Tootfinder

Emanant and emergent symmetry-topological-order from low-energy spectrum
Zixin Jessie Chen, \"Omer M. Aksoy, Cenke Xu, Xiao-Gang Wen
https://arxiv.org/abs/2509.08879 https:…

Emanant and emergent symmetry-topological-order from low-energy spectrum
Low-energy emergent and emanant symmetries can be anomalous, higher-group, or non-invertible. Such symmetries are systematically captured by topological orders in one higher dimension, known as symmetry topological orders (symTOs). Consequently, identifying the emergent or emanant symmetry of a system is not simply a matter of determining its group structure, but rather of computing the corresponding symTO. In this work, we develop a method to compute the symTO of 1+1D systems by analyzing thei…

Linear codes for $b$-symbol read channels attaining the Griesmer bound
Sascha Kurz
https://arxiv.org/abs/2507.07728 https://arxiv.org…

Linear codes for $b$-symbol read channels attaining the Griesmer bound
Reading channels where $b$-tuples of adjacent symbols are read at every step have e.g.\ applications in storage. Corresponding bounds and constructions of codes for the $b$-symbol metric, especially the pair-symbol metric where $b=2$, were intensively studied in the last fifteen years. Here we determine the optimal code parameters of linear codes in the $b$-symbol metric assuming that the minimum distance is sufficiently large. We also determine the optimal parameters of linear binary codes in …

Improved Bounds on Rainbow $k$-partite Matchings
Pitchayut Saengrungkongka
https://arxiv.org/abs/2508.07331 https://arxiv.org/pdf/2508.07331

Improved Bounds on Rainbow $k$-partite Matchings
Let $n$, $s$, and $k$ be positive integers. We say that a sequence $f_1,\dots,f_s$ of nonnegative integers is satisfying if for any collection of $s$ families $\mathcal F_1,\dots,\mathcal F_s\subseteq [n]^k$ such that $|\mathcal F_i|=f_i$ for all $i$, there exists a rainbow matching, i.e., a list of pairwise disjoint tuples $F_1\in\mathcal F_1$, $\dots$, $F_s\in\mathcal F_s$. We investigate the question, posed by Kupavskii and Popova, of determining the smallest $c=c(n,s,k)$ such that…

Clifford quantum cellular automata from topological quantum field theories and invertible subalgebras
Meng Sun, Bowen Yang, Zongyuan Wang, Nathanan Tantivasadakarn, Yu-An Chen
https://arxiv.org/abs/2509.07099

Clifford quantum cellular automata from topological quantum field theories and invertible subalgebras
We present a general framework for constructing quantum cellular automata (QCA) from topological quantum field theories (TQFT) and invertible subalgebras (ISA) using the cup-product formalism. This approach explicitly realizes all $\mathbb{Z}_2$ and $\mathbb{Z}_p$ Clifford QCAs (for prime $p$) in all admissible dimensions, in precise agreement with the classification predicted by algebraic $L$-theory. We determine the orders of these QCAs by explicitly showing that finite powers reduce to the i…

Ideals generated by corner-interval minors
Marie Amalore Nambi
https://arxiv.org/abs/2506.09618 https://arxiv.org/pdf/2506.09618

Ideals generated by corner-interval minors
In this article, we study binomial ideals generated by an arbitrary collection of corner-interval $2$-minors of a generic matrix. We determine the minimal prime ideals of such ideals and characterize their radicality in the special case of corner minors. Moreover, we discuss connectivity properties of contingency tables in algebraic statistics. We compute the Hilbert-Poincaré polynomial of the ideal generated by the set of all corner-interval minors and we derive the formula for the regularity…

Towards an Accurate and Effective Robot Vision (The Problem of Topological Localization for Mobile Robots)
Emanuela Boros
https://arxiv.org/abs/2509.04948 https://

Towards an Accurate and Effective Robot Vision (The Problem of Topological Localization for Mobile Robots)
Topological localization is a fundamental problem in mobile robotics, since robots must be able to determine their position in order to accomplish tasks. Visual localization and place recognition are challenging due to perceptual ambiguity, sensor noise, and illumination variations. This work addresses topological localization in an office environment using only images acquired with a perspective color camera mounted on a robot platform, without relying on temporal continuity of image sequences…

Componentwise Polish groupoids and equivalence relations
Ruiyuan Chen
https://arxiv.org/abs/2507.04138 https://arxiv.org/pdf/2507.041…

Componentwise Polish groupoids and equivalence relations
We study Borel equivalence relations equipped with a uniformly Borel family of Polish topologies on each equivalence class, and more generally, standard Borel groupoids equipped with such a family of topologies on each connected component. Such "componentwise Polish topologies" capture precisely the topological information determined by the Borel structure of a Polish group action, by the Becker--Kechris theorem. We prove that conversely, every abstract such Borel componentwise Polish groupoid …

Sober topologies on a set
Xiangrui Li, Qingguo Li, Dongsheng Zhao
https://arxiv.org/abs/2508.05419 https://arxiv.org/pdf/2508.05419

Sober topologies on a set
The collection of all topologies on a set X forms a complete lattice with respect to the inclusion order, which have been investigated by many researchers. Sobriety is one of the core and extensively studied properties in non-Hausdorff topology. This property plays a crucial role in characterizing the spectral spaces of commutative rings and topological spaces determined by their lattices of open sets. In this paper, we investigate the statute of sober topologies in the complete lattice of all …

Triplet Exciton-driven Topological Mott insulator at Finite Temperature
Peizhi Mai
https://arxiv.org/abs/2507.07178 https://arxiv.org…

Triplet Exciton-driven Topological Mott insulator at Finite Temperature
Motivated by experiments in which the quantum anomalous Hall (QAH) charge gap greatly exceeds the Curie temperature, we apply determinantal quantum Monte Carlo to two complementary lattice models with different geometries: the checkerboard quantum-spin-Hall-Hubbard model and the generalized Kane-Mele-Hubbard model. In both cases an incompressible QAH phase with total Chern number $C=\pm 1$ emerges at quarter filling well above the Curie temperature. Each spin channel carries its own nonquantize…

A spool for every quotient: One-loop partition functions in AdS$_3$ gravity
Robert Bourne, Jackson R. Fliss, Bob Knighton
https://arxiv.org/abs/2507.05364 …

A spool for every quotient: One-loop partition functions in AdS$_3$ gravity
The Wilson spool is a prescription for expressing one-loop determinants as topological line operators in three-dimensional gravity. We extend this program to describe massive spinning fields on all smooth, cusp-free, solutions of Euclidean gravity with a negative cosmological constant. Our prescription makes use of the expression of such solutions as a quotients of hyperbolic space. The result is a gauge-invariant topological operator, which can be promoted to an off-shell operator in the gravi…