{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YPHCUHEYUS2Q6GF62S4FJGTIQX","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":"a2f6850ae8e6e9aff20024b1ef6b50a4d044abf2d6c34b529509f36b57c7f7dc","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-04T11:06:15Z","title_canon_sha256":"3aa4cf5a1b2e87ea75e0ec6538cf1cfec42d3d61be6bb1c61bee8ae42f8f5cae"},"schema_version":"1.0","source":{"id":"1304.1317","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.1317","created_at":"2026-05-18T00:49:35Z"},{"alias_kind":"arxiv_version","alias_value":"1304.1317v2","created_at":"2026-05-18T00:49:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.1317","created_at":"2026-05-18T00:49:35Z"},{"alias_kind":"pith_short_12","alias_value":"YPHCUHEYUS2Q","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YPHCUHEYUS2Q6GF6","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YPHCUHEY","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:74e3040132d0dbebdc0457a85ad1fb33461cd0698f23fa1fe3e52bb6c0750957","target":"graph","created_at":"2026-05-18T00:49:35Z","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 reconstruct compactly supported potentials with only half a derivative in $L^2$ from the scattering amplitude at a fixed energy. For this we draw a connection between the recently introduced method of Bukhgeim, which uniquely determined the potential from the Dirichlet-to-Neumann map, and a question of Carleson regarding the convergence to initial data of solutions to time-dependent Schr\\\"odinger equations. We also provide examples of compactly supported potentials, with $s$ derivatives in $L^2$ for any $s<1/2$, which cannot be recovered by these means. Thus the recovery method has a differ","authors_text":"Daniel Faraco, Kari Astala, Keith M. Rogers","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-04T11:06:15Z","title":"Rough Potential Recovery in the Plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1317","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":"sha256:511351b3178a164a5cf467eb54e09dfec98a5952370b6cd719633019d1d5db54","target":"record","created_at":"2026-05-18T00:49:35Z","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":"a2f6850ae8e6e9aff20024b1ef6b50a4d044abf2d6c34b529509f36b57c7f7dc","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-04T11:06:15Z","title_canon_sha256":"3aa4cf5a1b2e87ea75e0ec6538cf1cfec42d3d61be6bb1c61bee8ae42f8f5cae"},"schema_version":"1.0","source":{"id":"1304.1317","kind":"arxiv","version":2}},"canonical_sha256":"c3ce2a1c98a4b50f18bed4b8549a6885fa4aef99d28bed60ee4ab639588619f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3ce2a1c98a4b50f18bed4b8549a6885fa4aef99d28bed60ee4ab639588619f2","first_computed_at":"2026-05-18T00:49:35.406743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:35.406743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VFc63L5ik8KJicikvgTRRt8GdgstLsYcaKsataX5622OKGGewg5Hes7mLSelLxjitsziSrzNOmRuxRaqJb+dBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:35.407565Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.1317","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:511351b3178a164a5cf467eb54e09dfec98a5952370b6cd719633019d1d5db54","sha256:74e3040132d0dbebdc0457a85ad1fb33461cd0698f23fa1fe3e52bb6c0750957"],"state_sha256":"ed5a3a0e366e4ac6b48bc15f355fd863bde3f5d88b20cde332636d55f37de7ad"}