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	Title	Source	Topics	Written	Found	Rel.	Status
	The Art of Computer Programming by Donald E. Knuth	Hacker News (front page)	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The Art of Computer Programming is a multi-volume work by Donald E. Knuth that comprehensively covers fundamental algorithms and their analysis, serving as an essential reference for computer scientists and programmers. It matters due to its authoritative depth and influence on the development of algorithmic thinking and software engineering practices. One concrete detail is that the series is renowned for introducing the Big O notation for describing the performance of algorithms. Open full article →
	A Matrix Model for Higher-Genus Fuss--Catalan Numbers	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article presents a two-matrix model that generates higher-genus Fuss-Catalan (FC) numbers for any $ p $ as coefficients in its $ 1/N $-expansion, extending the Gaussian matrix model's role in generating genus-$ g $ Catalan numbers for $ p=2 $. This work is significant as it provides exact sum rules and an explicit formula for higher-genus FC numbers, generalizing the Harer-Zagier formula to values of $ p > 2 $, and explores their relation to intersection numbers and the Euler characteristic of moduli spaces. Open full article →
	Improving SAT Solvers on Orthogonal Latin Square Problems	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The paper introduces a hybrid method combining SAT solvers with the Euler-Parker algorithm to improve the search for orthogonal Latin squares, which are challenging combinatorial problems. This approach effectively finds certain pairs of orthogonal Latin squares that were previously unknown, demonstrating a significant reduction in computational time compared to using SAT solvers alone; for instance, CaDiCaL augmented with the Euler-Parker algorithm solves the hardest cases in about 5,100 seconds on average. Open full article →
	Reconstructing Rational Functions on Finite Abelian Groups with Higher Autocorrelations	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The paper presents an algorithm for reconstructing rational-valued functions on finite Abelian groups from their higher-order autocorrelations, proving that autocorrelations up to order $3r+3$ are sufficient for reconstruction up to translation, where $r$ is the group's rank. This work has implications for various fields including X-ray crystallography and computer vision systems. The study also identifies a sharp upper bound on the separating degree of the regular representation in terms of the group’s rank, highlighting that functions are not determined by autocorrelations up to order $3r+2$. Open full article →
	Generalized Stein's lemma and asymptotic equipartition property for subalgebra entropies	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article presents a proof for the validity of the generalized quantum Stein's lemma when the second hypothesis is the state space of any finite-dimensional subalgebra, achieved through a strong asymptotic equipartition property for smooth subalgebra entropies. This finding links resource convertibility to quantum hypothesis testing and demonstrates that the relative entropy of a subalgebra represents the asymptotic dilution cost under suitable operations, offering insights into connecting different quantum resources based on subalgebras. Notably, this work provides an alternative proof using distinct operator-algebraic techniques compared to recent independent resolutions by Hayashi-Yamasaki and Lami. Open full article →
	An Accelerated Stochastic Variance-Reduced Algorithm for Entropic Wasserstein Barycenters	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study introduces an accelerated stochastic variance-reduced primal-dual algorithm for computing entropically regularized Wasserstein barycenters, which improves upon deterministic accelerated gradient methods by reducing dependency on support size by a square-root factor while maintaining efficiency with respect to target accuracy. Experiments across various datasets demonstrate the method's lower arithmetic costs compared to first-order baseline algorithms. Open full article →
	Almost Supermartingale Extensions of Olivier's Theorem	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article extends Olivier's 1827 theorem on the rate of convergence for decreasing summable sequences to the context of almost supermartingales, a stochastic process. This extension is significant for analyzing the convergence properties of stochastic iterative processes. One concrete detail involves applying these extensions to understand the behavior of general term decay in probabilistic settings akin to Olivier's original deterministic sequence analysis. Open full article →
	On a Theorem of Wang for Complex Homogeneous Manifolds	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article provides a new Lie theoretic proof for Wang's theorem regarding the sufficiency conditions for a compact homogeneous manifold $G/H$ to admit a $G$-invariant complex structure, relying solely on root space decomposition properties. This contrasts with Ni and Wallach’s recent work that employs more specialized Lie algebra objects like Borel subalgebras and Iwasawa decompositions. Open full article →
