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arXiv2026

Second-Order Problem Solving for Recursive Self-Improvement in Formal Verification

Recursive self-improvement (RSI) enables agents to iteratively optimize their workflows via execution feedback. However, standard RSI typically operates as a first-order optimizer: it repeatedly patches surface-level parameters in response to immediate failure symptoms, often leading to trial-and-error thrashing without resolving underlying mechanisms. To address this limitation, we introduce SO-RSI, a framework that elevates workflow optimization to a second-order diagnostic inquiry, investigating why failures occur before committing to structural interventions. SO-RSI passively monitors execution traces for three structural anomalies (recurrence, opposing edits, and expectation mismatch) to trigger targeted mechanism investigations. By executing lightweight diagnostic probes and maintaining persistent inquiry memory across RSI rounds, SO-RSI accumulates causal evidence to guide systematic workflow edits rather than parameter patches. Across Lean 4 proof generation and Verus-based verifiable code generation, SO-RSI improves final held-out pass rates over Naive RSI by 21.8 and 25.8 percentage points under matched 24-hour search budgets. Behavioral analyses further confirm that SO-RSI substantially suppresses failure recurrence and eliminates unproductive zero-progress optimization loops.

cs.AI↗
arXiv2026

Momentum-Space Path Integral Approach to Non-Hermitian Symmetry Breaking

A quantum-classical correspondence for non-Hermitian symmetry breaking has recently been established using coordinate-space path integrals, providing a semiclassical understanding of spectral transitions at the level of individual eigenstates. Here we develop its dual formulation in momentum space by constructing the corresponding trace formula and quantization condition. We show that the real or complex nature of individual eigenvalues is determined by the symmetry properties of the associated semiclassical orbits, as in the coordinate-space path-integral approach. Moreover, we demonstrate that the topology of semiclassical orbits determines the natural formulation of the quantization condition: the coordinate- and momentum-space formulations are equivalent for contractible periodic orbits in phase space, whereas for noncontractible orbits, the quantization condition along the winding direction remains valid, but its dual form must be corrected by a boundary term. In particular, real-space-winding and Brillouin-zone-winding orbits naturally select coordinate- and momentum-space quantization, respectively. As a nontrivial application, we investigate the boundary-induced spectral transition of Bloch oscillations in a finite non-Hermitian lattice, where Bloch-oscillation orbits winding across the Brillouin zone preserve the relevant symmetry and yield real energy levels, whereas boundary-reflected orbits form symmetry-related pairs and give rise to complex-conjugate eigenvalues. Our work completes the quantum-classical correspondence framework for non-Hermitian symmetry breaking, extending its applicability to a broader class of non-Hermitian problems.

quant-ph↗
arXiv2026

Biharmonic Lagrangian surfaces with constant Gaussian curvature in $2$-dimensional complex space forms

Constant curvature is one of the most fundamental intrinsic conditions in submanifold geometry. Investigating the existence and classification of biharmonic submanifolds under intrinsic curvature constraints is generally difficult, since the biharmonic equation is expressed in terms of extrinsic data. In this paper, we obtain a complete classification of biharmonic Lagrangian surfaces with constant Gaussian curvature in 2-dimensional complex space forms. As a consequence, we classify the biharmonic Lagrangian surfaces with flat normal bundle and we prove that pseudo-umbilical biharmonic Lagrangian surfaces are necessarily minimal.

math.DG↗
arXiv2026

Observability from Measurable Sets for One-Dimensional Heat Equations with Bounded Spacetime Potentials

This paper study observability for the Dirichlet heat equation on a bounded interval with a real bounded potential depending on space and time. We prove an observability inequality from every measurable subset of spacetime with positive measure. The constant is uniform over potentials with a prescribed $L^\infty$ bound. By duality, positive spacetime measure is equivalent to null controllability by square-integrable distributed controls. Controls can also be chosen bounded in time with values in $L^2$. If almost every spatial slice of the observation set has a fixed positive lower bound on its measure, the observability constant is bounded above by $C_0e^{C_1/T}$, uniformly in the locations of the slices. The proof combines observation estimates on finite-dimensional spaces transported by the evolution with decay estimates for the distance to those spaces.

