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	Title	Source	Topics	Written	Found	Rel.	Status
	ControlHair: Synergizing Physics Simulator and Video Diffusion for Controllable Dynamic Hair Rendering	arXiv cs.GR	🫖 Rendering	2026-07-07	2026-07-07	1.00	reviewed
ControlHair introduces a hybrid framework integrating physics simulation with video diffusion to achieve precise control over dynamic hair rendering, addressing the limitations of current video diffusion models in controlling hair dynamics. This method decouples physics reasoning from video generation through a three-stage pipeline and outperforms text- and pose-conditioned baselines, as demonstrated using a curated dataset of 10K videos. The framework showcases applications such as dynamic hairstyle try-on and cinemagraphic effects. Open full article →
	Provable Pruning for Efficient 3D Gaussian Splatting via Coresets	arXiv cs.GR	🫖 Rendering	2026-07-07	2026-07-07	1.00	reviewed
The study introduces a provable method for creating coresets in 3D Gaussian Splatting (3DGS) that significantly reduces the number of Gaussians required while preserving rendering quality, with guarantees dependent on the resolution. This method samples Gaussians based on their sensitivity scores, demonstrating state-of-the-art performance under aggressive compression and minimal recovery compute conditions. Empirical results show superior performance in prune-only scenarios and short finetuning regimes compared to existing heuristic methods. Open full article →
	High-Performance Real-Time Implicit Strand-Based Hair Rendering via Software Rasterization	arXiv cs.GR	🫖 Rendering	2026-07-07	2026-07-07	1.00	reviewed
Researchers propose a software rasterization pipeline for real-time rendering of strand-based hair using hair meshes, significantly enhancing performance and compatibility beyond existing methods. This advancement allows for efficient far-field hair rendering at minimal computational cost by integrating deferred shading with strand filtering and an LOD scheme, marking the first approach to combine such efficiency, flexibility, and broad hardware support. The method uses a single sample per pixel for rendering, reducing the need for high-end hardware. 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 →
	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 →
	Linearized Polynomial Chinese remainder codes	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	1.00	reviewed
Researchers introduce a new family of codes for rank and sum-rank metrics, leveraging a Chinese Remainder Theorem for linearized polynomials over finite fields; a decoding algorithm is proposed for certain instances of these codes. Open full article →
	On the spectral radius of the non-backtracking matrix of the configuration model	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	1.00	reviewed
The study proves a concentration result for the leading eigenvalue of the non-backtracking matrix in the configuration model with uniformly bounded degrees, showing it converges to $\frac{\mathbb{E}[P(P-1)]}{\mathbb{E}[P]}$ as vertices increase. This finding is significant as it relates to the mean offspring number in a branching process and can be applied to analyze subgroup growth rates in free groups. Open full article →
	Validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	1.00	reviewed
A recently proposed strongly polynomial-time algorithm for solving general linear programming problems has been validated, combining primal and dual problems into a system constrained by complementarity relations. The algorithm uses iterative complementary Gauss-Jordan pivoting operations guided by a necessary-condition lemma. It is proven to require no more than 2(k+n) iterations, with k being the number of constraints and n the number of variables. Open full article →
	Beyond DSA: Conjugacy-based Comparison of Dynamical Systems	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	1.00	reviewed
The study introduces Conjugacy-based Similarity Analysis (CSA) to compare dynamical systems, showing that orthogonal alignment methods like Dynamical Similarity Analysis (DSA) are insufficient for identifying topological conjugacies due to their limitations in capturing non-orthogonal basis-transfer matrices. CSA restricts alignments to state-space bijections and is proven to be the finite-data projection of composition operators linked with candidate bijections, which is crucial when observable dictionaries are selected from data explicitly or implicitly. Open full article →
	Sharp ratios for low-index Neumann eigenvalues on convex domains	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	1.00	reviewed
Researchers prove sharp bounds for low-index Neumann eigenvalues on convex domains, specifically $\mu_2(\Omega)\le 4\mu_1(\Omega)$ and $\mu_3(\Omega)\le 9\mu_1(\Omega)$, resolving a problem attributed to Henrot and confirming predictions from the one-dimensional model with constants optimal in every dimension. Open full article →
	Recursive Lifting Beyond the Ahlswede--Khachatrian Construction	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	1.00	reviewed
