{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PK7GDNP4AX3K7TED335CDART27","short_pith_number":"pith:PK7GDNP4","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"},"canonical_sha256":"7abe61b5fc05f6afcc83defa218233d7f08851ac4581daee7a90f61b2d7ee497","source":{"kind":"arxiv","id":"1302.0898","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0898","created_at":"2026-05-18T03:30:13Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0898v2","created_at":"2026-05-18T03:30:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0898","created_at":"2026-05-18T03:30:13Z"},{"alias_kind":"pith_short_12","alias_value":"PK7GDNP4AX3K","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PK7GDNP4AX3K7TED","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PK7GDNP4","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PK7GDNP4AX3K7TED335CDART27","target":"record","payload":{"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"},"canonical_sha256":"7abe61b5fc05f6afcc83defa218233d7f08851ac4581daee7a90f61b2d7ee497","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"},"source_kind":"arxiv","source_id":"1302.0898","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:30:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mxe/aSY9Z5/UZ/4NtWKhsaOhOVMPrbaNTrI+KTjtfH1y0ijN4U/SM2l8gVkp3ibgzVwl5nqb1aCwzu8ARK9JDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:10:21.220166Z"},"content_sha256":"82b6cc5b4c99accc83c67f271d96b022108952a50002ebdd4d22063112bdd15d","schema_version":"1.0","event_id":"sha256:82b6cc5b4c99accc83c67f271d96b022108952a50002ebdd4d22063112bdd15d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PK7GDNP4AX3K7TED335CDART27","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:30:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vI2vzZ80XU//70MNcQZEKMFCiVHblRJjZBCdBBzmUZHJsRACn5RhlhjtQJg7Evf1HPD17Bal9ltTxU1Ae08aCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:10:21.220825Z"},"content_sha256":"1cd2f8a52f552051dd65c8e32a8fe6c65654968bb73933d7d53e6b2f59c10a26","schema_version":"1.0","event_id":"sha256:1cd2f8a52f552051dd65c8e32a8fe6c65654968bb73933d7d53e6b2f59c10a26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PK7GDNP4AX3K7TED335CDART27/bundle.json","state_url":"https://pith.science/pith/PK7GDNP4AX3K7TED335CDART27/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PK7GDNP4AX3K7TED335CDART27/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T12:10:21Z","links":{"resolver":"https://pith.science/pith/PK7GDNP4AX3K7TED335CDART27","bundle":"https://pith.science/pith/PK7GDNP4AX3K7TED335CDART27/bundle.json","state":"https://pith.science/pith/PK7GDNP4AX3K7TED335CDART27/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PK7GDNP4AX3K7TED335CDART27/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PK7GDNP4AX3K7TED335CDART27","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":"ad0f3242ee6016a7e466489e709737133c1df88035271ba38c81c7cae0aa2160","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-04T23:04:12Z","title_canon_sha256":"67abbf40780422dbec43a45938fbe43bd5c1d973e6ee60df918416d1827711a3"},"schema_version":"1.0","source":{"id":"1302.0898","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0898","created_at":"2026-05-18T03:30:13Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0898v2","created_at":"2026-05-18T03:30:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0898","created_at":"2026-05-18T03:30:13Z"},{"alias_kind":"pith_short_12","alias_value":"PK7GDNP4AX3K","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PK7GDNP4AX3K7TED","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PK7GDNP4","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:1cd2f8a52f552051dd65c8e32a8fe6c65654968bb73933d7d53e6b2f59c10a26","target":"graph","created_at":"2026-05-18T03:30:13Z","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":"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","authors_text":"Andrea del Monaco, Pavel Gumenyuk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-04T23:04:12Z","title":"Chordal Loewner Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0898","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":"sha256:82b6cc5b4c99accc83c67f271d96b022108952a50002ebdd4d22063112bdd15d","target":"record","created_at":"2026-05-18T03:30:13Z","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":"ad0f3242ee6016a7e466489e709737133c1df88035271ba38c81c7cae0aa2160","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-02-04T23:04:12Z","title_canon_sha256":"67abbf40780422dbec43a45938fbe43bd5c1d973e6ee60df918416d1827711a3"},"schema_version":"1.0","source":{"id":"1302.0898","kind":"arxiv","version":2}},"canonical_sha256":"7abe61b5fc05f6afcc83defa218233d7f08851ac4581daee7a90f61b2d7ee497","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7abe61b5fc05f6afcc83defa218233d7f08851ac4581daee7a90f61b2d7ee497","first_computed_at":"2026-05-18T03:30:13.746209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:13.746209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8jrBOJtMvIUlDHTMh27OX2HyyFlOxmJGh61CoPlm9R6kPVrR4obhdEHP2fhYAwgNbyP46xSkAaoaWhdzbxHZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:13.746943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0898","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82b6cc5b4c99accc83c67f271d96b022108952a50002ebdd4d22063112bdd15d","sha256:1cd2f8a52f552051dd65c8e32a8fe6c65654968bb73933d7d53e6b2f59c10a26"],"state_sha256":"834efbbdda95ee52b799f6e24cbee86a0dc2ebc3204b72fb206be4113f1f9392"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ly43Kf6wJpuE/cLp/lK+FxKZznt2vXRezLcYkMFXhpphE7mAwSPu4cDC26+7UkH2yIywRogP6Lr3djGRU8LgAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:10:21.223354Z","bundle_sha256":"f749e749868d5c7a6e260d57cb778f910459d4495cc91ce125b76b1dc61b117c"}}