math.OC↗
arXiv2026

An Averaging Alternative to Pre-Trend Testing

We study difference-in-differences (DID) estimation of average treatment effects on the treated when the researcher is uncertain about which pre-treatment periods satisfy the parallel trends assumption. Roth (2022) shows that pre-trend testing can induce bias, complementing the statistical literature on post-selection inference. We propose the model averaged difference-in-differences (MADID) estimator, a weighted average of the candidate $2\times2$ DID estimators. The weights are normalized exponential functions of the candidate residual sums of squares, so implementation requires no specification test. We derive MADID's asymptotic properties under conditions that make invalid comparisons detectably more variable than at least one valid comparison. Under these conditions, MADID is consistent when the parallel trends assumption holds for at least one pre-treatment period. Although its joint limiting distribution across post-treatment periods is generally non-Gaussian, inference can be conducted by subsampling or simulation.

stat.ME↗
arXiv2026

Sharp planar Turán bounds for quasi-double stars

We study $W$-free planar graphs for $W\in\{W_{2,4},W_{2,5},W_{3,4}\}$, where the quasi-double star $W_{h,k}$ is obtained from a three-vertex path by attaching $h$ leaves to one endpoint and $k$ leaves to the other. We prove that every $W_{2,4}$-free planar graph on $n$ vertices has at most $9n/4$ edges, and the bound is attained whenever $8\mid n$. This determines the planar Turán density of $W_{2,4}$ as $9/4$. We also establish the sharp upper bound $5n/2$ for $W_{2,5}$. Combined with known constructions of planar graphs of maximum degree five, it yields $\ex_{\PP}(n,W_{2,5})=\lfloor5n/2\rfloor$ for every $n\ge15$. These results close the two corresponding coefficient gaps in the bounds of Liu et~al. Our proofs use structural restrictions on high-degree vertices, local deletions, and degree deficits in neighborhoods of radius two. For $W_{3,4}$, we characterize the planar graphs with a dominating vertex that avoid this tree and determine their exact extremal number, $\lfloor(5n-7)/2\rfloor$, for every $n\ge10$. Finally, $W$-free planar triangulations have at most eight, twelve, and eleven vertices for $W=W_{2,4},W_{2,5},W_{3,4}$, respectively; the first two bounds are sharp.

math.CO↗
arXiv2026

The conductivity problem with imperfect bonding interfaces and finite internal conductivities

We study the field concentration phenomenon between two closely spaced inclusions with imperfect bonding interfaces of low conductivity type. The inclusions are assumed to have finite conductivities. The problem is governed by a system of elliptic equations coupled with Robin-type boundary conditions. While it is known that finite-conductivity inclusions with ideal interfaces yield bounded gradients, in this paper we show that with imperfect bonding interfaces, the gradient of the solution may blow up as $\varepsilon$ (the distance between two inclusions) tends to zero when the bonding parameter $γ$ is large, while it is uniformly bounded independently of $\varepsilon$ when the bonding parameter $γ$ is small. Moreover, we identify the threshold of $γ$ and the optimal blow-up rates under certain symmetry assumptions. Compared to the case when the inclusions are perfect conductors, we find a novel logarithmic blow-up phenomenon at the critical value of $γ$.

math.AP↗
arXiv2026

Nexus: An Execution Fabric for AI Agents Across Cloud, Edge, and Devices

Language-model agents are evolving into long-running services that interact with models, tools, computers, mobile devices, and distributed environments. Existing agent frameworks simplify reasoning and tool invocation. However, cloud-centric designs face three limitations: centralized execution increases failure impact, scaling pressure, and compute cost; extending agents across computers, mobile devices, and edge environments requires a unified execution abstraction with permission control; and long-running executions require consistent lifecycle management across failures, recovery, results, usage, and settlement. We present Nexus, a cloud-edge platform that treats each invocation as a persistent task. Nexus uses an OpenWrt-based runtime for distributed serving, run-scoped delegation for authorized access to Computer and Mobile environments, and persistent records to track execution, outputs, failures, recovery, usage, and charging across cloud and edge components. We evaluate Nexus on controlled, cross-device, and model-driven workloads. All ten Computer-Android workflows succeed, and all six revocation tests block subsequent writes while preserving prior authorized reads. Under worker loss, journaling eliminates duplicate appends (six to zero per task), adding 0.933 s mean normal-path overhead. Across 24 matched task pairs, Nexus completes 24 tasks versus Dify's 22 and is a median 3.88 s faster on jointly successful pairs. In a separate workload, Nexus operates under a smaller tested incremental-runtime memory ceiling than Dapr (16 versus 64 MiB), although Dapr achieves lower successful-call latency. These results demonstrate how locality, operation-scoped authority, and persistent result identity support cloud-edge agent services with workload-dependent costs.

