Papers

Large Language Model (LLM)-based agents increasingly self-evolve by editing a persistent skill document that encodes their workflow, tool-use rules, and decision logic. This loop has two steps, an optimizer that proposes a candidate edit and a gate that accepts or rejects it. Prior work has concentrated on the optimizer, while the gate still follows a naive rule that keeps any edit which improves an aggregate validation score. We show that this rule fails in two ways. First, it admits permanent regressions, since an edit can raise the average while breaking items the skill already solves. Second, it is vulnerable to the Optimizer's Curse, since the best observed score on a finite and noisy validation set is upward biased. To solve the above two limitations, we propose a statistical acceptance gate for self-evolving agents (SAGE). Compared with previous work, SAGE has two contributions. First, SAGE proposes a per-item paired comparison that evaluates the current skill and the edited skill on identical validation items, which exposes regressions that an aggregate score hides and penalizes them asymmetrically. Second, SAGE also employs a one-sided paired test that commits an edit only when its wins are statistically reliable against its losses, and it abstains otherwise. SAGE is a conservative refinement of the standard gate that recovers the baseline exactly at a boundary setting. It commits only a subset of the baseline's edits, filtering out those whose gains are unreliable or purchased by breaking already-solved items. Across five benchmarks and four backbone LLMs under an equal-budget protocol, SAGE lowers the regression rate in 19 of 20 settings and matches the baseline in the remaining one, for example from 36.5% to 0% on LiveMath and from 42.8% to 0% on OfficeQA with DeepSeek-V4. SAGE also attains the highest final score in all 20 settings, raising LiveMath from 34.15 to 48.78.

We have detected for the first time the redshifting and blueshifting of X-ray photons due to the orbital motion of an X-ray telescope around the Earth. Current and planned X-ray telescopes like XRISM/Resolve and NewAthena can achieve energy resolutions $R = E / \Delta E \approx 1000$, requiring spectroscopic calibration of physical effects such as the local standard of rest and the orbit of the Earth around the Sun. We construct an a priori method for detecting a heretofore unexamined effect: the modulation of redshift due to the motion of an X-ray telescope around the Earth. We apply this pipeline to several XRISM/Resolve observations of narrow iron K$\alpha$ emission lines from galactic center molecular clouds, and we detect evidence of orbital redshift modulation in the K$\alpha$ emission at the 95% confidence level. Our findings suggest that orbital redshift modulation is already present and detectable in X-ray data and motivates reexamination of how X-ray photon data is packaged in the emerging era of high-resolution X-ray spectroscopy.

Metallic glasses exhibit pronounced composition-dependent mechanical properties, yet identifying the structural origins of these changes remains difficult. An outstanding issue is how to correlate different forms of medium range order (MRO), defined at different length scales and accessed through different experimental observables, and to understand their connection to properties. We combine synchrotron reduced density function, G(r), with machine-learning-assisted four dimensional scanning transmission electron microscopy (4D-STEM) to examine geometric and topological MRO in five Zr-based metallic glasses. Density wave analysis of G(r) provides a geometric MRO descriptor through the coherence length of atomic density correlations, while 4D-STEM reveals nanoscale topological and chemical MRO motifs, including crystal-like local ordering with distinct rotational symmetries. We show that the G(r)-derived coherence length captures an important baseline tendency for cooperative ductile relaxation, while composition-dependent topological MRO provides an additional structural contribution that helps explain the observed mechanical responses. In particular, increasing Zr content suppresses Cu-rich FCC-like MRO, increases the cooperative coherence volume, and promotes fine Zr-rich HCP-like local order associated with enhanced ductility. These results identify the combined structural influence of geometric and topological MRO as a key basis for composition-dependent mechanical response in metallic glasses.

We present formulas for the higher Alexander polynomials of satellite links.