	Foliated and Mather-Jacobian discrepancies via tangential arcs	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article introduces a tangential arc-space approach to calculate foliated discrepancies for logarithmic simple co-rank one foliations on threefolds, focusing on an invariant normal crossing separatrix divisor. This method links foliated adjunction with ordinary log pairs and applies the Ein-Mustață-Yasuda arc-space theorem to derive a tangential codimension formula, aligning logarithmic codimensions of toroidal tangential divisorial cylinders with their discrepancies. The theory supports a branch-conductor description for identifying non-lc and non-klt loci in foliated settings. Open full article →
	On Deranged Unit-Interval Parking Functions and the Deranged Bell Numbers	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article establishes a bijection between deranged ordered set partitions and deranged unit-interval parking functions ($\mathrm{DUPF}_n$), showing that their count is given by the deranged Bell numbers $\widetilde F_n$. This work introduces new structural insights into parking functions, including leader and lucky-car characterizations, a fixed-block stratification, and generating functions related to these structures. Open full article →
	A $3$-adic Recurrence for the Fixed Points of the Josephus Function $J_4$	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The paper establishes a $3$-adic recurrence to explain erratic fluctuations in fixed points of the Josephus function for stepsize four, where the survivor is initially positioned last; this alternation between two types of near-misses (falling short by one or two seats) differentiates it from solved cases with smaller stepsizes. The length of each block of near-misses corresponds to the number of times three divides a quantity derived from preceding circle sizes, enabling an efficient computation of the survivor's position for any circle size proportional to counting near-misses rather than iterating through all smaller circles. Open full article →
	A scheme for topological phases of the Weyl $C^*$-algebra	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article presents a classification scheme for topological phases of matter using the topology of pure states in a model $C^$-algebra, where phases are characterized by homotopy classes of state sections. This scheme generalizes the $K$-theoretic classification of gapped spectral projectors for A and AI type topological insulators when applied to translation-invariant Weyl $C^$-algebra states. Open full article →
	Prym-Brill-Noether Theory for General Covers	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study establishes new bounds on the dimension of the Prym-Brill-Noether variety for étale double covers of k-gonal curves, disproving a conjecture by Creech et al., and proposes a new conjecture. A key method involves analyzing the Prym-Brill-Noether variety of a double cover of a specific tropical curve called the loop of loops, utilizing Coxeter group combinatorics to prove topological properties. Open full article →
	Further Results on the Maximum Number of Stars in Graphs with Forbidden Properties	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study investigates the maximum number of $t$-stars in graphs that are not $k$-edge-hamiltonian, building on earlier work by Füredi et al. and Berikkyzy et al., who explored similar properties including traceability and hamiltonian-connectedness. The research reveals that a previously proposed conjecture fails at a critical value of $t$, leading to a threshold-type result for extremal graphs near this value. Open full article →
	Quandle homology and relative group homology	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article introduces a chain map connecting quandle homology to relative group homology, enabling the construction of quandle cocycles. This connection is significant for advancing algebraic structures in knot theory. The chain map's relation to Seifert (hyper)surfaces' triangulations of 1- and 2-dimensional links provides a geometric interpretation of these algebraic constructs. Open full article →
	A note on the second James-Hopf invariant	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The paper characterizes the stabilized second James-Hopf invariant through three defining axioms, notably its adherence to the Cartan formula and its vanishing property on suspensions. This work advances understanding in algebraic topology by uniquely specifying this invariant via natural transformations, utilizing a combination of the natural stable splitting of the James construction and Goodwillie calculus in its proof. Open full article →
	Exponential Mixing for 2D Stochastic Damped Euler Equation Driven by Bounded Noise	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
Researchers prove exponential mixing for a two-dimensional stochastic damped Euler equation on a torus, showing that with sufficiently large damping, a unique invariant measure exists and the system converges exponentially fast to equilibrium without viscous regularization. This result is novel as it establishes a $W^{1,\infty}$ estimate for vorticity, enabling a compact absorbing mechanism in $C(\mathbb{T}^2)$ and demonstrating that strong linear damping can replace viscosity's role in achieving mixing properties. Open full article →
