{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:YIH4FDA72ESTGTF3CNAPROGP47","short_pith_number":"pith:YIH4FDA7","schema_version":"1.0","canonical_sha256":"c20fc28c1fd125334cbb1340f8b8cfe7f685d72931457576d44b0e4ab1655316","source":{"kind":"arxiv","id":"2509.18003","version":2},"attestation_state":"computed","paper":{"title":"The $L^p$-continuity of wave operators for fractional order Schr\\\"odinger operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"M. Burak Erdogan, Michael Goldberg, William Green","submitted_at":"2025-09-22T16:41:13Z","abstract_excerpt":"We consider fractional Schr\\\"odinger operators $H=(-\\Delta)^\\alpha+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2\\alpha$, $\\alpha>1$. We show that the wave operators extend to bounded operators on $L^p(\\mathbb R^n)$ for all $1\\leq p\\leq\\infty$ under conditions on the potential that depend on $n$ and $\\alpha$ analogously to the case when $\\alpha\\in \\mathbb N$. As a consequence, we deduce a family of dispersive and Strichartz estimates for the perturbed fractional Schr\\\"odinger operator."},"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":"2509.18003","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-09-22T16:41:13Z","cross_cats_sorted":[],"title_canon_sha256":"a2c6d45b3496333d1230ca6dab8af1dd0e15956015d9d9f17fad1cddd7c2ff14","abstract_canon_sha256":"603fbb7142d262cfc942632aea1a208c81b0739726e78ac143dac6ff7c8c01cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-17T01:21:43.103937Z","signature_b64":"fvovvu+E0F7ZbMdAs94jN8LhVaW1LK/mz+oUcBW/m2/F8C+v7Ui0wEcDCBQRymEM1NZ+9IV7TqjAt1u7afw5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c20fc28c1fd125334cbb1340f8b8cfe7f685d72931457576d44b0e4ab1655316","last_reissued_at":"2026-07-17T01:21:43.103060Z","signature_status":"signed_v1","first_computed_at":"2026-07-17T01:21:43.103060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $L^p$-continuity of wave operators for fractional order Schr\\\"odinger operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"M. Burak Erdogan, Michael Goldberg, William Green","submitted_at":"2025-09-22T16:41:13Z","abstract_excerpt":"We consider fractional Schr\\\"odinger operators $H=(-\\Delta)^\\alpha+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2\\alpha$, $\\alpha>1$. We show that the wave operators extend to bounded operators on $L^p(\\mathbb R^n)$ for all $1\\leq p\\leq\\infty$ under conditions on the potential that depend on $n$ and $\\alpha$ analogously to the case when $\\alpha\\in \\mathbb N$. As a consequence, we deduce a family of dispersive and Strichartz estimates for the perturbed fractional Schr\\\"odinger operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.18003","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.18003/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2509.18003","created_at":"2026-07-17T01:21:43.103473+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.18003v2","created_at":"2026-07-17T01:21:43.103473+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.18003","created_at":"2026-07-17T01:21:43.103473+00:00"},{"alias_kind":"pith_short_12","alias_value":"YIH4FDA72EST","created_at":"2026-07-17T01:21:43.103473+00:00"},{"alias_kind":"pith_short_16","alias_value":"YIH4FDA72ESTGTF3","created_at":"2026-07-17T01:21:43.103473+00:00"},{"alias_kind":"pith_short_8","alias_value":"YIH4FDA7","created_at":"2026-07-17T01:21:43.103473+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2606.10685","citing_title":"Dynamical Amrein-Berthier Uncertainty for Fractional Schr\\\"odinger Flows","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YIH4FDA72ESTGTF3CNAPROGP47","json":"https://pith.science/pith/YIH4FDA72ESTGTF3CNAPROGP47.json","graph_json":"https://pith.science/api/pith-number/YIH4FDA72ESTGTF3CNAPROGP47/graph.json","events_json":"https://pith.science/api/pith-number/YIH4FDA72ESTGTF3CNAPROGP47/events.json","paper":"https://pith.science/paper/YIH4FDA7"},"agent_actions":{"view_html":"https://pith.science/pith/YIH4FDA72ESTGTF3CNAPROGP47","download_json":"https://pith.science/pith/YIH4FDA72ESTGTF3CNAPROGP47.json","view_paper":"https://pith.science/paper/YIH4FDA7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.18003&json=true","fetch_graph":"https://pith.science/api/pith-number/YIH4FDA72ESTGTF3CNAPROGP47/graph.json","fetch_events":"https://pith.science/api/pith-number/YIH4FDA72ESTGTF3CNAPROGP47/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YIH4FDA72ESTGTF3CNAPROGP47/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YIH4FDA72ESTGTF3CNAPROGP47/action/storage_attestation","attest_author":"https://pith.science/pith/YIH4FDA72ESTGTF3CNAPROGP47/action/author_attestation","sign_citation":"https://pith.science/pith/YIH4FDA72ESTGTF3CNAPROGP47/action/citation_signature","submit_replication":"https://pith.science/pith/YIH4FDA72ESTGTF3CNAPROGP47/action/replication_record"}},"created_at":"2026-07-17T01:21:43.103473+00:00","updated_at":"2026-07-17T01:21:43.103473+00:00"}