{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NOOXWEYX5LROJ3F6DMRAQDEVQK","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":"e0111a57a861eb6d60c94fe5883ccfe3c1bc487cfb91777071c3d98ca5b43dc9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-12T02:06:16Z","title_canon_sha256":"186b65e3af021f932f18f1ddd87a20ffd3ce9fc86561802b43d0ff651d5e35ee"},"schema_version":"1.0","source":{"id":"1601.02711","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02711","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02711v2","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02711","created_at":"2026-05-18T00:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"NOOXWEYX5LRO","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NOOXWEYX5LROJ3F6","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NOOXWEYX","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:0a6c97e2711555132a3686644d54aedc42cfacc50e5cdb05f0e5edd220d662fc","target":"graph","created_at":"2026-05-18T00:11:19Z","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":"We give a concrete sufficient condition for a simply-connected domain to be the image of the unit disk under a nonexpansive conformal map. This class of domains is also characterized by having sufficiently dense harmonic measure. The relation with the harmonic measure provides a natural higher-dimensional analogue of this problem, which is also addressed.","authors_text":"Leonid V. Kovalev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-12T02:06:16Z","title":"Conformal contractions and lower bounds on the density of harmonic measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02711","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":"sha256:347368fb932f3e91903577b9365a847c8a0375a22bd0f46f5a5f6909ab821692","target":"record","created_at":"2026-05-18T00:11:19Z","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":"e0111a57a861eb6d60c94fe5883ccfe3c1bc487cfb91777071c3d98ca5b43dc9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-01-12T02:06:16Z","title_canon_sha256":"186b65e3af021f932f18f1ddd87a20ffd3ce9fc86561802b43d0ff651d5e35ee"},"schema_version":"1.0","source":{"id":"1601.02711","kind":"arxiv","version":2}},"canonical_sha256":"6b9d7b1317eae2e4ecbe1b22080c958290812515a2e15e7cb5ed3dd42f0780f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b9d7b1317eae2e4ecbe1b22080c958290812515a2e15e7cb5ed3dd42f0780f3","first_computed_at":"2026-05-18T00:11:19.423850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:19.423850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mzZsNCRGJ/2/AzIfYinK4ZmQcDc4EcxJ3anFodyoqhwFW2qQgY2xAgrlauOdIXomR5XwmrPU61mPHLw3LDvTDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:19.424752Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02711","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:347368fb932f3e91903577b9365a847c8a0375a22bd0f46f5a5f6909ab821692","sha256:0a6c97e2711555132a3686644d54aedc42cfacc50e5cdb05f0e5edd220d662fc"],"state_sha256":"c029fc4a5d66f5330be9447f96f7af4e782fe8524f59af018bfdffa7aee14d67"}