	The Gruenberg-Kegel graph of finite solvable groups that are character-quadratic or semi-rational	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study classifies Gruenberg-Kegel graphs for finite solvable groups that are either character-quadratic or semi-rational, revealing specific structures and conditions under which these graphs can exist; notably, when the graph has up to three vertices in a nontrivial group setting, it belongs to an explicit list of 20 realizable graphs (with one possible exception), contingent upon the group's order not being divisible by 17 for semi-rational groups. Open full article →
	New columns in decomposition matrices of symmetric groups for every block	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
Researchers have identified new columns in decomposition matrices for symmetric groups labeled by partitions with even arm lengths for $p$-divisible hooks, solving at least one column for every block in odd characteristic $p$. These multiplicity-free columns are characterized using the recently introduced "odd sequence" statistic of partitions. This finding also determines the indecomposable summands of Foulkes modules $H^{(2^m)}$. Open full article →
	Distinguishing Gromov-Thurston manifolds using algebraic Dehn fillings	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study develops criteria to differentiate the homotopy types of Gromov-Thurston manifolds through an analysis of their fundamental groups as virtual Dehn fillings of relatively hyperbolic groups, providing a new method for manifold distinction. This matters as it offers a novel algebraic approach to geometric problems in topology. The key detail involves using the properties of virtual Dehn fillings to distinguish between these complex geometric structures. Open full article →
	A note on $\text{ded }\kappa$ and the part-whole principle	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article establishes a connection between the part-whole principle and $\text{ded }\kappa$, a characteristic related to Dedekind cuts in linear orders, which improves upon a previous result by Mancosu and Massas regarding generalized probability functions. This matters as it advances understanding in set theory and its applications to logical structures. Specifically, the work proposes new questions in this area following the improvement of the earlier probabilistic functions result. Open full article →
	The inverse reduction map in the quantum Littlewood-Richardson bijection	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article details a method to decompose a symplectic column into fixed and disjoint parts under parity involution, which uniquely determines the inverse of the reduction map in the quantum Littlewood-Richardson bijection; this decomposition enables explicit construction of the inverse using combinatorial $R$-matrices and shorter reduction maps as outlined by Watanabe. Open full article →
	Power series for roots of a trinomial and Kummer-like identities for higher order hypergeometric series	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article explores roots of the trinomial equation $x^n + px + q = 0$ using hypergeometric series, focusing on deriving alternative series solutions for cubic cases and generalizing these to higher orders through new identities akin to Kummer's. For the cubic case ($n=3$), the authors derive series in powers of the discriminant $D$ and its reciprocal, extending these methods to develop similar series for all $n \geq 3$. Open full article →
	Riemannian Positive Mass Theorem in All Dimensions in the Presence of Low-Codimension Singularities	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article proves the Riemannian positive mass theorem for asymptotically flat $L^\infty$-metrics with singular sets of subcritical Minkowski dimensions, showing nonnegative ADM mass in all ends and zero mass only in the Euclidean case. This work provides an analog to Schoen's codimension-three conjecture for positive scalar curvature in the context of manifolds with singularities. The proof involves a $\mu$-bubble dimension-descent argument adapted from previous works. Open full article →
	Standard Polynomials for Principal Subalgebras $\mathbb{K}Q_{\geq 1}$ of Path Algebras	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study explores standard polynomials for principal subalgebras $\mathbb{K}Q_{\geq 1}$ of path algebras, detailing their $PI$-theory and characterizing the centers and 3-centers through $St_2$ and $St_3$-elements. This work impacts understanding combinatorics on words in formal languages by providing algebraic explanations from a combinatorial viewpoint. Open full article →
	A Colombeau--Beurling criterion for the Riemann hypothesis	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The paper establishes an equivalence between the Riemann hypothesis and the properties of a specific moderate net within the Colombeau algebra $G(0,1)$, constructed through damped Bézout sums; this reformulates the Riemann hypothesis using generalized functions and weak association criteria. Two explicit damping strategies are introduced: one with exponential damping $\exp(-k\varepsilon^2)$ and super-exponential truncation, and another with polynomial damping $k^{-\delta(\varepsilon)}$ where $\delta(\varepsilon)=(\log(1/\varepsilon))^{-\alpha}$, illustrating the conditions under which these nets are moderate and uniformly $L^2$-bounded. Open full article →
