Tootfinder

I appreciate AOC cleaving apart the false “both sides are the same” equivalence of the word “populism” here. https://mastodon.online/@mastodonmigration/116082081470440947

Fanciful Figurines flip Free Flood-It -- Polynomial-Time Miniature Painting on Co-gem-free Graphs
Christian Rosenke, Mark Scheibner
https://arxiv.org/abs/2602.00690 https://arxiv.org/pdf/2602.00690 https://arxiv.org/html/2602.00690
arXiv:2602.00690v1 Announce Type: new
Abstract: Inspired by the eponymous hobby, we introduce Miniature Painting as the computational problem to paint a given graph $G=(V,E)$ according to a prescribed template $t \colon V \rightarrow C$, which assigns colors $C$ to the vertices of $G$. In this setting, the goal is to realize the template using a shortest possible sequence of brush strokes, where each stroke overwrites a connected vertex subset with a color in $C$. We show that this problem is equivalent to a reversal of the well-studied Free Flood-It game, in which a colored graph is decolored into a single color using as few moves as possible. This equivalence allows known complexity results for Free Flood-It to be transferred directly to Miniature Painting, including NP-hardness under severe structural restrictions, such as when $G$ is a grid, a tree, or a split graph. Our main contribution is a polynomial-time algorithm for Miniature Painting on graphs that are free of induced co-gems, a graph class that strictly generalizes cographs. As a direct consequence, Free Flood-It is also polynomial-time solvable on co-gem-free graphs, independent of the initial coloring.
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Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
[1/1]:
- Cartier integration of infinitesimal 2-braidings via 2-holonomy of the CMKZ 2-connection, II: The...
Cameron Kemp
https://arxiv.org/abs/2603.22694 https://mastoxiv.page/@arXiv_mathQA_bot/116288747056576727
- On the equivalence of Brantner's and Chu--Haugseng's approaches to enriched $\infty$-operads
Kensuke Arakawa
https://arxiv.org/abs/2603.23019 https://mastoxiv.page/@arXiv_mathAT_bot/116288685120443277
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How local rules generate emergent structure in cellular automata
Manuel Pita
https://arxiv.org/abs/2604.00273 https://arxiv.org/pdf/2604.00273 https://arxiv.org/html/2604.00273
arXiv:2604.00273v1 Announce Type: new
Abstract: Cellular automata generate spatially extended, temporally persistent emergent structures from local update rules. No general method derives the mechanisms of that generation from the rule itself; existing tools reconstruct structure from observed dynamics. This paper shows that the look-up table contains a readable causal architecture and introduces a forward model to extract it. The key observation in elementary cellular automata (ECA) is that adjacent cells share input positions, so the prime implicants of neighbouring transitions overlap. That overlap can couple the transitions causally or leave them independent. We formalize each pairwise interaction as a tile. A finite-state, tiling transducer, $\mathcal{T}$, composes tiles across the CA lattice, tracking how coupling and independence propagate from one cell pair to the next. Structural properties of $\mathcal{T}$ are used to classify ECA rules that can sustain regions of causal independence across space and time. We find that, in the 88 ECA equivalence classes, the number of local configurations at which coupling is structurally impossible -- computable from the look-up table -- predicts the prevalence of dynamically decoupled regions with Spearman $\rho = 0.89$ ($p < 10^{-31}$). The look-up table encodes not just what a rule computes but where it distributes causal coupling across the lattice; the framework reads that distribution forward, from local logical redundancy to emergent mesoscopic organization.
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A Modal de Finetti Theorem: Exchangeability under S4 and S5
Daniel Zantedeschi
https://arxiv.org/abs/2603.27547 https://arxiv.org/pdf/2603.27547 https://arxiv.org/html/2603.27547
arXiv:2603.27547v1 Announce Type: new
Abstract: We introduce modal exchangeability, a symmetry principle for probability measures on Kripke frames: invariance under those automorphisms of the frame that preserve the accessibility relation and fix a designated world. This principle characterizes when an agent's uncertainty over possible-world valuations respects the modal structure. We establish representation theorems that determine the probabilistic consequences of modal exchangeability for S4 and S5 frames. Under S5, where accessibility is an equivalence relation, the classical de Finetti theorem is recovered: valuations are conditionally i.i.d. given a single directing measure. Under S4, where accessibility is a preorder, the accessible cluster decomposes into orbits of the stabilizer group, and valuations within each orbit are conditionally i.i.d. with an orbit-specific directing measure. A rigidity constraint emerges: each directing measure must be constant across its orbit. Rigidity is not assumed but forced by symmetry; it is a theorem, not a modeling choice. The proofs are constructive, requiring only dependent choice (ZF DC), and yield computable representations for recursively presented frames. Rigidity has direct epistemic content: rational agents whose uncertainty respects modal structure cannot assign different latent parameters to worlds within the same orbit. The framework connects probabilistic representation theory to the S4/S5 distinction central to epistemic and temporal logic, with consequences for hyperintensional belief and rational learning under partial information.
