{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:6L2O7JIMKWQ3YEOOGV7536NT2H","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":"7887f7ecce0c779cac44117082b036587ac2af5b839ad98b4536aaa7abbc10cb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-05-30T11:46:43Z","title_canon_sha256":"e4a83538fde8c8008eab4c5f767820a2a5786821638217b29d1d546f4da93e26"},"schema_version":"1.0","source":{"id":"2505.24495","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.24495","created_at":"2026-07-05T11:12:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.24495v1","created_at":"2026-07-05T11:12:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24495","created_at":"2026-07-05T11:12:51Z"},{"alias_kind":"pith_short_12","alias_value":"6L2O7JIMKWQ3","created_at":"2026-07-05T11:12:51Z"},{"alias_kind":"pith_short_16","alias_value":"6L2O7JIMKWQ3YEOO","created_at":"2026-07-05T11:12:51Z"},{"alias_kind":"pith_short_8","alias_value":"6L2O7JIM","created_at":"2026-07-05T11:12:51Z"}],"graph_snapshots":[{"event_id":"sha256:748161b653ff93e088d2f25aa07601dba7932ff62bd1de6a9865ed00181f78cf","target":"graph","created_at":"2026-07-05T11:12:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.24495/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we characterize the convexity of the Berezin range for finite-rank operators acting on the weighted Hardy space $\\mathcal{H}_\\gamma (\\mathbb{D})$ over the unit disc $\\mathbb{D}$. We provide a complete classification in terms of convexity for concrete operators. Additionally, we address dynamical properties of finite-rank operators on Hardy and Bergman spaces. Several illustrative examples are discussed to support our theoretical findings. Additionally, geometrical interpretations have also been employed.","authors_text":"Gorachand Chakraborty, Sandip Kumar Maiti, Satyajit Sahoo","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-05-30T11:46:43Z","title":"Convexity of the Berezin range of operators on $\\mathcal{H}_\\gamma (\\mathbb{D})$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24495","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":"sha256:176db16a677725e9d390a7bd7b87d10ed2e7bf74ec799af6b5ff1104f7e0a2a4","target":"record","created_at":"2026-07-05T11:12:51Z","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":"7887f7ecce0c779cac44117082b036587ac2af5b839ad98b4536aaa7abbc10cb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2025-05-30T11:46:43Z","title_canon_sha256":"e4a83538fde8c8008eab4c5f767820a2a5786821638217b29d1d546f4da93e26"},"schema_version":"1.0","source":{"id":"2505.24495","kind":"arxiv","version":1}},"canonical_sha256":"f2f4efa50c55a1bc11ce357fddf9b3d1f0a062de635664b731db3d156620f97c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2f4efa50c55a1bc11ce357fddf9b3d1f0a062de635664b731db3d156620f97c","first_computed_at":"2026-07-05T11:12:51.055547Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:12:51.055547Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BfiERmDVzUQn/Hp6uc/vMz8H+ICs+edc2BPwVF2iTZSyq9nTcSq1TEQtYcWCDcMcAUTxSvWwSK2JgT2t+cTpBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:12:51.056074Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.24495","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:176db16a677725e9d390a7bd7b87d10ed2e7bf74ec799af6b5ff1104f7e0a2a4","sha256:748161b653ff93e088d2f25aa07601dba7932ff62bd1de6a9865ed00181f78cf"],"state_sha256":"ded462061a885271f1508ebc89ef957a4f819972d000be2d32e03239d972a876"}