{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4RF4HHWH7ZTKOJC5KXFJHTNMBD","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":"f35b26cec1f7303c1f5d8b0d79e9390592b073665c82575ee8a5a04b9f3f5b17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-02T17:07:16Z","title_canon_sha256":"51fe16930b438d864662cc43a5b3223bea8eb6def5ada9d6fc62fb7f9ad2a1cd"},"schema_version":"1.0","source":{"id":"1009.0478","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0478","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0478v1","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0478","created_at":"2026-05-18T03:43:05Z"},{"alias_kind":"pith_short_12","alias_value":"4RF4HHWH7ZTK","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"4RF4HHWH7ZTKOJC5","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"4RF4HHWH","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:ce499c1e982152816e87ea3b5e07d38a46e046285c1c9d3a44130e94af024490","target":"graph","created_at":"2026-05-18T03:43:05Z","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 be a Mori dream space together with an effective torus action of complexity one. In this note, we construct a polyhedral divisor on a suitable covering of the projective line P^1 which corresponds to the affine spectrum of the Cox ring of X. This description allows for a detailed study of torus orbits and deformations of the latter. Moreover, we present coverings of P^1 together with an action of a finite abelian group A in terms of so-called A-divisors of degree zero on P^1.","authors_text":"Klaus Altmann, Lars Petersen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-02T17:07:16Z","title":"Cox rings of rational complexity one T-varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0478","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:fabd7738ae80dae561e01cac093bc06a9e38b9fe31567336d5e667456773a51d","target":"record","created_at":"2026-05-18T03:43:05Z","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":"f35b26cec1f7303c1f5d8b0d79e9390592b073665c82575ee8a5a04b9f3f5b17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-02T17:07:16Z","title_canon_sha256":"51fe16930b438d864662cc43a5b3223bea8eb6def5ada9d6fc62fb7f9ad2a1cd"},"schema_version":"1.0","source":{"id":"1009.0478","kind":"arxiv","version":1}},"canonical_sha256":"e44bc39ec7fe66a7245d55ca93cdac08c49ca9cfea156dfebf42e5def1e19d56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e44bc39ec7fe66a7245d55ca93cdac08c49ca9cfea156dfebf42e5def1e19d56","first_computed_at":"2026-05-18T03:43:05.465736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:05.465736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PjW17xw68Q/QfIWwWbFr5HqfM/bBtExgZHkWpOfHyS7flO9jnFspIuSOi3DWcNBNXMDLViZVqbeftm2uXXgMBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:05.466444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0478","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fabd7738ae80dae561e01cac093bc06a9e38b9fe31567336d5e667456773a51d","sha256:ce499c1e982152816e87ea3b5e07d38a46e046285c1c9d3a44130e94af024490"],"state_sha256":"efd33d1be43ae0dbeb1c5eb15c2b23008abf69d8d44a577edaa8ab313baa8215"}