{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TT4XL25YF66III5WKKOLYRWLLE","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":"1fb9fc9f4bb09782d6c9761146898efe0e3fa55afa17a340c984f0fb72eceeef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-11-28T00:13:23Z","title_canon_sha256":"405906a5b3852022c8a1cf3fd75cd49667256bf135450d34ea7f35234123f41e"},"schema_version":"1.0","source":{"id":"1011.6007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.6007","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"arxiv_version","alias_value":"1011.6007v1","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.6007","created_at":"2026-05-18T04:34:37Z"},{"alias_kind":"pith_short_12","alias_value":"TT4XL25YF66I","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TT4XL25YF66III5W","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TT4XL25Y","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:d376128da93b1ff8d5ffcb1958f7dbfdfbbede30b0a49d98b6aa631bb47c167f","target":"graph","created_at":"2026-05-18T04:34:37Z","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":"The purpose of this note is to prove that there is an algebraic stack U parameterizing all curves. The curves that appear in the algebraic stack U are allowed to be arbitrarily singular, non-reduced, disconnected, and reducible. We also prove the boundedness of the open substack of U parameterizing geometrically connected curves with fixed arithmetic genus g and $\\leq$ e irreducible components. This is an updated and expanded version of [arXiv:0902.3690v2, Appendix B].","authors_text":"Jack Hall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-11-28T00:13:23Z","title":"Moduli of Singular Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6007","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":"sha256:8899378432d08b90f27a10443648aba144c6e74ddb98f306ef5d6df04a20aead","target":"record","created_at":"2026-05-18T04:34:37Z","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":"1fb9fc9f4bb09782d6c9761146898efe0e3fa55afa17a340c984f0fb72eceeef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-11-28T00:13:23Z","title_canon_sha256":"405906a5b3852022c8a1cf3fd75cd49667256bf135450d34ea7f35234123f41e"},"schema_version":"1.0","source":{"id":"1011.6007","kind":"arxiv","version":1}},"canonical_sha256":"9cf975ebb82fbc8423b6529cbc46cb591366d4094020710cb896b10fc758907b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cf975ebb82fbc8423b6529cbc46cb591366d4094020710cb896b10fc758907b","first_computed_at":"2026-05-18T04:34:37.703095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:37.703095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XqVrx9zGdQtS6pXYCRmjAhGVwUjUg4XliiK4R4TxpyZMPjzUqNLktHmvYlnJMvm1QjxBLz++f5RwS5tJhAkJBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:37.703514Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.6007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8899378432d08b90f27a10443648aba144c6e74ddb98f306ef5d6df04a20aead","sha256:d376128da93b1ff8d5ffcb1958f7dbfdfbbede30b0a49d98b6aa631bb47c167f"],"state_sha256":"ea9376db17c061c3d8eae8d758ed1cb2bc7a9758c85bf3ba88acc351791984af"}