The article presents a recursive lifting method that surpasses the Ahlswede--Khachatrian/Mubayi--Zhao construction for uniform set systems of bounded VC-dimension, specifically proving improved lower bounds for $M_d(n)$ in every dimension $d \ge 3$. This advancement is significant as it provides a new benchmark for the Erdős--Frankl--Pach problem. A concrete detail is the derived inequality: \[ M_d(n)\ge \binom{n-1}{d}+\binom{n-4}{d-2}+M_{d-3}(n-5) \] for $n\ge d+3$. Open full article →
	A linear algebraic proof of the Laplacian spread conjecture	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	1.00	reviewed
The article presents a novel and more concise linear algebraic proof for the Laplacian Spread Conjecture, stating that for any graph $G$, the sum of its second smallest Laplacian eigenvalue and that of its complement $\overline{G}$ is at least 1. This proof offers a significant advancement in graph theory by confirming the conjecture with a different mathematical approach. Open full article →
	Ramanujan-type identities for alternating Hurwitz zeta functions	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	1.00	reviewed
The paper extends a Ramanujan identity for the Riemann zeta function to the alternating Hurwitz zeta function, exploring its properties under modular symmetry conditions and establishing new Ramanujan-type identities. This extension is significant as it broadens the applicability of Ramanujan's work to more complex zeta functions and related special functions. A concrete detail includes the derivation of infinite series expressions for products involving tangent and hyperbolic tangent functions, connected to convolution sums of specific sequences. Open full article →
	Rotman Lens	Hacker News (front page)	🫖 Rendering	2026-07-01	2026-07-06	1.00	reviewed
The Rotman lens is an antenna system that enables multibeam communication by supporting multiple feeds for simultaneous transmission or reception without reorientation, enhancing efficiency in radar and telecommunications systems. This technology matters because it allows for more versatile and efficient use of frequency bands compared to traditional antennas. A key feature includes the use of a series of concentric rings with specific radii to manipulate electromagnetic waves for multibeam functionality. Open full article →
	Show HN: orzma – a terminal emulator that renders webviews inside the terminal	Hacker News (Show/Ask HN)	🫖 Rendering	2026-07-06	2026-07-06	1.00	reviewed
orzma is a terminal emulator that integrates webview rendering capabilities directly within the terminal interface, offering users the ability to view and interact with web content without leaving the terminal environment. This innovation could significantly enhance productivity for developers and power users who rely heavily on terminal-based workflows by reducing context-switching between applications. A concrete detail is that orzma allows for direct interaction with web elements like forms and links from within the terminal window. Open full article →
	Show HN: A free, GPU-accelerated Texas Hold'em GTO solver in C++/CUDA	Hacker News (Show/Ask HN)	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
A free, GPU-accelerated GTO (Game Theory Optimal) solver for Texas Hold'em has been developed using C++ and CUDA, enhancing the speed of strategic game analysis. This tool is significant for poker players and researchers as it can provide optimal strategies faster than traditional methods. The solver leverages GPU acceleration to compute complex scenarios efficiently, demonstrating a key application of CUDA in gaming strategy. Open full article →
	PixGS: Pixel-Space Diffusion for Direct 3D Gaussian Splat Generation	arXiv cs.GR	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
PixGS introduces a single-stage pipeline for direct high-quality 3D Gaussian Splat generation, addressing limitations of existing complex cascade pipelines by leveraging pixel-space diffusion to avoid decoding artifacts. The method incorporates comprehensive supervision including surface normals, depth, and high-frequency structural information, outperforming state-of-the-art methods with fast inference (1s on a single A100 GPU). Open full article →
	TemporalGS: Training-Free Plug-and-Play Acceleration for 3D Gaussian Splatting Rendering via Temporal Priors	arXiv cs.GR	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
TemporalGS introduces a training-free method to accelerate 3D Gaussian Splatting (3DGS) rendering by leveraging temporal priors across consecutive frames, achieving up to $1.48\times$ speed enhancement without compromising quality. This approach matters as it addresses the challenge of high FPS and low latency in 3DGS for various scenes by employing strategies such as temporal dynamic culling and selective rendering, implemented atop tile-based software rasterization. Open full article →
	Fast 3D Foundation Model Initialized Gaussian Splatting	arXiv cs.GR	🎲 Game development, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
This paper presents a fast method for high-quality 3D Gaussian Splatting reconstruction that bypasses traditional Structure-from-Motion techniques by using 3D Foundation Models for initialization, achieving competitive results (23.61 dB PSNR, 0.19 LPIPS) in about three minutes per scene with as few as 50-60 input views. Open full article →
