发表机构
Australian National University（澳大利亚国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出带符号加权仿射p-adic残差目标作为有限域约束的原生编码，通过坐标支配定理确保全局极小值在有限域内，并以数独案例验证其有效性。
AI 中文摘要
我们研究带符号的加权仿射$p$-adic残差目标，作为有限域约束的原生编码。对于分离有限字母表的素数，充分加权的正一元行将每个系数固定到其允许集合，而负行则奖励不等端点或子句满足。一个坐标支配定理将每个全局极小值置于有限域内；在那里，损失（至多相差一个加性常数）等于全不同冲突计数或满足的CNF子句数的负值。标准数独提供了一个无需one-hot提升的81系数案例研究。客户端实现展示了生成的数据框、算术、诊断和搜索。
英文摘要
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.
Comments31 pages, 7 figures. Accepted for publication in p-Adic Numbers, Ultrametric Analysis and Applications