	Note On Gaussian Random Fields \& Underlying Markov Processes Through a Central Limit Theorem	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	1.00	reviewed
The paper introduces universal Gaussian random fields (UGRF) for an underlying ergodic Markov process through a central limit theorem, demonstrating their connection to previously studied Gaussian random fields associated with transient Markov processes. A Lamperti-type time change is applied to achieve an infinite-dimensional stationary Ornstein-Uhlenbeck evolution, showing that Itô's deterministic component vanishes under this transformation and establishing connections under specific conditions on the infinitesimal generator of the process. Open full article →
	Occupation Patterns and Parikh Images in Markov Support Dynamics	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article introduces a commutative-algebraic framework using occupation patterns and Parikh images to study state trajectories in discrete-time Markov chains, embedding these patterns into combinatorial commutative algebra through monomial ideals. This method distinguishes three levels of support complexity (reachability growth, trajectory growth, and occupation-pattern growth) and demonstrates how occupation ideals reflect various dynamic behaviors like branching and recurrence within the graph structure. For instance, at each time step n, a monomial ideal is generated by Parikh monomials of all admissible trajectories of length n, with its minimal generators corresponding one-to-one to distinct occupation patterns realized at that time. Open full article →
	Spectral Properties of Dense Barab\'asi-Albert Graphs	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study examines the adjacency spectra of dense Barab\'asi-Albert graphs, revealing that as graph size increases, the expected adjacency matrix converges to a rank-one kernel, with fluctuations forming a random matrix having a calculable variance profile. This finding is significant for understanding the spectral properties of real-world networks characterized by preferential attachment and uneven degree distributions. Notably, the research derives the limiting bulk spectral distribution using the quadratic vector equation approach and identifies the asymptotic location of the leading eigenvalue influenced by the rank-one mean component. Open full article →
	Determination of separable perturbations of an unbounded potential in the two-dimensional Schr\"odinger equation	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study establishes uniqueness and stability for determining separable perturbations of an unbounded potential in a two-dimensional Schrödinger equation using the Dirichlet-to-Neumann map, which is crucial for inverse problems in quantum mechanics. The proof leverages a particular Carleman inequality to achieve these results. Open full article →
	The integral closedness of lattice simplices with large lattice length	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study proves that every $n$-dimensional lattice simplex $P$, where the lattice length $L(P)\ge n-1$, is integrally closed, impacting the understanding of projective normality for ample line bundles on $\mathbb{Q}$-factorial toric Fano varieties with Picard number one. A key detail involves refining this result using the invariant $\Gamma_{P}$. Open full article →
	On Perfectoidizaiton of Finite Algebras over a Perfectoid Ring	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study explores properties of perfectoidization for finite algebras over a perfectoid ring, proving that if $A=R[t]/(m(t))$ with $R$ being perfectoid and the discriminant $d$ of $m(t)$ a non-zero divisor meeting a bounded torsion condition, then $dA_{\mathrm{pfd}}\subset A$. This work aids in providing explicit descriptions of algebraic structures under perfectoid conditions. Open full article →
	Algebraic Hodge generic points are dense	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study proves that algebraic Hodge generic points are dense within complex varieties over $\overline{\mathbb{Q}}$, contributing to the Grothendieck period conjecture under a large monodromy condition, and it establishes new cases of the Mumford-Tate conjecture. A key technical achievement is a novel result on relations among solutions of $G$-operators, utilizing height estimates by Bombieri and André. Open full article →
	A closed subspace of a Gateaux differentiability space is a Gateaux differentiability space : over 46 years of open problem solved	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The paper solves a 46-year-old problem by proving that a closed subspace of a Gateaux differentiability space is itself a Gateaux differentiability space, using a novel technique involving weak$^{}$ slices and an iterative selection process. This breakthrough advances the understanding of geometric properties within non-metric frameworks and introduces new methods for analyzing dual convex sets under pure weak$^{}$ topology. As a result, if $X$ is a weak Asplund space and $M$ is a closed subspace of $X$, then $M$ is confirmed to be a Gateaux differentiability space. Open full article →
