{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:X2BAN4BEKRT7FNUTVWU2I32KXC","short_pith_number":"pith:X2BAN4BE","schema_version":"1.0","canonical_sha256":"be8206f0245467f2b693ada9a46f4ab88007c380c0b0c4bc6c021ac629012197","source":{"kind":"arxiv","id":"1811.10715","version":1},"attestation_state":"computed","paper":{"title":"Plemelj-Sokhotski isomorphism for quasicircles in Riemann surfaces and the Schiffer operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Eric Schippers, Wolfgang Staubach","submitted_at":"2018-11-26T22:13:09Z","abstract_excerpt":"Let $R$ be a compact Riemann surface and $\\Gamma$ be a Jordan curve separating $R$ into connected components $\\Sigma_1$ and $\\Sigma_2$. We consider Calder\\'on-Zygmund type operators $T(\\Sigma_1,\\Sigma_k)$ taking the space of $L^2$ anti-holomorphic one-forms on $\\Sigma_1$ to the space of $L^2$ holomorphic one-forms on $\\Sigma_k$, which we call the Schiffer operators. We extend results of Menahem M. Schiffer and others, which where confined to analytic Jordan curves $\\Gamma$, to general quasicircles in a characterizing manner, and prove new identities for adjoints of the Schiffer operators. Furt"},"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":"1811.10715","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-11-26T22:13:09Z","cross_cats_sorted":[],"title_canon_sha256":"a7829dc86767c444590624c72aaca816b0b1929abe08957d278e0d750e78da2e","abstract_canon_sha256":"fe6813670af22c8986ba654463cf964af8c35eb7ae138b6ad06f9dc7732bf35b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:47.752923Z","signature_b64":"DHsfj+QN7kU7ZkcCtcHEKSrb5eqN2GrOr1hQ9Kq9JiH60cW3G+D77q5mhoRrYEwmGTs8GnY9A5s08YizbkCbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be8206f0245467f2b693ada9a46f4ab88007c380c0b0c4bc6c021ac629012197","last_reissued_at":"2026-05-17T23:59:47.752508Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:47.752508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Plemelj-Sokhotski isomorphism for quasicircles in Riemann surfaces and the Schiffer operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Eric Schippers, Wolfgang Staubach","submitted_at":"2018-11-26T22:13:09Z","abstract_excerpt":"Let $R$ be a compact Riemann surface and $\\Gamma$ be a Jordan curve separating $R$ into connected components $\\Sigma_1$ and $\\Sigma_2$. We consider Calder\\'on-Zygmund type operators $T(\\Sigma_1,\\Sigma_k)$ taking the space of $L^2$ anti-holomorphic one-forms on $\\Sigma_1$ to the space of $L^2$ holomorphic one-forms on $\\Sigma_k$, which we call the Schiffer operators. We extend results of Menahem M. Schiffer and others, which where confined to analytic Jordan curves $\\Gamma$, to general quasicircles in a characterizing manner, and prove new identities for adjoints of the Schiffer operators. Furt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10715","kind":"arxiv","version":1},"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":"1811.10715","created_at":"2026-05-17T23:59:47.752577+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.10715v1","created_at":"2026-05-17T23:59:47.752577+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.10715","created_at":"2026-05-17T23:59:47.752577+00:00"},{"alias_kind":"pith_short_12","alias_value":"X2BAN4BEKRT7","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"X2BAN4BEKRT7FNUT","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"X2BAN4BE","created_at":"2026-05-18T12:33:01.666342+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/X2BAN4BEKRT7FNUTVWU2I32KXC","json":"https://pith.science/pith/X2BAN4BEKRT7FNUTVWU2I32KXC.json","graph_json":"https://pith.science/api/pith-number/X2BAN4BEKRT7FNUTVWU2I32KXC/graph.json","events_json":"https://pith.science/api/pith-number/X2BAN4BEKRT7FNUTVWU2I32KXC/events.json","paper":"https://pith.science/paper/X2BAN4BE"},"agent_actions":{"view_html":"https://pith.science/pith/X2BAN4BEKRT7FNUTVWU2I32KXC","download_json":"https://pith.science/pith/X2BAN4BEKRT7FNUTVWU2I32KXC.json","view_paper":"https://pith.science/paper/X2BAN4BE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.10715&json=true","fetch_graph":"https://pith.science/api/pith-number/X2BAN4BEKRT7FNUTVWU2I32KXC/graph.json","fetch_events":"https://pith.science/api/pith-number/X2BAN4BEKRT7FNUTVWU2I32KXC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X2BAN4BEKRT7FNUTVWU2I32KXC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X2BAN4BEKRT7FNUTVWU2I32KXC/action/storage_attestation","attest_author":"https://pith.science/pith/X2BAN4BEKRT7FNUTVWU2I32KXC/action/author_attestation","sign_citation":"https://pith.science/pith/X2BAN4BEKRT7FNUTVWU2I32KXC/action/citation_signature","submit_replication":"https://pith.science/pith/X2BAN4BEKRT7FNUTVWU2I32KXC/action/replication_record"}},"created_at":"2026-05-17T23:59:47.752577+00:00","updated_at":"2026-05-17T23:59:47.752577+00:00"}