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Tefft","submitted_at":"2025-02-05T16:38:49Z","abstract_excerpt":"Let $D$ be an endomorphism on $\\mathbb{Z}_m^n$ so that \\[D(x_1, x_2, ..., x_n)=(x_1+x_2 \\; \\text{mod} \\; m, x_2+x_3 \\; \\text{mod} \\; m, ..., x_n+x_1 \\; \\text{mod} \\; m).\\] We call the sequence $\\{D^{\\alpha}(\\mathbf{u})\\}_{\\alpha=0}^{\\infty}$ the Ducci sequence of $\\mathbf{u} \\in \\mathbb{Z}_m^n$, which always enters a cycle. Now let $H$ be an endomorphism on $\\mathbb{Z}_m^n$ such that \\[H(x_1, x_2, ..., x_n)=(x_2, x_3, ..., x_n, x_1).\\] In this paper, we will talk about a few cases when $\\mathbf{u}$ and $H^{\\beta}(\\mathbf{u})$ have the same Ducci cycle for $\\beta > 0$, as well as prove a few ca"},"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":"2502.03345","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-02-05T16:38:49Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"3c9395357ed9c45f0ba508070011efd8a04c48ce8b8e54b7252e69e18f522026","abstract_canon_sha256":"f055c49281d75477755e43360339daf8cf4513349bfc418b132dbb492c82d563"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:10:03.459044Z","signature_b64":"9QkHuZHGxS/BHlONvic8O9xwulx8vCKBAM5ZEau2rN3Lh4bfca1ZvOAdsto6z/awyVjqQ4SKbF2EDQutpAo0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8bc75ce26e5637beef17bc36bcb0939426d971f4c36684850f4e704ecae40671","last_reissued_at":"2026-07-05T10:10:03.458600Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:10:03.458600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Examining $H$-Closed Ducci Sequences on $\\mathbb{Z}_m^n$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.NT","authors_text":"Mark L. 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