{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:VUI6JPNBKGDNZ4FLWSF3DNVIH5","short_pith_number":"pith:VUI6JPNB","schema_version":"1.0","canonical_sha256":"ad11e4bda15186dcf0abb48bb1b6a83f63cfd7c064d91c738685804db110717a","source":{"kind":"arxiv","id":"1805.09161","version":5},"attestation_state":"computed","paper":{"title":"Partial Data Calder\\'on Problems for $L^{n/2}$ Potentials on Admissible Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Leo Tzou","submitted_at":"2018-05-22T12:00:35Z","abstract_excerpt":"We solve the partial data Calder\\'on problem on conformally transversallly anisotropic (CTA) manifolds with $L^{n/2}$ potentials - on par with sharp unique continuation result of \\cite{JerKen}. A trivial consequence of this is the sharp regularity improvement to the result of Kenig-Sj\\\"ostrand-Uhlmann \\cite{ksu}. This is done by constructing a \"Green's function\" which possesses both desirable boundary conditions {\\em and} satisfies semiclassical type estimates in the suitable $L^{p}$ spaces. No Carleman estimates were used in the writing of this article which makes it starkly different from th"},"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":"1805.09161","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-05-22T12:00:35Z","cross_cats_sorted":[],"title_canon_sha256":"00aec00ff5ff64f09a72bc97e561a67dfaf345ef9fec49b20662b659a00215d7","abstract_canon_sha256":"7dfc73c731a4f444ca551d4f886594f174a899d9bd9f1637b13674622a6d424b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:49.418742Z","signature_b64":"IokT5GCyCkyIgUGTeSH87wRyS/hR3Y/kzUgd9qtTY24B4RrRfauh2X7vJAYhYo8xbYM8Ac1rEg6H3UE78lIbBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad11e4bda15186dcf0abb48bb1b6a83f63cfd7c064d91c738685804db110717a","last_reissued_at":"2026-05-18T00:07:49.417901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:49.417901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Partial Data Calder\\'on Problems for $L^{n/2}$ Potentials on Admissible Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Leo Tzou","submitted_at":"2018-05-22T12:00:35Z","abstract_excerpt":"We solve the partial data Calder\\'on problem on conformally transversallly anisotropic (CTA) manifolds with $L^{n/2}$ potentials - on par with sharp unique continuation result of \\cite{JerKen}. A trivial consequence of this is the sharp regularity improvement to the result of Kenig-Sj\\\"ostrand-Uhlmann \\cite{ksu}. This is done by constructing a \"Green's function\" which possesses both desirable boundary conditions {\\em and} satisfies semiclassical type estimates in the suitable $L^{p}$ spaces. No Carleman estimates were used in the writing of this article which makes it starkly different from th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09161","kind":"arxiv","version":5},"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":"1805.09161","created_at":"2026-05-18T00:07:49.418042+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.09161v5","created_at":"2026-05-18T00:07:49.418042+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09161","created_at":"2026-05-18T00:07:49.418042+00:00"},{"alias_kind":"pith_short_12","alias_value":"VUI6JPNBKGDN","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_16","alias_value":"VUI6JPNBKGDNZ4FL","created_at":"2026-05-18T12:32:59.047623+00:00"},{"alias_kind":"pith_short_8","alias_value":"VUI6JPNB","created_at":"2026-05-18T12:32:59.047623+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/VUI6JPNBKGDNZ4FLWSF3DNVIH5","json":"https://pith.science/pith/VUI6JPNBKGDNZ4FLWSF3DNVIH5.json","graph_json":"https://pith.science/api/pith-number/VUI6JPNBKGDNZ4FLWSF3DNVIH5/graph.json","events_json":"https://pith.science/api/pith-number/VUI6JPNBKGDNZ4FLWSF3DNVIH5/events.json","paper":"https://pith.science/paper/VUI6JPNB"},"agent_actions":{"view_html":"https://pith.science/pith/VUI6JPNBKGDNZ4FLWSF3DNVIH5","download_json":"https://pith.science/pith/VUI6JPNBKGDNZ4FLWSF3DNVIH5.json","view_paper":"https://pith.science/paper/VUI6JPNB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.09161&json=true","fetch_graph":"https://pith.science/api/pith-number/VUI6JPNBKGDNZ4FLWSF3DNVIH5/graph.json","fetch_events":"https://pith.science/api/pith-number/VUI6JPNBKGDNZ4FLWSF3DNVIH5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VUI6JPNBKGDNZ4FLWSF3DNVIH5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VUI6JPNBKGDNZ4FLWSF3DNVIH5/action/storage_attestation","attest_author":"https://pith.science/pith/VUI6JPNBKGDNZ4FLWSF3DNVIH5/action/author_attestation","sign_citation":"https://pith.science/pith/VUI6JPNBKGDNZ4FLWSF3DNVIH5/action/citation_signature","submit_replication":"https://pith.science/pith/VUI6JPNBKGDNZ4FLWSF3DNVIH5/action/replication_record"}},"created_at":"2026-05-18T00:07:49.418042+00:00","updated_at":"2026-05-18T00:07:49.418042+00:00"}