{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YNBWIYX7GMZIUZG4YQXXWWOR4M","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":"b19fcfebf053203254b5e62d2558dfee6d5a1c61cfdf7bfe4d0f0c951270d268","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-02-29T22:07:50Z","title_canon_sha256":"83bdbfb8fa032fb9599bc5861bb2c95916e105c6783cf95e5f5042e6572ffa30"},"schema_version":"1.0","source":{"id":"1603.00071","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00071","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00071v3","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00071","created_at":"2026-05-18T01:03:19Z"},{"alias_kind":"pith_short_12","alias_value":"YNBWIYX7GMZI","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YNBWIYX7GMZIUZG4","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YNBWIYX7","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:815a18bf89d91f108c91c239f7a077075283ca57605b9a8cbd87707fbd5938d3","target":"graph","created_at":"2026-05-18T01:03:19Z","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 $G\\subseteq GL(n)$ be a finite group without pseudo-reflections. We present an algorithm to compute and verify a candidate for the Cox ring of a resolution $X\\rightarrow \\mathbb{C}^n/G$, which is based just on the geometry of the singularity $\\mathbb{C}^n/G$, without further knowledge of its resolutions. We explain the use of our implementation of the algorithms in Singular. As an application, we determine the Cox rings of resolutions $X\\rightarrow \\mathbb{C}^3/G$ for all $G\\subseteq GL(3)$ with the aforementioned property and of order $|G|\\leq 12$. We also provide examples in dimension 4.","authors_text":"Maria Donten-Bury, Simon Keicher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-02-29T22:07:50Z","title":"Computing resolutions of quotient singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00071","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":"sha256:9bcc280fa6b9115f06742047519c07405801bc63dade9bd10b02e75d544516f5","target":"record","created_at":"2026-05-18T01:03:19Z","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":"b19fcfebf053203254b5e62d2558dfee6d5a1c61cfdf7bfe4d0f0c951270d268","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-02-29T22:07:50Z","title_canon_sha256":"83bdbfb8fa032fb9599bc5861bb2c95916e105c6783cf95e5f5042e6572ffa30"},"schema_version":"1.0","source":{"id":"1603.00071","kind":"arxiv","version":3}},"canonical_sha256":"c3436462ff33328a64dcc42f7b59d1e32b27b5ff26b0dc095432ecadf3b2deaa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3436462ff33328a64dcc42f7b59d1e32b27b5ff26b0dc095432ecadf3b2deaa","first_computed_at":"2026-05-18T01:03:19.652230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:19.652230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0CzBSJpG4Q1O7Xq188mz252GGB0Ocyz2DNbDVpx6qSe5P/quwYvQqG+D10iDBCByvPPixVFmuNCBzFpaU2+IAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:19.652805Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.00071","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bcc280fa6b9115f06742047519c07405801bc63dade9bd10b02e75d544516f5","sha256:815a18bf89d91f108c91c239f7a077075283ca57605b9a8cbd87707fbd5938d3"],"state_sha256":"b711942a843249c7b379389a712a9c13d92c1ffa5b63c8a27353e1fbf798b09a"}