{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:2AIJV76UYUBJMUWSLT4PEL7F63","short_pith_number":"pith:2AIJV76U","schema_version":"1.0","canonical_sha256":"d0109affd4c5029652d25cf8f22fe5f6c334ecc891298e3510c934c16cdd2776","source":{"kind":"arxiv","id":"1201.5573","version":2},"attestation_state":"computed","paper":{"title":"Semiclassical estimates of the cut-off resolvent for trapping perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Jean-Francois Bony, Vesselin Petkov","submitted_at":"2012-01-26T16:35:47Z","abstract_excerpt":"This paper is devoted to the study of a semiclassical \"black box\" operator $P$. We estimate the norm of its resolvent truncated near the trapped set by the norm of its resolvent truncated on rings far away from the origin. For $z$ in the unphysical sheet with $- h |ln h| < Im z < 0$, we prove that this estimate holds with a constant $h |Im z|^{-1} e^{C|Im z|/h}$. We also obtain analogous bounds for the resonances states of $P$. These results hold without any assumption on the trapped set neither any assumption on the multiplicity of the resonances."},"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":"1201.5573","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-01-26T16:35:47Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"7b2411e13b52e8dd8aa96023c41aa6b5df7f7b071fd3bb09845cb94c5736ec01","abstract_canon_sha256":"ea898e353f3dbf2506cffe1ac1fd009f7726eab83ecf19736872b474a0caea58"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:10.667876Z","signature_b64":"o5P/P/enYFmiTNHFk3qXQvl7wPIbdk4M+GOVPLjezsFpvqoN4frztsonp5NF3NCipCMgWe/xbPunmxdSMgNyDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0109affd4c5029652d25cf8f22fe5f6c334ecc891298e3510c934c16cdd2776","last_reissued_at":"2026-05-18T03:45:10.667193Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:10.667193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semiclassical estimates of the cut-off resolvent for trapping perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Jean-Francois Bony, Vesselin Petkov","submitted_at":"2012-01-26T16:35:47Z","abstract_excerpt":"This paper is devoted to the study of a semiclassical \"black box\" operator $P$. We estimate the norm of its resolvent truncated near the trapped set by the norm of its resolvent truncated on rings far away from the origin. For $z$ in the unphysical sheet with $- h |ln h| < Im z < 0$, we prove that this estimate holds with a constant $h |Im z|^{-1} e^{C|Im z|/h}$. We also obtain analogous bounds for the resonances states of $P$. These results hold without any assumption on the trapped set neither any assumption on the multiplicity of the resonances."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5573","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":"1201.5573","created_at":"2026-05-18T03:45:10.667307+00:00"},{"alias_kind":"arxiv_version","alias_value":"1201.5573v2","created_at":"2026-05-18T03:45:10.667307+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5573","created_at":"2026-05-18T03:45:10.667307+00:00"},{"alias_kind":"pith_short_12","alias_value":"2AIJV76UYUBJ","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_16","alias_value":"2AIJV76UYUBJMUWS","created_at":"2026-05-18T12:26:50.516681+00:00"},{"alias_kind":"pith_short_8","alias_value":"2AIJV76U","created_at":"2026-05-18T12:26:50.516681+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/2AIJV76UYUBJMUWSLT4PEL7F63","json":"https://pith.science/pith/2AIJV76UYUBJMUWSLT4PEL7F63.json","graph_json":"https://pith.science/api/pith-number/2AIJV76UYUBJMUWSLT4PEL7F63/graph.json","events_json":"https://pith.science/api/pith-number/2AIJV76UYUBJMUWSLT4PEL7F63/events.json","paper":"https://pith.science/paper/2AIJV76U"},"agent_actions":{"view_html":"https://pith.science/pith/2AIJV76UYUBJMUWSLT4PEL7F63","download_json":"https://pith.science/pith/2AIJV76UYUBJMUWSLT4PEL7F63.json","view_paper":"https://pith.science/paper/2AIJV76U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1201.5573&json=true","fetch_graph":"https://pith.science/api/pith-number/2AIJV76UYUBJMUWSLT4PEL7F63/graph.json","fetch_events":"https://pith.science/api/pith-number/2AIJV76UYUBJMUWSLT4PEL7F63/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2AIJV76UYUBJMUWSLT4PEL7F63/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2AIJV76UYUBJMUWSLT4PEL7F63/action/storage_attestation","attest_author":"https://pith.science/pith/2AIJV76UYUBJMUWSLT4PEL7F63/action/author_attestation","sign_citation":"https://pith.science/pith/2AIJV76UYUBJMUWSLT4PEL7F63/action/citation_signature","submit_replication":"https://pith.science/pith/2AIJV76UYUBJMUWSLT4PEL7F63/action/replication_record"}},"created_at":"2026-05-18T03:45:10.667307+00:00","updated_at":"2026-05-18T03:45:10.667307+00:00"}