{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:IODFLBFK5AIGCFH44AE5QLHI5L","short_pith_number":"pith:IODFLBFK","schema_version":"1.0","canonical_sha256":"43865584aae8106114fce009d82ce8eacaf4513bb4ec9b327ac698f26dc40754","source":{"kind":"arxiv","id":"1010.4034","version":1},"attestation_state":"computed","paper":{"title":"Roots of the affine Cremona group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alvaro Liendo","submitted_at":"2010-10-19T20:03:40Z","abstract_excerpt":"Let k[x_1,...,x_n] be the polynomial algebra in n variables and let A^n=Spec k[x_1,...,x_n]. In this note we show that the root vectors of the affine Cremona group Aut(A^n) with respect to the diagonal torus are exactly the locally nilpotent derivations x^a\\times d/dx_i, where x^a is any monomial not depending on x_i. This answers a question due to Popov."},"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":"1010.4034","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-19T20:03:40Z","cross_cats_sorted":[],"title_canon_sha256":"81ea1c0699c9e33eb31c57f353702dd5ed61a414328b535660c851ff8c5773b4","abstract_canon_sha256":"794959c23c50ba71e59a94a662f2e05007b59b21d78f9819c8ceef7406bde941"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:43.562997Z","signature_b64":"pb0nV3UeeG26KBtBrHFMBeeBERPIG/JbQwckX21sXMDEi5brwwKiwbhClSL8J5IjKm/2k/SWpkXfQYCom+U6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43865584aae8106114fce009d82ce8eacaf4513bb4ec9b327ac698f26dc40754","last_reissued_at":"2026-05-18T04:03:43.562221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:43.562221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Roots of the affine Cremona group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alvaro Liendo","submitted_at":"2010-10-19T20:03:40Z","abstract_excerpt":"Let k[x_1,...,x_n] be the polynomial algebra in n variables and let A^n=Spec k[x_1,...,x_n]. In this note we show that the root vectors of the affine Cremona group Aut(A^n) with respect to the diagonal torus are exactly the locally nilpotent derivations x^a\\times d/dx_i, where x^a is any monomial not depending on x_i. This answers a question due to Popov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4034","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":"1010.4034","created_at":"2026-05-18T04:03:43.562351+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.4034v1","created_at":"2026-05-18T04:03:43.562351+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4034","created_at":"2026-05-18T04:03:43.562351+00:00"},{"alias_kind":"pith_short_12","alias_value":"IODFLBFK5AIG","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"IODFLBFK5AIGCFH4","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"IODFLBFK","created_at":"2026-05-18T12:26:09.077623+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/IODFLBFK5AIGCFH44AE5QLHI5L","json":"https://pith.science/pith/IODFLBFK5AIGCFH44AE5QLHI5L.json","graph_json":"https://pith.science/api/pith-number/IODFLBFK5AIGCFH44AE5QLHI5L/graph.json","events_json":"https://pith.science/api/pith-number/IODFLBFK5AIGCFH44AE5QLHI5L/events.json","paper":"https://pith.science/paper/IODFLBFK"},"agent_actions":{"view_html":"https://pith.science/pith/IODFLBFK5AIGCFH44AE5QLHI5L","download_json":"https://pith.science/pith/IODFLBFK5AIGCFH44AE5QLHI5L.json","view_paper":"https://pith.science/paper/IODFLBFK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.4034&json=true","fetch_graph":"https://pith.science/api/pith-number/IODFLBFK5AIGCFH44AE5QLHI5L/graph.json","fetch_events":"https://pith.science/api/pith-number/IODFLBFK5AIGCFH44AE5QLHI5L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IODFLBFK5AIGCFH44AE5QLHI5L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IODFLBFK5AIGCFH44AE5QLHI5L/action/storage_attestation","attest_author":"https://pith.science/pith/IODFLBFK5AIGCFH44AE5QLHI5L/action/author_attestation","sign_citation":"https://pith.science/pith/IODFLBFK5AIGCFH44AE5QLHI5L/action/citation_signature","submit_replication":"https://pith.science/pith/IODFLBFK5AIGCFH44AE5QLHI5L/action/replication_record"}},"created_at":"2026-05-18T04:03:43.562351+00:00","updated_at":"2026-05-18T04:03:43.562351+00:00"}