Clay weekly context brief for the Maths category (ISO week 2026-W35).

Clay tracks publications from the Maths feed list. Below are recent items from this category, each with its source and a short description of what the publication covers when one is available in the source feed.

Recent publications:
1. $F$-intersection flatness of dagger and Berkovich Tate algebras
   Source: math.AC (Commutative Algebra)
   Link: https://arxiv.org/abs/2511.00753
   We show, using the techniques developed in arXiv:2504.06444 and arXiv:2305.11139, that dagger algebras and Tate algebras in the sense of Berkovich in prime characteristic $p > 0$ have intersection flat Frobenius.
2. Geometrically multiplicative non-archimedean norms
   Source: math.AG (Algebraic Geometry)
   Link: https://arxiv.org/abs/2608.19481
   Universally (or geometrically) multiplicative norms on Banach algebras over complete non-archimedean fields were used by Berkovich in his works on non-archimedean geometry, and later they were studied in some detail by Poineau.
3. Topological Effects on Bubbling in the Critical Dirichlet Problem on Hyperbolic Domains: $3\leq N \leq5$
   Source: math.AP (Analysis of PDEs)
   Link: https://arxiv.org/abs/2608.19356
   Let \(\Omega\Subset\mathbb H^N\), \(N\in\{3,4,5\}\), be a bounded connected \(C^2\) domain.
4. Real polynomials with given multiplicities of real roots: Complete conjectural description of homology
   Source: math.AT (Algebraic Topology)
   Link: https://arxiv.org/abs/2608.19733
   Following \cite {KSW} we continue the study the cellular complexes formed by polynomials of a given degree having a given sequence of multiplicities of real roots.
5. Factorization and Atomic Decomposition in Hardy-Orlicz Spaces on the Upper Half-Plane with Applications to Hankel Operators
   Source: math.CA (Classical Analysis and ODEs)
   Link: https://arxiv.org/abs/2608.19451
   In this work, we establish a strong factorization for Hardy-Orlicz spaces on the upper half-plane.
6. Counting thresholds for perfect matchings in hypergraphs
   Source: math.CO (Combinatorics)
   Link: https://arxiv.org/abs/2608.19345
   In a $k$-uniform hypergraph, the minimum $d$-degree for some $0\le d\le k-1$ is the minimum number of edges containing any given $d$-set of vertices.
7. Norm of the generalized Hilbert operator on Hardy spaces
   Source: math.CV (Complex Variables)
   Link: https://arxiv.org/abs/2608.19660
   We study the generalized Hilbert operator \[ \mathcal{H}_b f(z)=\int_0^1 f(t)\,\frac{(1-t)^b}{(1-tz)^{b+1}}\,dt, \qquad b>0, \] acting on the Hardy spaces $H^p$ for $1\leq p\leq \infty$.
8. Outer Contact Billiards
   Source: math.DS (Dynamical Systems)
   Link: https://arxiv.org/abs/2608.19393
   We introduce outer contact billiards as an odd dimensional counterpart to outer symplectic billiards.
9. Nonexistence of Frame Measures for Separated Uniform Consecutive-Digit Bernoulli Convolutions
   Source: math.FA (Functional Analysis)
   Link: https://arxiv.org/abs/2608.19676
   We investigate the existence problem of frame measures for uniform consecutive-digit Bernoulli convolutions under the separated scaling condition.
10. The Second Edge Theorem: The Asymptotic Collapse of Sample-Dependent Information Geometry to the Canonical Flat Canvas of Conventional Statistics in Large
   Source: math.GM (General Mathematics)
   Link: https://arxiv.org/abs/2608.19251
   This paper establishes the global proof of the Second Edge Theorem: as sample size tends to infinity, sample-dependent information-geometric manifolds---formed by the parameter space, sample-scaled Fisher metric, and dual alpha-connections---undergo metric-topological collapse onto the flat tangent space of Conventional Statistics at the true parameter.
11. Soft Bitopological Groups via Soft Elements
   Source: math.GN (General Topology)
   Link: https://arxiv.org/abs/2602.12678
   Let $F$ be a soft group over a parameter set $A$.
12. Products of nonconjugate maximal subgroups
   Source: math.GR (Group Theory)
   Link: https://arxiv.org/abs/2608.19478
   We prove that a finite group $G$ is solvable whenever $MN=G$ for every pair of nonconjugate maximal subgroups $M,N<G$.
13. Deciding if a shadow resolves into a given link: linear-time algorithms
   Source: math.GT (Geometric Topology)
   Link: https://arxiv.org/abs/2608.19484
   A {\em shadow} (or {\em projection}) is obtained from a link diagram by ignoring the over/under information at each crossing.
14. Mathematics in the age of the reproduction of intelligence
   Source: math.HO (History and Overview)
   Link: https://arxiv.org/abs/2608.16378
   Drawing on Walter Benjamin's account of technological reproducibility and aura in relation to art, together with insights from Yehuda Rav and Ludwig Wittgenstein, this speculative essay reflects on the impact of AI systems on the practice of pure mathematics.
15. Tri-Hybrid Beamforming for T-RIS-Enabled Base Station
   Source: math.IT (Information Theory)
   Link: https://arxiv.org/abs/2608.19736