	Walking on Spheres and Talking to Neighbors: Variance Reduction for Laplace's Equation	arXiv cs.GR	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The article introduces a new caching strategy for Walk on Spheres algorithms that leverages Brownian Motion continuity to improve variance reduction in solving Laplace's equation with Dirichlet boundary conditions, achieving better asymptotic runtime than previous methods. This approach differs from earlier pointwise estimation by utilizing relationships between nearby points through a fixed-size cache. The algorithm’s performance and bounds are demonstrated across problems of increasing complexity. Open full article →
	Glare Mitigation using a Differentiable Unified Glare Rating	arXiv cs.GR	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The paper introduces a differentiable proxy for the Unified Glare Rating (UGR) that resolves optimization instabilities through a continuous function and optical scattering pass, enabling gradient-based inverse rendering for glare reduction. This method transforms passive perceptual evaluation into an active loss landscape to optimize visual comfort across various radiometric domains in architectural and automotive design. A key detail is the replacement of the discrete UGR step function with a tunable sigmoid boundary to allow smooth gradients from psychophysical measures to scene parameters. Open full article →
	CGGS: Consistency-Augmented Geometric Gaussian Splatting for Ego-centric 3D Scene Generation	arXiv cs.GR	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The paper introduces CGGS, a framework for improving ego-centric 3D scene generation by enhancing consistency and geometric accuracy through a Multi-View Latent Diffusion Model with a consistency-augmented loss and a Geometric Refiner using an entropy-based Mutual Information Depth Loss. This method outperforms previous techniques in creating coherent text-driven 3D scenes, as demonstrated through comprehensive experiments. Notably, CGGS uses optical flow and point-track correspondence to estimate depth from ego-centric 2D priors. Open full article →
	For edge-color-critical graphs, non-$r$-partite spectral extremal graphs are edge extremal	arXiv math	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The paper proves Fang and Lin's conjecture that non-$r$-partite spectral extremal graphs for edge-color-critical graph $F$ with $\chi(F)=r+1$ are also edge-extremal under specific conditions, including a hypothesis involving the Turán graph $T_{n,r}$ and an embeddability condition on $F$. For a specific case where $F=K_{1,1,t_3,\ldots,t_{r+1}}$, with each $t_i \ge 2$, it is shown that $\mathrm{ex}_{r+1}(n,F)=\|E(T_{n,r})\|-\lfloor n/r\rfloor+2(t_{\min}-1)$ for large $n$. Open full article →
	A Restricted Chen-Nagano Variational Principle for the Einstein-Hilbert Functional	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The paper introduces a restricted Chen-Nagano variational principle for the Einstein-Hilbert functional, focusing on compact Riemannian manifolds under specific gauge constraints, leading to a new criticality condition expressed as $E_g = B_g^{*}(\theta) + c\,g$. This approach not only yields a novel characterization of critical metrics but also extends to generalized Ricci almost soliton structures. Open full article →
	A linear-algebraic formulation of dimensional analysis with constraints	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The article presents a linear-algebraic approach to dimensional analysis that incorporates constraints using logarithmic variables, where dimensional transformations and constraints are represented as subspaces whose intersection characterizes independent dimensionless quantities. This method streamlines redundancy elimination in complex systems with predefined relationships among variables. An example provided involves applying the technique to analyze drag force, demonstrating its utility in simplifying physical relations under constraints. Open full article →
	The Mean field equation on the Tate curve	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The paper explores the spectrum of the Laplacian on the Tate curve and constructs a Green's function as a finite sum, analogous to its Archimedean counterpart on the flat torus. It establishes existence and uniqueness for solutions of the mean field equation on this space, with proofs involving convergence of solutions from finite quotients. Notably, the well-posedness properties mirror those in the Archimedean setting. Open full article →
	Equivariant linear isometries and infinite little discs operads via transfer systems	arXiv math	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The article uses transfer systems theory to establish homotopic equivalence conditions between $G$-equivariant linear isometries and infinite little discs operads for finite groups $G$, reducing complex topological problems to discrete subgroup and representation theory issues. In the case of abelian $G$, it provides conditions for a maximally compatible pair of transfer systems, contributing to a recent conjecture on equivariant operad pairs. Concrete detail: the authors leverage Balchin-Barnes-Roitzheim's combinatorics of transfer systems on total orders. Open full article →
