{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UMFECQQPJJBT54SKHTBY3BW6KK","short_pith_number":"pith:UMFECQQP","canonical_record":{"source":{"id":"1408.1373","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-06T18:46:27Z","cross_cats_sorted":[],"title_canon_sha256":"809e71c4968eeb81d329ceed95a975aec3bc15e4c324bf8d63c1a1b909496ed5","abstract_canon_sha256":"bbd3c466f3d80f76fd812bbccfac720965e53161dc0618fc40963ed2b7dc1bc9"},"schema_version":"1.0"},"canonical_sha256":"a30a41420f4a433ef24a3cc38d86de528067a3c0e4a9723bb5b82c6a06c7a909","source":{"kind":"arxiv","id":"1408.1373","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1373","created_at":"2026-05-18T01:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1373v2","created_at":"2026-05-18T01:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1373","created_at":"2026-05-18T01:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"UMFECQQPJJBT","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UMFECQQPJJBT54SK","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UMFECQQP","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UMFECQQPJJBT54SKHTBY3BW6KK","target":"record","payload":{"canonical_record":{"source":{"id":"1408.1373","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-06T18:46:27Z","cross_cats_sorted":[],"title_canon_sha256":"809e71c4968eeb81d329ceed95a975aec3bc15e4c324bf8d63c1a1b909496ed5","abstract_canon_sha256":"bbd3c466f3d80f76fd812bbccfac720965e53161dc0618fc40963ed2b7dc1bc9"},"schema_version":"1.0"},"canonical_sha256":"a30a41420f4a433ef24a3cc38d86de528067a3c0e4a9723bb5b82c6a06c7a909","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:49.416149Z","signature_b64":"OVSWzZgKQlN+Cekg06PWdlPejBKN2lqMFq7Ww2MAZjxXnVYoqtcPSbXAkoGy3FSIFIM5TonrQ9liz5MfKcbsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a30a41420f4a433ef24a3cc38d86de528067a3c0e4a9723bb5b82c6a06c7a909","last_reissued_at":"2026-05-18T01:21:49.415372Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:49.415372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.1373","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":"2026-05-18T01:21:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9G2bpbDtih0yvlrddIASDk5x9tPDHzoa4sxNTL8V7ASsiyWpKL0wK9wW+/zsNV6ePQ3viIQhvaDAs5lO9XeUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:35:20.150230Z"},"content_sha256":"bb69857bc0753b620140e16707ec86346afec4e4f66ce6e15a1e08da8ff2eb35","schema_version":"1.0","event_id":"sha256:bb69857bc0753b620140e16707ec86346afec4e4f66ce6e15a1e08da8ff2eb35"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UMFECQQPJJBT54SKHTBY3BW6KK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Additive group actions on affine T-varieties of complexity one in arbitrary characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alvaro Liendo, Kevin Langlois","submitted_at":"2014-08-06T18:46:27Z","abstract_excerpt":"Let X be a normal affine T-variety of complexity at most one over a perfect field k, where T stands for the split algebraic torus. Our main result is a classification of additive group actions on X that are normalized by the T-action. This generalizes the classification given by the second author in the particular case where k is algebraically closed and of characteristic zero.\n  With the assumption that the characteristic of k is positive, we introduce the notion of rationally homogeneous locally finite iterative higher derivations which corresponds geometrically to additive group actions on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1373","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":"2026-05-18T01:21:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZW2R6pNGt47M+TrMr7tvzS99niffCIUJpcjs8OQdgiYifhlGn/XoxDhGbT0bGBZ5th66zl/UCsaa9/+F6jXvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:35:20.150584Z"},"content_sha256":"25baa775bc66ca37d6456ac481aec0aaeaec48d47371540a15c3c0e40d527d87","schema_version":"1.0","event_id":"sha256:25baa775bc66ca37d6456ac481aec0aaeaec48d47371540a15c3c0e40d527d87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UMFECQQPJJBT54SKHTBY3BW6KK/bundle.json","state_url":"https://pith.science