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Let $D_{\\sqrt{\\rho}}$ denote the Hamilton vector field of the Grauert tube function $\\sqrt{\\rho}$ acting as a differential operator. We prove scaling asymptotics for the spectral localization kernel of the Toeplitz operator $\\Pi_\\tau D_{\\sqrt{\\rho}} \\Pi_\\tau$. We also prove scaling asymptotics for the tempered spectral projections kernel $P_"},"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":"2107.05105","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SP","submitted_at":"2021-07-11T17:56:23Z","cross_cats_sorted":["math.AP","math.CV"],"title_canon_sha256":"27b9f4e945d9ee58ae2204f7ade4a7ed88505da66bfd3c5b86f5360b1f369658","abstract_canon_sha256":"4bad1e8f43ba9b69bade220e431b15a24ebcecc3f594a9b96d77ce4932324469"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:06:27.889073Z","signature_b64":"HAZ/ANqqkVKnIIhge0fVvGGYns+ym1B080lAVmUDsPgjj9nDYS7QjNFsY5QeBpVrCl+mMChEXe2SX++gt3FzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36eb973208cdd42e80b9663c65215984c265756debf494190dc873ba8b05b95f","last_reissued_at":"2026-07-05T05:06:27.888680Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:06:27.888680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scaling asymptotics for Szeg\\H{o} kernels on Grauert tubes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.CV"],"primary_cat":"math.SP","authors_text":"Abraham Rabinowitz, Robert Chang","submitted_at":"2021-07-11T17:56:23Z","abstract_excerpt":"Let $M_\\tau$ be the Grauert tube of radius $\\tau$ of a closed, real analytic manifold $M$. Associated to the Grauert tube boundary is the orthogonal projection $\\Pi_\\tau \\colon L^2(\\partial M_\\tau) \\to H^2(\\partial M_\\tau)$, called the Szeg\\H{o} projector. Let $D_{\\sqrt{\\rho}}$ denote the Hamilton vector field of the Grauert tube function $\\sqrt{\\rho}$ acting as a differential operator. We prove scaling asymptotics for the spectral localization kernel of the Toeplitz operator $\\Pi_\\tau D_{\\sqrt{\\rho}} \\Pi_\\tau$. We also prove scaling asymptotics for the tempered spectral projections kernel $P_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.05105","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2107.05105/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":"2107.05105","created_at":"2026-07-05T05:06:27.888735+00:00"},{"alias_kind":"arxiv_version","alias_value":"2107.05105v2","created_at":"2026-07-05T05:06:27.888735+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.05105","created_at":"2026-07-05T05:06:27.888735+00:00"},{"alias_kind":"pith_short_12","alias_value":"G3VZOMQIZXKC","created_at":"2026-07-05T05:06:27.888735+00:00"},{"alias_kind":"pith_short_16","alias_value":"G3VZOMQIZXKC5AFZ","created_at":"2026-07-05T05:06:27.888735+00:00"},{"alias_kind":"pith_short_8","alias_value":"G3VZOMQI","created_at":"2026-07-05T05:06:27.888735+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/G3VZOMQIZXKC5AFZMY6GKIKZQT","json":"https://pith.science/pith/G3VZOMQIZXKC5AFZMY6GKIKZQT.json","graph_json":"https://pith.science/api/pith-number/G3VZOMQIZXKC5AFZMY6GKIKZQT/graph.json","events_json":"https://pith.science/api/pith-number/G3VZOMQIZXKC5AFZMY6GKIKZQT/events.json","paper":"https://pith.science/paper/G3VZOMQI"},"agent_actions":{"view_html":"https://pith.science/pith/G3VZOMQIZXKC5AFZMY6GKIKZQT","download_json":"https://pith.science/pith/G3VZOMQIZXKC5AFZMY6GKIKZQT.json","view_paper":"https://pith.science/paper/G3VZOMQI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2107.05105&json=true","fetch_graph":"https://pith.science/api/pith-number/G3VZOMQIZXKC5AFZMY6GKIKZQT/graph.json","fetch_events":"https://pith.science/api/pith-number/G3VZOMQIZXKC5AFZMY6GKIKZQT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G3VZOMQIZXKC5AFZMY6GKIKZQT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G3VZOMQIZXKC5AFZMY6GKIKZQT/action/storage_attestation","attest_author":"https://pith.science/pith/G3VZOMQIZXKC5AFZMY6GKIKZQT/action/author_attestation","sign_citation":"https://pith.science/pith/G3VZOMQIZXKC5AFZMY6GKIKZQT/action/citation_signature","submit_replication":"https://pith.science/pith/G3VZOMQIZXKC5AFZMY6GKIKZQT/action/replication_record"}},"created_at":"2026-07-05T05:06:27.888735+00:00","updated_at":"2026-07-05T05:06:27.888735+00:00"}