Author

T. Nguyen

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Preprint Sep 2026

Bouvier's Conjecture and Dimension Sequences of Unique Factorization Domains

We prove Bouvier's conjecture. More generally, an integer sequence $(a_n)_{n \ge 0}$ with $a_0=d \ge 0$ is realized by a unique factorization domain (UFD) $R$ with $\dim R[X_1,\ldots,X_n]=a_n$ for every $n \ge 0$ if and only if $$ a_n+1\le a_{n+1} \le a_n+\left\lfloor\frac{a_n+1}{n+1}\right\rfloor \qquad(n\ge0) $$ and $a_1 \le 2d$ whenever $d \ge 1$.

Viet Anh Khoa Tran, Thieu N. Vo, T. Nguyen · 0 citations

Preprint Sep 2026

Bouvier's Conjecture Is True

We construct a local UFD $A$ with $\dim A = 2$ and $\dim A[X]=4$. Since every UFD is a Krull domain, $A$ is a finite-dimensional non-Jaffard Krull domain, proving Bouvier's conjecture.

Viet Anh Khoa Tran, Thieu N. Vo, T. Nguyen · 0 citations

#machine learning Preprint Sep 2026

Topological Steering

This work proposes Topological Steering, a new framework for steering LLM behavior through the topological representation of activation spaces, and shows that Topological Steering consistently modifies LLM behavior across multiple model families and model sizes.

Benoît Guérand, T. Nguyen · 0 citations