{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IOCNIYJ453KDVMS2AGIXP3AJTS","short_pith_number":"pith:IOCNIYJ4","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"},"canonical_sha256":"4384d4613ceed43ab25a019177ec099cb7f50cbc9e832b7540b6d17ed95f3d01","source":{"kind":"arxiv","id":"1003.1125","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1125","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1125v1","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1125","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"IOCNIYJ453KD","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IOCNIYJ453KDVMS2","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IOCNIYJ4","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IOCNIYJ453KDVMS2AGIXP3AJTS","target":"record","payload":{"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"},"canonical_sha256":"4384d4613ceed43ab25a019177ec099cb7f50cbc9e832b7540b6d17ed95f3d01","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"},"source_kind":"arxiv","source_id":"1003.1125","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kdaOrG787V/dRwiTiwCoDNFiI5KpaBWXbw1x9B814XZKlt0xtbbXvgtfEhWV+r9Vzi4+i9Oya5OC4fqSSDIqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:37:59.962343Z"},"content_sha256":"a005065ab4c9f84c60c199d3a4ef62900771e3153dba93799e9a141c633bd981","schema_version":"1.0","event_id":"sha256:a005065ab4c9f84c60c199d3a4ef62900771e3153dba93799e9a141c633bd981"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IOCNIYJ453KDVMS2AGIXP3AJTS","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:11:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8D4KGqb7cPifxIWnl4xoHNeZdZyQ3a7PanuDlHyPggCI5qR/KrKOUSw6tT9LvdtGSCyb5IGEl/rzdmpYNgXxDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:37:59.963054Z"},"content_sha256":"6afdea0b0ce574e3abc6e0c1d815d5bbf057f88877868b839e700d2ffbd8a4e0","schema_version":"1.0","event_id":"sha256:6afdea0b0ce574e3abc6e0c1d815d5bbf057f88877868b839e700d2ffbd8a4e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IOCNIYJ453KDVMS2AGIXP3AJTS/bundle.json","state_url":"https://pith.science/pith/IOCNIYJ453KDVMS2AGIXP3AJTS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IOCNIYJ453KDVMS2AGIXP3AJTS/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":"2026-06-09T08:37:59Z","links":{"resolver":"https://pith.science/pith/IOCNIYJ453KDVMS2AGIXP3AJTS","bundle":"https://pith.science/pith/IOCNIYJ453KDVMS2AGIXP3AJTS/bundle.json","state":"https://pith.science/pith/IOCNIYJ453KDVMS2AGIXP3AJTS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IOCNIYJ453KDVMS2AGIXP3AJTS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IOCNIYJ453KDVMS2AGIXP3AJTS","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":"aefae46ac82d4172307c6f49ff9a4527a38e83bd6f54827e27da0adfe615cfcf","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-03-04T20:57:57Z","title_canon_sha256":"78ab7195105fc889849a34370a258303ae2baa550bf65ab7c8024954d681bc14"},"schema_version":"1.0","source":{"id":"1003.1125","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.1125","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"arxiv_version","alias_value":"1003.1125v1","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.1125","created_at":"2026-05-18T01:11:55Z"},{"alias_kind":"pith_short_12","alias_value":"IOCNIYJ453KD","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IOCNIYJ453KDVMS2","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IOCNIYJ4","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:6afdea0b0ce574e3abc6e0c1d815d5bbf057f88877868b839e700d2ffbd8a4e0","target":"graph","created_at":"2026-05-18T01:11:55Z","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":"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.","authors_text":"Laurent Bartholdi","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-03-04T20:57:57Z","title":"Self-similar Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.1125","kind":"arxiv","version":1},"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:a005065ab4c9f84c60c199d3a4ef62900771e3153dba93799e9a141c633bd981","target":"record","created_at":"2026-05-18T01:11:55Z","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":"aefae46ac82d4172307c6f49ff9a4527a38e83bd6f54827e27da0adfe615cfcf","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-03-04T20:57:57Z","title_canon_sha256":"78ab7195105fc889849a34370a258303ae2baa550bf65ab7c8024954d681bc14"},"schema_version":"1.0","source":{"id":"1003.1125","kind":"arxiv","version":1}},"canonical_sha256":"4384d4613ceed43ab25a019177ec099cb7f50cbc9e832b7540b6d17ed95f3d01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4384d4613ceed43ab25a019177ec099cb7f50cbc9e832b7540b6d17ed95f3d01","first_computed_at":"2026-05-18T01:11:55.606954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:55.606954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kj63qv1eCrhJcuazuSyMuy/NeFFKCLLuIHEbz5wOdfSiW3jXlZfRxcwLLxSMmjtn1uEzcSja6kQiQYkZDRxKCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:55.607282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.1125","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a005065ab4c9f84c60c199d3a4ef62900771e3153dba93799e9a141c633bd981","sha256:6afdea0b0ce574e3abc6e0c1d815d5bbf057f88877868b839e700d2ffbd8a4e0"],"state_sha256":"325f0d821102d4ed76eeae91b39cafa81ddb4ddb22780b302ed2f8d66ffd81a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gIeRotzbqOv2oEC6YijaAVWcCsThsSJZ5BohwIT8hfG/TwZbld4bqkkoC8sX1yMZy9AVrjWhEiVEoiiT+DIOCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:37:59.967115Z","bundle_sha256":"b2ee21677fcb1d150e41b9d69552ed001ac690104633f0595298fbdf43aa2ee3"}}