cs.DC↗
arXiv2026

Chirality-induced spin selectivity as a nonequilibrium effect: a unified test of competing mechanisms

For two decades, the origin of Chirality-Induced Spin Selectivity (CISS), the spin polarization of electrons by nonmagnetic chiral systems without magnetic fields, has remained unsettled. Here, we establish a single exact rule defining the fundamental conditions for the effect: in nonmagnetic, time-reversal-invariant conductors, all measurable CISS signals are time-reversal odd and vanish near equilibrium, proving that structural chirality alone is insufficient. By evaluating leading theoretical mechanisms across four levels of nonequilibrium transport, from coherent classical driving to fully non-Markovian quantum baths, we verify this selection rule to machine precision. We show that coherent chiral vibrations generate substantial collinear polarization (up to 10 percent across 0.5-6 THz) that reverses with handedness, whereas incoherent vibrations yield under 1 percent, and non-Markovian bath memory further suppresses the signal. The chiral geometry first makes the electronic motion chiral by accumulating orbital angular momentum; spin-orbit coupling (SOC) then converts that into spin. CISS therefore acts as both a spin polarizer and a spin filter, the latter an order of magnitude weaker. The polarization grows with molecular length and then saturates, matching trends reported for DNA and peptides. Reversing the drive converts decaying spin into a handedness-locked charge-current pulse (inverse-CISS). We find that once the system is driven, the polarization magnitude scales with an effective spin-orbit coupling: making heavy atoms and curved light-atom backbones indistinguishable at equivalent effective SOC. This enables us to chart how geometry, driving field, and length separate those routes.

cond-mat.mes-hall↗
arXiv2026

From Pixels, Without Pre-training: Joint Generative and Self-Supervised Representation Learning in One Model

Strong image generation models are conditioned on class labels, aligned to frozen pretrained encoders, or built on separately trained autoencoders. While effective, generation then depends on supervision or pretraining: labels must be annotated, and encoders or autoencoders pretrained for the target domain. We study joint generative and self-supervised representation learning in a single model, enabling self-conditioned generation without labels or pretrained models. This is challenging because the objectives are mismatched: contrastive learning consumes clean augmented views and favors coarse, invariant semantics, while flow matching consumes noisy images and must preserve the fine detail and spatial layout that contrastive learning discards. We propose SCION (Self-conditioned Generation on Self-supervised representation), whose core is a single pixel-space encoder conditioned on the flow timestep and an embedding. For representation learning, this conditioning embedding is a learned global vector shared across images, with the encoder's [CLS] token yielding the semantic representation trained by the contrastive loss. For generative training, the conditioning embedding is the image's own [CLS] representation, while patch tokens pass through a decoder to predict the image. To sample without a reference image at inference, we jointly learn a prior over the embedding. Gradient-norm balancing and stop-gradient mechanisms enable joint optimization in one run. SCION is self-supervised and self-contained, with no labels or pretrained models. On ImageNet 256x256, with the JiT-B recipe and no representation guidance, SCION reaches 8.92 FID, surpassing class-unconditional iREPA, which aligns to pretrained DINOv2 (46.44), and RCG, which conditions on it (14.27). With JiT-L, SCION achieves 5.89 FID without guidance and 3.47 with representation guidance, outperforming RCG with the ADM recipe (6.24).

cs.LG↗
arXiv2026

SimpleMark: Fast Multi-Bit Text Watermarking under f -Divergence Constraints

We introduce a framework for multi-bit text watermarking with security defined directly through $f$-divergence from the base language model distribution. Unlike prior approaches that focus on average-key distortion-freeness or a particular statistical distance, our formulation supports general $f$-divergences, including total variation and KL divergence, and enforces the guarantee for each realized key and embedded message. We develop a coding-based watermarking scheme that optimally biases next-token distributions subject to a prescribed divergence budget, and characterize the resulting tradeoff between embedding rate, decoding reliability, and statistical security. Experimentally, we compare our method against prior multi-bit watermarking schemes across modern language models and payload regimes. Our approach achieves substantially lower watermark detectability while maintaining competitive message-recovery performance and generation quality. Our results provide a unified view of secure multi-bit watermarking and recover several commonly used security notions as special cases.

