{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:AWI4NC3E6GDZWHIMSMRMN3TXOY","short_pith_number":"pith:AWI4NC3E","schema_version":"1.0","canonical_sha256":"0591c68b64f1879b1d0c9322c6ee77761bc464de4457a7649987668d5faff912","source":{"kind":"arxiv","id":"1305.1965","version":3},"attestation_state":"computed","paper":{"title":"The proof of the Kontsevich periodicity conjecture on noncommutative birational transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP","math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Natalia Iyudu, Stanislav Shkarin","submitted_at":"2013-05-08T21:59:47Z","abstract_excerpt":"For an arbitrary associative unital ring $R$, let $J_1$ and $J_2$ be the following noncommutative birational partly defined involutions on the set $M_3(R)$ of $3\\times 3$ matrices over $R$: $J_1(M)=M^{-1}$ (the usual matrix inverse) and $J_2(M)_{jk}=(M_{kj})^{-1}\\,$ (the transpose of the Hadamard inverse).\n  We prove the following surprising conjecture by Kontsevich saying that $(J_2\\circ J_1)^3$ is the identity map modulo the ${\\rm Diag}_{L} \\times \\rm{Diag}_R$ action $(D_1,D_2)(M)=D_1^{-1}MD_2$ of pairs of invertible diagonal matrices.\n  That is, we show that for each $M$ in the domain where"},"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":"1305.1965","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-05-08T21:59:47Z","cross_cats_sorted":["math-ph","math.DS","math.MP","math.QA","math.RT"],"title_canon_sha256":"d0368df0b7face5d39def6cbc04f9cbf8912a213cc6452f3f825210a4cd0dd00","abstract_canon_sha256":"f83dca0509fe949cdf4d5e863645a7ecfbb9966d18c3133a724dba2e68741ae6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:06.241031Z","signature_b64":"kD51jhBTUDR8frc6p13SyDmX3NjT4bfvOTpMtrTabYM2dbq21PYS7S4x8f0h/k+53kbn51/ZnDVJcmDhhje2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0591c68b64f1879b1d0c9322c6ee77761bc464de4457a7649987668d5faff912","last_reissued_at":"2026-05-18T01:28:06.240367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:06.240367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The proof of the Kontsevich periodicity conjecture on noncommutative birational transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP","math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Natalia Iyudu, Stanislav Shkarin","submitted_at":"2013-05-08T21:59:47Z","abstract_excerpt":"For an arbitrary associative unital ring $R$, let $J_1$ and $J_2$ be the following noncommutative birational partly defined involutions on the set $M_3(R)$ of $3\\times 3$ matrices over $R$: $J_1(M)=M^{-1}$ (the usual matrix inverse) and $J_2(M)_{jk}=(M_{kj})^{-1}\\,$ (the transpose of the Hadamard inverse).\n  We prove the following surprising conjecture by Kontsevich saying that $(J_2\\circ J_1)^3$ is the identity map modulo the ${\\rm Diag}_{L} \\times \\rm{Diag}_R$ action $(D_1,D_2)(M)=D_1^{-1}MD_2$ of pairs of invertible diagonal matrices.\n  That is, we show that for each $M$ in the domain 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