/pith/UMFECQQPJJBT54SKHTBY3BW6KK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UMFECQQPJJBT54SKHTBY3BW6KK/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":"2026-06-02T02:35:20Z","links":{"resolver":"https://pith.science/pith/UMFECQQPJJBT54SKHTBY3BW6KK","bundle":"https://pith.science/pith/UMFECQQPJJBT54SKHTBY3BW6KK/bundle.json","state":"https://pith.science/pith/UMFECQQPJJBT54SKHTBY3BW6KK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UMFECQQPJJBT54SKHTBY3BW6KK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UMFECQQPJJBT54SKHTBY3BW6KK","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":"bbd3c466f3d80f76fd812bbccfac720965e53161dc0618fc40963ed2b7dc1bc9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-06T18:46:27Z","title_canon_sha256":"809e71c4968eeb81d329ceed95a975aec3bc15e4c324bf8d63c1a1b909496ed5"},"schema_version":"1.0","source":{"id":"1408.1373","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1373","created_at":"2026-05-18T01:21:49Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1373v2","created_at":"2026-05-18T01:21:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1373","created_at":"2026-05-18T01:21:49Z"},{"alias_kind":"pith_short_12","alias_value":"UMFECQQPJJBT","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UMFECQQPJJBT54SK","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UMFECQQP","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:25baa775bc66ca37d6456ac481aec0aaeaec48d47371540a15c3c0e40d527d87","target":"graph","created_at":"2026-05-18T01:21:49Z","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 normal affine T-variety of complexity at most one over a perfect field k, where T stands for the split algebraic torus. Our main result is a classification of additive group actions on X that are normalized by the T-action. This generalizes the classification given by the second author in the particular case where k is algebraically closed and of characteristic zero.\n  With the assumption that the characteristic of k is positive, we introduce the notion of rationally homogeneous locally finite iterative higher derivations which corresponds geometrically to additive group actions on ","authors_text":"Alvaro Liendo, Kevin Langlois","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-06T18:46:27Z","title":"Additive group actions on affine T-varieties of complexity one in arbitrary characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1373","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:bb69857bc0753b620140e16707ec86346afec4e4f66ce6e15a1e08da8ff2eb35","target":"record","created_at":"2026-05-18T01:21:49Z","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":"bbd3c466f3d80f76fd812bbccfac720965e53161dc0618fc40963ed2b7dc1bc9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-08-06T18:46:27Z","title_canon_sha256":"809e71c4968eeb81d329ceed95a975aec3bc15e4c324bf8d63c1a1b909496ed5"},"schema_version":"1.0","source":{"id":"1408.1373","kind":"arxiv","version":2}},"canonical_sha256":"a30a41420f4a433ef24a3cc38d86de528067a3c0e4a9723bb5b82c6a06c7a909","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a30a41420f4a433ef24a3cc38d86de528067a3c0e4a9723bb5b82c6a06c7a909","first_computed_at":"2026-05-18T01:21:49.415372Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:49.415372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OVSWzZgKQlN+Cekg06PWdlPejBKN2lqMFq7Ww2MAZjxXnVYoqtcPSbXAkoGy3FSIFIM5TonrQ9liz5MfKcbsAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:49.416149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.1373","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb69857bc0753b620140e16707ec86346afec4e4f66ce6e15a1e08da8ff2eb35","sha256:25baa775bc66ca37d6456ac481aec0aaeaec48d47371540a15c3c0e40d527d87"],"state_sha256":"e144dc00035cbcbccf9d30975f95255b1dc49e26272f1029de6a5f1a42b4e029"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Vz01CZUzBNz75zrQhm8oaqbCaFaONFTbkdTzZtDEa5rt6pAXVVNlpyH70kF6zwAgFd8FTWEYwrc0qQ+ti/FDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:35:20.152433Z","bundle_sha256":"a3c22bef260d347a3f27b9efa23c19bbbaf111dfe0d43fa1db14406e623e6bff"}}