[Submitted on 13 Sep 2026]
[View PDF](https://arxiv.org/pdf/2609.16063)
[HTML (experimental)](https://arxiv.org/html/2609.16063v1)
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.
References & Citations
...
Bibliographic Explorer
(What is the Explorer?) Connected Papers
(What is Connected Papers?) Litmaps
(What is Litmaps?) scite Smart Citations
(What are Smart Citations?) alphaXiv
(What is alphaXiv?) CatalyzeX Code Finder for Papers
(What is CatalyzeX?) DagsHub
(What is DagsHub?) Gotit.pub
(What is GotitPub?) Hugging Face
(What is Huggingface?) ScienceCast
(What is ScienceCast?) Influence Flower
(What are Influence Flowers?) CORE Recommender
(What is CORE?) IArxiv Recommender
(What is IArxiv?) arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.