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Tefft","submitted_at":"2024-01-30T23:29:21Z","abstract_excerpt":"Let the Ducci function $D: \\mathbb{Z}_m^n \\to \\mathbb{Z}_m^n$ be defined as\n  \\[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)\\]\n  and let the Ducci sequence of $\\mathbf{u}$ be the sequence $\\{D^{\\alpha}(\\mathbf{u})\\}_{\\alpha=0}^{\\infty}$.\n  %In this paper, we will prove that if $n,m$ are powers of $2$, then repeatedly applying $D$ will eventually result in $(0,0,...,0)$, as well as establish an upper bound for how many iterations it will take for this to happen.\n  In this paper, we will provide another proof that for $n=2^k$ and"},"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":"2401.17502","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2024-01-30T23:29:21Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"21dbfff051aeff0155c2f3be30b9262d615d46ea40d2661a77b8ea6906171a6e","abstract_canon_sha256":"8c26164ef548726d438ae2c7f53abdcc3b915b547c0a796501e97389edf9c149"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:00:35.944869Z","signature_b64":"16HGEwh+k3wnJtd2wdrA0tHHzFXoRRI04OvUb7XxVtFZNS12neBmEMBBodLC3anGFIwIpXNont7fp+vb1szbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a0e5969b554d145bb4838f8646e05eb154cf554637b4c04a4d99cfe6228f7b8","last_reissued_at":"2026-07-05T09:00:35.944427Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:00:35.944427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Period of Ducci Cycles on $\\mathbb{Z}_{2^l}$ for Tuples of Length $2^k$","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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