{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:PK7GDNP4AX3K7TED335CDART27","short_pith_number":"pith:PK7GDNP4","schema_version":"1.0","canonical_sha256":"7abe61b5fc05f6afcc83defa218233d7f08851ac4581daee7a90f61b2d7ee497","source":{"kind":"arxiv","id":"1302.0898","version":2},"attestation_state":"computed","paper":{"title":"Chordal Loewner Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andrea del Monaco, Pavel Gumenyuk","submitted_at":"2013-02-04T23:04:12Z","abstract_excerpt":"The aim of this survey paper is to present a complete direct proof of the well celebrated cornerstone result in Loewner Theory, originally due to Kufarev et al [Trudy Tomsk. Gos. Univ. Ser. Meh.-Mat. 200 (1968) 142-164. MR0257336 (41 #1987)], stating that the family of the hydrodynamically normalized conformal self-maps of the upper-half plane onto the complement of a gradually erased slit satisfies, under a suitable parametrization, the chordal Loewner differential equation. The proof is based solely on basic theorems of Geometric Function Theory combined with some elementary topological fact"},"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":"1302.0898","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-04T23:04:12Z","cross_cats_sorted":[],"title_canon_sha256":"67abbf40780422dbec43a45938fbe43bd5c1d973e6ee60df918416d1827711a3","abstract_canon_sha256":"ad0f3242ee6016a7e466489e709737133c1df88035271ba38c81c7cae0aa2160"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:13.746943Z","signature_b64":"8jrBOJtMvIUlDHTMh27OX2HyyFlOxmJGh61CoPlm9R6kPVrR4obhdEHP2fhYAwgNbyP46xSkAaoaWhdzbxHZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7abe61b5fc05f6afcc83defa218233d7f08851ac4581daee7a90f61b2d7ee497","last_reissued_at":"2026-05-18T03:30:13.746209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:13.746209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chordal Loewner Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andrea del Monaco, Pavel Gumenyuk","submitted_at":"2013-02-04T23:04:12Z","abstract_excerpt":"The aim of this survey paper is to present a complete direct proof of the well celebrated cornerstone result in Loewner Theory, originally due to Kufarev et al [Trudy Tomsk. Gos. Univ. Ser. Meh.-Mat. 200 (1968) 142-164. MR0257336 (41 #1987)], stating that the family of the hydrodynamically normalized conformal self-maps of the upper-half plane onto the complement of a gradually erased slit satisfies, under a suitable parametrization, the chordal Loewner differential equation. The proof is based solely on basic theorems of Geometric Function Theory combined with some elementary topological fact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0898","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":"1302.0898","created_at":"2026-05-18T03:30:13.746380+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.0898v2","created_at":"2026-05-18T03:30:13.746380+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0898","created_at":"2026-05-18T03:30:13.746380+00:00"},{"alias_kind":"pith_short_12","alias_value":"PK7GDNP4AX3K","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_16","alias_value":"PK7GDNP4AX3K7TED","created_at":"2026-05-18T12:27:54.935989+00:00"},{"alias_kind":"pith_short_8","alias_value":"PK7GDNP4","created_at":"2026-05-18T12:27:54.935989+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/PK7GDNP4AX3K7TED335CDART27","json":"https://pith.science/pith/PK7GDNP4AX3K7TED335CDART27.json","graph_json":"https://pith.science/api/pith-number/PK7GDNP4AX3K7TED335CDART27/graph.json","events_json":"https://pith.science/api/pith-number/PK7GDNP4AX3K7TED335CDART27/events.json","paper":"https://pith.science/paper/PK7GDNP4"},"agent_actions":{"view_html":"https://pith.science/pith/PK7GDNP4AX3K7TED335CDART27","download_json":"https://pith.science/pith/PK7GDNP4AX3K7TED335CDART27.json","view_paper":"https://pith.science/paper/PK7GDNP4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.0898&json=true","fetch_graph":"https://pith.science/api/pith-number/PK7GDNP4AX3K7TED335CDART27/graph.json","fetch_events":"https://pith.science/api/pith-number/PK7GDNP4AX3K7TED335CDART27/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PK7GDNP4AX3K7TED335CDART27/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PK7GDNP4AX3K7TED335CDART27/action/storage_attestation","attest_author":"https://pith.science/pith/PK7GDNP4AX3K7TED335CDART27/action/author_attestation","sign_citation":"https://pith.science/pith/PK7GDNP4AX3K7TED335CDART27/action/citation_signature","submit_replication":"https://pith.science/pith/PK7GDNP4AX3K7TED335CDART27/action/replication_record"}},"created_at":"2026-05-18T03:30:13.746380+00:00","updated_at":"2026-05-18T03:30:13.746380+00:00"}