{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:7HOPRCCQCMEMQ4RKKPQ5BGPJ43","short_pith_number":"pith:7HOPRCCQ","schema_version":"1.0","canonical_sha256":"f9dcf888501308c8722a53e1d099e9e6d1b0efece766bd8d64abc7f521b2a73c","source":{"kind":"arxiv","id":"2505.13014","version":1},"attestation_state":"computed","paper":{"title":"Spectral asymptotics of semi-classical Toeplitz operators on Levi non-degenerate CR manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.CV","authors_text":"Wei-Chuan Shen","submitted_at":"2025-05-19T11:59:18Z","abstract_excerpt":"We consider any compact CR manifold whose Levi form is non-degenerate of constant signature $(n_-,n_+)$, $n_-+n_+=n$. For $\\lambda>0$ and $q\\in\\{0,\\cdots,n\\}$, we let $\\Pi_\\lambda^{(q)}$ be the spectral projection of the Kohn Laplacian of $(0,q)$-forms corresponding to the interval $[0,\\lambda]$. For certain classical pseudodifferential operators $P$, we study a class of generalized elliptic Toeplitz operators $T_{P,\\lambda}^{(q)}:=\\Pi_\\lambda^{(q)}\\circ P\\circ \\Pi_\\lambda^{(q)}$. For any cut-off $\\chi\\in\\mathscr C^\\infty_c(\\mathbb R\\setminus\\{0\\})$, we establish the full asymptotics of the se"},"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":"2505.13014","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2025-05-19T11:59:18Z","cross_cats_sorted":["math.AP","math.SP"],"title_canon_sha256":"92f27a14397301847dc9cddf87bfb9df0da9e789b29432932927ae85d6a104c1","abstract_canon_sha256":"74120b167b9621dd3c98758126b2de0f1aa1c9c7bf014b0571179a648b3a0d46"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:05:13.761682Z","signature_b64":"H+xYPnZxmeKgJlFGMpfgbgV424LW+5VunIoq2wst6lD35j4H4ZU17oqsEb8W0ln91Si1h1sQIG75AUj9MctwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9dcf888501308c8722a53e1d099e9e6d1b0efece766bd8d64abc7f521b2a73c","last_reissued_at":"2026-07-05T11:05:13.761222Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:05:13.761222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral asymptotics of semi-classical Toeplitz operators on Levi non-degenerate CR manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SP"],"primary_cat":"math.CV","authors_text":"Wei-Chuan Shen","submitted_at":"2025-05-19T11:59:18Z","abstract_excerpt":"We consider any compact CR manifold whose Levi form is non-degenerate of constant signature $(n_-,n_+)$, $n_-+n_+=n$. For $\\lambda>0$ and $q\\in\\{0,\\cdots,n\\}$, we let $\\Pi_\\lambda^{(q)}$ be the spectral projection of the Kohn Laplacian of $(0,q)$-forms corresponding to the interval $[0,\\lambda]$. For certain classical pseudodifferential operators $P$, we study a class of generalized elliptic Toeplitz operators $T_{P,\\lambda}^{(q)}:=\\Pi_\\lambda^{(q)}\\circ P\\circ \\Pi_\\lambda^{(q)}$. For any cut-off $\\chi\\in\\mathscr C^\\infty_c(\\mathbb R\\setminus\\{0\\})$, we establish the full asymptotics of the se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.13014","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.13014/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2505.13014","created_at":"2026-07-05T11:05:13.761279+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.13014v1","created_at":"2026-07-05T11:05:13.761279+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.13014","created_at":"2026-07-05T11:05:13.761279+00:00"},{"alias_kind":"pith_short_12","alias_value":"7HOPRCCQCMEM","created_at":"2026-07-05T11:05:13.761279+00:00"},{"alias_kind":"pith_short_16","alias_value":"7HOPRCCQCMEMQ4RK","created_at":"2026-07-05T11:05:13.761279+00:00"},{"alias_kind":"pith_short_8","alias_value":"7HOPRCCQ","created_at":"2026-07-05T11:05:13.761279+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/7HOPRCCQCMEMQ4RKKPQ5BGPJ43","json":"https://pith.science/pith/7HOPRCCQCMEMQ4RKKPQ5BGPJ43.json","graph_json":"https://pith.science/api/pith-number/7HOPRCCQCMEMQ4RKKPQ5BGPJ43/graph.json","events_json":"https://pith.science/api/pith-number/7HOPRCCQCMEMQ4RKKPQ5BGPJ43/events.json","paper":"https://pith.science/paper/7HOPRCCQ"},"agent_actions":{"view_html":"https://pith.science/pith/7HOPRCCQCMEMQ4RKKPQ5BGPJ43","download_json":"https://pith.science/pith/7HOPRCCQCMEMQ4RKKPQ5BGPJ43.json","view_paper":"https://pith.science/paper/7HOPRCCQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.13014&json=true","fetch_graph":"https://pith.science/api/pith-number/7HOPRCCQCMEMQ4RKKPQ5BGPJ43/graph.json","fetch_events":"https://pith.science/api/pith-number/7HOPRCCQCMEMQ4RKKPQ5BGPJ43/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7HOPRCCQCMEMQ4RKKPQ5BGPJ43/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7HOPRCCQCMEMQ4RKKPQ5BGPJ43/action/storage_attestation","attest_author":"https://pith.science/pith/7HOPRCCQCMEMQ4RKKPQ5BGPJ43/action/author_attestation","sign_citation":"https://pith.science/pith/7HOPRCCQCMEMQ4RKKPQ5BGPJ43/action/citation_signature","submit_replication":"https://pith.science/pith/7HOPRCCQCMEMQ4RKKPQ5BGPJ43/action/replication_record"}},"created_at":"2026-07-05T11:05:13.761279+00:00","updated_at":"2026-07-05T11:05:13.761279+00:00"}