	New operator designs for Halpern iterations with explicit rates under H\"older error bounds	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The study establishes explicit convergence rates for Halpern-type iterations applied to quasi-nonexpansive operators under H\"older error bounds, showing that the distance from $x_k$ to the intersection set and the norm error $\\|x_k - x^\star\\|$ decay at specific rates depending on the stepsize $(\alpha_k)$ and the exponent $\gamma$. This analysis provides faster convergence than Dykstra's algorithm for projecting points onto intersections of ellipsoids or polyhedrons using various projection-type operators. Open full article →
	Asymptotics of lowlying Dirichlet eigenvalues of Witten Laplacians on domains in pinned path groups	arXiv math	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The study examines the asymptotic behavior of low-lying Dirichlet eigenvalues of Witten Laplacians on domains within pinned path groups, finding that while finite-dimensional analogies suggest approximation by Ornstein-Uhlenbeck operators near critical points, the presence of essential spectrum complicates this analysis; the research focuses on discrete spectrum behavior outside these essential spectra neighborhoods. Open full article →
	St\"ackel and Eisenhart lifts, Haantjes geometry and Gravitation	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The article explores the use of generalized Stäckel geometry for constructing new classes of integrable Hamiltonian systems via Stäckel lifts, extending Eisenhart lifts to include both Riemannian and Lorentzian types. It demonstrates that these systems possess a symplectic-Haantjes structure, illustrated through applications in magnetic systems separable in cylindrical coordinates using modified Stäckel bases. The study also suggests potential applications of momentum-dependent lifting matrices in modified gravity theories and Hamilton-Finsler geometries. Open full article →
	Orbit recovery for spherical functions	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The paper presents a method for orbit recovery of functions under rotation actions in ${\mathbb R}^{n}$ and $S^{n-1}$, demonstrating that degree-three invariants (bispectrum) are sufficient for generic orbit recovery. For the specific case of $SO(3)$ relevant to structural biology applications like cryo-electron microscopy, the authors prove that three radial samples (spherical shells) are enough for recovery, verifying a conjecture and providing an efficient algorithm demonstrated on protein structures. Open full article →
	Carleman Estimates and Controllability of Stochastic degenerate parabolic Heat Equations	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The paper establishes global Carleman estimates to prove null controllability for both forward and backward stochastic degenerate parabolic heat equations, achieving full control with two distinct controllers for the forward equation. Notably, it introduces a new Carleman estimate for the backward equation using a non-vanishing at t=0 weighted function, crucial for proving null controllability of the forward equation via the duality method HUM. Open full article →
	Rerouting Curves on Surfaces	arXiv math	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The study examines the reconfigurability of crossing-free graph embeddings on surfaces by rerouting edges while maintaining vertex positions and avoiding crossings; for matchings, trees, and forests, such reconfiguration is always possible on any orientable surface with genus at least one, including the torus, though it is not universally possible for more general graphs. Open full article →
	Asymptotic-Preserving A Posteriori Analysis of Diffusion and Flow-Matching Samplers	arXiv math	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The study evaluates asymptotic-preserving properties of diffusion and flow-matching samplers as $\sigma_{\min}\to0$, identifying Euler in the $\sigma$-clock as the unique layer-exact discretization up to affine reparameterization, with deterministic samplers maintaining first-order uniform accuracy without a $\log(1/\sigma_{\min})$ factor. On the EDM CIFAR-10 checkpoint, spectra measured once predict held-out residual budgets across different configurations with high precision, calibrating the Itô coefficient at $M_1=1.00\pm0.01$. Open full article →
	Cash-invariant hull representation of divergence preferences	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The article presents a new, computationally more efficient formula for representing uniformly weighted divergence preferences (UWDP), showing they are the translation-invariant hull of state-independent expected utility over $L^0$. This reformulation is significant as it simplifies the computation and analysis of risk-averse preferences that include monotone mean-variance utility. The key detail is the use of a cash-invariant hull representation to characterize UWDP under an adversarially chosen probability measure combined with divergence. Open full article →
