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We investigate the structure of the groups $Aut End A$ and $Aut \\mathcal{A}^{\\circ}$, where $\\mathcal{A}^{\\circ}$ is the category of finitely generated free algebras from $\\mathcal{A}$. We prove that the group $Aut End A$ is generated by semi-inner and mirror automorphisms of $End F$ and the group $Aut \\mathcal{A}^{\\circ}$ is generated by sem"},"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":"math/0512273","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.RA","submitted_at":"2005-12-13T14:26:16Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"63e895d03420ea8e74d38822ad0b45f96d1b6a288be5dc90057863adb4abad9b","abstract_canon_sha256":"24a82679cfaff483333ccc9078d2bf36528382e7cc40ff7b2700a07a54a5fa02"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:02.181401Z","signature_b64":"ib+lbf5fhvUKAohWTLAyz+1wAzAUpxZzlWvXWPE+QMCAXvbi4YNwZPnxIQAmHoP6cUaqfML/YGMIngQkXw0FAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63973e7b3ccd73e9423c8c217dc2dc64450c28f0a123349bec6a9e3fb1a371a2","last_reissued_at":"2026-05-18T00:29:02.180718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:02.180718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Automorphisms of the semigroup of endomorphisms of free associative algebras","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"A. 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We prove that the group $Aut End A$ is generated by semi-inner and mirror automorphisms of $End F$ and the group $Aut \\mathcal{A}^{\\circ}$ is generated by sem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0512273","kind":"arxiv","version":3},"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":"math/0512273","created_at":"2026-05-18T00:29:02.180827+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0512273v3","created_at":"2026-05-18T00:29:02.180827+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0512273","created_at":"2026-05-18T00:29:02.180827+00:00"},{"alias_kind":"pith_short_12","alias_value":"MOLT46Z4ZVZ6","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"MOLT46Z4ZVZ6SQR4","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"MOLT46Z4","created_at":"2026-05-18T12:25:53.335082+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/MOLT46Z4ZVZ6SQR4RQQX3QW4MR","json":"https://pith.science/pith/MOLT46Z4ZVZ6SQR4RQQX3QW4MR.json","graph_json":"https://pith.science/api/pith-number/MOLT46Z4ZVZ6SQR4RQQX3QW4MR/graph.json","events_json":"https://pith.science/api/pith-number/MOLT46Z4ZVZ6SQR4RQQX3QW4MR/events.json","paper":"https://pith.science/paper/MOLT46Z4"},"agent_actions":{"view_html":"https://pith.science/pith/MOLT46Z4ZVZ6SQR4RQQX3QW4MR","download_json":"https://pith.science/pith/MOLT46Z4ZVZ6SQR4RQQX3QW4MR.json","view_paper":"https://pith.science/paper/MOLT46Z4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0512273&json=true","fetch_graph":"https://pith.science/api/pith-number/MOLT46Z4ZVZ6SQR4RQQX3QW4MR/graph.json","fetch_events":"https://pith.science/api/pith-number/MOLT46Z4ZVZ6SQR4RQQX3QW4MR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MOLT46Z4ZVZ6SQR4RQQX3QW4MR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MOLT46Z4ZVZ6SQR4RQQX3QW4MR/action/storage_attestation","attest_author":"https://pith.science/pith/MOLT46Z4ZVZ6SQR4RQQX3QW4MR/action/author_attestation","sign_citation":"https://pith.science/pith/MOLT46Z4ZVZ6SQR4RQQX3QW4MR/action/citation_signature","submit_replication":"https://pith.science/pith/MOLT46Z4ZVZ6SQR4RQQX3QW4MR/action/replication_record"}},"created_at":"2026-05-18T00:29:02.180827+00:00","updated_at":"2026-05-18T00:29:02.180827+00:00"}