{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MGD5EFLNIYQXZIW6NHWH4D7M6F","short_pith_number":"pith:MGD5EFLN","schema_version":"1.0","canonical_sha256":"6187d2156d46217ca2de69ec7e0fecf16c8a9d7509ce5931fb9e95289eeb8fa9","source":{"kind":"arxiv","id":"1501.02321","version":2},"attestation_state":"computed","paper":{"title":"Spectral multipliers for the Kohn Laplacian on forms on the sphere in $\\mathbb{C}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Adam Sikora, Alessio Martini, Michael G. Cowling, Valentina Casarino","submitted_at":"2015-01-10T08:53:39Z","abstract_excerpt":"The unit sphere $\\mathbb{S}$ in $\\mathbb{C}^n$ is equipped with the tangential Cauchy-Riemann complex and the associated Laplacian $\\Box_b$. We prove a H\\\"ormander spectral multiplier theorem for $\\Box_b$ with critical index $n-1/2$, that is, half the topological dimension of $\\mathbb{S}$. Our proof is mainly based on representation theory and on a detailed analysis of the spaces of differential forms on $\\mathbb{S}$."},"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":"1501.02321","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-10T08:53:39Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"8329f64c8b1beef2e4bdefaf0dc7d38ff61fa841b3c59266dd783c2ae94af5ee","abstract_canon_sha256":"9e876cb80a99b909e8c0adc2b750b7a22a32d5857e49b64bf837b0cd83a18a41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:15.352599Z","signature_b64":"7uA4rwv5uExBuM2xU4FblUmDwQmN0QjXOwNOtUtsmt6Fv7bb+gQrmbLrqTZUyUBZoRQ1DQ0mWJWGYenktphjAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6187d2156d46217ca2de69ec7e0fecf16c8a9d7509ce5931fb9e95289eeb8fa9","last_reissued_at":"2026-05-17T23:58:15.352105Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:15.352105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral multipliers for the Kohn Laplacian on forms on the sphere in $\\mathbb{C}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Adam Sikora, Alessio Martini, Michael G. Cowling, Valentina Casarino","submitted_at":"2015-01-10T08:53:39Z","abstract_excerpt":"The unit sphere $\\mathbb{S}$ in $\\mathbb{C}^n$ is equipped with the tangential Cauchy-Riemann complex and the associated Laplacian $\\Box_b$. We prove a H\\\"ormander spectral multiplier theorem for $\\Box_b$ with critical index $n-1/2$, that is, half the topological dimension of $\\mathbb{S}$. Our proof is mainly based on representation theory and on a detailed analysis of the spaces of differential forms on $\\mathbb{S}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.02321","kind":"arxiv","version":2},"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":"1501.02321","created_at":"2026-05-17T23:58:15.352198+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.02321v2","created_at":"2026-05-17T23:58:15.352198+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.02321","created_at":"2026-05-17T23:58:15.352198+00:00"},{"alias_kind":"pith_short_12","alias_value":"MGD5EFLNIYQX","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MGD5EFLNIYQXZIW6","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MGD5EFLN","created_at":"2026-05-18T12:29:32.376354+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/MGD5EFLNIYQXZIW6NHWH4D7M6F","json":"https://pith.science/pith/MGD5EFLNIYQXZIW6NHWH4D7M6F.json","graph_json":"https://pith.science/api/pith-number/MGD5EFLNIYQXZIW6NHWH4D7M6F/graph.json","events_json":"https://pith.science/api/pith-number/MGD5EFLNIYQXZIW6NHWH4D7M6F/events.json","paper":"https://pith.science/paper/MGD5EFLN"},"agent_actions":{"view_html":"https://pith.science/pith/MGD5EFLNIYQXZIW6NHWH4D7M6F","download_json":"https://pith.science/pith/MGD5EFLNIYQXZIW6NHWH4D7M6F.json","view_paper":"https://pith.science/paper/MGD5EFLN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.02321&json=true","fetch_graph":"https://pith.science/api/pith-number/MGD5EFLNIYQXZIW6NHWH4D7M6F/graph.json","fetch_events":"https://pith.science/api/pith-number/MGD5EFLNIYQXZIW6NHWH4D7M6F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MGD5EFLNIYQXZIW6NHWH4D7M6F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MGD5EFLNIYQXZIW6NHWH4D7M6F/action/storage_attestation","attest_author":"https://pith.science/pith/MGD5EFLNIYQXZIW6NHWH4D7M6F/action/author_attestation","sign_citation":"https://pith.science/pith/MGD5EFLNIYQXZIW6NHWH4D7M6F/action/citation_signature","submit_replication":"https://pith.science/pith/MGD5EFLNIYQXZIW6NHWH4D7M6F/action/replication_record"}},"created_at":"2026-05-17T23:58:15.352198+00:00","updated_at":"2026-05-17T23:58:15.352198+00:00"}