{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WLPKPZVGULUE4WGRNW4MKLRKET","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9769587eb120e4354be9d685121c800be1567d8b2a367e2c85f542bbc58e076d","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-06T22:32:25Z","title_canon_sha256":"41016768f7101a7060fe6585af2e07552e84af46ab579bf65f3dabeb3642129e"},"schema_version":"1.0","source":{"id":"1803.02450","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02450","created_at":"2026-05-17T23:59:53Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02450v2","created_at":"2026-05-17T23:59:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02450","created_at":"2026-05-17T23:59:53Z"},{"alias_kind":"pith_short_12","alias_value":"WLPKPZVGULUE","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WLPKPZVGULUE4WGR","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WLPKPZVG","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:15b9cd2e97a3867c3199616927711f78eb6dcd2f80244732a813760902612f19","target":"graph","created_at":"2026-05-17T23:59:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the cut-off resolvent of semiclassical Schr{\\\"o}dinger operators on $\\mathbb{R}^d$ with bounded compactly supported potentials $V$. We prove that for real energies $\\lambda^2$ in a compact interval in $\\mathbb{R}_+$ and for any smooth cut-off function $\\chi$ supported in a ball near the support of the potential $V$, for some constant $C>0$, one has\n  \\begin{equation*}\n  \\| \\chi (-h^2\\Delta + V-\\lambda^2)^{-1} \\chi \\|_{L^2\\to H^1} \\leq C\n  \\,\\mathrm{e}^{Ch^{-4/3}\\log \\frac{1}{h} }.\n  \\end{equation*} This bound shows in particular an upper bound on the imaginary parts of the resonances ","authors_text":"Fr\\'ed\\'eric Klopp, Martin Vogel","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-06T22:32:25Z","title":"Semiclassical resolvent estimates for bounded potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02450","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f95eea0ca4cc61cd03a89486702e28db9a8ca2c8a7302b34df0bad010629c435","target":"record","created_at":"2026-05-17T23:59:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9769587eb120e4354be9d685121c800be1567d8b2a367e2c85f542bbc58e076d","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-06T22:32:25Z","title_canon_sha256":"41016768f7101a7060fe6585af2e07552e84af46ab579bf65f3dabeb3642129e"},"schema_version":"1.0","source":{"id":"1803.02450","kind":"arxiv","version":2}},"canonical_sha256":"b2dea7e6a6a2e84e58d16db8c52e2a24f8234d2cc518e8c6610faf40b09f345e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2dea7e6a6a2e84e58d16db8c52e2a24f8234d2cc518e8c6610faf40b09f345e","first_computed_at":"2026-05-17T23:59:53.112282Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:53.112282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"umuZFtFEvWR2usc9N1RxK+nDC6tI1j6QH4RivSR/bUKedVge2Lw9oMY604lfAA8/ZMojrhz/uQZ/u8lJywceCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:53.112821Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.02450","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f95eea0ca4cc61cd03a89486702e28db9a8ca2c8a7302b34df0bad010629c435","sha256:15b9cd2e97a3867c3199616927711f78eb6dcd2f80244732a813760902612f19"],"state_sha256":"905fba2797aa3eec8e907aa395ec4c4931c483dc89145a689c2dc6c863d8da07"}