	Palindrome complexity versus factor complexity	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study establishes a new relationship indicating that for non-ultimately periodic infinite words, the limit of the ratio of palindrome complexity adjusted logarithmically to factor complexity approaches zero as n increases. This finding highlights a fundamental connection between palindromic and general subsequential structures in infinite sequences; notably, the study also confirms the essential optimality of the numerator in this limiting expression. Open full article →
	On varieties where $\mathrm{CS}\mathfrak{X}$ implies $\mathfrak{X}\mathrm{T}$	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article provides new examples of varieties where the property $\mathrm{CS}\mathfrak{X}$ (all maximal $\mathfrak{X}$-subgroups are malnormal) implies $\mathfrak{X}\mathrm{T}$ (any two $\mathfrak{X}$-subgroups with a nontrivial intersection generate an $\mathfrak{X}$-subgroup), extending the findings from previous work. This implication matters as it clarifies the relationship between these group properties within specific varieties, contributing to the broader understanding of $\CSX$- and $\XT$-groups. One concrete detail is that while $\mathrm{CS}\mathfrak{X}$ does not generally imply $\mathfrak{X}\mathrm{T}$, certain identified varieties indeed satisfy this implication. Open full article →
	Decomposition Theorem for Perfectoid Rings along General Ideals	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article presents a tameness theorem for torsion in perfectoid rings, showing that if $ R $ is a perfectoid ring and $ I \subset R $ an ideal, then the $ I $-torsion in $ R $ is $ I_{\mathrm{perfd}} $-almost zero, leading to an excision-type decomposition. This result matters as it offers new structural insights into perfectoid rings using Andr\'e's lemma and $p$-complete arc descent techniques. Open full article →
	Random Permutations from Bott-Samelson Varieties	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study examines probability distributions on $S_n$ derived from Bott-Samelson varieties over finite fields, showing that for reduced words $R_1$ and $R_2$, their associated distributions $\mathbb{P}_{R_1,q}$ and $\mathbb{P}_{R_2,q}$ are equal if and only if $R_1$ and $R_2$ belong to the same commutation class, indicating that distribution equality implies the words represent the same permutation. Open full article →
	S-Equivalence of Band-Twisted Genus One Knots	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article proves that a genus-one knot $K$ and its band-twisted variant $K(\ell,0)$ are $S$-equivalent if and only if the $(2,2)$-entry of their Seifert matrix is zero and the sum of off-diagonal entries divides $\ell$. This equivalence is shown to yield infinite families of $S$-equivalent but inequivalent genus-one knots, such as the knot $9_{46}$. Open full article →
	Ramsey numbers of multiple copies of a graph and the random Ramsey theorem	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The paper extends the determination of $2$-colour Ramsey numbers to $r$-colour cases for multiple copies of a fixed graph $H$, specifically for $r=3$ and when $H$'s chromatic number is at least $r$, using $(H,r)$-gadgets and linear programming. It also derives the $r$-colour Ramsey number for complete bipartite graphs up to a linear error term, linking to the clique-edge-covering problem, and proves random versions of these results, generalizing the Rödl-Ruciński theorem. Open full article →
	A Matrix-Theoretic Exact Formula for Counting Primes in Intervals Between Consecutive Odd Squares	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article presents a matrix-theoretic exact formula to count primes in intervals between consecutive odd squares, defining matrix multiplicity and proving an identity that calculates the number of primes in each interval without primality testing. The formula confirms at least one prime exists in such intervals up to $1.37 \times 10^{17}$, establishing a combinatorial condition equivalent to this property. Open full article →
	A probabilistic bijection between twenty-vertex configurations with a free west boundary and Gelfand-Tsetlin patterns avoiding three equal entries in a row	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study establishes a probabilistic bijection between twenty-vertex configurations on quadrangular domains with a free west boundary and Gelfand-Tsetlin patterns that avoid having three consecutive equal entries, revealing a correspondence explained by the alignment of their enumeration formulas. This connection is significant as it links two distinct combinatorial structures through a novel mapping where the west boundary of vertex configurations corresponds to the bottom row of Gelfand-Tsetlin patterns; specifically, when the west boundary is fixed, it aligns with the pattern's bottom row being $(1, 2, \ldots, n)$. Open full article →
	Quasi-Polish spaces and spaces of filters in second-order arithmetic	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The paper formalizes quasi-Polish spaces and their equivalent representations, such as UF spaces and $\mathbf{\Pi}_2^0$ subspaces of $\mathcal{P}(\mathbb{N})$, within second-order arithmetic to conduct a reverse mathematical analysis of the transitions between these structures. This work matters as it provides foundational insights into the logical strength required for equivalences among different representations of quasi-Polish spaces, enhancing understanding in descriptive set theory and topology. Open full article →