Machine learning (ML) and deep learning (DL) have dominated Intrusion Detection System (IDS) research in recent years. Unfortunately, many existing studies have produced inflated results and unreliable benchmarks due to critical oversights and mistakes in the ML and DL pipeline, from data collection and labeling to feature engineering and model training and evaluation. CIC-IDS2017 is a standard benchmark for network intrusion detection. Still, many published results on this dataset are difficult to compare due to labeling errors, inconsistent flow extraction, potential leakage, and performance evaluation metrics dominated by benign traffic. In this paper, we present a comprehensive benchmark with corrected PCAP-level labeling and a complete evaluation pipeline with diverse ML models. We evaluate eleven tabular classifiers at three nested levels: binary attack detection, nine-class attack-family attribution, and fifteen-class fine-grained classification. A soft-voting ensemble of Random Forest, XGBoost, and LightGBM obtains the best fine-tier macro-F1 of 0.955, with coarse and binary macro-F1 scores of 0.980 and 0.999, respectively. We further conducted a feature selection study based on an analysis of feature importance. This comprehensive benchmark pipeline is configurable and open-source, enabling new feature extraction and model plugins for new datasets. Future work should use this pipeline as a reference point for richer features, rare-class analysis, and model generalization towards new datasets and attack classes.

Neutrino oscillations offer an interferometric setting for open-system dynamics, quantum resources, and parameter estimation. We distinguish two often-conflated statistical families: propagation-basis dephasing uses a survival factor $\eta_p$ to damp interference before flavor projection, changing flavor probabilities; effective flavor-mode dephasing suppresses only off-diagonal coherence of a single-particle, two-mode state while fixing its populations. For the two-flavor mode state, we derive exact concurrence, entanglement of formation, and local quantum uncertainty, and reduce one-sided projective discord to a one-parameter optimization. For $0<P<1$ and $0<\eta_m<1$, the QFIM in $(P,\chi,\eta_m)$ is diagonal, with $\mathcal{H}^{\rm mode}_{\chi\chi}=C_{\eta_m}^2$ and $\mathcal{H}^{\rm mode}_{\xi_m\xi_m}=C_{\eta_m}^2/(1-\eta_m^2)$, where $\xi_m=-\ln\eta_m$. For propagation-basis dephasing, basis-matched QFI and flavor FI separate dynamical information loss from measurement inaccessibility for the mixing angle, mass-squared splitting, and dephasing rate. A monochromatic three-flavor benchmark evaluates the mixed-state QFIM, flavor FIM, and SLD incompatibility for $(\theta_{23},\delta_{\rm CP},\xi_{31},g)$ at DUNE-like, T2HK-like, and ESSnuSB-inspired points. At $\Gamma_0=10^{-23}\,\mathrm{GeV}$, the fixed-coordinate ratio $\mathcal{F}^{\rm flav}_{\delta\delta}/\mathcal{H}_{\delta\delta}$ is approximately $0.010$, $0.013$, and $0.105$, respectively; all three points show strong $\theta_{23}$–$\xi_{31}$ incompatibility. A single-energy flavor measurement supplies only two independent probabilities, so its four-parameter FIM is rank deficient: these diagonal ratios are conditional diagnostics, not joint four-parameter sensitivities. These are state-level information-geometric benchmarks, not event-level sensitivity forecasts.

The icy dwarf planets in the outer solar system are among the most enigmatic bodies known, showing activity ranging from atmospheric resurfacing to possible cryovolcanism. Yet the study of their interiors remains largely theoretical, with few empirical measurements to guide our understanding. The orbits of their moons offer a way to break this deadlock, providing a direct probe of dwarf planet interiors. Here we present a detailed investigation of Haumea's interior derived from the motion of its satellite system. Fitting a new dynamical model to two decades of precise Hubble Space Telescope astrometry, we simultaneously measure Haumea's dynamical oblateness, $J_2$, and the masses of its satellites. Our analysis of the $J_2$ measurement combined with occultation-derived shape models conclusively shows that Haumea has a dense rocky core overlaid with an ice-rich mantle. However, the current dataset is not constraining enough to fully determine the detailed internal structure (core/mantle density, two-layer vs. three-layer, etc.). We do find a slight preference for models where Haumea retains a frozen-in fossil figure, but more data are needed to statistically confirm this. Future observations of the satellite system, as well as observations of stellar occultations, are needed to fully test this hypothesis and should substantially tighten constraints on Haumea's interior. Taken together with other recent evidence for geophysical and geochemical evolution of dwarf planets, our work shows that dense rocky cores and subsurface oceans are likely to be ubiquitous among the trans-Neptunian dwarf planets.

We investigate a two-dimensional electron system in an external magnetic field. An intrinsic four-particle excitation of the electron system, which we term a magnetoplasmon molecule, is observed. The molecule comprises two identical electrons and two Fermi holes with opposite spins. Both electrons and one Fermi hole participate in the collective plasma oscillations of the electron system, whereas the second Fermi hole neutralizes the excess electronic charge. We examine the interaction between the magnetoplasmon molecule and a magnetoexciton condensate.

