{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XT6COAL4WZEIHAHS2LZFWMVODX","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":"c3cec01c1ab5dfa084ed260e13ecb6a08141df3d7594ecdaadb57fa10e4f6d8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-05T12:18:38Z","title_canon_sha256":"13a3b7b8457017e0bd07bab45e2b0c0a827c6cae44b95e8fafffbdc920bdd169"},"schema_version":"1.0","source":{"id":"1312.1516","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1516","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1516v1","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1516","created_at":"2026-05-18T03:05:27Z"},{"alias_kind":"pith_short_12","alias_value":"XT6COAL4WZEI","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XT6COAL4WZEIHAHS","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XT6COAL4","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:3114aa7394c49e335da86f810f949f21dd658017d4d0c00f275364205afd7d4e","target":"graph","created_at":"2026-05-18T03:05:27Z","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":"We provide an estimate for the essential norm of a weighted composition operator $W_{\\psi,\\varphi}\\colon f\\mapsto \\psi(f\\circ\\varphi)$ acting on the space $BMOA$ in terms of the weight function $\\psi$ and the $n$-th power $\\varphi^n$ of the analytic self-map $\\varphi$ of the open unit disc $\\mathbb{D}$. We also provide a new estimate for the norm of the weighted composition operator on $BMOA$.","authors_text":"Jussi Laitila, Mikael Lindstr\\\"om","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-05T12:18:38Z","title":"The essential norm of a weighted composition operator on BMOA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1516","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:d95fbd9707e451c7a021d25a67daf7826c6d4e45914669d3a5743b99aab6eba8","target":"record","created_at":"2026-05-18T03:05:27Z","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":"c3cec01c1ab5dfa084ed260e13ecb6a08141df3d7594ecdaadb57fa10e4f6d8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-05T12:18:38Z","title_canon_sha256":"13a3b7b8457017e0bd07bab45e2b0c0a827c6cae44b95e8fafffbdc920bdd169"},"schema_version":"1.0","source":{"id":"1312.1516","kind":"arxiv","version":1}},"canonical_sha256":"bcfc27017cb6488380f2d2f25b32ae1dea2e0e2908472a7f46017b68acfc9ba7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcfc27017cb6488380f2d2f25b32ae1dea2e0e2908472a7f46017b68acfc9ba7","first_computed_at":"2026-05-18T03:05:27.060913Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:27.060913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PQ/S+zhHP33vUnks79D72LZDZHjb331P6wB5d7loGMfgBvQ7U72ao8c7KWLNb4UkWfwmyT3FJUtpwdMI9WwmDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:27.061386Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1516","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d95fbd9707e451c7a021d25a67daf7826c6d4e45914669d3a5743b99aab6eba8","sha256:3114aa7394c49e335da86f810f949f21dd658017d4d0c00f275364205afd7d4e"],"state_sha256":"60ef362580ef711578ef68b2ae010635b1326c0a4db27e61c839c4aeeb7074fc"}