{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:NS5NU6B77MNL4NKHHNOQRUA27L","short_pith_number":"pith:NS5NU6B7","schema_version":"1.0","canonical_sha256":"6cbada783ffb1abe35473b5d08d01afacad5c6dc11aab7935493dd1365def8a5","source":{"kind":"arxiv","id":"1410.1825","version":2},"attestation_state":"computed","paper":{"title":"The Loewner Equation for Multiple Slits, Multiply Connected Domains and Branch Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Christoph B\\\"ohm, Sebastian Schlei{\\ss}inger","submitted_at":"2014-10-07T17:59:24Z","abstract_excerpt":"Let $\\gamma_1,\\gamma_2:[0,T]\\to \\overline{\\mathbb{D}}\\setminus\\{0\\}$ be parametrizations of two slits $\\Gamma_1:=\\gamma(0,T], \\Gamma_2=\\gamma_2(0,T]$ such that $\\Gamma_1$ and $\\Gamma_2$ are disjoint. \\\\ Let $g_t$ to be the unique normalized conformal mapping from $\\mathbb{D}\\setminus (\\gamma_1[0,t]\\cup \\gamma_2[0,t])$ onto $\\mathbb{D}$ with $g_t(0)=0,$ $g'_t(0)>0$. Furthermore, for $k=1,2$, denote by $h_{k;t}$ the unique normalized conformal mapping from $\\mathbb{D}\\setminus \\gamma_k[0,t]$ onto $\\mathbb{D}$ with $h_{k;t}(0)=0,$ ${h'_{k;t}(0)}>0$.\\\\ Loewner's famous theorem (\\cite{Loewner:1923}"},"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":"1410.1825","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-10-07T17:59:24Z","cross_cats_sorted":[],"title_canon_sha256":"60660f433a1307844c63c51d01f6d3daaa00bb6969b1704d89530963d5fd909b","abstract_canon_sha256":"4c0002366c466c46c94194b4b3b96181daeced17e2611619b3fe7447d6c533cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:16.147852Z","signature_b64":"wbiUAJfAKj8REU7bmEaB0XhX8XoFHMBcd4w8Hn1Wl5wnLiAOhiPkyYg9FxvCol1Zb4TeGCVo/pcj93ZkYThiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cbada783ffb1abe35473b5d08d01afacad5c6dc11aab7935493dd1365def8a5","last_reissued_at":"2026-05-18T01:25:16.147278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:16.147278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Loewner Equation for Multiple Slits, Multiply Connected Domains and Branch Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Christoph B\\\"ohm, Sebastian Schlei{\\ss}inger","submitted_at":"2014-10-07T17:59:24Z","abstract_excerpt":"Let $\\gamma_1,\\gamma_2:[0,T]\\to \\overline{\\mathbb{D}}\\setminus\\{0\\}$ be parametrizations of two slits $\\Gamma_1:=\\gamma(0,T], \\Gamma_2=\\gamma_2(0,T]$ such that $\\Gamma_1$ and $\\Gamma_2$ are disjoint. \\\\ Let $g_t$ to be the unique normalized conformal mapping from $\\mathbb{D}\\setminus (\\gamma_1[0,t]\\cup \\gamma_2[0,t])$ onto $\\mathbb{D}$ with $g_t(0)=0,$ $g'_t(0)>0$. Furthermore, for $k=1,2$, denote by $h_{k;t}$ the unique normalized conformal mapping from $\\mathbb{D}\\setminus \\gamma_k[0,t]$ onto $\\mathbb{D}$ with $h_{k;t}(0)=0,$ ${h'_{k;t}(0)}>0$.\\\\ Loewner's famous theorem (\\cite{Loewner:1923}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.1825","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":""},"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":"1410.1825","created_at":"2026-05-18T01:25:16.147379+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.1825v2","created_at":"2026-05-18T01:25:16.147379+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.1825","created_at":"2026-05-18T01:25:16.147379+00:00"},{"alias_kind":"pith_short_12","alias_value":"NS5NU6B77MNL","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_16","alias_value":"NS5NU6B77MNL4NKH","created_at":"2026-05-18T12:28:41.024544+00:00"},{"alias_kind":"pith_short_8","alias_value":"NS5NU6B7","created_at":"2026-05-18T12:28:41.024544+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/NS5NU6B77MNL4NKHHNOQRUA27L","json":"https://pith.science/pith/NS5NU6B77MNL4NKHHNOQRUA27L.json","graph_json":"https://pith.science/api/pith-number/NS5NU6B77MNL4NKHHNOQRUA27L/graph.json","events_json":"https://pith.science/api/pith-number/NS5NU6B77MNL4NKHHNOQRUA27L/events.json","paper":"https://pith.science/paper/NS5NU6B7"},"agent_actions":{"view_html":"https://pith.science/pith/NS5NU6B77MNL4NKHHNOQRUA27L","download_json":"https://pith.science/pith/NS5NU6B77MNL4NKHHNOQRUA27L.json","view_paper":"https://pith.science/paper/NS5NU6B7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.1825&json=true","fetch_graph":"https://pith.science/api/pith-number/NS5NU6B77MNL4NKHHNOQRUA27L/graph.json","fetch_events":"https://pith.science/api/pith-number/NS5NU6B77MNL4NKHHNOQRUA27L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NS5NU6B77MNL4NKHHNOQRUA27L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NS5NU6B77MNL4NKHHNOQRUA27L/action/storage_attestation","attest_author":"https://pith.science/pith/NS5NU6B77MNL4NKHHNOQRUA27L/action/author_attestation","sign_citation":"https://pith.science/pith/NS5NU6B77MNL4NKHHNOQRUA27L/action/citation_signature","submit_replication":"https://pith.science/pith/NS5NU6B77MNL4NKHHNOQRUA27L/action/replication_record"}},"created_at":"2026-05-18T01:25:16.147379+00:00","updated_at":"2026-05-18T01:25:16.147379+00:00"}