We develop a general criterion for establishing absolute continuity of convolutions of fractal measures on the line, and more generally of prescribed line projections of fractal measures in the plane. The crucial new ingredient is exact scaling covariance of the \(L^1\)-norm of Littlewood-Paley pieces of the projected measure, under affine renormalization. We apply this criterion in three key settings. First, we show that the convolution of two measures on the line is absolutely continuous whenever their dimensions sum to more than one, provided one is a self-conformal measure whose defining IFS is not \(C^2\)-conjugate to linear, and the other is either self-conformal or Ahlfors–David regular. Second, we show that every line projection of a planar complex-analytic self-conformal measure of dimension greater than one is absolutely continuous, under natural nonlinearity and nondegeneracy assumptions. Finally, we show that every line projection of a planar self-affine measure is absolutely continuous, under natural irreducibility and proximality assumptions, whenever the correlation dimension of the measure and the Frostman dimension of its Furstenberg measure sum to more than two.

We investigate aspects of the relationship between global sections of divisors and birational geometry. We show that for varieties $X$ of klt Calabi-Yau type, global sections are governed by the same birational data that control the $D$-minimal model program ($D$-MMP). As a consequence, global sections of arbitrary big divisors can be systematically reduced to Euler characteristics $\chi(Y,\mathcal O_Y(D))$ on suitable birational models $Y$ using vanishing theorems, extending classical positivity-based methods beyond the movable cone. The reduction proceeds by removing fixed divisorial components, which do not contribute to the space of global sections, either directly by subtraction or birationally by contraction to a suitable $D$-minimal model. We obtain piecewise quasipolynomial formulae for global sections on the big cone, whose domains are the Mori chambers of the $D$-MMP. Restricting to the subclass of Fano type varieties extends such formulae to the entire effective cone. These formulae can be constructed from just the small birational class of $X$, yet encode properties of all birational contractions of $X$. Alongside the computation of global sections from birational geometry, we study the inverse process, wherein finite computations of $h^0(X,\mathcal O_X(D))$ determine aspects of the chamber decomposition and the associated birational models.

Among distinct optimal acceleration mechanisms for deterministic monotone root-finding problems and fixed-point problems, dual-anchoring has recently been shown to admit a more robust direct stochastic extension than standard anchor acceleration. However, without additional strong monotonicity, the existing stochastic dual-anchoring guarantee has two limitations: first, it requires cocoercivity in expectation, and second, it attains only $O(\epsilon^{-3})$ oracle complexity, leaving a gap to the near-optimal $\tilde{O}(\epsilon^{-2})$ complexity achieved by other methods. In this work, we address both of these limitations by combining dual-anchoring with stochastic resolvent approximation and optimized variance control. For unbiased stochastic oracles with variance bounded by $\sigma^2$, where sample operators are monotone and uniformly $L$-Lipschitz, our algorithm finds a point with $\epsilon$-residual with a near-optimal oracle complexity of $O ( (LD / \epsilon) \ell + (\sigma^2 / \epsilon^2) \ell^2)$, where $\ell = \log (1 + LD / \epsilon)$ and $D$ is the initial distance to a solution. This result improves the best known oracle complexity in the noise-dominated regime under these samplewise assumptions, reducing the poly-logarithmic factor from cubic to quadratic.

Uniform random rotations are an effective preprocessing step for quantization: they make normalized coordinate distributions approximately Gaussian, enabling the use of codebooks optimized offline. We introduce TORQUE, a framework that improves on previous quantization works that use random rotations by jointly optimizing how many and which coordinates to preserve at high precision both before and after rotation, under a fixed overall expected bit budget. Intuitively, before rotation, preserving large input coordinates at high precision can reduce overall error by preventing the rotation from spreading their values across many coordinates. Likewise, after rotation, preserving a small fraction of the largest-magnitude coordinates at high precision allows the remaining values to be quantized more accurately using codebooks optimized offline for the resulting truncated Gaussian distribution. We derive a quantization error upper bound and prove that top-$k$ pre-rotation retention minimizes it for each $k$. This reduces the search over coordinate subsets to an optimization over $k$, enabling a fast optimizer that uses offline codebooks and parallel parameter selection for practical implementation. We demonstrate an improved tradeoff between reconstruction accuracy and storage cost through numerical evaluation under the Gaussian model and experiments on nearest-neighbor retrieval, KV-cache compression, and activation compression.