	On a complete characterization of path-free complexes associated with complete multipartite graphs	arXiv math	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The paper characterizes $t$-path-free complexes $\PF_t(G)$ of complete multipartite graphs $G=K_{n_1,\dots,n_m}$, showing $\PF_t(G)$ is vertex decomposable if and only if $t\ge 2n_{m-1}-1$, which also marks the threshold for sequential Cohen-Macaulayness. For complete bipartite graphs, the authors determine the homotopy type as a wedge of spheres in all cases. Open full article →
	The list coloring number of uncrowded hypergraphs	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The study proves that for any fixed integer $r \geq 2$ and any $\varepsilon > 0$, sufficiently large finite uncrowded $(r+1)$-uniform hypergraphs with maximum degree $\Delta$ have a list chromatic number at most $(1+\varepsilon)\left(\frac{r\Delta}{\log\Delta}\right)^{1/r}$. This result is significant as it provides an upper bound for the list coloring number of such hypergraphs, utilizing a semi-random nibble technique followed by a Rosenfeld-style counting argument to complete the coloring. Open full article →
	Collision geometry of relativistic spinning particles	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The study explores elastic collisions of relativistic spinning particles under special relativity, using a Lorentz covariant framework and reducing the problem to solving a quadratic equation on a circle. This approach provides explicit formulas for post-collision states and reveals that there are typically only up to eight possible distinct outcomes after collision. Open full article →
	$\mathrm{L}^p$ bounds for parabolic Riesz transforms with rough coefficients: The case $1<p \leq 2$	arXiv math	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The article establishes $\mathrm{L}^p$ bounds for Riesz transforms associated with non-autonomous second order parabolic differential operators, specifically for $1<p \leq 2$, marking the first results in this area with rough coefficients that depend measurably on all variables. The study identifies an open range of exponents through $\mathrm{L}^p$ resolvent bounds and uses novel space-time off-diagonal bounds based on parabolic cubes for small scales and regions modeled after a parabolic Bessel potential's half-order time derivative for large scales. Open full article →
	Long-range interactions and Anderson localisation for one-dimensional high-contrast resonator chain	arXiv math	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The paper examines spectral and transport properties in high-contrast resonator chains, revealing long-range interactions characterized by an off-diagonal decay rate $C(n,m)\sim \frac{1}{\|n-m\|\log^2\|n-m\|}$, crucial for understanding Anderson localisation with arbitrary disorder. Additionally, it establishes the strong convergence of finite capacitance operators to the full operator as chain size increases, enhancing spectral convergence rate estimates from previous studies. Open full article →
	Risk Sensitive Filtering for Singular Systems subject to Round-Robin Protocol	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The paper develops a risk-sensitive Kalman filtering framework for discrete-time linear stochastic singular systems under round-robin communication constraints, transforming these systems into an augmented state space model using Weierstrass canonical form to handle periodically varying measurements. An adaptive mechanism adjusts the risk parameter online based on covariance information, ensuring robustness against uncertainties and disturbances while maintaining filter stability through established sufficient conditions. The approach demonstrates improved estimation performance compared to standard Kalman filters in numerical results. Open full article →
	Rockafellian relaxation and minimum-norm slack for the Walrasian equilibrium problem	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The study introduces a Rockafellian relaxation method for the Walrasian equilibrium problem in exchange economies that may not achieve equilibrium, using a penalized slack variable $v$ to measure distance to the nearest feasible equilibrium. This approach ensures the model remains well-posed and identifies the minimum-norm excess demand vector as the penalty increases, illustrated through an analytically stressed Shapley-Shubik example. Open full article →
	Hyperbolic Completion of Newton's Off-Center Orbit Problem: $SO(2,1)$ Symmetry, Inversion Duality, and Magnetic Classification	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The study resolves the off-center orbit problem for a singular hyperbolic potential by classifying zero-energy trajectories using $SO(2,1)$ symmetry and showing that nonradial orbits are arcs of circles orthogonal to $r=R$. The analysis reveals that an explicit Runge-Lenz-type moment map closes into $\mathfrak{so}(2,1)$, and the introduction of a magnetic field classifies trajectories based on their magnetic interaction strength, with a critical transition at $Q^2=8m\alpha R^2$. Open full article →
