[Submitted on 13 Sep 2026]
Title:Signed p-adic Residual Encodings of Finite-Domain All-Different Systems with a Sudoku Case Study
View a PDF of the paper titled Signed p-adic Residual Encodings of Finite-Domain All-Different Systems with a Sudoku Case Study, by Greg Baker
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Abstract:We study signed, weighted affine $p$-adic residual objectives as native encodings of finite-domain constraints. For primes that separate the finite alphabet, sufficiently weighted positive unary rows pin each coefficient to its allowed set, while negative rows reward unequal endpoints or clause satisfaction. A coordinatewise domination theorem places every global minimiser in the finite domain; there the loss is, up to an additive constant, the all-different conflict count or the negative number of satisfied CNF clauses. Standard Sudoku provides an $81$-coefficient case study without a one-hot lift. A client-side implementation exposes the generated dataframes, arithmetic, diagnostics, and searches.
Comments: 31 pages, 7 figures. Accepted for publication in p-Adic Numbers, Ultrametric Analysis and Applications
Subjects:
Machine Learning (cs.LG)
Cite as: arXiv:2609.16063 [cs.LG]
(or arXiv:2609.16063v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.16063
arXiv-issued DOI via DataCite
Submission history
From: Greg Baker [view email] [v1] Sun, 13 Sep 2026 10:42:59 UTC (528 KB)
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