cs.CR↗
arXiv2026

Current selects the helicity of a chiral phonon

The emergence of spin-polarized electrons from nonmagnetic chiral molecules and crystals is called Chirality-induced spin selectivity (CISS). A chiral phonon of definite wavevector $q$ can strongly enhance it, but near equilibrium the two helicities $+q$ and $-q$ are equally populated: they are time-reversal partners and their contributions cancel. We show that in a biased chiral conductor the current causes the phonon of one helicity to damp less than the other. The damping asymmetry is odd in the current, odd under $q\rightarrow-q$, invariant under a mirror that reverses the structural handedness, and equal, mode for mode, to the current-induced nonconservative Berry force on the phonon coordinate. Closing the phonon kinetics with a rate equation turns the asymmetry into a net lattice helicity: at any finite bias one helicity is preferentially populated, with no threshold, growing linearly with the current as $V\rightarrow0$; above a threshold that helicity becomes a self-sustained coherent travelling wave. We demonstrate this effect in elemental tellurium, treated as an open quantum system (electronic Hamiltonian, phonon bath, and electron-phonon coupling) within a quasi-ab initio framework. The electronic Hamiltonian is supplied by a vertex-corrected quasiparticle self-consistent $GW$ (QSGW) potential with spin-orbit coupling; nuclear displacements are modeled with a machine-learned interatomic potential, which yields chiral phonon modes at finite $\pm q_z$ on the $Γ$-A line. The perturbation to the electronic Hamiltonian from a nuclear displacement is approximated by a frozen-phonon deformation potential. No optical pump is needed: a bias alone drives the current and selects the phonon helicity; reversing the current reverses the selection.

cond-mat.mes-hall↗
arXiv2026

Rotated, but How Far? Diagnosing and Improving Object-Rotation Reasoning in VLMs

Vision-language models (VLMs) can detect that an object has rotated across views, but cannot reliably tell by how much. We introduce OR-Bench, a fine-grained benchmark for object-rotation reasoning with eight tasks covering rotation detection, rotation magnitude estimation, and multi-view rotation reasoning. Across 12 VLMs, the gap is stark: the strongest models approach 100% accuracy on detection, yet even coarse magnitude estimation is near chance. When asked for exact angles, models place 91.8--100% of their predictions on just $0^\circ$, $90^\circ$, and $180^\circ$, a failure we term canonical-angle collapse. This collapse persists even without visual input. Representation probing shows that missing information is only part of the explanation. Although rotation information becomes less recoverable at finer granularity, substantial coarse-grained information remains, and a simple linear probe outperforms the models' generated answers. This suggests that VLMs underuse rotation information they already encode. We therefore propose RotationCue, a lightweight decoder that recovers coarse rotation information from the VLM's own frozen representations and feeds it back to the model as intermediate textual context. Across three VLMs, RotationCue improves every model--task combination on OR-Bench, raising macro-average accuracy by 7.9--12.6 points while preserving general capabilities.

cs.CV↗
arXiv2026

The Riemann theta function near soliton limit

It has been known that (the square of) Jacobi elliptic function can be expressed by an infinite sum of single solitons of $\sech^2$ shape. In this paper, we show that there exists a similar structure for higher genus cases. It turns out that this is just a consequence of the quasi-periodicity of the Riemann $θ$-function. More precisely, we show that the second derivative of $\log θ$ with the \emph{real} Riemann $θ$-function of genus $g$ near soliton limit can be well approximated by the \emph{sum} of \emph{real} and \emph{regular} $g$-soliton solutions of Hirota-type in $g$-dimensional real space $\R^g$. This leads to a tessellation of $\R^g$, whose tile is an oblique prism divided into $2^g$ sections by hyper-planes of dominant exponents in the theta function. We apply the results to study quasi-periodic solutions to the KdV and KP equations. We construct the quasi-periodic solutions using the Schottky group, which uniformizes the corresponding Riemann surfaces. We also discuss solitons on quasi-periodic background by pinching some of the homological cycles

nlin.SI↗
arXiv2026

Retrieval-Based In-Context Learning: A Domain Adaptation Framework

In-context retrieval (ICR) is a retrieval-based form of in-context learning (ICL) in which demonstrations are retrieved from a source database based on similarity to the query, rather than sampled independently. In this work, we formulate ICR as a type of domain adaptation problem, where the source distribution $P$ of the database may differ from the target distribution $Q$ of the test query-label pair. We investigate the performance of ICR under a flexible class of distributional shifts that substantially extends prior work \citep{li2024fine,guo2025retrieval}, and establish theoretical guarantees that quantify the benefits and pitfalls of this learning paradigm. Our theory is verified by experiments on synthetic and language tasks.