	Hecke monoids, their homomorphisms and parabolicity	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study explores homomorphisms in Hecke monoids, focusing on the properties and classification of parabolic and injective homomorphisms, revealing a rich structure of parabolic homomorphisms and classifying locally injective connected homomorphisms between classical types, which unexpectedly provides insight into all homomorphisms between Hecke monoids. Open full article →
	Conformally Invariant Besov Spaces on Chord-Arc Domains	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article introduces Besov-type spaces on simply connected domains, proving that on quasidisks, first-order Besov spaces are isomorphic to higher-order counterparts, which preserve conformal quasi-invariance. This characterization of chord-arc domains through the isomorphism between first-order and boundary Besov spaces extends previous Dirichlet space ($p=2$) results to all $1 < p < \infty$. Open full article →
	Topological complexity sequences of groups	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article defines the topological complexity sequence for groups based on their Milnor constructions, providing an intrinsic refinement that applies to groups with infinite cohomological dimensions. This sequence is shown to be weakly increasing and unbounded for such groups. For a finite group of even order, the asymptotic behavior of this sequence has been determined. Open full article →
	Compactness of products and commutators of inner projections	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The paper characterizes the compactness of products and commutators of inner projections in Hardy spaces over unit disks and polydisks, using Douglas algebra for single-variable cases. It identifies a rigidity phenomenon where on the bidisc, the product of two inner projections is compact only if it has finite rank, contrasting with triviality in higher-dimensional polydiscs. Open full article →
	Large deviations for maximum local time of simple random walk in dimensions $d\ge 3$	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study provides precise asymptotic probabilities for upward and downward deviations of the maximum local time of simple random walks on $\mathbb{Z}^d$ for dimensions $d\ge 3$, both in discrete- and continuous-time settings, with Gumbel-type distributions identified at the logarithmic scale. The research matters as it completes the understanding of local time deviations through a loop-pruning construction that proves matching discrete-time lower bounds. A concrete detail is the derivation of sharp continuous-time asymptotics for downward deviations alongside establishing discrete-time upper bounds. Open full article →
	Geometric bounds for Steklov and weighted Neumann eigenvalues on Euclidean domains	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	1.00	reviewed
The study establishes sharp upper bounds for the first two nonzero Steklov eigenvalues in Euclidean spaces of dimension $d \geq 7$, normalized by volume and boundary measure, and derives strict upper bounds for dimensions $3 \leq d \leq 6$. Additionally, it extends previous results to provide strict upper bounds for all higher Steklov eigenvalues on planar simply connected domains with continuous boundaries. Open full article →
	Asymptotic theory and first-order bias of the Wallace--Freeman estimator	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The Wallace--Freeman estimator is shown to be equivalent to a penalized likelihood criterion with a $n^{-1}$ penalty weight in regular parametric models, establishing its asymptotic properties within standard theory; this equivalence also reveals an explicit $O(n^{-1})$ bias difference from the maximum likelihood estimator. The findings are illustrated for the Weibull model, where the Wallace--Freeman penalty modifies the leading bias of the shape parameter's estimation. Open full article →
	Cohomological invariants of hermitian forms that detect hyperbolicity	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
Researchers constructed cohomological invariants for hermitian forms using unramified cohomology groups that detect hyperbolicity, applicable across any type (orthogonal, symplectic, unitary) and over fields with any characteristic; this method shows that hermitian pairs over quaternion algebras with trivial classical invariants are hyperbolic in fields of separable dimension 3. Open full article →
	Semi-Cosimplicial Hilbert Spaces with Isometric Coface Operators	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article introduces and develops semi-cosimplicial Hilbert spaces with isometric coface operators, linking to non-commutative probability theory through the concept of spreadability. This work explores applications in areas such as cohomology, representation theory, and graph decomposition, offering a new framework for understanding distributional symmetry. A key detail involves the classification and extensions of semi-cosimplicial sets with injective coface maps, providing foundational insights into their structure and potential theoretical applications. Open full article →