Learning from human videos offers a promising route to acquiring diverse manipulation skills. Extending this capability beyond tabletop settings to long-horizon mobile manipulation requires adapting and composing demonstrated interactions across changing scenes and robot configurations. We present Skill Assembly and Kinematic Imitation (SAKI), a framework connecting human-video skill acquisition, cross-demonstration assembly and closed-loop whole-body execution. SAKI prepares reusable object-centric skills that preserve task-critical interactions while allowing transfer paths to adapt. Given a goal and supplied task dependencies, it selects and orders skills, binds their object roles to the current scene, and carries scene estimates and robot configuration between successive skills. Whole-body kinematic imitation generates coordinated base, arm and gripper motion. During execution, persistent object estimates maintain task references across viewpoint changes, while visual feedback updates remaining trajectories. Real-robot experiments demonstrate skill reuse across layouts and the composition of independently demonstrated interactions into continuous mobile tasks, including tidying and wiping. Ablation results show that task-conditioned reference preparation substantially improves long-horizon task completion with whole-body optimisation and visual feedback held fixed. Check https://aus.bot/research/saki/ for video demos!

The lack of rigorous safety and performance certificates remains a key bottleneck to the deployment of modern learning-based methods. Sample compression has recently emerged as a powerful tool for deriving such certificates, with particularly sharp bounds available for algorithms satisfying a so-called preference property – also known as stability in the learning theory literature. These bounds find direct application across domains as different as the Scenario Approach, Pick-to-Learn, and Support Vector methods. However, whether they are tight has remained an open problem. In this paper we resolve this question affirmatively and show that the state-of-the-art bound for preferent compressions is provably tight. We establish this by exhibiting an explicit construction based on the uniform distribution and order statistics that attains the bound in the limit. Along the way, we also provide a considerably shorter and more accessible proof of this bound, requiring only elementary counting arguments and no infinite-dimensional duality.

Out-of-time-ordered correlators (OTOCs) provide a powerful probe of quantum chaos and scrambling. While the Lindblad formalism is often used to describe OTOCs in open systems, microscopic mechanisms that give rise to the Lindblad equation at the level of time-ordered correlation functions do not necessarily justify this approach at the level of OTOCs. Starting from a microscopic model of a subsystem coupled to a random bath, we show that the resulting OTOC dynamics contains an additional contribution compared to the standard Lindblad approach. This contribution, induced by correlations between different replicas, allows key properties of the underlying unitary dynamics such as long-time freeness to be retained and information scrambling to be captured more faithfully. As an application, we show that this extended formalism can be used to numerically study OTOCs in large closed systems by replacing part of the system with a dissipative boundary, offering a way to study operator spreading and higher-order correlations beyond directly accessible system sizes.

Using $e^+ e^-$ collision data collected with the BESIII detector at center-of-mass energies between $4.128$ and $4.226$ GeV, corresponding to an integrated luminosity of $7.33~{\rm fb}^{-1}$, the inclusive branching fractions of the decays $D_s^+ \to \eta X$ and $D_s^+ \to \eta^\prime X$ ($X$ denotes any possible particles) are measured to be $(30.72 \pm 0.90 \pm 0.46)\%$ and $(12.30 \pm 0.94 \pm 0.37)\%$, where the first uncertainties are statistical and the second systematic. The results are consistent with the previous CLEO measurements, with precision improved by factors of 2.8 and 1.9 for $D_s^+ \to \eta X$ and $D_s^+ \to \eta^\prime X$, respectively.

