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If none of the eigenvalues of the matrices A_i is a root of unity, then we prove that the set of pairs (n_1,n_2) of non-negative integers such that f_1^{n_1}(x_1)=f_2^{n_2}(x_2) is a finite union of sets of the form (m_1k + \\ell_1, m_2k + \\ell_2) where m_1, m_2, \\ell_1, \\ell_2 are given non-negative integers, and k "},"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":"1604.02529","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-04-09T06:39:04Z","cross_cats_sorted":["math.AG","math.DS"],"title_canon_sha256":"c8102692eb0b796db91af75beabc0fc548ac21f22f4ca9dcb307473ab9677501","abstract_canon_sha256":"b2e7d3638e0dc0324c5f903ca90d2b3cded36be5c1315b2b84fe9d378b875b1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:22.711162Z","signature_b64":"vBGwVCdOdbvYlu/DiPKP8VUYsKAHSkn2hDmYdTyahIIp+vRUQ3Qt2XoSOO3qDK3m9fShvTWofpel8+ciTI0qCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81d850de8dce96de529bccbba5d08180d5fb89db36dbf0745a822f9d9bf2d47a","last_reissued_at":"2026-05-18T01:17:22.710722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:22.710722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The orbit intersection problem for linear spaces and semiabelian varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.DS"],"primary_cat":"math.NT","authors_text":"Dragos Ghioca, Khoa Nguyen","submitted_at":"2016-04-09T06:39:04Z","abstract_excerpt":"Let f_1 and f_2 be affine maps of the N-th dimensional affine space over the complex numbers, i.e., f_i(x):=A_i x + y_i (where each A_i is an N-by-N matrix and y_i is a given vector), and let x_1 and x_2 be vectors such that x_i is not preperiodic under the action of f_i for i=1,2. 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