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Replaced article(s) found for math.CA. https://arxiv.org/list/math.CA/new
[1/1]:
- On the equivalence between moderate growth-type conditions in the weight matrix setting II
Gerhard Schindl

A tautological continuous field of Roe bimodules
Vladimir Manuilov
https://arxiv.org/abs/2603.23366 https://arxiv.org/pdf/2603.23366 https://arxiv.org/html/2603.23366
arXiv:2603.23366v1 Announce Type: new
Abstract: We generalize the notion of a continuous field of C*-algebras to that of Hilbert C*-bimodules. Given a partially ordered set $P$ and a monotonically non-decreasing family of ternary rings of operators (TROs) assigned to the points of $P$, we equip $P$ with a certain zero-dimensional Hausdorff topology and use a certain compactification $\gamma P$ to get the base space for a continuous field of Hilbert C*-bimodules over $\gamma P$.
As a motivating example, we consider the set $D(X,Y)$ of coarse equivalence classes of metrics on the disjoint union of two metric spaces, $X$ and $Y$. Each such class gives rise to a uniform Roe bimodule, a TRO linking the uniform Roe algebras of $X$ and $Y$. The resulting family of TROs is non-decreasing with respect to the natural partial order on $D(X,Y)$ and thus yields a tautological continuous field of Hilbert C*-bimodules over $\gamma D(X,Y)$.
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A synthetic construction of universal cocartesian fibrations
Christian Sattler, David W\"arn
https://arxiv.org/abs/2603.28688 https://arxiv.org/pdf/2603.28688 https://arxiv.org/html/2603.28688
arXiv:2603.28688v1 Announce Type: new
Abstract: We give a model-independent construction of directed univalent cocartesian fibrations of $(\infty,1)$-categories, and prove a straightening equivalence against such fibrations. The key step is showing that cocartesian fibrations descend along localisations, which we accomplish by analysing mapping spaces of localisations. Along the way we introduce a directed version of the join construction, giving a sequential colimit description of the full image of any functor.
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Speedability of computably approximable reals and their approximations
George Barmpalias, Nan Fang, Wolfgang Merkle, Ivan Titov
https://arxiv.org/abs/2603.26484 https://arxiv.org/pdf/2603.26484 https://arxiv.org/html/2603.26484
arXiv:2603.26484v1 Announce Type: new
Abstract: An approximation of a real is a sequence of rational numbers that converges to the real. An approximation is left-c.e. if it is computable and nondecreasing and is d.c.e. if it is computable and has bounded variation. A real is computably approximable if it has some computable approximation, and left-c.e. and d.c.e. reals are defined accordingly.
An approximation $\{a_s\}_{s \in \omega}$ is speedable if there exists a nondecreasing computable function $f$ such that the approximation $\{a_{f(s)}\}_{s \in \omega}$ converges in a certain formal sense faster than $\{a_s\}_{s \in \omega}$. This leads to various notions of speedability for reals, e.g., one may require for a computably approximable real that either all or some of its approximations of a specific type are speedable.
Merkle and Titov established the equivalence of several speedability notions for left-c.e. reals that are defined in terms of left-c.e. approximations. We extend these results to d.c.e. reals and d.c.e. approximations, and we prove that in this setting, being speedable is equivalent to not being Martin-L\"{o}f random. Finally, we demonstrate that every computably approximable real has a computable approximation that is speedable.
