{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:A45JPGEGJ2G75TJZW7DMOBUQZO","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":"4e7d6ed78fd1c8ff4b53a1c93949d137ddf28557e86c62d6d658d33605dc0a6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-27T08:01:54Z","title_canon_sha256":"ba1347a5a4b04706aad3683dddb98ef440b1b5ef6ce4e7ccb01cf3b3cc99295e"},"schema_version":"1.0","source":{"id":"1707.08768","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.08768","created_at":"2026-05-18T00:39:19Z"},{"alias_kind":"arxiv_version","alias_value":"1707.08768v1","created_at":"2026-05-18T00:39:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08768","created_at":"2026-05-18T00:39:19Z"},{"alias_kind":"pith_short_12","alias_value":"A45JPGEGJ2G7","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"A45JPGEGJ2G75TJZ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"A45JPGEG","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:44efdb499cec2d8bdc8ec77caeb9cc89d435d9cf1566b603ba2dc93f9809e18c","target":"graph","created_at":"2026-05-18T00:39:19Z","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":"Motivated by the study of the structure of algebraic actions the additive group on affine threefolds X, we consider a special class of such varieties whose algebraic quotient morphisms X $\\rightarrow$ X//Ga restrict to principal homogeneous bundles over the complement of a smooth point of the quotient. We establish basic general properties of these varieties and construct families of examples illustrating their rich geometry. In particular, we give a complete classification of a natural subclass consisting of threefolds X endowed with proper Ga-actions, whose algebraic quotient morphisms $\\pi$","authors_text":"Adrien Dubouloz (IMB), Isac Hed\\'en (RIMS), Takashi Kishimoto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-27T08:01:54Z","title":"Equivariant extensions of Ga-torsors over punctured surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08768","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":"sha256:395084e866331906961fbacaa58ebcefde7c0f5db6506bf0ad70cd3140e2321f","target":"record","created_at":"2026-05-18T00:39:19Z","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":"4e7d6ed78fd1c8ff4b53a1c93949d137ddf28557e86c62d6d658d33605dc0a6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-27T08:01:54Z","title_canon_sha256":"ba1347a5a4b04706aad3683dddb98ef440b1b5ef6ce4e7ccb01cf3b3cc99295e"},"schema_version":"1.0","source":{"id":"1707.08768","kind":"arxiv","version":1}},"canonical_sha256":"073a9798864e8dfecd39b7c6c70690cb96b6ad062b50dc513ab734dacf879b1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"073a9798864e8dfecd39b7c6c70690cb96b6ad062b50dc513ab734dacf879b1c","first_computed_at":"2026-05-18T00:39:19.534014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:19.534014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NxWhYWExBzkczQaR7sNwtHDMJfElr1wZ/1hfYRzzAwLVC5xwWvvB1Bz3LYo3c7U+TB2a4s2rFZDw0OuDQyF5BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:19.534661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.08768","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:395084e866331906961fbacaa58ebcefde7c0f5db6506bf0ad70cd3140e2321f","sha256:44efdb499cec2d8bdc8ec77caeb9cc89d435d9cf1566b603ba2dc93f9809e18c"],"state_sha256":"56b1fdc902850d56a35bb6eaa4526c5fb038c64cb98d42a813e2cae719afda49"}