{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:7CXTL6INXZ7U5QKDYRM3IWUNAQ","short_pith_number":"pith:7CXTL6IN","schema_version":"1.0","canonical_sha256":"f8af35f90dbe7f4ec143c459b45a8d04013662a40238f6574e6d4f9b2d17f512","source":{"kind":"arxiv","id":"1407.6305","version":2},"attestation_state":"computed","paper":{"title":"On the singularities of the Szeg\\\"o projections on lower energy forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Chin-Yu Hsiao, George Marinescu","submitted_at":"2014-07-23T17:34:39Z","abstract_excerpt":"Let $X$ be an abstract not necessarily compact orientable CR manifold of dimension $2n-1$, $n\\geqslant2$. Let $\\Box^{(q)}_{b}$ be the Gaffney extension of Kohn Laplacian for $(0,q)$-forms. We show that the spectral function of $\\Box^{(q)}_b$ admits a full asymptotic expansion on the non-degenerate part of the Levi form. As a corollary, we deduce that if $X$ is compact and the Levi form is non-degenerate of constant signature on $X$, then the spectrum of $\\Box^{(q)}_b$ in $]0,\\infty[$ consists of point eigenvalues of finite multiplicity. Moreover, we show that a certain microlocal conjugation o"},"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":"1407.6305","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-07-23T17:34:39Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"78a0890a0d91add46b7bcf440f14732b1f3e58683263ccb56f0626c20b219e0a","abstract_canon_sha256":"577e31d5d97da8dbd40d798514994485c104c9f8d4b15f35e2759de45a31ce8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:32.040802Z","signature_b64":"QKwIfN9nFLAQwu3VrH/vu0hiASf64X+0SscgKS9F/bUk+lLBrhpF3FZmw+PUZCZYpDap5XRGGCewEchJoDy2Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f8af35f90dbe7f4ec143c459b45a8d04013662a40238f6574e6d4f9b2d17f512","last_reissued_at":"2026-05-18T00:34:32.040471Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:32.040471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the singularities of the Szeg\\\"o projections on lower energy forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CV","authors_text":"Chin-Yu Hsiao, George Marinescu","submitted_at":"2014-07-23T17:34:39Z","abstract_excerpt":"Let $X$ be an abstract not necessarily compact orientable CR manifold of dimension $2n-1$, $n\\geqslant2$. Let $\\Box^{(q)}_{b}$ be the Gaffney extension of Kohn Laplacian for $(0,q)$-forms. We show that the spectral function of $\\Box^{(q)}_b$ admits a full asymptotic expansion on the non-degenerate part of the Levi form. As a corollary, we deduce that if $X$ is compact and the Levi form is non-degenerate of constant signature on $X$, then the spectrum of $\\Box^{(q)}_b$ in $]0,\\infty[$ consists of point eigenvalues of finite multiplicity. Moreover, we show that a certain microlocal conjugation o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6305","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":"1407.6305","created_at":"2026-05-18T00:34:32.040521+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.6305v2","created_at":"2026-05-18T00:34:32.040521+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6305","created_at":"2026-05-18T00:34:32.040521+00:00"},{"alias_kind":"pith_short_12","alias_value":"7CXTL6INXZ7U","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"7CXTL6INXZ7U5QKD","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"7CXTL6IN","created_at":"2026-05-18T12:28:16.859392+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/7CXTL6INXZ7U5QKDYRM3IWUNAQ","json":"https://pith.science/pith/7CXTL6INXZ7U5QKDYRM3IWUNAQ.json","graph_json":"https://pith.science/api/pith-number/7CXTL6INXZ7U5QKDYRM3IWUNAQ/graph.json","events_json":"https://pith.science/api/pith-number/7CXTL6INXZ7U5QKDYRM3IWUNAQ/events.json","paper":"https://pith.science/paper/7CXTL6IN"},"agent_actions":{"view_html":"https://pith.science/pith/7CXTL6INXZ7U5QKDYRM3IWUNAQ","download_json":"https://pith.science/pith/7CXTL6INXZ7U5QKDYRM3IWUNAQ.json","view_paper":"https://pith.science/paper/7CXTL6IN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.6305&json=true","fetch_graph":"https://pith.science/api/pith-number/7CXTL6INXZ7U5QKDYRM3IWUNAQ/graph.json","fetch_events":"https://pith.science/api/pith-number/7CXTL6INXZ7U5QKDYRM3IWUNAQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7CXTL6INXZ7U5QKDYRM3IWUNAQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7CXTL6INXZ7U5QKDYRM3IWUNAQ/action/storage_attestation","attest_author":"https://pith.science/pith/7CXTL6INXZ7U5QKDYRM3IWUNAQ/action/author_attestation","sign_citation":"https://pith.science/pith/7CXTL6INXZ7U5QKDYRM3IWUNAQ/action/citation_signature","submit_replication":"https://pith.science/pith/7CXTL6INXZ7U5QKDYRM3IWUNAQ/action/replication_record"}},"created_at":"2026-05-18T00:34:32.040521+00:00","updated_at":"2026-05-18T00:34:32.040521+00:00"}