{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7CABSEGMPJACOKLHDTNXMLHRMB","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":"8e301d5dcf6424e410c5d56305abfd081abfe4b9e6e686808781bbd24260637f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-08T20:48:41Z","title_canon_sha256":"dcee8127dc8f25f1f4cb2c050561c48bef4e2263c7e92ad870645cd15caef33a"},"schema_version":"1.0","source":{"id":"1603.02668","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02668","created_at":"2026-05-18T01:19:22Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02668v1","created_at":"2026-05-18T01:19:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02668","created_at":"2026-05-18T01:19:22Z"},{"alias_kind":"pith_short_12","alias_value":"7CABSEGMPJAC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7CABSEGMPJACOKLH","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7CABSEGM","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:0c0686404f9f606dfa9cbabda4e228083b09bb023f8578521d70af3bee0cc319","target":"graph","created_at":"2026-05-18T01:19:22Z","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":"In 1968, Krzyz conjectured that for non-vanishing holomorphic functions $f(z) = c_0 + c_1 z + \\dots$ in the unit disk with $|f(z)| \\leq 1$, we have the sharp bound $|c_n| \\leq 2/e$ for all $n \\geq 1$, with equality only for the function $f(z) = exp [(z^n - 1)/(z^n + 1)]$ and its rotations. This conjecture was considered by many researchers, but only partial results have been established. The desired estimate has been proved only for $n \\leq 5$.\n  We provide here two different proofs of this conjecture and its generalizations based on completely different ideas.","authors_text":"Samuel L. Krushkal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-08T20:48:41Z","title":"Hyperbolic geodesics, Krzyz's conjecture and beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02668","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":"sha256:9bd9b57e5da066f636a4b760e85544066e11f269291bd7972f076bb1ba36daca","target":"record","created_at":"2026-05-18T01:19:22Z","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":"8e301d5dcf6424e410c5d56305abfd081abfe4b9e6e686808781bbd24260637f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-08T20:48:41Z","title_canon_sha256":"dcee8127dc8f25f1f4cb2c050561c48bef4e2263c7e92ad870645cd15caef33a"},"schema_version":"1.0","source":{"id":"1603.02668","kind":"arxiv","version":1}},"canonical_sha256":"f8801910cc7a402729671cdb762cf16044d5ebaa39397028b395970abaf27a34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8801910cc7a402729671cdb762cf16044d5ebaa39397028b395970abaf27a34","first_computed_at":"2026-05-18T01:19:22.646784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:22.646784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k0nr85UZhqxT1KU7oyn/XiapO0afBl05JhOx9riAdHN4RlzOoPhSnWuxOx9MIHvrqAE2gwMkcgr1tCSjGLxjDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:22.647582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.02668","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bd9b57e5da066f636a4b760e85544066e11f269291bd7972f076bb1ba36daca","sha256:0c0686404f9f606dfa9cbabda4e228083b09bb023f8578521d70af3bee0cc319"],"state_sha256":"a86f1a219a531b2dc9314590970f09ee9e10c316f56c1524d23b7a8dde38d353"}