stat.ML↗
arXiv2026

ReMaD: Tuning-free Domain Adaptation for Classification and Out-of-Distribution Detection

We introduce Reduced-rank Mahalanobis Distance (ReMaD), a novel prototypical distance-based refinement to classification and out-of-distribution (OOD) detection using pretrained models without finetuning. We use embeddings of the target dataset to fit closed-form distribution statistics in the model's latent space which can classify in-distribution samples and detect OOD samples, all without training or prior knowledge of the OOD data. Building on prototype classification and OOD detection, we analyze the distribution properties of large pretrained models when processing new datasets; based on this analysis, we formulate a simple modification to Mahalanobis Distance to adapt models' latent space distributions to new domains by removing unused features, without the finetuning or hyperparameter searches required by other adaptation procedures. We demonstrate the efficacy of this method to adapt existing large pretrained image embedding models to new classification domains outside their trained capabilities by testing across four target datasets, with competitive performance in both classification and OOD detection.

cs.LG↗
arXiv2026

When to Switch: Reliable Action-Chunk Extension for Vision-Language-Action Models

Vision-Language-Action (VLA) models serve as unified policies for robotic manipulation, yet their expensive inference forces robots to pause between policy calls, resulting in stop-and-go execution that interrupts smooth motion and prolongs task completion. Extending the action chunk reduces policy calls and hence these pauses, but predicting farther into the future makes long-chunk execution unreliable. To understand where this unreliability arises, we analyze action errors within long chunks and find that they concentrate around transitions between manipulation subskills, growing sharply with chunk length. This suggests the importance of transition timing, i.e., when to switch subskills within a chunk. Motivated by this observation, we introduce RACE (Reliable Action-Chunk Extension), a framework that predicts the transition timing from an auxiliary one-step denoising pass and conditions action generation on it. By learning and conditioning on transition timing, RACE reduces errors at subskill transitions and enables reliable execution of longer action chunks. Across simulation benchmarks, RACE outperforms fine-tuning at the same chunk length; with 2x longer chunks, it surpasses recent state-of-the-art and efficient VLAs in success rate, and with 4x longer chunks, it remains competitive. On a real robot, RACE uses 4x longer chunks, which reduces the idle time caused by stop-and-go execution by about 5x, while achieving a higher success rate than fine-tuning with the same chunk length. Code and a real-robot demo are available at https://github.com/Seonghoon-Yu/RACE-VLA

cs.RO↗
arXiv2026

A Physically Motivated Compact Parameterization of Neutron Star Atmosphere Emission for Thermal X-ray Pulse-Profile Modeling

Thermal X-ray pulse-profile modeling depends on the angular and spectral properties of neutron star atmosphere emission. We construct a compact empirical approximation to the specific intensity using eight coefficients for the angular dependence and five for a normalized spectral kernel. The angular prescription is motivated by the formal solution of the radiative-transfer equation, while the spectral normalization preserves a specified bolometric flux. We calibrate this family to numerical atmosphere tables, focusing on return-current-heated and fully ionized hydrogen atmospheres. When incorporated into a semi-analytic pulse-profile model, the approximation reproduces profiles normalized by their phase-averaged flux to within approximately $4\%$ for antipodal hot spots and $5\%$ for non-antipodal hot spots in the tested heated-atmosphere configurations. We also analyze synthetic eXTP observations using different beaming prescriptions to test the conclusion in our previous work based on a linear description of the angular dependence of the emission. The comparisons suggest that the angular dependence of the intensity cannot be simply characterized by a linear function of the cosine value of the emission angle, because its detailed shape and energy dependence will affect the parameter inference. This parameterization can significantly increase the efficiency for analytic and numerical models, and provide a compact framework for examining how atmosphere assumptions affect neutron star pulse profiles and the inferred stellar properties.

astro-ph.HE↗