{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OWXVVU6GZVSEPZCQCR6JP6GOBM","short_pith_number":"pith:OWXVVU6G","canonical_record":{"source":{"id":"1405.6288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-24T10:21:29Z","cross_cats_sorted":[],"title_canon_sha256":"202639f6d6c43801b4f13adbdf35adf2aa3b045c5a0968716912cd26bcaaa9a8","abstract_canon_sha256":"807d1fb6d98305a45fd3f5aeb270ad5d4b0681b8e7dab5ad72b2dfa076ca716d"},"schema_version":"1.0"},"canonical_sha256":"75af5ad3c6cd6447e450147c97f8ce0b3f8e270f3f1477242b9e477f6257a30a","source":{"kind":"arxiv","id":"1405.6288","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6288","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6288v1","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6288","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"pith_short_12","alias_value":"OWXVVU6GZVSE","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OWXVVU6GZVSEPZCQ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OWXVVU6G","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OWXVVU6GZVSEPZCQCR6JP6GOBM","target":"record","payload":{"canonical_record":{"source":{"id":"1405.6288","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-24T10:21:29Z","cross_cats_sorted":[],"title_canon_sha256":"202639f6d6c43801b4f13adbdf35adf2aa3b045c5a0968716912cd26bcaaa9a8","abstract_canon_sha256":"807d1fb6d98305a45fd3f5aeb270ad5d4b0681b8e7dab5ad72b2dfa076ca716d"},"schema_version":"1.0"},"canonical_sha256":"75af5ad3c6cd6447e450147c97f8ce0b3f8e270f3f1477242b9e477f6257a30a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:07.590575Z","signature_b64":"J9nNWO657iqqrhKRP7rkmBXnvOAn+pJ5L0ge5yCBFjU4QkmqguB72NZqdcHguUsdEE1Tf7SMwu5jA8WkgSKiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75af5ad3c6cd6447e450147c97f8ce0b3f8e270f3f1477242b9e477f6257a30a","last_reissued_at":"2026-05-18T02:51:07.589987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:07.589987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.6288","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":"2026-05-18T02:51:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rfB+MMXDyCIinybtgqxBZyo+/nvHmnMnCK3owSu3zUXTwNzcEvVzTcbETng/CtOLcL5YJ8Ly+eD0t0ADYO48AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T03:59:33.258759Z"},"content_sha256":"b9c918b77f6f5f64a5180728ba197419df75a88b2e2ee0a6b7108d3251638747","schema_version":"1.0","event_id":"sha256:b9c918b77f6f5f64a5180728ba197419df75a88b2e2ee0a6b7108d3251638747"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OWXVVU6GZVSEPZCQCR6JP6GOBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper central series for the group of unitriangular automorphisms of a free associative algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Mikhail V. Neshchadim, Valeriy G. Bardakov","submitted_at":"2014-05-24T10:21:29Z","abstract_excerpt":"We study some subgroups of the group of unitriangular automorphisms $U_n$ of a free associative algebra over a field of characteristic zero. We find the center of $U_n$ and describe the hypercenters of $U_2$ and $U_3$. In particular, we prove that the upper central series for $U_2$ has infinite length. As consequence, we prove that the groups $U_n$ are non-linear for all $n \\geq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6288","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":"2026-05-18T02:51:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m7OZ8Qs+3ttJxrd1/9kTKg/dWtOHVTOlu7JdU5tLZ2FIazMpK4Dd8aUzkezDZcOGt5RjFf3MqNOvF812IRRtCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T03:59:33.259441Z"},"content_sha256":"843f1939c8793070563e69e3aa1126512cacc57dcac44a73ef07bebbaccc85d9","schema_version":"1.0","event_id":"sha256:843f1939c8793070563e69e3aa1126512cacc57dcac44a73ef07bebbaccc85d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OWXVVU6GZVSEPZCQCR6JP6GOBM/bundle.json","state_url":"https://pith.science/pith/OWXVVU6GZVSEPZCQCR6JP6GOBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OWXVVU6GZVSEPZCQCR6JP6GOBM/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":"2026-06-06T03:59:33Z","links":{"resolver":"https://pith.science/pith/OWXVVU6GZVSEPZCQCR6JP6GOBM","bundle":"https://pith.science/pith/OWXVVU6GZVSEPZCQCR6JP6GOBM/bundle.json","state":"https://pith.science/pith/OWXVVU6GZVSEPZCQCR6JP6GOBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OWXVVU6GZVSEPZCQCR6JP6GOBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OWXVVU6GZVSEPZCQCR6JP6GOBM","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":"807d1fb6d98305a45fd3f5aeb270ad5d4b0681b8e7dab5ad72b2dfa076ca716d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-24T10:21:29Z","title_canon_sha256":"202639f6d6c43801b4f13adbdf35adf2aa3b045c5a0968716912cd26bcaaa9a8"},"schema_version":"1.0","source":{"id":"1405.6288","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6288","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6288v1","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6288","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"pith_short_12","alias_value":"OWXVVU6GZVSE","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OWXVVU6GZVSEPZCQ","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OWXVVU6G","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:843f1939c8793070563e69e3aa1126512cacc57dcac44a73ef07bebbaccc85d9","target":"graph","created_at":"2026-05-18T02:51:07Z","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 study some subgroups of the group of unitriangular automorphisms $U_n$ of a free associative algebra over a field of characteristic zero. We find the center of $U_n$ and describe the hypercenters of $U_2$ and $U_3$. In particular, we prove that the upper central series for $U_2$ has infinite length. As consequence, we prove that the groups $U_n$ are non-linear for all $n \\geq 2$.","authors_text":"Mikhail V. Neshchadim, Valeriy G. Bardakov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-24T10:21:29Z","title":"Upper central series for the group of unitriangular automorphisms of a free associative algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6288","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:b9c918b77f6f5f64a5180728ba197419df75a88b2e2ee0a6b7108d3251638747","target":"record","created_at":"2026-05-18T02:51:07Z","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":"807d1fb6d98305a45fd3f5aeb270ad5d4b0681b8e7dab5ad72b2dfa076ca716d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-05-24T10:21:29Z","title_canon_sha256":"202639f6d6c43801b4f13adbdf35adf2aa3b045c5a0968716912cd26bcaaa9a8"},"schema_version":"1.0","source":{"id":"1405.6288","kind":"arxiv","version":1}},"canonical_sha256":"75af5ad3c6cd6447e450147c97f8ce0b3f8e270f3f1477242b9e477f6257a30a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75af5ad3c6cd6447e450147c97f8ce0b3f8e270f3f1477242b9e477f6257a30a","first_computed_at":"2026-05-18T02:51:07.589987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:07.589987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J9nNWO657iqqrhKRP7rkmBXnvOAn+pJ5L0ge5yCBFjU4QkmqguB72NZqdcHguUsdEE1Tf7SMwu5jA8WkgSKiBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:07.590575Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6288","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9c918b77f6f5f64a5180728ba197419df75a88b2e2ee0a6b7108d3251638747","sha256:843f1939c8793070563e69e3aa1126512cacc57dcac44a73ef07bebbaccc85d9"],"state_sha256":"4d7b28d0ab886cac62c326e851bae4da68c8b1c56547c045e26f54abae2d963c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w7/jFLTPkk6rSdBpPzfJyWru3qs7L6jXYSp78H5OrjYoTS2UNzK0Iob5mdgPzAM4aX0zUkX8FMUmrX3k4QJjAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T03:59:33.262939Z","bundle_sha256":"7ea1add21bec0dd3e860f9e4953dd751e2b9cd48bac88fffc844a9b8835cdd61"}}