{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:D7UKMOUNSNIIWVR5S6YWZIGB6W","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":"1b51f74da8d8f91dd284e8deb194eccb572bee9171aee28c1d3cfab77c3030e3","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-25T23:55:27Z","title_canon_sha256":"a2de641662bafd0f6dd53febd0ec47fea8c3e457c064b227860a21ea6e02ec80"},"schema_version":"1.0","source":{"id":"1108.5214","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5214","created_at":"2026-05-18T04:12:57Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5214v3","created_at":"2026-05-18T04:12:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5214","created_at":"2026-05-18T04:12:57Z"},{"alias_kind":"pith_short_12","alias_value":"D7UKMOUNSNII","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"D7UKMOUNSNIIWVR5","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"D7UKMOUN","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:77fb2732ef7800a90be0ea668524dc7895b912b905fa755c19c46d7aa8594119","target":"graph","created_at":"2026-05-18T04:12:57Z","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":"Let $G_n$ be the genus of a two-dimensional surface obtained by gluing, uniformly at random, the sides of an $n$-gon. Recently Linial and Nowik proved, via an enumerational formula due to Harer and Zagier, that the expected value of $G_n$ is asymptotic to $(n - \\ln n)/2$ for $n\\to\\infty$. We prove a local limit theorem for the distribution of $G_n$, which implies that $G_n$ is asymptotically Gaussian, with mean $(n-\\ln n)/2$ and variance $(\\ln n)/4$.","authors_text":"Boris Pittel, Sergei Chmutov","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-25T23:55:27Z","title":"The genus of a random chord diagram is asymptotically normal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5214","kind":"arxiv","version":3},"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":"sha256:2202de04d80fe48ec7f71cbd939be350bf3d4c67ba436f265adf938a0642e967","target":"record","created_at":"2026-05-18T04:12:57Z","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":"1b51f74da8d8f91dd284e8deb194eccb572bee9171aee28c1d3cfab77c3030e3","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-08-25T23:55:27Z","title_canon_sha256":"a2de641662bafd0f6dd53febd0ec47fea8c3e457c064b227860a21ea6e02ec80"},"schema_version":"1.0","source":{"id":"1108.5214","kind":"arxiv","version":3}},"canonical_sha256":"1fe8a63a8d93508b563d97b16ca0c1f5a084af57a60ed5466331696fcf356767","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1fe8a63a8d93508b563d97b16ca0c1f5a084af57a60ed5466331696fcf356767","first_computed_at":"2026-05-18T04:12:57.328474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:57.328474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uuf7/WspWWxsOcN23LJdAJbtxc985c21jaqN20jQTgNF2xhKd6jUdZv1++zaWqTT+94fpxgrzZPVvQlyXo0+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:57.329184Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5214","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2202de04d80fe48ec7f71cbd939be350bf3d4c67ba436f265adf938a0642e967","sha256:77fb2732ef7800a90be0ea668524dc7895b912b905fa755c19c46d7aa8594119"],"state_sha256":"e61605bd02669dcc5d8374450a451d87a507a8fdb252630ae8c1820773b4db76"}