{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YP2AGQXQVDH4RJXNIE2Y2JYV6V","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":"e538d1e01b83224cb1d5b5df1ac5bcea1a164feb26fec7ce026a32e030978568","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-03T14:55:43Z","title_canon_sha256":"06e266f7515ca475e5c5c9179e7d37bc3079f3e8e7c26bc8f8177f8e6509c7f5"},"schema_version":"1.0","source":{"id":"1502.00879","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.00879","created_at":"2026-05-18T00:15:42Z"},{"alias_kind":"arxiv_version","alias_value":"1502.00879v3","created_at":"2026-05-18T00:15:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.00879","created_at":"2026-05-18T00:15:42Z"},{"alias_kind":"pith_short_12","alias_value":"YP2AGQXQVDH4","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YP2AGQXQVDH4RJXN","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YP2AGQXQ","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:69ec15e8c1cd2481afffb53727c36c9cf32ab4b55cd516b4b92ac3ca615c338e","target":"graph","created_at":"2026-05-18T00:15:42Z","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 prove that every Q-factorial complete toric variety is a finite quotient of a poly weighted space (PWS), as defined in our previous work arXiv:1501.05244. This generalizes the Batyrev-Cox and Conrads description of a Q-factorial complete toric variety of Picard number 1, as a finite quotient of a weighted projective space (WPS) \\cite[Lemma~2.11]{BC} and \\cite[Prop.~4.7]{Conrads}, to every possible Picard number, by replacing the covering WPS with a PWS. As a consequence we describe the bases of the subgroup of Cartier divisors inside the free group of Weil divisors and the bases of the Pica","authors_text":"Lea Terracini, Michele Rossi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-03T14:55:43Z","title":"A Q-factorial complete toric variety is a quotient of a poly weighted space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00879","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":"sha256:84cf20866ab6651f9061ccc1ab97f8d415cc83e198c3bbbfb2db505cba706db5","target":"record","created_at":"2026-05-18T00:15:42Z","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":"e538d1e01b83224cb1d5b5df1ac5bcea1a164feb26fec7ce026a32e030978568","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-03T14:55:43Z","title_canon_sha256":"06e266f7515ca475e5c5c9179e7d37bc3079f3e8e7c26bc8f8177f8e6509c7f5"},"schema_version":"1.0","source":{"id":"1502.00879","kind":"arxiv","version":3}},"canonical_sha256":"c3f40342f0a8cfc8a6ed41358d2715f546099c953387634ad8a9342a09de4da3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3f40342f0a8cfc8a6ed41358d2715f546099c953387634ad8a9342a09de4da3","first_computed_at":"2026-05-18T00:15:42.509522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:42.509522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T+6nl9s3ndmEFkV2wDPYOK9OqxIw0rFURYVmOusfnBGAR3S98kveYLhgfwxrvnzR7wbo98MljcRHx34YtDFQBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:42.509980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.00879","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84cf20866ab6651f9061ccc1ab97f8d415cc83e198c3bbbfb2db505cba706db5","sha256:69ec15e8c1cd2481afffb53727c36c9cf32ab4b55cd516b4b92ac3ca615c338e"],"state_sha256":"9e0e3ba3af04ee16015172b7cb6cbd5bf5b5fadcd68881d751032c39cbf2e445"}