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...
Viet Anh Khoa Tran, Thieu N. Vo, T. Nguyen· 0 citations
We prove locality of the critical probability for Bernoulli site percolation on infinite, connected, locally finite, vertex-transitive graphs, under the usual assumption that the critical probabilities stay uniformly below one. The proof develops site-percolation forms of the two-ghost inequality, sharp-threshold and s...
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
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
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