{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:PD3QC2MKQHZ2RN2YLZTXD6TGUI","short_pith_number":"pith:PD3QC2MK","schema_version":"1.0","canonical_sha256":"78f701698a81f3a8b7585e6771fa66a214c561feccfe2c18ad14f1af4c147f25","source":{"kind":"arxiv","id":"1408.1992","version":2},"attestation_state":"computed","paper":{"title":"Quantitative unique continuation principle for Schr\\\"odinger Operators with Singular Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Abel Klein, C.S. Sidney Tsang","submitted_at":"2014-08-08T22:52:10Z","abstract_excerpt":"We prove a quantitative unique continuation principle for Schr\\\"odinger operators $H=-\\Delta+V$ on $\\mathrm{L}^2(\\Omega)$, where $\\Omega$ is an open subset of $\\mathbb{R}^d$ and $V$ is a singular potential: $V \\in \\mathrm{L}^\\infty(\\Omega) + \\mathrm{L}^p(\\Omega)$. As an application, we derive a unique continuation principle for spectral projections of Schr\\\"odinger operators with singular potentials."},"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":"1408.1992","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-08-08T22:52:10Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ae7b41200fd29a8f7c6b030cc41bcf2232f4c86aed5342d03099e06ae9861cfd","abstract_canon_sha256":"382104114a3aca2283c0d64131360ec17482d92114c09c74c0cbe0e473144727"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:10.766809Z","signature_b64":"in1ucLRpcHGccuOE7ZY/qmeRlQlbL/+R4VSw4YcPk9dmnAVQmXxvmAor8vmbf9UPSv7qbcFqFKcTXErnUqlZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78f701698a81f3a8b7585e6771fa66a214c561feccfe2c18ad14f1af4c147f25","last_reissued_at":"2026-05-18T02:29:10.766145Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:10.766145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantitative unique continuation principle for Schr\\\"odinger Operators with Singular Potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Abel Klein, C.S. Sidney Tsang","submitted_at":"2014-08-08T22:52:10Z","abstract_excerpt":"We prove a quantitative unique continuation principle for Schr\\\"odinger operators $H=-\\Delta+V$ on $\\mathrm{L}^2(\\Omega)$, where $\\Omega$ is an open subset of $\\mathbb{R}^d$ and $V$ is a singular potential: $V \\in \\mathrm{L}^\\infty(\\Omega) + \\mathrm{L}^p(\\Omega)$. As an application, we derive a unique continuation principle for spectral projections of Schr\\\"odinger operators with singular potentials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1992","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":"1408.1992","created_at":"2026-05-18T02:29:10.766232+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.1992v2","created_at":"2026-05-18T02:29:10.766232+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1992","created_at":"2026-05-18T02:29:10.766232+00:00"},{"alias_kind":"pith_short_12","alias_value":"PD3QC2MKQHZ2","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PD3QC2MKQHZ2RN2Y","created_at":"2026-05-18T12:28:43.426989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PD3QC2MK","created_at":"2026-05-18T12:28:43.426989+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/PD3QC2MKQHZ2RN2YLZTXD6TGUI","json":"https://pith.science/pith/PD3QC2MKQHZ2RN2YLZTXD6TGUI.json","graph_json":"https://pith.science/api/pith-number/PD3QC2MKQHZ2RN2YLZTXD6TGUI/graph.json","events_json":"https://pith.science/api/pith-number/PD3QC2MKQHZ2RN2YLZTXD6TGUI/events.json","paper":"https://pith.science/paper/PD3QC2MK"},"agent_actions":{"view_html":"https://pith.science/pith/PD3QC2MKQHZ2RN2YLZTXD6TGUI","download_json":"https://pith.science/pith/PD3QC2MKQHZ2RN2YLZTXD6TGUI.json","view_paper":"https://pith.science/paper/PD3QC2MK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.1992&json=true","fetch_graph":"https://pith.science/api/pith-number/PD3QC2MKQHZ2RN2YLZTXD6TGUI/graph.json","fetch_events":"https://pith.science/api/pith-number/PD3QC2MKQHZ2RN2YLZTXD6TGUI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PD3QC2MKQHZ2RN2YLZTXD6TGUI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PD3QC2MKQHZ2RN2YLZTXD6TGUI/action/storage_attestation","attest_author":"https://pith.science/pith/PD3QC2MKQHZ2RN2YLZTXD6TGUI/action/author_attestation","sign_citation":"https://pith.science/pith/PD3QC2MKQHZ2RN2YLZTXD6TGUI/action/citation_signature","submit_replication":"https://pith.science/pith/PD3QC2MKQHZ2RN2YLZTXD6TGUI/action/replication_record"}},"created_at":"2026-05-18T02:29:10.766232+00:00","updated_at":"2026-05-18T02:29:10.766232+00:00"}