{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:N4EJ23CDHVT5ADMBZP2DPTVRXE","short_pith_number":"pith:N4EJ23CD","canonical_record":{"source":{"id":"1411.2480","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-10T16:02:56Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"69288877636894026d78521141295817b85427919692c964ab539c0d27631e17","abstract_canon_sha256":"6c66f615417dcf454affe6a91e47032cb47e3d9f96bb264e382dcd60a4ebd605"},"schema_version":"1.0"},"canonical_sha256":"6f089d6c433d67d00d81cbf437ceb1b92784f81da4856d24491ff0c1435c3b56","source":{"kind":"arxiv","id":"1411.2480","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2480","created_at":"2026-05-18T01:37:28Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2480v2","created_at":"2026-05-18T01:37:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2480","created_at":"2026-05-18T01:37:28Z"},{"alias_kind":"pith_short_12","alias_value":"N4EJ23CDHVT5","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N4EJ23CDHVT5ADMB","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N4EJ23CD","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:N4EJ23CDHVT5ADMBZP2DPTVRXE","target":"record","payload":{"canonical_record":{"source":{"id":"1411.2480","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-10T16:02:56Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"69288877636894026d78521141295817b85427919692c964ab539c0d27631e17","abstract_canon_sha256":"6c66f615417dcf454affe6a91e47032cb47e3d9f96bb264e382dcd60a4ebd605"},"schema_version":"1.0"},"canonical_sha256":"6f089d6c433d67d00d81cbf437ceb1b92784f81da4856d24491ff0c1435c3b56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:28.575412Z","signature_b64":"lJJH5X5/Y56rFIEOAdP0FwEol1s3hKZUwECYp2Rz3TvXyQiXD3ZaQf9f9zO9z/gwpy6GZVarz5m72KFUIZWdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f089d6c433d67d00d81cbf437ceb1b92784f81da4856d24491ff0c1435c3b56","last_reissued_at":"2026-05-18T01:37:28.574617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:28.574617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.2480","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rFR3K8pFoNsntPJkoGw6nsvva9Yi43VQJ6w6dtwy1qu468WylVCEjkNW/b9QS5jiQ3/6S1fxgt7wTOLXQZn0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:34:48.333421Z"},"content_sha256":"5d9f83d4389d91367d41ac7d0b76592283aaa26b96dade10d620baeebc71062e","schema_version":"1.0","event_id":"sha256:5d9f83d4389d91367d41ac7d0b76592283aaa26b96dade10d620baeebc71062e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:N4EJ23CDHVT5ADMBZP2DPTVRXE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the geometry of normal horospherical G-varieties of complexity one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Kevin Langlois, Ronan Terpereau","submitted_at":"2014-11-10T16:02:56Z","abstract_excerpt":"Let G be a connected simply-connected reductive algebraic group. In this article, we consider the normal algebraic varieties equipped with a horospherical G-action such that the quotient of a G-stable open subset is a curve. Let X be such a G-variety. Using the combinatorial description of Timashev, we describe the class group of X by generators and relations and we give a representative of the canonical class. Moreover, we obtain a smoothness criterion for X and a criterion to determine whether the singularities of X are rational or log-terminal respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2480","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"461k+sRrsBI4ILgQf1e2tmlFyDV8pFLbqmoPKnZHfe47dP18UmLSSC4A5OeTMSzgUJ2kpwVLjEIZLcDLZWEdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:34:48.334011Z"},"content_sha256":"96601efbdae7b79682d273bf4b90ce47a574e2d293c2f6ce52a97523ae834665","schema_version":"1.0","event_id":"sha256:96601efbdae7b79682d273bf4b90ce47a574e2d293c2f6ce52a97523ae834665"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N4EJ23CDHVT5ADMBZP2DPTVRXE/bundle.json","state_url":"https://pith.science/pith/N4EJ23CDHVT5ADMBZP2DPTVRXE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N4EJ23CDHVT5ADMBZP2DPTVRXE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T19:34:48Z","links":{"resolver":"https://pith.science/pith/N4EJ23CDHVT5ADMBZP2DPTVRXE","bundle":"https://pith.science/pith/N4EJ23CDHVT5ADMBZP2DPTVRXE/bundle.json","state":"https://pith.science/pith/N4EJ23CDHVT5ADMBZP2DPTVRXE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N4EJ23CDHVT5ADMBZP2DPTVRXE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:N4EJ23CDHVT5ADMBZP2DPTVRXE","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":"6c66f615417dcf454affe6a91e47032cb47e3d9f96bb264e382dcd60a4ebd605","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-10T16:02:56Z","title_canon_sha256":"69288877636894026d78521141295817b85427919692c964ab539c0d27631e17"},"schema_version":"1.0","source":{"id":"1411.2480","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2480","created_at":"2026-05-18T01:37:28Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2480v2","created_at":"2026-05-18T01:37:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2480","created_at":"2026-05-18T01:37:28Z"},{"alias_kind":"pith_short_12","alias_value":"N4EJ23CDHVT5","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"N4EJ23CDHVT5ADMB","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"N4EJ23CD","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:96601efbdae7b79682d273bf4b90ce47a574e2d293c2f6ce52a97523ae834665","target":"graph","created_at":"2026-05-18T01:37:28Z","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 be a connected simply-connected reductive algebraic group. In this article, we consider the normal algebraic varieties equipped with a horospherical G-action such that the quotient of a G-stable open subset is a curve. Let X be such a G-variety. Using the combinatorial description of Timashev, we describe the class group of X by generators and relations and we give a representative of the canonical class. Moreover, we obtain a smoothness criterion for X and a criterion to determine whether the singularities of X are rational or log-terminal respectively.","authors_text":"Kevin Langlois, Ronan Terpereau","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-10T16:02:56Z","title":"On the geometry of normal horospherical G-varieties of complexity one"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2480","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":"sha256:5d9f83d4389d91367d41ac7d0b76592283aaa26b96dade10d620baeebc71062e","target":"record","created_at":"2026-05-18T01:37:28Z","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":"6c66f615417dcf454affe6a91e47032cb47e3d9f96bb264e382dcd60a4ebd605","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-11-10T16:02:56Z","title_canon_sha256":"69288877636894026d78521141295817b85427919692c964ab539c0d27631e17"},"schema_version":"1.0","source":{"id":"1411.2480","kind":"arxiv","version":2}},"canonical_sha256":"6f089d6c433d67d00d81cbf437ceb1b92784f81da4856d24491ff0c1435c3b56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f089d6c433d67d00d81cbf437ceb1b92784f81da4856d24491ff0c1435c3b56","first_computed_at":"2026-05-18T01:37:28.574617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:28.574617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lJJH5X5/Y56rFIEOAdP0FwEol1s3hKZUwECYp2Rz3TvXyQiXD3ZaQf9f9zO9z/gwpy6GZVarz5m72KFUIZWdBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:28.575412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2480","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d9f83d4389d91367d41ac7d0b76592283aaa26b96dade10d620baeebc71062e","sha256:96601efbdae7b79682d273bf4b90ce47a574e2d293c2f6ce52a97523ae834665"],"state_sha256":"4ec68c8d138132a23558e7a9f5aa15c743169ffebc23e55e09c183b00aef5928"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BoF6+yDmwXVjmuN9V3DE8AT/QtcKgXiWGw9iRoJLRpIa/8i5xSYW+5RHhEjGc3w3x3/SZcHmRsM7zG59ky8rAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:34:48.336242Z","bundle_sha256":"eea1b25480fbe1cab7d65695a7ac83df28e3dbe136cfbbda49a59cb09c120ab5"}}