{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VG5LDK2VFZE5FNBM4BHZ526GCO","short_pith_number":"pith:VG5LDK2V","schema_version":"1.0","canonical_sha256":"a9bab1ab552e49d2b42ce04f9eebc613a43c1ecf0118f6c1cf5b9e0379cbb17a","source":{"kind":"arxiv","id":"1512.08886","version":1},"attestation_state":"computed","paper":{"title":"$\\beta$-admissibility of observation and control operators for hypercontractive semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Andrew Wynn, Birgit Jacob, Jonathan R. Partington, Sandra Pott","submitted_at":"2015-12-30T09:16:39Z","abstract_excerpt":"We prove a Weiss conjecture on $\\beta$-admissibility of control and observation operators for discrete and continuous $\\gamma$-hypercontractive semigroups of operators, by representing them in terms of shifts on weighted Bergman spaces and using a reproducing kernel thesis for Hankel operators. Particular attention is paid to the case $\\gamma=2$, which corresponds to the unweighted Bergman shift."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1512.08886","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-30T09:16:39Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"a84ab3e76823b9167d91df3da44ee470404000001381dcf300222ae5543261b1","abstract_canon_sha256":"97927fa090f93a6090a0f3eb4e11947d90616da13ff25fbd9b08430ddac90a52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:53.661636Z","signature_b64":"+zfXmowgguRW6pTf8YY8jiyQN3jNrQSBZqfd25ZPln4Q9iUOfmfJsaV0aRFgCJofu3F4w3aO8na2x/YC02B2BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9bab1ab552e49d2b42ce04f9eebc613a43c1ecf0118f6c1cf5b9e0379cbb17a","last_reissued_at":"2026-05-18T01:22:53.660891Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:53.660891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\beta$-admissibility of observation and control operators for hypercontractive semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Andrew Wynn, Birgit Jacob, Jonathan R. Partington, Sandra Pott","submitted_at":"2015-12-30T09:16:39Z","abstract_excerpt":"We prove a Weiss conjecture on $\\beta$-admissibility of control and observation operators for discrete and continuous $\\gamma$-hypercontractive semigroups of operators, by representing them in terms of shifts on weighted Bergman spaces and using a reproducing kernel thesis for Hankel operators. Particular attention is paid to the case $\\gamma=2$, which corresponds to the unweighted Bergman shift."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08886","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1512.08886","created_at":"2026-05-18T01:22:53.661029+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.08886v1","created_at":"2026-05-18T01:22:53.661029+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08886","created_at":"2026-05-18T01:22:53.661029+00:00"},{"alias_kind":"pith_short_12","alias_value":"VG5LDK2VFZE5","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"VG5LDK2VFZE5FNBM","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"VG5LDK2V","created_at":"2026-05-18T12:29:44.643036+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VG5LDK2VFZE5FNBM4BHZ526GCO","json":"https://pith.science/pith/VG5LDK2VFZE5FNBM4BHZ526GCO.json","graph_json":"https://pith.science/api/pith-number/VG5LDK2VFZE5FNBM4BHZ526GCO/graph.json","events_json":"https://pith.science/api/pith-number/VG5LDK2VFZE5FNBM4BHZ526GCO/events.json","paper":"https://pith.science/paper/VG5LDK2V"},"agent_actions":{"view_html":"https://pith.science/pith/VG5LDK2VFZE5FNBM4BHZ526GCO","download_json":"https://pith.science/pith/VG5LDK2VFZE5FNBM4BHZ526GCO.json","view_paper":"https://pith.science/paper/VG5LDK2V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.08886&json=true","fetch_graph":"https://pith.science/api/pith-number/VG5LDK2VFZE5FNBM4BHZ526GCO/graph.json","fetch_events":"https://pith.science/api/pith-number/VG5LDK2VFZE5FNBM4BHZ526GCO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VG5LDK2VFZE5FNBM4BHZ526GCO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VG5LDK2VFZE5FNBM4BHZ526GCO/action/storage_attestation","attest_author":"https://pith.science/pith/VG5LDK2VFZE5FNBM4BHZ526GCO/action/author_attestation","sign_citation":"https://pith.science/pith/VG5LDK2VFZE5FNBM4BHZ526GCO/action/citation_signature","submit_replication":"https://pith.science/pith/VG5LDK2VFZE5FNBM4BHZ526GCO/action/replication_record"}},"created_at":"2026-05-18T01:22:53.661029+00:00","updated_at":"2026-05-18T01:22:53.661029+00:00"}