{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MP7O6VMYZ7YMFUWMILZR4YW6IZ","short_pith_number":"pith:MP7O6VMY","schema_version":"1.0","canonical_sha256":"63feef5598cff0c2d2cc42f31e62de4648841839a12b3b12a4fff1d8acd82914","source":{"kind":"arxiv","id":"1303.1032","version":1},"attestation_state":"computed","paper":{"title":"Proper triangular Ga-actions on A^4 are translations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Adrien Dubouloz (IMB), David Finston, Imad Jaradat","submitted_at":"2013-03-05T13:42:15Z","abstract_excerpt":"We describe the structure of geometric quotients for proper locally triangulable additve group actions on locally trivial A^3-bundles over a noetherian normal base scheme X defined over a field of characteristic 0. In the case where dim X=1, we show in particular that every such action is a translation with geometric quotient isomorphic to the total space of a vector bundle of rank 2 over X. As a consequence, every proper triangulable Ga-action on the affine four space A^4 over a field of characteristic 0 is a translation with geometric quotient isomorphic to A^3."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1303.1032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-03-05T13:42:15Z","cross_cats_sorted":[],"title_canon_sha256":"5b9539c85829997b3c9cfad27f3710379c0584ee9303a0db4e347b8b0325bfb8","abstract_canon_sha256":"9fbd75837c2d4b309ccb9fbf12962add4bf56147c42ce23bad2c4068cf76ce86"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:25.630556Z","signature_b64":"kVemdFehxNMSsso+SEzuuW/jjs95bvdRYZyjYeJ30JN+R0fAnCWAEfevb+Qr/sEU3pOWIcAB8on+fJMNbQrnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63feef5598cff0c2d2cc42f31e62de4648841839a12b3b12a4fff1d8acd82914","last_reissued_at":"2026-05-18T01:22:25.629854Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:25.629854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proper triangular Ga-actions on A^4 are translations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Adrien Dubouloz (IMB), David Finston, Imad Jaradat","submitted_at":"2013-03-05T13:42:15Z","abstract_excerpt":"We describe the structure of geometric quotients for proper locally triangulable additve group actions on locally trivial A^3-bundles over a noetherian normal base scheme X defined over a field of characteristic 0. In the case where dim X=1, we show in particular that every such action is a translation with geometric quotient isomorphic to the total space of a vector bundle of rank 2 over X. As a consequence, every proper triangulable Ga-action on the affine four space A^4 over a field of characteristic 0 is a translation with geometric quotient isomorphic to A^3."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1032","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.1032","created_at":"2026-05-18T01:22:25.629973+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.1032v1","created_at":"2026-05-18T01:22:25.629973+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1032","created_at":"2026-05-18T01:22:25.629973+00:00"},{"alias_kind":"pith_short_12","alias_value":"MP7O6VMYZ7YM","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"MP7O6VMYZ7YMFUWM","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"MP7O6VMY","created_at":"2026-05-18T12:27:52.871228+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MP7O6VMYZ7YMFUWMILZR4YW6IZ","json":"https://pith.science/pith/MP7O6VMYZ7YMFUWMILZR4YW6IZ.json","graph_json":"https://pith.science/api/pith-number/MP7O6VMYZ7YMFUWMILZR4YW6IZ/graph.json","events_json":"https://pith.science/api/pith-number/MP7O6VMYZ7YMFUWMILZR4YW6IZ/events.json","paper":"https://pith.science/paper/MP7O6VMY"},"agent_actions":{"view_html":"https://pith.science/pith/MP7O6VMYZ7YMFUWMILZR4YW6IZ","download_json":"https://pith.science/pith/MP7O6VMYZ7YMFUWMILZR4YW6IZ.json","view_paper":"https://pith.science/paper/MP7O6VMY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.1032&json=true","fetch_graph":"https://pith.science/api/pith-number/MP7O6VMYZ7YMFUWMILZR4YW6IZ/graph.json","fetch_events":"https://pith.science/api/pith-number/MP7O6VMYZ7YMFUWMILZR4YW6IZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MP7O6VMYZ7YMFUWMILZR4YW6IZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MP7O6VMYZ7YMFUWMILZR4YW6IZ/action/storage_attestation","attest_author":"https://pith.science/pith/MP7O6VMYZ7YMFUWMILZR4YW6IZ/action/author_attestation","sign_citation":"https://pith.science/pith/MP7O6VMYZ7YMFUWMILZR4YW6IZ/action/citation_signature","submit_replication":"https://pith.science/pith/MP7O6VMYZ7YMFUWMILZR4YW6IZ/action/replication_record"}},"created_at":"2026-05-18T01:22:25.629973+00:00","updated_at":"2026-05-18T01:22:25.629973+00:00"}