   Transmissive reconfigurable intelligent surfaces (T-RISs) integrated into the transmitter provide a viable realization of tri-hybrid multiple-input multiple-output (MIMO), where spatial processing is distributed across the digital, analog radio-frequency (RF), and electromagnetic (EM) domains.
16. The Additive Arithmetic of Linear Orders
   Source: math.LO (Logic)
   Link: https://arxiv.org/abs/2608.20309
   We present a systematic development of the arithmetic of the class of linear orders under the ordered sum $(LO, +)$ and prove a number of new results.
17. Dangling points in area-minimizing Meissner polyhedra
   Source: math.MG (Metric Geometry)
   Link: https://arxiv.org/abs/2608.19747
   Meissner polyhedra are constant-width bodies obtained from extremal finite sets of unit diameter.
18. 3D Einstein action from 6D Kodaira-Spencer gravity
   Source: math-ph (Mathematical Physics)
   Link: https://arxiv.org/abs/2608.19309
   In view of embedding 3D gravity into topological string theory, we show that the dimensional reduction of 6D Kodaira-Spencer gravity on $\text{AdS}_3\times S^3$, i.e.
19. A High-Order Rank-Adaptive Implicit Algorithm for Solving High Dimensional Diffusion Equations using the Hierarchical Tucker Decomposition
   Source: math.NA (Numerical Analysis)
   Link: https://arxiv.org/abs/2608.19368
   This paper presents a high-order rank-adaptive implicit integrator for the tensor solution of high-dimensional diffusion equations.
20. A Cheeger-type inequality for the drift Laplacian with Wentzell-type boundary condition
   Source: math.SP (Spectral Theory)
   Link: https://arxiv.org/abs/2503.16093
   We prove lower bounds for the first non-trivial eigenvalue of the drift Laplacian on manifolds with Wentzell-type boundary condition in terms of some Cheeger-type constants for bulk-boundary interactions. Our results are in the spirit of Cheeger's classical inequality.
21. An equidistribution conjecture for quotient-closed and submodule-closed subcategories
   Source: math.RA (Rings and Algebras)
   Link: https://arxiv.org/abs/2608.18024
   We study subcategories of the module category of a finite-dimensional algebra that are closed under quotients or submodules.
22. Monoidal seeds of the categories $\mathcal{C}_{wv}$ over quiver Hecke algebras
   Source: math.QA (Quantum Algebra)
   Link: https://arxiv.org/abs/2608.15020
   In this paper, when the quiver Hecke algebra R is symmetric, we present a new construction of quantum monoidal seeds $ \mathscr{S}_{w,v}$ for $\mathcal{C}_{wv}$ using the reflection functors $\mathcal{F}_i$ and the newly introduced operators $\mathcal{K}_i$.
23. Complexity rank one implies real rank zero
   Source: math.OA (Operator Algebras)
   Link: https://arxiv.org/abs/2608.12089
   We show that $C^*$-algebras with complexity rank one have real rank zero, as an application, the uniform Roe algebra $C_u^*|\mathbb{Z}|$ has real rank zero.
24. Weighted Recursions for the Smallest Parts Function
   Source: math.NT (Number Theory)
   Link: https://arxiv.org/abs/2606.07885
   We establish new polynomial-weighted recursions for Andrews' smallest parts function.
25. The van der Waerden Simplicial Complex and its Lefschetz Properties
   Source: math.AC (Commutative Algebra)
   Link: https://arxiv.org/abs/2603.29978
   The van der Waerden simplicial complex, denoted ${\tt vdw}(n,k)$, is the simpicial complex whose facets correspond to the arithmetic progressions of length $k$ in the set $\{1,\ldots,n\}$.
26. Quadratic generation of ideals defining nonsigular toric 3-folds
   Source: math.AG (Algebraic Geometry)
   Link: https://arxiv.org/abs/2608.19577
   Let $X$ be a projective line bundle over a nonsingular toric surface which is a blowup the projective plane along at most 4 invariant points, or a blowup the product of the projective lines along at most 4 invariant points.
27. Heat--Airy Transport of Differential Operators and Moving Boundaries
   Source: math.AP (Analysis of PDEs)
   Link: https://arxiv.org/abs/2608.19434
   We study the transport of polynomial differential operators under the two-parameter commuting evolution \[ P_{t,s} = \exp\left( \frac{t}{2}D^2-\frac{s}{3}D^3 \right), \qquad D=\frac{d}{dx}.

Sources in this brief: math-ph (Mathematical Physics); math.AC (Commutative Algebra); math.AG (Algebraic Geometry); math.AP (Analysis of PDEs); math.AT (Algebraic Topology); math.CA (Classical Analysis and ODEs); math.CO (Combinatorics); math.CV (Complex Variables); math.DS (Dynamical Systems); math.FA (Functional Analysis); math.GM (General Mathematics); math.GN (General Topology); math.GR (Group Theory); math.GT (Geometric Topology); math.HO (History and Overview); math.IT (Information Theory); math.LO (Logic); math.MG (Metric Geometry); math.NA (Numerical Analysis); math.NT (Number Theory); math.OA (Operator Algebras); math.QA (Quantum Algebra); math.RA (Rings and Algebras); math.SP (Spectral Theory).
Selected 27 of 250 available items for this weekly brief.