{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:IOCNIYJ453KDVMS2AGIXP3AJTS","short_pith_number":"pith:IOCNIYJ4","schema_version":"1.0","canonical_sha256":"4384d4613ceed43ab25a019177ec099cb7f50cbc9e832b7540b6d17ed95f3d01","source":{"kind":"arxiv","id":"1003.1125","version":1},"attestation_state":"computed","paper":{"title":"Self-similar Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Laurent Bartholdi","submitted_at":"2010-03-04T20:57:57Z","abstract_excerpt":"We give a general definition of self-similar Lie algebras, and show that important examples of Lie algebras fall into that class. We give sufficient conditions for a self-similar Lie algebra to be nil, and prove in this manner that the self-similar algebras associated with Grigorchuk's and Gupta-Sidki's torsion groups are nil as well as self-similar. We derive the same results for a class of examples constructed by Petrogradsky, Shestakov and Zelmanov."},"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":"1003.1125","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-03-04T20:57:57Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"78ab7195105fc889849a34370a258303ae2baa550bf65ab7c8024954d681bc14","abstract_canon_sha256":"aefae46ac82d4172307c6f49ff9a4527a38e83bd6f54827e27da0adfe615cfcf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:55.607282Z","signature_b64":"Kj63qv1eCrhJcuazuSyMuy/NeFFKCLLuIHEbz5wOdfSiW3jXlZfRxcwLLxSMmjtn1uEzcSja6kQiQYkZDRxKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4384d4613ceed43ab25a019177ec099cb7f50cbc9e832b7540b6d17ed95f3d01","last_reissued_at":"2026-05-18T01:11:55.606954Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:55.606954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-similar Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Laurent Bartholdi","submitted_at":"2010-03-04T20:57:57Z","abstract_excerpt":"We give a general definition of self-similar Lie algebras, and show that important examples of Lie algebras fall into that class. We give sufficient conditions for a self-similar Lie algebra to be nil, and prove in this manner that the self-similar algebras associated with Grigorchuk's and Gupta-Sidki's torsion groups are nil as well as self-similar. We derive the same results for a class of examples constructed by Petrogradsky, Shestakov and Zelmanov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1125","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":"1003.1125","created_at":"2026-05-18T01:11:55.607009+00:00"},{"alias_kind":"arxiv_version","alias_value":"1003.1125v1","created_at":"2026-05-18T01:11:55.607009+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1125","created_at":"2026-05-18T01:11:55.607009+00:00"},{"alias_kind":"pith_short_12","alias_value":"IOCNIYJ453KD","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"IOCNIYJ453KDVMS2","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"IOCNIYJ4","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/IOCNIYJ453KDVMS2AGIXP3AJTS","json":"https://pith.science/pith/IOCNIYJ453KDVMS2AGIXP3AJTS.json","graph_json":"https://pith.science/api/pith-number/IOCNIYJ453KDVMS2AGIXP3AJTS/graph.json","events_json":"https://pith.science/api/pith-number/IOCNIYJ453KDVMS2AGIXP3AJTS/events.json","paper":"https://pith.science/paper/IOCNIYJ4"},"agent_actions":{"view_html":"https://pith.science/pith/IOCNIYJ453KDVMS2AGIXP3AJTS","download_json":"https://pith.science/pith/IOCNIYJ453KDVMS2AGIXP3AJTS.json","view_paper":"https://pith.science/paper/IOCNIYJ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1003.1125&json=true","fetch_graph":"https://pith.science/api/pith-number/IOCNIYJ453KDVMS2AGIXP3AJTS/graph.json","fetch_events":"https://pith.science/api/pith-number/IOCNIYJ453KDVMS2AGIXP3AJTS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IOCNIYJ453KDVMS2AGIXP3AJTS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IOCNIYJ453KDVMS2AGIXP3AJTS/action/storage_attestation","attest_author":"https://pith.science/pith/IOCNIYJ453KDVMS2AGIXP3AJTS/action/author_attestation","sign_citation":"https://pith.science/pith/IOCNIYJ453KDVMS2AGIXP3AJTS/action/citation_signature","submit_replication":"https://pith.science/pith/IOCNIYJ453KDVMS2AGIXP3AJTS/action/replication_record"}},"created_at":"2026-05-18T01:11:55.607009+00:00","updated_at":"2026-05-18T01:11:55.607009+00:00"}