{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OPIHIHMVTCABO65OJJ6OHY7NG2","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":"583853ad53bd1d40509caea70a161a549367d79e6f105ff041a44349b7ee82e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-20T17:43:32Z","title_canon_sha256":"97d8599f9c21b9aaaea8764f4ab90d70687ccc33c870281dfdec07c33b05e7b3"},"schema_version":"1.0","source":{"id":"1805.07804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.07804","created_at":"2026-05-18T00:15:32Z"},{"alias_kind":"arxiv_version","alias_value":"1805.07804v1","created_at":"2026-05-18T00:15:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.07804","created_at":"2026-05-18T00:15:32Z"},{"alias_kind":"pith_short_12","alias_value":"OPIHIHMVTCAB","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OPIHIHMVTCABO65O","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OPIHIHMV","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:6469b31ad57506b064d0f029a999839a0ab69d54e652a5c86e8751134b7e04d2","target":"graph","created_at":"2026-05-18T00:15:32Z","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":"Very recently, Bo\\v{z}in and Karapetrovi\\'c solved a conjecture by proving that the norm of the Hilbert matrix operator $\\mathcal{H}$ on the Bergman space $A^p$ is equal to $\\frac{\\pi}{\\sin(\\frac{2\\pi}{p})}$ for $2 < p < 4.$ In this article we present a partly new and simplified proof of this result. Moreover, we calculate the exact value of the norm of $\\mathcal{H}$ defined on the Korenblum spaces $H^\\infty_\\alpha$ for $0 < \\alpha \\le 2/3$ and an upper bound for the norm on the scale $2/3 < \\alpha < 1$.","authors_text":"Mikael Lindstr\\\"om, Niklas Wikman, Santeri Miihkinen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-20T17:43:32Z","title":"Norm estimates of weighted composition operators pertaining to the Hilbert Matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07804","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":"sha256:8e55559d64e087df5dc94ac66e21fe8a2e4a19e3cb81fbb50eac876a990e0b77","target":"record","created_at":"2026-05-18T00:15:32Z","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":"583853ad53bd1d40509caea70a161a549367d79e6f105ff041a44349b7ee82e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-20T17:43:32Z","title_canon_sha256":"97d8599f9c21b9aaaea8764f4ab90d70687ccc33c870281dfdec07c33b05e7b3"},"schema_version":"1.0","source":{"id":"1805.07804","kind":"arxiv","version":1}},"canonical_sha256":"73d0741d959880177bae4a7ce3e3ed36bf8059be5fb71bad9b38eb0d0182a805","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73d0741d959880177bae4a7ce3e3ed36bf8059be5fb71bad9b38eb0d0182a805","first_computed_at":"2026-05-18T00:15:32.498026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:32.498026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/+UfbSXg4U5pdw3nm0hwGTjRDP1dYen4rnbfjulqSzgx4GgLphOH4Fg4Mj6DPFT/PrbJxXQqUEG+sdtkauQOBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:32.498629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.07804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e55559d64e087df5dc94ac66e21fe8a2e4a19e3cb81fbb50eac876a990e0b77","sha256:6469b31ad57506b064d0f029a999839a0ab69d54e652a5c86e8751134b7e04d2"],"state_sha256":"6754c5a0f6446650bab8175e1d7a7f2fbdd915275e49dff6a28a716e8124c038"}