{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:M7YZ7YUO6ZZAHBX5KNWO3NZVNQ","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":"2860dba0125bc4e279915cb7eacd4c7fbf38f516b8a0c3159b211a2bfa814c87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-12-03T20:36:21Z","title_canon_sha256":"7fbc92b2001f9b06c152e3376fb17a62b87b0e8db005e3753cce4f5036a1f629"},"schema_version":"1.0","source":{"id":"0812.0802","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.0802","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"arxiv_version","alias_value":"0812.0802v2","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0802","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"pith_short_12","alias_value":"M7YZ7YUO6ZZA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"M7YZ7YUO6ZZAHBX5","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"M7YZ7YUO","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:aa87f2981df66e29129e633f8dbc16687f32ba73417101af1f65df399c0b29b6","target":"graph","created_at":"2026-05-18T02:24:56Z","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 X=spec A be a normal affine variety over an algebraically closed field k of characteristic 0 endowed with an effective action of a torus T of dimension n. Let also D be a homogeneous locally nilpotent derivation on the normal affine Z^n-graded domain A, so that D generates a k_+-action on X that is normalized by the T-action. We provide a complete classification of pairs (X,D) in two cases: for toric varieties (n=\\dim X) and in the case where n=\\dim X-1. This generalizes previously known results for surfaces due to Flenner and Zaidenberg. As an application we compute the homogeneous Makar-","authors_text":"Alvaro Liendo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-12-03T20:36:21Z","title":"Affine T-varieties of complexity one and locally nilpotent derivations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0802","kind":"arxiv","version":2},"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":"sha256:1cf6cccd9eb3716da2346901e471b996b07540522e76a63fcdaaef8f6abf5bdc","target":"record","created_at":"2026-05-18T02:24:56Z","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":"2860dba0125bc4e279915cb7eacd4c7fbf38f516b8a0c3159b211a2bfa814c87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-12-03T20:36:21Z","title_canon_sha256":"7fbc92b2001f9b06c152e3376fb17a62b87b0e8db005e3753cce4f5036a1f629"},"schema_version":"1.0","source":{"id":"0812.0802","kind":"arxiv","version":2}},"canonical_sha256":"67f19fe28ef6720386fd536cedb7356c25ec50f9a339d5f5c91e3fd389d77ccd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67f19fe28ef6720386fd536cedb7356c25ec50f9a339d5f5c91e3fd389d77ccd","first_computed_at":"2026-05-18T02:24:56.750931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:56.750931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"52XgULoA1RL0Xg+7IkHlb2WP+dH/iEo1R4EI6/uSGUvHMazDhGriBq0slcV5CwJrN5JVPpEo2UYNxJxVUo0KCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:56.751627Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.0802","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cf6cccd9eb3716da2346901e471b996b07540522e76a63fcdaaef8f6abf5bdc","sha256:aa87f2981df66e29129e633f8dbc16687f32ba73417101af1f65df399c0b29b6"],"state_sha256":"80db63de718d862bd2cf994628716962d50b2803b293e5ccd5fa59b2d5ea0c63"}