{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BXF2K54J6DXGEF2IMNOITQA5S2","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":"d42131ea8ab347384f5c0ac3dbb7d99f867099ead567a4edd699d5106edac6d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-06-15T12:12:36Z","title_canon_sha256":"71506830479c941db95b618ed65b4e872e3308279abf8d4697594683eca29067"},"schema_version":"1.0","source":{"id":"1706.04833","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04833","created_at":"2026-05-18T00:38:39Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04833v2","created_at":"2026-05-18T00:38:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04833","created_at":"2026-05-18T00:38:39Z"},{"alias_kind":"pith_short_12","alias_value":"BXF2K54J6DXG","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BXF2K54J6DXGEF2I","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BXF2K54J","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:e68b1329c4015661b525775b8a4987ad5e663bfde4edf18359e69bf1ce4e8349","target":"graph","created_at":"2026-05-18T00:38:39Z","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":"Suppose $\\varphi$ is a holomorphic self map of the unit disk and $C_\\varphi$ is a composition operator with symbol $\\varphi$ that fixes the origin and $0<|\\varphi'(0)|<1$. This work explores sufficient conditions that ensure all holomorphic solutions of Schr\\\"oder equation for the composition operator $C_\\varphi$ belong to a Bloch-type space $\\mathcal{B}_\\alpha$ for some $\\alpha>0$. The results from composition operators have been extended to weighted composition operators in the second part of this work.","authors_text":"Bhupendra Paudyal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-06-15T12:12:36Z","title":"Eigenfunctions of Composition Operators on Bloch-type Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04833","kind":"arxiv","version":2},"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":"sha256:9527006d87c1f476379d9560ee73f0ff64c406fb3990d3d252494def451396d1","target":"record","created_at":"2026-05-18T00:38:39Z","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":"d42131ea8ab347384f5c0ac3dbb7d99f867099ead567a4edd699d5106edac6d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-06-15T12:12:36Z","title_canon_sha256":"71506830479c941db95b618ed65b4e872e3308279abf8d4697594683eca29067"},"schema_version":"1.0","source":{"id":"1706.04833","kind":"arxiv","version":2}},"canonical_sha256":"0dcba57789f0ee621748635c89c01d96a354e532ed323db73039acd34774c123","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0dcba57789f0ee621748635c89c01d96a354e532ed323db73039acd34774c123","first_computed_at":"2026-05-18T00:38:39.573014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:39.573014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MFBhZa0nxapi8DbzkKIMQZyZy0o6dU/5Lp6xSzzbr9O+pEyFm16xV2RyHE7RJADrZxP69uqDxF2Vw24JM19uDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:39.573497Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04833","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9527006d87c1f476379d9560ee73f0ff64c406fb3990d3d252494def451396d1","sha256:e68b1329c4015661b525775b8a4987ad5e663bfde4edf18359e69bf1ce4e8349"],"state_sha256":"d4a066a07d3f4c889dab72cadc4f2d661a18beb8cbd56247175e1d3947fd49d2"}