{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MUVFJX632P4EJ6N42JNG5C43L7","short_pith_number":"pith:MUVFJX63","schema_version":"1.0","canonical_sha256":"652a54dfdbd3f844f9bcd25a6e8b9b5fc812c14b2d814ab957cd434abf9cff08","source":{"kind":"arxiv","id":"1505.06355","version":1},"attestation_state":"computed","paper":{"title":"Bijections preserving commutators and automorphisms of unitriangular group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexei Stepanov, Waldemar Holubowski","submitted_at":"2015-05-23T17:40:30Z","abstract_excerpt":"We complete characterization of bijections preserving commutators (PC-maps) in the group of unitriangular matrices $UT(n,F)$ over a field $F$, where $n$ is a natural number or infinity. PC-maps were recently described up to almost identity PC-maps by M.Chen, D.Wang, and H.Zhai (2011) for finite $n$ and by R.Slowik (2013) for $n=\\infty$. An almost identity map is a map, preserving elementary transvections. We show that an almost identity PC-map is a multiplication by a central element. In particular, if $n=\\infty$, then an almost identity map is identity. Together with the result of R.Slowik th"},"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":"1505.06355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-05-23T17:40:30Z","cross_cats_sorted":[],"title_canon_sha256":"d997bda05dd4d08f18107409632a9da1bd06746bdf1ab75d89d8ecac5b374eb0","abstract_canon_sha256":"eb20620bc9e11408d572616fd76cfa2edb83ef1cea1587430fda220c54560c8b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:47.515405Z","signature_b64":"ep05NK+zKmk6wVWUtQygjiH+OJQ1cSVamqIRXtK+aBLC6elGXwRBC90H+1NUBjCWP06QMrI9GSkUeB68Bx2TBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"652a54dfdbd3f844f9bcd25a6e8b9b5fc812c14b2d814ab957cd434abf9cff08","last_reissued_at":"2026-05-18T02:03:47.514723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:47.514723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bijections preserving commutators and automorphisms of unitriangular group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alexei Stepanov, Waldemar Holubowski","submitted_at":"2015-05-23T17:40:30Z","abstract_excerpt":"We complete characterization of bijections preserving commutators (PC-maps) in the group of unitriangular matrices $UT(n,F)$ over a field $F$, where $n$ is a natural number or infinity. PC-maps were recently described up to almost identity PC-maps by M.Chen, D.Wang, and H.Zhai (2011) for finite $n$ and by R.Slowik (2013) for $n=\\infty$. An almost identity map is a map, preserving elementary transvections. We show that an almost identity PC-map is a multiplication by a central element. In particular, if $n=\\infty$, then an almost identity map is identity. Together with the result of R.Slowik th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06355","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":"1505.06355","created_at":"2026-05-18T02:03:47.514819+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.06355v1","created_at":"2026-05-18T02:03:47.514819+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06355","created_at":"2026-05-18T02:03:47.514819+00:00"},{"alias_kind":"pith_short_12","alias_value":"MUVFJX632P4E","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MUVFJX632P4EJ6N4","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MUVFJX63","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/MUVFJX632P4EJ6N42JNG5C43L7","json":"https://pith.science/pith/MUVFJX632P4EJ6N42JNG5C43L7.json","graph_json":"https://pith.science/api/pith-number/MUVFJX632P4EJ6N42JNG5C43L7/graph.json","events_json":"https://pith.science/api/pith-number/MUVFJX632P4EJ6N42JNG5C43L7/events.json","paper":"https://pith.science/paper/MUVFJX63"},"agent_actions":{"view_html":"https://pith.science/pith/MUVFJX632P4EJ6N42JNG5C43L7","download_json":"https://pith.science/pith/MUVFJX632P4EJ6N42JNG5C43L7.json","view_paper":"https://pith.science/paper/MUVFJX63","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.06355&json=true","fetch_graph":"https://pith.science/api/pith-number/MUVFJX632P4EJ6N42JNG5C43L7/graph.json","fetch_events":"https://pith.science/api/pith-number/MUVFJX632P4EJ6N42JNG5C43L7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MUVFJX632P4EJ6N42JNG5C43L7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MUVFJX632P4EJ6N42JNG5C43L7/action/storage_attestation","attest_author":"https://pith.science/pith/MUVFJX632P4EJ6N42JNG5C43L7/action/author_attestation","sign_citation":"https://pith.science/pith/MUVFJX632P4EJ6N42JNG5C43L7/action/citation_signature","submit_replication":"https://pith.science/pith/MUVFJX632P4EJ6N42JNG5C43L7/action/replication_record"}},"created_at":"2026-05-18T02:03:47.514819+00:00","updated_at":"2026-05-18T02:03:47.514819+00:00"}