	Proof of Sun's conjectures on hyperbolic cosine series via the Eisenstein--Lambert method	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article proves two conjectures by Zhi-Wei Sun on hyperbolic cosine Lambert series, including the evaluation of a series $S_m$ for integers $m \geq 0$, where specific values for $S_0$ and $S_1$ are derived as $S_0=\frac{1}{12}$ and $S_1=\frac{1}{2\pi^2}$, with $S_m=0$ for $m>1$. The proof employs the Eisenstein--Lambert method, leveraging modular transformations for Eisenstein series. Open full article →
	Duality for Delsarte's extremal problem on compact Gelfand pairs	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The study explores Delsarte-type extremal problems for positive definite functions on compact Gelfand pairs using infinite-dimensional linear programming, with implications for Turán and Delsarte problems in number theory, sphere packing, and statistics. The paper establishes and proves a strong duality statement for these problems. Notably, the research includes compact Abelian groups as a specific case. Open full article →
	The group identification problem for $p$-groups of small order	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
Research identifies effective group-theoretic invariants and develops an algorithm to distinguish among non-isomorphic p-groups, specifically applied to the $10,494,213$ groups of order $2^9$. Notably, 56 pairs of these groups are particularly challenging to differentiate using invariants. Open full article →
	On the stable Hopf invariant	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article presents a simplified approach to the stable Hopf invariant, offering elementary proofs for key formulas including the Cartan Formula. It extends these results to the stable category of $\pi$-spaces when $\pi$ is a discrete group, enhancing applicability and understanding of the invariant's uniqueness. Open full article →
	Comparison theorems for the extreme eigenvalues of a random symmetric matrix	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The paper establishes a comparison theorem showing that the maximum eigenvalue of a sum of independent random symmetric matrices is dominated by that of a matching Gaussian random matrix, strengthening previous results and providing corollaries for minimum eigenvalues and spectral norms. This methodology enhances existing bounds on eigenvalues in various fields including spectral graph theory and quantum information theory, and provides the first complete proof for the injectivity properties of sparse random dimension reduction maps conjectured by Nelson & Nguyen in 2013. Open full article →
	Bi-twisted conjugacy in finite groups	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
Researchers offer two methods to calculate the number of bi-twisted conjugacy classes in finite groups—one through irreducible characters and another using ordinary conjugacy classes—highlighting new equalities and inequalities for Reidemeister numbers. The study also establishes connections between bi-twisted conjugacy, representation theory, and fixed-point free automorphisms. One concrete detail includes the derivation of sharp inequalities for Reidemeister numbers related to these conjugacy classes. Open full article →
	Riemann-Wirtinger integrals on the product of two one-dimensional complex tori	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article introduces the Riemann-Wirtinger integral extended to the product of two one-dimensional complex tori, generalizing its application beyond a single complex torus. This extension is significant for understanding the structure of associated twisted cohomology groups and deriving related differential equations. The study derives a specific system of differential equations satisfied by this new form of Riemann-Wirtinger integral. Open full article →
	Pure extension of the theta divisor over the moduli space of abelian varieties	arXiv math	📐 Math	2026-07-07	2026-07-07	1.00	reviewed
The article extends the theta divisor over the moduli space of abelian varieties, showing that its pure weight 2 extension differs from the Zariski closure by a tropicalization of the Riemann theta function; this work applies Moret-Bailly's "key formula" to derive a universal formula for the Néron-Tate height of a point. Open full article →

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Source	Kind	State	Last status	Every
Ars Technica	rss	active	ok: 20 seen / 0 new	60m
arXiv cs.GR	rss	active	ok: 24 seen / 0 new	60m
arXiv math	rss	active	ok: 1134 seen / 0 new	60m
Game Developer	rss	active	ok: 50 seen / 0 new	60m
Hacker News (front page)	api	active	ok: 50 seen / 3 new	60m
Hacker News (Show/Ask HN)	api	active	ok: 50 seen / 10 new	60m
Lobsters	rss	active	ok: 25 seen / 3 new	60m
Quanta Magazine	rss	active	ok: 5 seen / 0 new	60m
r/gamedev	rss	active	ok: 25 seen / 0 new	60m
Slashdot	rss	active	ok: 15 seen / 0 new	60m
Terence Tao blog	rss	active	ok: 10 seen / 0 new	60m
a16z	rss	off	unverified	60m
GDC Vault	scrape	off	deferred	60m
IndieHackers	rss	off	disabled	60m
Inigo Quilez	rss	off	unverified	60m
Ke-Sen Huang SIGGRAPH index	scrape	off	deferred	60m
LinkedIn	api	off	inactive	60m
Real-Time Rendering blog	rss	off	blocked	60m
Shadertoy blog	rss	off	unverified	60m

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