Strong electron-phonon coupling can destabilize both Chern insulators (CIs) and fractional Chern insulators (FCIs) in favor of charge order, but whether the instabilities in CI and FCI share a common microscopic mechanism remains unclear. In this paper, we address this question by studying a flat-band Haldane model coupled to dynamical Holstein phonons at integer and fractional fillings using density-matrix renormalization group with local basis optimization. We find that the low-energy effects of phonons are dominated by their dressing of charge-neutral collective modes. In the CI and FCI, phonons dress excitons and magnetorotons into composite modes that we identify as exciton polarons and magnetoroton polarons, respectively. These modes soften strongly upon approaching the transition, while the momenta of their energy minima anticipate the ordering wave vectors of the charge-ordered phases. The phonon spectrum, in turn, acquires dispersive features inherited from the exciton and magnetoroton modes, providing direct lattice signatures of these neutral excitations. Within the FCI phase, electron-phonon coupling also enhances the opposite-chirality spectral weight of the graviton response, thereby resulting in a chirality deficit. Our results provide a unified excitation-based picture of phonon-driven instabilities in CIs and FCIs and establish lattice dynamics as a probe of their neutral collective modes.

The degenerate geometry of a null boundary admits an enlarged local conformal freedom: in two dimensions, a Carrollian coframe allows two independent Weyl rescalings, one modulating and the other preserving the boundary volume form. We investigate whether both transformations can be realized as charged asymptotic symmetries in three-dimensional flat holography. We show that Einstein gravity canonically realizes the volume-modulating Carroll-Weyl transformation, together with local Carroll boosts, but does not admit the volume-preserving rescaling as an additional independent asymptotic symmetry. We trace this obstruction both back to the conformal completion of null infinity and to the absence of two independent commuting semisimple generators in the Poincaré algebra. Conformal gravity overcomes this obstruction through bulk dilatations, which supply the missing algebraic direction. We construct an asymptotically flat phase space of conformal gravity in which both types of Carroll-Weyl transformations and local Carroll boosts admit finite, integrable, and generically nonvanishing canonical charges, and derive their centrally extended algebra. Finally, we show that these central extensions arise from boundary anomalies through symplectic descent, yielding a gravitational prediction for Carroll-Weyl anomalies in flat holography.

We investigate the implications of causality and positivity for the tidal Love numbers of gravitating objects. We work within the framework of point-particle effective field theory, where the Love numbers correspond to the Wilson coefficients of operators constructed from the curvature tensor and its derivatives. For simplicity, we focus on the quadrupolar gravito-electric sector, which provides the leading contribution to tidal deformability. We show that requiring the tidal response to be retarded and to decay at high frequencies, together with the assumption of passivity, leads to nontrivial bounds on the Love numbers. These bounds delineate an allowed region in the parameter space of the effective theory and apply to any localized object. In particular, we study their application to neutron stars. We compute the dynamical Love numbers through fourth order in the frequency expansion for a representative set of polytropic and tabulated neutron-star equations of state and show that, in the low-compactness regime, the bounds translate into constraints on the first oscillation mode of the star. Importantly, these constraints are conceptually independent of the stability and thermodynamic conditions commonly imposed in the literature. While our focus is primarily on conservative systems, we also discuss how the bounds are modified in the presence of dissipation. Our results lay the ground for a systematic framework to derive bounds on compact objects from fundamental principles.

Reconstructing simulation-ready 3D scenes from real-world observations enables robotics, gaming, and immersive applications, yet existing methods largely assume rigid objects. This leaves an important gap for deformables, whose simulation-ready geometry depends on dimensionality (curves, surfaces, or volumes) and whose behavior may require models beyond elasticity. We present CoDimRecon, an agentic framework that reconstructs editable scenes containing rigid, articulated, and deformable objects from multi-view RGB observations. Scene-level geometric priors ground scale and layout, while object-level generated meshes guide the agent toward detailed, compact geometry; articulated rigid objects are decomposed into movable parts with explicit joints. For deformables, category-wise agent sessions reconstruct curves as centerlines with radii, surfaces as manifold shells with thickness, and volumes as watertight solids for volumetric meshing. Reusable simulator skills initialize compatible physical models and parameters, while agent-guided behavioral tests expose mismatches and trigger targeted revisions of motion, geometry, numerics, or material modeling. On evaluated Replica and ScanNet++ scenes, CoDimRecon achieves competitive compositional reconstruction accuracy while additionally producing deformable assets for rod, shell, and solid simulation. We further demonstrate robot interactions across all three representations, including a controlled paper-folding case in which behavioral testing motivates plastic bending.