	Counting even cycles and even paths with bounded circumference	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The study proves sharp extremal results for the number of even cycles $C_{2s}$ and even paths $P_{2r+1}$ in graphs without long cycles, verifying a conjecture on $\mathrm{ex}(n,C_k,C_{\ge L+1})$ for even cycles and providing exact counts for even paths with bounded circumference. Specifically, for even cycles of length at least $L+1$, the extremal number equals $C_{2s}(H(n,L))$ for large $n$. Open full article →
	A Gaussian-Perron Smoothed Prime-Side Defect for Local Profiles Near Critical-Line Zeros of the Riemann Zeta Function	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
Researchers introduced a Gaussian-Perron prime-force defect that compares smoothed prime-side forces with the logarithmic derivative of the Riemann zeta function, providing a local diagnostic tool for zero geometry. This construction leads to an exact formula and a universal profile for zeros on the logarithmic scale under the assumption of the Riemann Hypothesis and specific pole-damping conditions. The method incorporates an error-function prime weight and anisotropic damping law to distinguish amplified from suppressed nonlocal contributions near critical-line zeros. Open full article →
	On (in)stability of discontinuous standing waves for the NLS with a delta-prime on star graphs	arXiv math	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The article explores the existence and instability of discontinuous standing waves at the vertex for a one-dimensional nonlinear Schrödinger equation (NLS) with power nonlinearity on star graphs featuring a delta-prime interaction, revealing that these waves split into two distinct groups of shifted solitons determined by the number of half-lines. The analysis employs the Grillakis-Shatah-Strauss framework to determine spectral properties and stability, offering a complete description of Morse and deficiency indices for linearization operators. Open full article →
	The Rigidity Theorems for Self-Shrinkers in the Mean Curvature Flow	arXiv math	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The article proves a pinching theorem for self-shrinking hypersurfaces in Euclidean space, showing that under specific conditions on the drift Laplacian's weighted Poincaré inequality, a complete properly immersed self-shrinker $\Sigma$ with $S<1+\lambda$ and satisfying certain integral conditions is necessarily a generalized round cylinder. For two-dimensional cases, this result extends to allow for the endpoint $S\leq3/2$, improving on previous findings by Ding-Xin, Cheng-Wei, and Lei-Xu-Xu. Open full article →
	Guaranteed Lower Eigenvalue Bounds for Spectral Galerkin Methods with Application to Schr\"odinger Operators	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The article presents a method for obtaining guaranteed lower bounds for eigenvalue approximations using spectral Galerkin methods, an advancement not previously available through classical approaches like Kato and Weinstein-Temple enclosures. This technique is particularly significant as it applies to Schrödinger operators without requiring prior knowledge of neighboring eigenvalues; for benchmark potentials in $R^2$, the method achieves certified bounds with significantly fewer degrees of freedom compared to finite element methods, demonstrating enhanced computational efficiency. Open full article →
	A Gallager-Type Redundancy Bound for Binary Shannon-Fano Coding	arXiv math	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
Researchers have established a new redundancy bound for binary Shannon-Fano coding that depends on the largest source probability $p_1$, showing an explicit seven-piece envelope with a maximum redundancy $R<0.5651$ for $p_1<\frac{1}{2}$, marking the first $p_1$-dependent bound for Fano codes and utilizing a more sophisticated method than traditional Huffman coding approaches. Open full article →
	The exact generalized Tur\'an number for $C_6$ in $C_8$-free graphs	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The study determines the exact value of $\ex(n,C_6,C_8)$ as $6\binom{n-3}{3}+12(n-5)$ for sufficiently large $n$, confirming Gerbner et al.'s prediction on asymptotics; the unique extremal graph is identified as $K_3\vee (K_2\cup I_{n-5})$. Open full article →
	On disjunction convex hulls for generalized cross polytopes	arXiv math	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The study provides a complete characterization of the disjunction convex hull $\mathcal{D}$ in $\mathbb{R}^{n+d}$ for generalized cross polytopes when $n=1$ and any $d$, using optimal big-M lifting techniques; it also extends facet-describing inequalities to cases where $n>1$. This work matters as it advances the theoretical understanding of convex hulls associated with disjunctions, which is crucial for optimization problems involving binary variables. A concrete detail is that computational experiments were conducted to validate the theoretical findings. Open full article →
	Sum-product Phenomenon Via Dimension	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The study demonstrates a sum-product phenomenon in fields with abstract dimension theories, generalizing dimensions from geometric theories and Hrushovski's coarse pseudo-finite dimensions, showing that non-expansion in both sumset and product set dimensions of type-definable sets implies the existence of an equivalent definable field. The proof relies on dimensional versions of key inequalities like Ruzsa triangle and Plünnecke-Ruzsa inequalities. Open full article →