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Crosslisted article(s) found for math.DG. https://arxiv.org/list/math.DG/new
[1/1]:
- Smooth Fractal Trees: Analytic Generators and Discrete Equivalence
Henk Mulder

Uniformity and isotypic smallness for quantum-group representations
Alexandru Chirvasitu
https://arxiv.org/abs/2603.24855 https://arxiv.org/pdf/2603.24855 https://arxiv.org/html/2603.24855
arXiv:2603.24855v1 Announce Type: new
Abstract: Compact-group representations on Banach spaces are known to be norm-continuous precisely when they have finite spectra. For a quantum group with continuous-function algebra $\mathcal{C}(\mathbb{G})$ norm continuity can be cast analogously as the bounded weak$^*$-norm continuity of the representation's attached map $\mathcal{C}(\mathbb{G})^*\to \mathrm{End}(E)$. While the uniformity/isotypic finiteness equivalence no longer holds generally, it does for compact quantum groups either coamenable or having dimension-bounded irreducible representations. This generalizes the aforementioned classical variant, providing two independent quantum-specific mechanisms of recovering it.
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Introducing pixelation with applications
J. Daisie Rock
https://arxiv.org/abs/2603.25432 https://arxiv.org/pdf/2603.25432 https://arxiv.org/html/2603.25432
arXiv:2603.25432v1 Announce Type: new
Abstract: Motivated by the desire for a new kind of approximation, we define a type of localization called pixelation. We present how pixelation manifests in representation theory and in the study of sites and sheaves. A path category is constructed from a set, a collection of "paths" into the set, and an equivalence relation on the paths. A screen is a partition of the set that respects the paths and equivalence relation. For a commutative ring, we also enrich the path category over its modules (=linearize the category with respect to the ring) and quotient by an ideal generated by paths (possibly 0). The pixelation is the localization of a path category, or the enriched quotient, with respect to a screen. The localization has useful properties and serves as an approximation of the original category. As applications, we use pixelations to provide a new point of view of the Zariski topology of localized ring spectra, provide a parallel story to a ringed space and sheaves of modules, and construct a categorical generalization of higher Auslander algebras of type $A$.
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The Unitary Conjugation Groupoid as a Universal Mediator of the Baum--Connes Assembly Map
Shih-Yu Chang
https://arxiv.org/abs/2603.22162 https://arxiv.org/pdf/2603.22162 https://arxiv.org/html/2603.22162
arXiv:2603.22162v1 Announce Type: new
Abstract: We show that the Baum--Connes assembly map factors canonically through the unitary conjugation groupoid, which serves as a universal mediator among groupoid models that are Morita equivalent to a given transformation groupoid. This establishes a structural link between groupoid-based index theory and the Baum--Connes program at the level of K-theory. Building on our previous development of unitary conjugation groupoids and their associated index theory, we extend the $K_1$ index framework beyond the Type I setting to non-Type I examples, including the irrational rotation algebra and amenable crossed products. Using Morita equivalence, we relate unitary conjugation groupoids to transformation and action groupoids, enabling the transfer of descent-type index constructions to these settings. Our main result shows that, among all groupoid realizations that are Morita equivalent to a transformation groupoid, the factorization through the unitary conjugation groupoid is canonical at the level of K-theory. This identifies the unitary conjugation groupoid as a universal intermediary for the Baum--Connes assembly map. As applications, we recover the classical index pairing with the tracial state for the irrational rotation algebra in the sense of Connes, and we prove that for amenable crossed products the descent construction agrees with the analytic Baum--Connes assembly map under Morita equivalence. These results provide a conceptual interpretation of the assembly map in terms of internal symmetries of crossed product algebras and suggest a unified framework connecting Fredholm-type index data with equivariant K-theory via groupoid methods.
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On the equivalence of two approaches to multiplicative homotopy theories
Kensuke Arakawa
https://arxiv.org/abs/2603.23018 https://arxiv.org/pdf/2603.23018 https://arxiv.org/html/2603.23018
arXiv:2603.23018v1 Announce Type: new
Abstract: We study the relation of two frameworks for multiplicative homotopy theories: Presentably symmetric monoidal $\infty$-categories and combinatorial symmetric monoidal model categories. Our main theorem establishes an equivalence of their homotopy theories.
As consequences, we solve Pavlov's conjecture and obtain a solution to a special case of Hovey's 10th problem. We also prove several variations of the main theorem, such as an analog for non-symmetric monoidal semi-model categories.
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