We address the breakdown of fixed-order perturbation theory due to logarithms in $s/p_t^2$ for processes involving two jets or more at the energies currently explored at the LHC. The problem manifests itself in various ways: an obvious breakdown of the perturbative series for some kinematic distributions, highly asymmetric scale variations in other distributions, and the need for an artificially large renormalisation scale to even achieve numerical stability. As we demonstrate, the problem is solved through the resummation of these high-energy logarithms. The customary choice of a large renormalisation scale of $m_{j_1j_2}$ offers no systematic resolution. This breakdown in fixed order predictions is illustrated for the production of $Z$+dijets. We show that resummed predictions obtained using \HighEJ matched to fixed order obtain accurate predictions for all the relevant distributions investigated in a recent ATLAS measurement.

Let $d \geq 5$, $0 < \gamma < d - 2$, and $\Omega_N$ be the binomial random subset of $Q_N = [-N,N]^d \cap \mathbb Z^d$ with retention probability $p_N = N^{-\gamma}$. We prove that, with failure probability of optimal exponential order, every subset $B \subseteq \Omega_N$ of fixed positive relative density realizes, at each scale $p_N^{-2/(d - 2)} \lesssim \lambda \lesssim N^2$, a squared distance of the form $q^2 \lambda$, where $q$ belongs to a fixed finite set depending only on the dimension and the density. The lower scale $p_N^{-2/(d - 2)}$ is sharp. As a consequence,the squared-distance set $D^2(B)$ of $B$ has maximal order $N^2$ and contains affine copies of every fixed finite subset of $\mathbb Z$. The main new input is a finite multidilate supersaturation theorem for dense subsets of $Q_N$, which, together with boundedness estimates for the associated spherical distance graphs down to the sharp scale, allows us to apply Schacht's transference theorem.

Let $R$ be a commutative Artinian ring. We consider two graphs associated to $R$, namely the compressed zero-divisor graph $\Gamma_E(R)$ and the associate class graph $\Gamma_A(R)$. Partitioning the vertex set of a zero-divisor graph into its core and its boundary, we count the core vertices that dominate the core. This count is a graph invariant, and we estimate it for $\Gamma(R)$, $\Gamma_A(R)$ and $\Gamma_E(R)$. We prove that the count for $\Gamma_A(R)$ is bounded below by the count for $\Gamma_E(R)$, and that the lower bound is attained precisely when $R$ is Gorenstein. As a consequence we obtain that $R$ is Gorenstein if and only if $\Gamma_A(R)\cong\Gamma_E(R)$ as graphs, the isomorphism being an arbitrary one and not merely the natural compression map. Using the same counting technique we then answer, for Artinian rings, a question of Anderson and LaGrange by showing that $\Gamma(R)\cong\Gamma_E(R)$ if and only if $R\cong \mathbb Z_2^{\,n}$ for some $n\ge2$, or $R\cong\mathbb Z_4$, or $R\cong\mathbb Z_2[x]/(x^2)$.

In this article, we introduce a new rewriting method for computing hom-bases of diagrammatic categories. Our approach is based on stratified presentations, obtained by partitioning an equational presentation into strata according to the rewriting behavior of its relations. We establish modularity principles for termination and confluence in stratified rewriting systems with coefficients in a ring. We then introduce a completion procedure that transforms a stratified presentation into a normalized one, in which mixed interactions between successive strata are absorbed into the normalized rewriting rules, thereby inducing modularity of confluence. This leads to a stratified hom-basis theorem for diagrammatic categories. We illustrate the method by applying it to the $q$-Schur category, for which we construct a new hom-basis.

Electric dipole moments (EDMs) provide some of the most sensitive probes of CP-violating interactions beyond the Standard Model (SM). Within the Standard Model Effective Field Theory (SMEFT), we investigate constraints on CP-violating top-quark interactions using current and projected leptonic and hadronic EDM measurements. Our analysis incorporates the complete chain of relevant effects, including one- and two-loop matching, Barr-Zee contributions, Weinberg operator and heavy-quark threshold corrections, and renormalization-group induced operator mixing. We demonstrate the strong complementarity between leptonic and hadronic EDM observables and show that future proton EDM searches could significantly strengthen constraints on several CP-violating top-quark interactions.

