{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:YSSC2ZLNNFE76YQQR2VMFIPILF","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":"e0c11618fd2c9f580cc97be1f3a12f33f65110bf8ad9a461797d9717b7d00b81","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-01-13T01:16:16Z","title_canon_sha256":"accfcf874e4530535c2f444548f4ddcfecefcf6074d434f0bfb7c2d7374dfb1c"},"schema_version":"1.0","source":{"id":"2201.04758","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.04758","created_at":"2026-07-05T08:33:25Z"},{"alias_kind":"arxiv_version","alias_value":"2201.04758v3","created_at":"2026-07-05T08:33:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.04758","created_at":"2026-07-05T08:33:25Z"},{"alias_kind":"pith_short_12","alias_value":"YSSC2ZLNNFE7","created_at":"2026-07-05T08:33:25Z"},{"alias_kind":"pith_short_16","alias_value":"YSSC2ZLNNFE76YQQ","created_at":"2026-07-05T08:33:25Z"},{"alias_kind":"pith_short_8","alias_value":"YSSC2ZLN","created_at":"2026-07-05T08:33:25Z"}],"graph_snapshots":[{"event_id":"sha256:fb98a11529611a50bb163fe475cd5ea433204150bfe29dbedda1d5a842c2adcd","target":"graph","created_at":"2026-07-05T08:33:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2201.04758/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is devoted to establishing several types of $L^p$-boundedness of wave operators $W_\\pm=W_\\pm(H, \\Delta^2)$ associated with the bi-Schr\\\"odinger operators $H=\\Delta^{2}+V(x)$ on the line $\\mathbb{R}$. Given suitable decay potentials $V$, we firstly prove that the wave and dual wave operators are bounded on $L^p(\\mathbb{R})$ for all $1<p<\\infty$: $$ \\|W_\\pm f\\|_{L^p(\\mathbb{R})}+\\|W_\\pm^* f\\|_{L^p(\\mathbb{R})}\\lesssim \\|f\\|_{L^p(\\mathbb{R})},$$ which are further extended to the $L^p$-boundedness on the weighted spaces $L^p(\\mathbb{R},w)$ with general even $A_p$-weights $w$ and to the ","authors_text":"Haruya Mizutani, Xiaohua Yao, Zijun Wan","cross_cats":["math-ph","math.CA","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-01-13T01:16:16Z","title":"$L^p$-boundedness of wave operators for bi-Schr\\\"odinger operators on the line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.04758","kind":"arxiv","version":3},"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":"sha256:21b95b402a08d662710cfa7a35f873453bf2f55d9ddddc809f4870303eef8285","target":"record","created_at":"2026-07-05T08:33:25Z","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":"e0c11618fd2c9f580cc97be1f3a12f33f65110bf8ad9a461797d9717b7d00b81","cross_cats_sorted":["math-ph","math.CA","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-01-13T01:16:16Z","title_canon_sha256":"accfcf874e4530535c2f444548f4ddcfecefcf6074d434f0bfb7c2d7374dfb1c"},"schema_version":"1.0","source":{"id":"2201.04758","kind":"arxiv","version":3}},"canonical_sha256":"c4a42d656d6949ff62108eaac2a1e8595cc08446bd6b07137801c64eb701f740","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4a42d656d6949ff62108eaac2a1e8595cc08446bd6b07137801c64eb701f740","first_computed_at":"2026-07-05T08:33:25.248505Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:33:25.248505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w9rgv4kfo5WS4brK30OPWTYHZKiLSpEA5pRD6hnmHeipy8QRab2AYr3u0dZRGU8ia2m2i5y9HCDYM87bBnBxDg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:33:25.248976Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.04758","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21b95b402a08d662710cfa7a35f873453bf2f55d9ddddc809f4870303eef8285","sha256:fb98a11529611a50bb163fe475cd5ea433204150bfe29dbedda1d5a842c2adcd"],"state_sha256":"d1e270264781ad3aec1aca479647077def9861beb1e59a7db93e69d304346b89"}