256":"68c48c4983fd7d744590ab9f4f22f12fc3046c30a6ad9a5a12d4e4acc74cc7a1"},"schema_version":"1.0","source":{"id":"1802.01828","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.01828","created_at":"2026-05-18T00:24:21Z"},{"alias_kind":"arxiv_version","alias_value":"1802.01828v1","created_at":"2026-05-18T00:24:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01828","created_at":"2026-05-18T00:24:21Z"},{"alias_kind":"pith_short_12","alias_value":"47BHEJPKD2DH","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"47BHEJPKD2DHTSDS","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"47BHEJPK","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:13892f9b3df7ade43e16d64c5d7fcc62cc11cc618d2ceae4a6fd7be0815089fe","target":"graph","created_at":"2026-05-18T00:24:21Z","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":"In this article, we study the weighted composition operators preserving the class $\\mathcal{P}_{\\alpha}$ of analytic functions subordinate to $\\frac{1+\\alpha z}{1-z}$ for $|\\alpha|\\leq 1, \\alpha \\neq -1$. Some of its consequences and examples for some special cases are presented. Furthermore, we discuss about the fixed points of weighted composition operators.","authors_text":"Perumal Muthukumar, Saminathan Ponnusamy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-06T07:30:38Z","title":"Weighted composition operators on the class of subordinate functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01828","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":"sha256:744d213ed9c1ad9f4903ba3be4a83ee66323031ef55e6942dcd9896f0b5f47b9","target":"record","created_at":"2026-05-18T00:24:21Z","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":"4b6bae51777023009512d48217d81c0d12cca3868d290ae663159a985dbc2bd7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-06T07:30:38Z","title_canon_sha256":"68c48c4983fd7d744590ab9f4f22f12fc3046c30a6ad9a5a12d4e4acc74cc7a1"},"schema_version":"1.0","source":{"id":"1802.01828","kind":"arxiv","version":1}},"canonical_sha256":"e7c27225ea1e8679c87293314caed54d55f44f0ffb33f8f7fd405ff5418b7a49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7c27225ea1e8679c87293314caed54d55f44f0ffb33f8f7fd405ff5418b7a49","first_computed_at":"2026-05-18T00:24:21.167480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:21.167480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kQBbYNfQ6C19WwkPjVdBW8oxT5L9sibuhfOxQ4yoQlTZkgUhLzFFcL2HIzOsLRpVoB83cZ5ffzPHIUgVFwGVDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:21.167925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.01828","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:744d213ed9c1ad9f4903ba3be4a83ee66323031ef55e6942dcd9896f0b5f47b9","sha256:13892f9b3df7ade43e16d64c5d7fcc62cc11cc618d2ceae4a6fd7be0815089fe"],"state_sha256":"2b5413ce377e3830b24eb0311248dca2b6843904533be7d5f130f9765132caec"}