{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:MGAJB4N7DU4IJEJEETLZROUWQ6","short_pith_number":"pith:MGAJB4N7","canonical_record":{"source":{"id":"1201.4750","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-01-23T16:00:17Z","cross_cats_sorted":[],"title_canon_sha256":"19185ceb50e0dbd4a5beff62ad6185eeddf9ec20ce400fcea35cd99f48e1d00a","abstract_canon_sha256":"0d9868bd053659c232508bd17addce0f5d45a75995ca1f613cfbb77ac654b9e3"},"schema_version":"1.0"},"canonical_sha256":"618090f1bf1d3884912424d798ba96879937cdd56140876dc8e01684b5bf632e","source":{"kind":"arxiv","id":"1201.4750","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4750","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4750v1","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4750","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"pith_short_12","alias_value":"MGAJB4N7DU4I","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MGAJB4N7DU4IJEJE","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MGAJB4N7","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:MGAJB4N7DU4IJEJEETLZROUWQ6","target":"record","payload":{"canonical_record":{"source":{"id":"1201.4750","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-01-23T16:00:17Z","cross_cats_sorted":[],"title_canon_sha256":"19185ceb50e0dbd4a5beff62ad6185eeddf9ec20ce400fcea35cd99f48e1d00a","abstract_canon_sha256":"0d9868bd053659c232508bd17addce0f5d45a75995ca1f613cfbb77ac654b9e3"},"schema_version":"1.0"},"canonical_sha256":"618090f1bf1d3884912424d798ba96879937cdd56140876dc8e01684b5bf632e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:05.269743Z","signature_b64":"arVgWwxpAr+IoiIg9bHMQUe7WFUSQIbicjxzhnzm5iE/GYbcqkUWlWmA9dQx6iFpRpBP9mkTll6iUScrDTuzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"618090f1bf1d3884912424d798ba96879937cdd56140876dc8e01684b5bf632e","last_reissued_at":"2026-05-18T04:04:05.268949Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:05.268949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.4750","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:04:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QizXGfIYB+MFxc56tLj8vMf11v2uk1TWO+Vu0qAY+Jmjo7wxCPN2Yn846giLA1TKUSJG8cCqJoVSamDR8P9qDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:43:55.799338Z"},"content_sha256":"34e0b7de1660601f70e5cfdc1213db27b1e0a795d8231d420e269d50c42c8194","schema_version":"1.0","event_id":"sha256:34e0b7de1660601f70e5cfdc1213db27b1e0a795d8231d420e269d50c42c8194"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:MGAJB4N7DU4IJEJEETLZROUWQ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Harmonic measures of slit sides perpendicular to the domain boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Andrey Zakharov, Dmitri Prokhorov","submitted_at":"2012-01-23T16:00:17Z","abstract_excerpt":"The article is devoted to the geometry of solutions to the chordal Loewner equation which is based on comparison of singular solutions and harmonic measures for the sides of a slit in domains generated by a driving term. It is proved that harmonic measures of two sides of a slit in the upper half-plane which is perpendicular to the real axis are asymptotically equal to each other."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4750","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:04:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E7ju1Q/fMNEMc69WM0+8Pi25sBvhKc3DUww2CiSS1Z1KYM6bLEiLxhztvDjQeFxgTgZJb67RmvZDZzAjVQUFAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T19:43:55.799692Z"},"content_sha256":"59959c9f5836caa22ca5620ce0b5f437803820a305fb7920216043c771264e18","schema_version":"1.0","event_id":"sha256:59959c9f5836caa22ca5620ce0b5f437803820a305fb7920216043c771264e18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MGAJB4N7DU4IJEJEETLZROUWQ6/bundle.json","state_url":"https://pith.science/pith/MGAJB4N7DU4IJEJEETLZROUWQ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MGAJB4N7DU4IJEJEETLZROUWQ6/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":"2026-05-28T19:43:55Z","links":{"resolver":"https://pith.science/pith/MGAJB4N7DU4IJEJEETLZROUWQ6","bundle":"https://pith.science/pith/MGAJB4N7DU4IJEJEETLZROUWQ6/bundle.json","state":"https://pith.science/pith/MGAJB4N7DU4IJEJEETLZROUWQ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MGAJB4N7DU4IJEJEETLZROUWQ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MGAJB4N7DU4IJEJEETLZROUWQ6","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":"0d9868bd053659c232508bd17addce0f5d45a75995ca1f613cfbb77ac654b9e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-01-23T16:00:17Z","title_canon_sha256":"19185ceb50e0dbd4a5beff62ad6185eeddf9ec20ce400fcea35cd99f48e1d00a"},"schema_version":"1.0","source":{"id":"1201.4750","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4750","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4750v1","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4750","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"pith_short_12","alias_value":"MGAJB4N7DU4I","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MGAJB4N7DU4IJEJE","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MGAJB4N7","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:59959c9f5836caa22ca5620ce0b5f437803820a305fb7920216043c771264e18","target":"graph","created_at":"2026-05-18T04:04:05Z","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 article is devoted to the geometry of solutions to the chordal Loewner equation which is based on comparison of singular solutions and harmonic measures for the sides of a slit in domains generated by a driving term. It is proved that harmonic measures of two sides of a slit in the upper half-plane which is perpendicular to the real axis are asymptotically equal to each other.","authors_text":"Andrey Zakharov, Dmitri Prokhorov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-01-23T16:00:17Z","title":"Harmonic measures of slit sides perpendicular to the domain boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4750","kind":"arxiv","version":1},"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":"sha256:34e0b7de1660601f70e5cfdc1213db27b1e0a795d8231d420e269d50c42c8194","target":"record","created_at":"2026-05-18T04:04:05Z","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":"0d9868bd053659c232508bd17addce0f5d45a75995ca1f613cfbb77ac654b9e3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-01-23T16:00:17Z","title_canon_sha256":"19185ceb50e0dbd4a5beff62ad6185eeddf9ec20ce400fcea35cd99f48e1d00a"},"schema_version":"1.0","source":{"id":"1201.4750","kind":"arxiv","version":1}},"canonical_sha256":"618090f1bf1d3884912424d798ba96879937cdd56140876dc8e01684b5bf632e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"618090f1bf1d3884912424d798ba96879937cdd56140876dc8e01684b5bf632e","first_computed_at":"2026-05-18T04:04:05.268949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:05.268949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"arVgWwxpAr+IoiIg9bHMQUe7WFUSQIbicjxzhnzm5iE/GYbcqkUWlWmA9dQx6iFpRpBP9mkTll6iUScrDTuzDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:05.269743Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.4750","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34e0b7de1660601f70e5cfdc1213db27b1e0a795d8231d420e269d50c42c8194","sha256:59959c9f5836caa22ca5620ce0b5f437803820a305fb7920216043c771264e18"],"state_sha256":"81c6a424dbefe7403d5990316d545635c9c0ffde30f601543431f0ce93eff5c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MSjHTY3XHgZmG+7DBOlqByADSgZEfXlg1Lr05LOxLRrqygpaCDmtMeBP95eAm5vgiNod2KPUT/JOVIAsL+YzAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T19:43:55.801766Z","bundle_sha256":"af67e6061e9eb5713bd151b68e77a29570df3b9807a0407d549aa2e6787724ad"}}