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Elements of $I$ can be interpreted as identities $[A(a,b),a]=[B(a,b),b]$ in Lie rings. The kernel $I$ can be decomposed into a direct sum $I=\\bigoplus_{n,m} I_{n,m},$ where elements of $I_{n,m}$ correspond to identities on commutators of weight $n+m,$ where the letter $a$ occurs $n$ times and the"},"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":"1805.02734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-05-07T20:34:34Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"a3bdc2af2761c9aafc3287aa4e866d788e535d7c7ffc68b49529f5d0b9cc814d","abstract_canon_sha256":"afd3048e23b355a695c03ce2f863724302a8ce2f0794c78d93719b8f3ca8e3b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:35.869887Z","signature_b64":"Hzvg9QT3ajYcbrtf5I7iUCGfOfX7A/W5W3RaZkfTWNW1a1ALnQAjTcmfdCpj0zfkYMBugPGcdxKS3tR7gp/TAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f9e339a081490b93214e2868f3cc30c07f23b7c2a341c7b22079f96a02b6b57","last_reissued_at":"2026-05-18T00:16:35.869251Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:35.869251Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On two letter identities in Lie rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.GR","authors_text":"Boris Baranov, Savelii Novikov, Sergei O. 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