{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:GTE7HT6S5ZXYTSQ3S5W424LT4Y","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":"88d01d12021d22a716b94ce850474750d9e75c8674b9da84b805b434f3a943e3","cross_cats_sorted":[],"license":"","primary_cat":"math.CV","submitted_at":"2002-09-25T02:49:43Z","title_canon_sha256":"a89534236bb01cfae95f45bbd58156b7536ce5171c7d3c881b087e49117bd26b"},"schema_version":"1.0","source":{"id":"math/0209334","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0209334","created_at":"2026-07-04T14:36:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0209334v2","created_at":"2026-07-04T14:36:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0209334","created_at":"2026-07-04T14:36:28Z"},{"alias_kind":"pith_short_12","alias_value":"GTE7HT6S5ZXY","created_at":"2026-07-04T14:36:28Z"},{"alias_kind":"pith_short_16","alias_value":"GTE7HT6S5ZXYTSQ3","created_at":"2026-07-04T14:36:28Z"},{"alias_kind":"pith_short_8","alias_value":"GTE7HT6S","created_at":"2026-07-04T14:36:28Z"}],"graph_snapshots":[{"event_id":"sha256:6c5199725c24bab38b7d95d2d5c6fbf072896c97734b7be19fba0174a09faeac","target":"graph","created_at":"2026-07-04T14:36:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0209334/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider a simply connected Riemann surface represented by a Speiser graph. Nevanlinna asked if the type of the surface is determined by the mean excess of the graph: whether mean excess zero implies that the surface is parabolic and negative mean excess implies that the surface is hyperbolic. Teichmuller gave an example of a hyperbolic simply connected Riemann surface whose mean excess is zero, disproving the first of these implications. We give an example of a simply connected parabolic Riemann surface with negative mean excess, thus disproving the other part. We also construct an example of","authors_text":"Itai Benjamini, Oded Schramm, Sergei Merenkov","cross_cats":[],"headline":"","license":"","primary_cat":"math.CV","submitted_at":"2002-09-25T02:49:43Z","title":"A negative answer to Nevanlinna's type question and a parabolic surface with a lot of negative curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0209334","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":"sha256:5d49cad45548e7295b68a3bd298d69e4169c4303ab5c314d11cc639de0f81136","target":"record","created_at":"2026-07-04T14:36:28Z","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":"88d01d12021d22a716b94ce850474750d9e75c8674b9da84b805b434f3a943e3","cross_cats_sorted":[],"license":"","primary_cat":"math.CV","submitted_at":"2002-09-25T02:49:43Z","title_canon_sha256":"a89534236bb01cfae95f45bbd58156b7536ce5171c7d3c881b087e49117bd26b"},"schema_version":"1.0","source":{"id":"math/0209334","kind":"arxiv","version":2}},"canonical_sha256":"34c9f3cfd2ee6f89ca1b976dcd7173e61722bf2598f49ab9403d5c33bb710cca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34c9f3cfd2ee6f89ca1b976dcd7173e61722bf2598f49ab9403d5c33bb710cca","first_computed_at":"2026-07-04T14:36:28.725869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:36:28.725869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q3gJZW+lh1gp8VMDJQmhHqoFeZJSbJ8HdAw3EtotlJTCkMevNXH5mXVwZoZUDjrELqhT77/hM+6HxD2CzFShCg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:36:28.726293Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0209334","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d49cad45548e7295b68a3bd298d69e4169c4303ab5c314d11cc639de0f81136","sha256:6c5199725c24bab38b7d95d2d5c6fbf072896c97734b7be19fba0174a09faeac"],"state_sha256":"eed9fd6cc3c697daf0db85cc0d4ef84ac49773e889921154c308c73684845075"}