{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HRXUJKHK6WERGM2PG65VSJGAXO","short_pith_number":"pith:HRXUJKHK","schema_version":"1.0","canonical_sha256":"3c6f44a8eaf58913334f37bb5924c0bbbba54812b4b234a03ef00cf90e0b4b96","source":{"kind":"arxiv","id":"1706.01530","version":2},"attestation_state":"computed","paper":{"title":"On the $L^p$ boundedness of wave operators for two-dimensional Schr\\\"odinger operators with threshold obstructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Burak Erdogan, Michael Goldberg, William R. Green","submitted_at":"2017-06-05T20:32:29Z","abstract_excerpt":"Let $H=-\\Delta+V$ be a Schr\\\"odinger operator on $L^2(\\mathbb R^2)$ with real-valued potential $V$, and let $H_0=-\\Delta$. If $V$ has sufficient pointwise decay, the wave operators $W_{\\pm}=s-\\lim_{t\\to \\pm\\infty} e^{itH}e^{-itH_0}$ are known to be bounded on $L^p(\\mathbb R^2)$ for all $1< p< \\infty$ if zero is not an eigenvalue or resonance. We show that if there is an s-wave resonance or an eigenvalue only at zero, then the wave operators are bounded on $L^p(\\mathbb R^2)$ for $1 < p<\\infty$. This result stands in contrast to results in higher dimensions, where the presence of zero energy obs"},"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":"1706.01530","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-05T20:32:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"79664af261931431706c81003687813a19ff57bf1cfb30e3aedda95fe826e871","abstract_canon_sha256":"59e336991ec647bcd77fd41602616a9a70f2d3c708af251f1e0fd90184ca995b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:56.689608Z","signature_b64":"2NS1N6gxhuBtwx5omq5GLmK4DH5Al8OG3nBt4E3IJ3M2rP0OLyWL7329ZBYTBpfGpkuAAjvXM/AbMsqijiTdAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c6f44a8eaf58913334f37bb5924c0bbbba54812b4b234a03ef00cf90e0b4b96","last_reissued_at":"2026-05-18T00:05:56.689161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:56.689161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the $L^p$ boundedness of wave operators for two-dimensional Schr\\\"odinger operators with threshold obstructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Burak Erdogan, Michael Goldberg, William R. Green","submitted_at":"2017-06-05T20:32:29Z","abstract_excerpt":"Let $H=-\\Delta+V$ be a Schr\\\"odinger operator on $L^2(\\mathbb R^2)$ with real-valued potential $V$, and let $H_0=-\\Delta$. If $V$ has sufficient pointwise decay, the wave operators $W_{\\pm}=s-\\lim_{t\\to \\pm\\infty} e^{itH}e^{-itH_0}$ are known to be bounded on $L^p(\\mathbb R^2)$ for all $1< p< \\infty$ if zero is not an eigenvalue or resonance. We show that if there is an s-wave resonance or an eigenvalue only at zero, then the wave operators are bounded on $L^p(\\mathbb R^2)$ for $1 < p<\\infty$. This result stands in contrast to results in higher dimensions, where the presence of zero energy obs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01530","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":"1706.01530","created_at":"2026-05-18T00:05:56.689229+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.01530v2","created_at":"2026-05-18T00:05:56.689229+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01530","created_at":"2026-05-18T00:05:56.689229+00:00"},{"alias_kind":"pith_short_12","alias_value":"HRXUJKHK6WER","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HRXUJKHK6WERGM2P","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HRXUJKHK","created_at":"2026-05-18T12:31:18.294218+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/HRXUJKHK6WERGM2PG65VSJGAXO","json":"https://pith.science/pith/HRXUJKHK6WERGM2PG65VSJGAXO.json","graph_json":"https://pith.science/api/pith-number/HRXUJKHK6WERGM2PG65VSJGAXO/graph.json","events_json":"https://pith.science/api/pith-number/HRXUJKHK6WERGM2PG65VSJGAXO/events.json","paper":"https://pith.science/paper/HRXUJKHK"},"agent_actions":{"view_html":"https://pith.science/pith/HRXUJKHK6WERGM2PG65VSJGAXO","download_json":"https://pith.science/pith/HRXUJKHK6WERGM2PG65VSJGAXO.json","view_paper":"https://pith.science/paper/HRXUJKHK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.01530&json=true","fetch_graph":"https://pith.science/api/pith-number/HRXUJKHK6WERGM2PG65VSJGAXO/graph.json","fetch_events":"https://pith.science/api/pith-number/HRXUJKHK6WERGM2PG65VSJGAXO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HRXUJKHK6WERGM2PG65VSJGAXO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HRXUJKHK6WERGM2PG65VSJGAXO/action/storage_attestation","attest_author":"https://pith.science/pith/HRXUJKHK6WERGM2PG65VSJGAXO/action/author_attestation","sign_citation":"https://pith.science/pith/HRXUJKHK6WERGM2PG65VSJGAXO/action/citation_signature","submit_replication":"https://pith.science/pith/HRXUJKHK6WERGM2PG65VSJGAXO/action/replication_record"}},"created_at":"2026-05-18T00:05:56.689229+00:00","updated_at":"2026-05-18T00:05:56.689229+00:00"}