{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q3UTOQCISXT4XTNRIVEYS6BLAB","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":"9cee1f557602d0f6cdff000579e78d2e46171ca77b9c29f602a665299e29a1aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-04T12:39:19Z","title_canon_sha256":"8a247d5c8cfb49490d207148540e49ab2c2f478c370d52807b87d9a46c1548e2"},"schema_version":"1.0","source":{"id":"1312.1141","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1141","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1141v2","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1141","created_at":"2026-05-18T02:55:27Z"},{"alias_kind":"pith_short_12","alias_value":"Q3UTOQCISXT4","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q3UTOQCISXT4XTNR","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q3UTOQCI","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:aa552fe423ec53ef35c4352a1b38067d0780c0dba00bcd6ebe5b1d349a5be9c8","target":"graph","created_at":"2026-05-18T02:55:27Z","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 present the generating function for the numbers of isomorphism classes of coverings of the two-dimensional sphere by the genus $g$ compact oriented surface not ramified outside of a given set of $m+1$ points in the target, fixed ramification type over one point, and arbitrary ramification types over the remaining $m$ points. We present the genus expansion of this generating function and prove, that the generating function of coverings of genus $0$ satisfies some system of differential equations. We show that this generating function is a specialization of the function from paper \\cite{GJ} a","authors_text":"Boris Bychkov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-04T12:39:19Z","title":"On the number of coverings of the sphere ramified over given points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1141","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:e206c497a57c0e7257e6ca3837f900800978083a67823ddf3b84e8697eba00e2","target":"record","created_at":"2026-05-18T02:55:27Z","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":"9cee1f557602d0f6cdff000579e78d2e46171ca77b9c29f602a665299e29a1aa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-04T12:39:19Z","title_canon_sha256":"8a247d5c8cfb49490d207148540e49ab2c2f478c370d52807b87d9a46c1548e2"},"schema_version":"1.0","source":{"id":"1312.1141","kind":"arxiv","version":2}},"canonical_sha256":"86e937404895e7cbcdb1454989782b0076656385eb697256a71e07da44ef9597","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86e937404895e7cbcdb1454989782b0076656385eb697256a71e07da44ef9597","first_computed_at":"2026-05-18T02:55:27.366293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:27.366293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FoTfYRosptcvw6l2SYw9zVsmkMd1hVBfvhgcd9T+2PhLJZ2nVTdajt5j5T48zFF2eE0fsuxqojQvooaK+zsmDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:27.366873Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1141","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e206c497a57c0e7257e6ca3837f900800978083a67823ddf3b84e8697eba00e2","sha256:aa552fe423ec53ef35c4352a1b38067d0780c0dba00bcd6ebe5b1d349a5be9c8"],"state_sha256":"5f9b59d5434aef42450f8ef0797d81cf684a0ee755dfbce8c7a0fcde94eddabf"}