We prove that the relative log canonical algebra of a semi-dlt pair $(X,\Delta_X)$ projective over a scheme $T$ is finitely generated, equivalently, that $(X,\Delta_X)$ admits a relative stable model, provided that the normalization admits a log canonical model over $T$, that $(X,\Delta_X)$ admits a stable model over an open dense subscheme $T^0\subset T$ whose exceptional locus does not contain any stratum of the conductor, and that the log centers contained in the conductor have images meeting $T^0$. Our main contribution is a direct proof that avoids Kollár's gluing theory entirely. As a consequence, we recover demi-normal versions of results of Hacon–Xu and Birkar. Furthermore, we derive the existence of certain MMP steps for slc pairs, recovering results of Ambro and Kollár. Finally, these results lay the groundwork for a streamlined proof of the properness of the Kollár–Shepherd-Barron–Alexeev moduli space of stable pairs, to be completed in forthcoming work.

Adaptive circuits use measurements and outcome-conditioned feedback to implement nonreciprocal dynamics without postselection. We show that fermion circuits host independently tunable density and coherence skin effects. The stationary state has an exact density tilt set only by measurement strength and feedback displacement: conditioned-gate details cancel, yielding an exponential one-particle profile and, at any filling, a tilted ensemble of configuration weights. Decaying coherences instead obey, in the bulk, an effective Hatano-Nelson generator controlled by the conditioned gates through a relative occupation phase. Tuning this phase drives a point-gap topological transition and reverses coherence localization at fixed density, allowing density and coherence to localize at opposite edges. We derive both exponents for conditioned $U(2)$ gates and propose a correlator-ratio probe using ensemble-averaged observables.

Several physically interesting Lindbladians, such as those describing generic open quantum system models as well as engineered state preparation processes, are often rapidly mixing, that is, they relax to steady states in time scaling polylogarithmically with the system size. Owing to the short mixing times, it is physically expected that local perturbations do not substantially increase the mixing time. In this work we question this expectation and ask whether rapid mixing survives. We provide counterexamples showing that rapid mixing is not stable in general, even when the perturbation does not change the steady state. We also show that arbitrarily weak local Hamiltonian perturbations can destroy rapid mixing. Complementing these results, we develop an array of sufficient conditions which imply stable rapid mixing, including several classes of quasifree fermionic systems, commuting Lindbladians, and local spin systems. We also identify conditions under which modified logarithmic Sobolev inequalities (MLSIs), a stronger form of convergence, lead to stable rapid mixing. As a further implication of our results, we show that rapid mixing does not imply a positive MLSI constant.

We study entanglement entropy in a certain ansatz of matrix quantum mechanics (MQM) wavefunctions which behave as generating functionals for a planar 't Hooft expansion. We argue that these 't Hooft diagrammatics can directly probe aspects of the topology of the bulk dual, such as the contractibility of a thermal or replica $S^1$ cycle. Our argument relies on treating 't Hooft diagrams as a non-perturbative definition of off-shell string theory worldsheets in which contractibility of replica cycle leads to worldsheets punctured by a conical deficit (as first described by Susskind and Uglum). We describe how a deconfinement transition in the MQM is tied to the exchange of dominant topologies, as well as to a candidate description of open string 'edge modes' of Susskind and Uglum. Lastly, we study toy models of black hole evaporation and show that the boundary planar expansion itself diagnoses the exchange of dominance between the disconnected topology and replica wormhole topology, without ensemble averaging and without independently postulating which bulk saddles should be included.

Pixel-space diffusion Transformers (DiTs) directly operate on high-dimensional visual data, yet their hidden representations typically undergo uniform refinement across depth. Natural images, however, are inherently organized at different levels of granularity. Global structure can often be represented compactly, whereas local textures and fine details require richer representations. Motivated by this, we introduce heterogeneous refinement in pixel-space DiTs, assigning different feature groups distinct refinement budgets across depth. Consequently, an ordered feature specialization emerges: sparsely refined features predominantly encode global visual structure, whereas more frequently refined features increasingly specialize toward localized, high-frequency details. We refer to these two groups as persistent and active features, respectively. Building on this emergent specialization, we introduce Persistence Forcing (PerF), which explicitly exploits this persistent–active feature organization for pixel-space image generation. This enables persistent features to continuously condition actively refined features, allowing stable global information to guide the ongoing refinement of finer visual details. During generative sampling, this interaction further induces a meaningful guidance direction that promotes coherent global structure and naturally complements classifier-free guidance. On ImageNet $256\times256$, PerF-L achieves FID of $1.91$, approaching $1.86$ of JiT-H with only half the parameters, while PerF-H further achieves FID of $1.63$ and $1.76$ on ImageNet $256\times256$ and $512\times512$, respectively.