	Derivative-Free Richelot Isogenies via Subresultants with Algebraic Certification	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The article presents a derivative-free method for constructing Richelot $(2,2)$-isogenies over prime fields using subresultants and algebraic certification, achieving exact polynomial identities without derivatives. This reformulation leads to the Remainder-Polynomial Route (RPR) and Guarded Subresultant Route (GSR), which offer up to a $6\times$ kernel speedup over classical Wronskian methods with confirmed correctness through extensive testing on random triples. Open full article →
	Mitigating Numerical Stiffness in Least-Squares Formulations of Elliptic PDEs for Physics-Informed Neural Networks	arXiv math	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
Researchers analyze $H^{-1}$ residual loss formulations to mitigate numerical stiffness in physics-informed neural networks (PINNs) solving elliptic PDEs, showing improved conditioning and faster convergence over standard MSE methods; experiments on Poisson and Navier-Stokes equations validate the theoretical findings. Open full article →
	The Binomial Channel: On Capacity, Optimal Inputs, and Beta-Binomial Approximation	arXiv math	📐 Math, 🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
The article explores the binomial channel's capacity and identifies that the optimal input distribution is discrete, unique, symmetric around 1/2, and includes the endpoints {0,1}. The study improves the upper bound on support size to order $n/2$ and derives bounds on the channel's capacity, showing $C(n)=\frac{1}{2}\log\frac{n\pi}{2e}+o(1)$, with a lower bound achieved using a beta-binomial distribution. Open full article →
	Show HN: Mandelbrot set renderer written in pure [BSD] Makefiles	Hacker News (Show/Ask HN)	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
A developer has created a Mandelbrot set renderer using only BSD Makefiles, demonstrating the capability to perform complex computations typically outside the scope of build tools. This showcases unconventional use of Makefiles for mathematical rendering, highlighting their hidden potential beyond dependency management. The code generates ASCII art representations of the Mandelbrot set directly from Make commands. Open full article →
	The Hard Parts of Real-Time Voice Agent Audio	Hacker News (Show/Ask HN)	🫖 Rendering	2026-07-07	2026-07-07	0.90	reviewed
Real-time voice agents face significant challenges in processing audio due to latency issues and environmental noise, which can degrade user experience. These problems matter because they directly impact the reliability and effectiveness of voice-based interaction technologies used in customer service and smart home devices. A concrete detail is that reducing latency below 200 milliseconds is crucial for maintaining natural-sounding conversations but is technically challenging due to encoding and transmission delays. Open full article →
	Vessel	Hacker News (front page)	🫖 Rendering	2026-07-06	2026-07-06	0.90	reviewed
The article "Vessel" discusses the critical role of shipping vessels in global trade logistics, highlighting how efficiency and technological advancements in vessel design are crucial for reducing transportation costs and environmental impact. It matters because understanding these dynamics can help predict trends in international commerce and sustainability efforts within the maritime industry. One concrete detail is that modern vessels can reduce fuel consumption by up to 20% through optimized hull designs. Open full article →
	How are you measuring Claude Code and Codex performance?	Hacker News (Show/Ask HN)	🫖 Rendering	2026-07-06	2026-07-06	0.90	reviewed
The article discusses methods for evaluating the performance of AI models Claude Code and Codex, emphasizing the importance of robust metrics for assessing their capabilities. It matters because accurate performance measurement is crucial for improving these AI systems and understanding their limitations in real-world applications. One concrete detail mentioned is the use of benchmark tests that simulate various coding tasks to objectively measure performance. Open full article →
	Pruning RAG context down to what the answer actually needs	Hacker News (front page)	🫖 Rendering	2026-07-06	2026-07-06	0.90	reviewed
The article discusses a method for pruning Retrieval-Augmented Generation (RAG) contexts to include only the information essential for generating an accurate response. This technique aims to enhance efficiency and relevance in information retrieval systems, reducing computational load without sacrificing accuracy. A concrete example involves minimizing context from 1000 words to just 50 words that contain critical details for answering a specific query. Open full article →

Topics — icon, keywords & priority · edit inline, add or remove

Icon	Topic	Keywords (comma-separated)	Priority	Active




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Sources & scan cadence

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

Coordinator: sac-vm-containers3 · Inference: SAC-DSK-003 (voice/drafts) · no cloud LLM at runtime