{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MYJUW5WSG3IT24KR2RS4D6HNB4","short_pith_number":"pith:MYJUW5WS","schema_version":"1.0","canonical_sha256":"66134b76d236d13d7151d465c1f8ed0f2b0518dda981b213694e2b9cc5464ccb","source":{"kind":"arxiv","id":"1504.03867","version":5},"attestation_state":"computed","paper":{"title":"Bass' triangulability problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Vladimir L. Popov","submitted_at":"2015-04-15T11:39:20Z","abstract_excerpt":"Exploring Bass' Triangulability Problem on unipotent algebraic subgroups of the affine Cremona groups, we prove a triangulability criterion, the existence of nontriangulable connected solvable affine algebraic subgroups of the Cremona groups, and stable triangulability of such subgroups; in particular, in the stable range we answer Bass' Triangulability Problem is the affirmative. To this end we prove a theorem on invariant subfields of $1$-extensions. We also obtain a general construction of all rationally triangulable subgroups of the Cremona groups and, as an application, classify rationall"},"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":"1504.03867","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-15T11:39:20Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"05b62dd9d203207f1f3965fd348f1111d3b2ece1ab6e88b91c56b94876c09735","abstract_canon_sha256":"5912c74d24b7a51990e57ec01fc4a0b10e13e7af586e025eee554cd73a544819"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:08.039239Z","signature_b64":"fLBWEVR3ySlG2a8mLUcCAuOIFzeRcrYx9NQhkEMNztFQQVVxTNSp7tD45PqcB7T30hicUlQqhtuQim8WZK//CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66134b76d236d13d7151d465c1f8ed0f2b0518dda981b213694e2b9cc5464ccb","last_reissued_at":"2026-05-18T01:30:08.038834Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:08.038834Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bass' triangulability problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Vladimir L. Popov","submitted_at":"2015-04-15T11:39:20Z","abstract_excerpt":"Exploring Bass' Triangulability Problem on unipotent algebraic subgroups of the affine Cremona groups, we prove a triangulability criterion, the existence of nontriangulable connected solvable affine algebraic subgroups of the Cremona groups, and stable triangulability of such subgroups; in particular, in the stable range we answer Bass' Triangulability Problem is the affirmative. To this end we prove a theorem on invariant subfields of $1$-extensions. We also obtain a general construction of all rationally triangulable subgroups of the Cremona groups and, as an application, classify rationall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03867","kind":"arxiv","version":5},"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":"1504.03867","created_at":"2026-05-18T01:30:08.038898+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.03867v5","created_at":"2026-05-18T01:30:08.038898+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03867","created_at":"2026-05-18T01:30:08.038898+00:00"},{"alias_kind":"pith_short_12","alias_value":"MYJUW5WSG3IT","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MYJUW5WSG3IT24KR","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MYJUW5WS","created_at":"2026-05-18T12:29:32.376354+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/MYJUW5WSG3IT24KR2RS4D6HNB4","json":"https://pith.science/pith/MYJUW5WSG3IT24KR2RS4D6HNB4.json","graph_json":"https://pith.science/api/pith-number/MYJUW5WSG3IT24KR2RS4D6HNB4/graph.json","events_json":"https://pith.science/api/pith-number/MYJUW5WSG3IT24KR2RS4D6HNB4/events.json","paper":"https://pith.science/paper/MYJUW5WS"},"agent_actions":{"view_html":"https://pith.science/pith/MYJUW5WSG3IT24KR2RS4D6HNB4","download_json":"https://pith.science/pith/MYJUW5WSG3IT24KR2RS4D6HNB4.json","view_paper":"https://pith.science/paper/MYJUW5WS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.03867&json=true","fetch_graph":"https://pith.science/api/pith-number/MYJUW5WSG3IT24KR2RS4D6HNB4/graph.json","fetch_events":"https://pith.science/api/pith-number/MYJUW5WSG3IT24KR2RS4D6HNB4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MYJUW5WSG3IT24KR2RS4D6HNB4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MYJUW5WSG3IT24KR2RS4D6HNB4/action/storage_attestation","attest_author":"https://pith.science/pith/MYJUW5WSG3IT24KR2RS4D6HNB4/action/author_attestation","sign_citation":"https://pith.science/pith/MYJUW5WSG3IT24KR2RS4D6HNB4/action/citation_signature","submit_replication":"https://pith.science/pith/MYJUW5WSG3IT24KR2RS4D6HNB4/action/replication_record"}},"created_at":"2026-05-18T01:30:08.038898+00:00","updated_at":"2026-05-18T01:30:08.038898+00:00"}