{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:I35IVQWLN6DLGRRKGH4YOTZFGS","short_pith_number":"pith:I35IVQWL","canonical_record":{"source":{"id":"1503.01130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-03T21:18:48Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"8024441ef48fe854598c63f09b9233b2c90b956cf961129f6c15263af01e424d","abstract_canon_sha256":"eedd6d3a9217a9dcc7106ac5b1428f476aa6b55b51433570adba8fc751fa7882"},"schema_version":"1.0"},"canonical_sha256":"46fa8ac2cb6f86b3462a31f9874f2534a6e3ab4bd92b3fceee11b06c006ff8d2","source":{"kind":"arxiv","id":"1503.01130","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01130","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01130v1","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01130","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"pith_short_12","alias_value":"I35IVQWLN6DL","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I35IVQWLN6DLGRRK","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I35IVQWL","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:I35IVQWLN6DLGRRKGH4YOTZFGS","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01130","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-03T21:18:48Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"8024441ef48fe854598c63f09b9233b2c90b956cf961129f6c15263af01e424d","abstract_canon_sha256":"eedd6d3a9217a9dcc7106ac5b1428f476aa6b55b51433570adba8fc751fa7882"},"schema_version":"1.0"},"canonical_sha256":"46fa8ac2cb6f86b3462a31f9874f2534a6e3ab4bd92b3fceee11b06c006ff8d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:39.815599Z","signature_b64":"O43mi/4l7eOpg1eQGqbW/P6tbRszw7xjF+zQH2TkuimRNo85splJMj1GIxNVCMqvdVz0Uu6XkgvzKw9SRIJNDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46fa8ac2cb6f86b3462a31f9874f2534a6e3ab4bd92b3fceee11b06c006ff8d2","last_reissued_at":"2026-05-18T02:25:39.815146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:39.815146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01130","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:25:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X2TRN+jaMImLjO5zZFQqPUngmwSRGWPM+ncBIHlOaI8xa526BY3n45npixAqSOgI05Sxx1n5X+1tu6miLfFHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:14:49.846128Z"},"content_sha256":"17b8575a4fe6008845d49888583592bef48babc3e8589d76b63a1b329bdb296b","schema_version":"1.0","event_id":"sha256:17b8575a4fe6008845d49888583592bef48babc3e8589d76b63a1b329bdb296b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:I35IVQWLN6DLGRRKGH4YOTZFGS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted composition operators on the Dirichlet space: boundedness and spectral properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"E. A. Gallardo-Guti\\'errez, I. Chalendar, J.R. Partington","submitted_at":"2015-03-03T21:18:48Z","abstract_excerpt":"Boundedness of weighted composition operators $W_{u,\\varphi}$ acting on the classical Dirichlet space $\\mathcal{D}$ as $W_{u,\\varphi}f= u\\, (f\\circ \\varphi)$ is studied in terms of the multiplier space associated to the symbol $\\varphi$, i.e., ${\\mathcal{M}(\\phi)}=\\{ u \\in {\\mathcal D}: W_{u,\\phi} \\hbox{ is bounded on } {\\mathcal D} \\}$. A prominent role is played by the multipliers of the Dirichlet space. As a consequence, the spectrum of $W_{u,\\varphi}$ in $\\mathcal{D}$ whenever $\\varphi$ is an automorphism of the unit disc is studied, extending a recent work of Hyv\\\"arinen, Lindstr\\\"om, Nie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01130","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:25:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zO3ZRvfzq+pmXPH0nZNE6Q3A6VRNzxecmKn2dIg8HiELwNiRJ9YJmHcuXHPkaJnaEQ8dKU7eOtIet/yH6fjFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:14:49.846477Z"},"content_sha256":"cda051f9a6a1a63dc5d2c33b489d713d736cd33aa8d2f2a6873c1aa90312e2bd","schema_version":"1.0","event_id":"sha256:cda051f9a6a1a63dc5d2c33b489d713d736cd33aa8d2f2a6873c1aa90312e2bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I35IVQWLN6DLGRRKGH4YOTZFGS/bundle.json","state_url":"https://pith.science/pith/I35IVQWLN6DLGRRKGH4YOTZFGS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I35IVQWLN6DLGRRKGH4YOTZFGS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T04:14:49Z","links":{"resolver":"https://pith.science/pith/I35IVQWLN6DLGRRKGH4YOTZFGS","bundle":"https://pith.science/pith/I35IVQWLN6DLGRRKGH4YOTZFGS/bundle.json","state":"https://pith.science/pith/I35IVQWLN6DLGRRKGH4YOTZFGS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I35IVQWLN6DLGRRKGH4YOTZFGS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:I35IVQWLN6DLGRRKGH4YOTZFGS","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":"eedd6d3a9217a9dcc7106ac5b1428f476aa6b55b51433570adba8fc751fa7882","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-03T21:18:48Z","title_canon_sha256":"8024441ef48fe854598c63f09b9233b2c90b956cf961129f6c15263af01e424d"},"schema_version":"1.0","source":{"id":"1503.01130","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01130","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01130v1","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01130","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"pith_short_12","alias_value":"I35IVQWLN6DL","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"I35IVQWLN6DLGRRK","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"I35IVQWL","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:cda051f9a6a1a63dc5d2c33b489d713d736cd33aa8d2f2a6873c1aa90312e2bd","target":"graph","created_at":"2026-05-18T02:25:39Z","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":"Boundedness of weighted composition operators $W_{u,\\varphi}$ acting on the classical Dirichlet space $\\mathcal{D}$ as $W_{u,\\varphi}f= u\\, (f\\circ \\varphi)$ is studied in terms of the multiplier space associated to the symbol $\\varphi$, i.e., ${\\mathcal{M}(\\phi)}=\\{ u \\in {\\mathcal D}: W_{u,\\phi} \\hbox{ is bounded on } {\\mathcal D} \\}$. A prominent role is played by the multipliers of the Dirichlet space. As a consequence, the spectrum of $W_{u,\\varphi}$ in $\\mathcal{D}$ whenever $\\varphi$ is an automorphism of the unit disc is studied, extending a recent work of Hyv\\\"arinen, Lindstr\\\"om, Nie","authors_text":"E. A. Gallardo-Guti\\'errez, I. Chalendar, J.R. Partington","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-03T21:18:48Z","title":"Weighted composition operators on the Dirichlet space: boundedness and spectral properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01130","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":"sha256:17b8575a4fe6008845d49888583592bef48babc3e8589d76b63a1b329bdb296b","target":"record","created_at":"2026-05-18T02:25:39Z","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":"eedd6d3a9217a9dcc7106ac5b1428f476aa6b55b51433570adba8fc751fa7882","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-03T21:18:48Z","title_canon_sha256":"8024441ef48fe854598c63f09b9233b2c90b956cf961129f6c15263af01e424d"},"schema_version":"1.0","source":{"id":"1503.01130","kind":"arxiv","version":1}},"canonical_sha256":"46fa8ac2cb6f86b3462a31f9874f2534a6e3ab4bd92b3fceee11b06c006ff8d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46fa8ac2cb6f86b3462a31f9874f2534a6e3ab4bd92b3fceee11b06c006ff8d2","first_computed_at":"2026-05-18T02:25:39.815146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:39.815146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O43mi/4l7eOpg1eQGqbW/P6tbRszw7xjF+zQH2TkuimRNo85splJMj1GIxNVCMqvdVz0Uu6XkgvzKw9SRIJNDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:39.815599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01130","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17b8575a4fe6008845d49888583592bef48babc3e8589d76b63a1b329bdb296b","sha256:cda051f9a6a1a63dc5d2c33b489d713d736cd33aa8d2f2a6873c1aa90312e2bd"],"state_sha256":"7794a0a4367c49c13740861788fea36d8e868b1e6d7d4f99edf1fa45f5af995e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WajCs55TysRCJeRRToL6Juk+BRMSfkO4U2K0Tir68+3hmKtZnOtYp8orADoLMEzfDw5AkRBQ71row4s7OTlNAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:14:49.848332Z","bundle_sha256":"292ea24746f2524215a250587213d0de77f9cf23386d20989745dc7bf5a1a5d6"}}