{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:WZTPFSAZX4YH5FAX3S3LTZCMF3","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":"d9f583618657d40c1b0b115fcc25f0a9427bab76067b99a8f2908ff293b91955","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1994-10-05T11:27:39Z","title_canon_sha256":"bd1e9b6ec036e5801230711e8f48bbbd330f32c417d5761b93ef1d360b1d5ce0"},"schema_version":"1.0","source":{"id":"alg-geom/9410003","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9410003","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9410003v1","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9410003","created_at":"2026-05-18T01:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"WZTPFSAZX4YH","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"WZTPFSAZX4YH5FAX","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"WZTPFSAZ","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:3a0c64ed4bcb536d535b33b70323ee00abeff7dd26b1672b8dc841dfdb8b3f80","target":"graph","created_at":"2026-05-18T01:37:43Z","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 construct and prove the projectiveness of the moduli spaces which are natural generalizations to the case of surfaces of the following:\n  1) $M_{g,n}$, the moduli space of $n$-marked stable curves,\n  2) $M_{g,n}(W)$, the moduli space of $n$-marked stable maps to a variety $W$.","authors_text":"Valery Alexeev","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1994-10-05T11:27:39Z","title":"Moduli spaces $M_{g,n}(W)$ for surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9410003","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:f29469b3b0840a46523006384db0c152c71b1fd7171bfb12d79806c83122dc0d","target":"record","created_at":"2026-05-18T01:37:43Z","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":"d9f583618657d40c1b0b115fcc25f0a9427bab76067b99a8f2908ff293b91955","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1994-10-05T11:27:39Z","title_canon_sha256":"bd1e9b6ec036e5801230711e8f48bbbd330f32c417d5761b93ef1d360b1d5ce0"},"schema_version":"1.0","source":{"id":"alg-geom/9410003","kind":"arxiv","version":1}},"canonical_sha256":"b666f2c819bf307e9417dcb6b9e44c2eef734b9efd9084f5ac7a29323e6f350a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b666f2c819bf307e9417dcb6b9e44c2eef734b9efd9084f5ac7a29323e6f350a","first_computed_at":"2026-05-18T01:37:43.133835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:43.133835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0+uZKYnP9BYUP2JzeI9mbgpvL4xH5apqkfRdmiNSiVEC8um9FiHUi7cNa1ejGlByAK/QVHJYsGfoCJkiJgMpBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:43.134362Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9410003","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f29469b3b0840a46523006384db0c152c71b1fd7171bfb12d79806c83122dc0d","sha256:3a0c64ed4bcb536d535b33b70323ee00abeff7dd26b1672b8dc841dfdb8b3f80"],"state_sha256":"e4870e784894b4a17a490029ff3eb7688e4def708af768fd18570421bb31d460"}