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arXiv2026

Control Synthesis against LTL Specifications with Long-Run Visit Proportion Objectives

This paper investigates the path-planning problem for systems required to satisfy a linear temporal logic (LTL) specification while achieving a desired long-run visit proportion. For a path represented in prefix-suffix structure, the long-run visit proportion quantifies the asymptotic occurrence proportion of an atomic proposition (AP) sequence of interest in the suffix trace. Such a quantitative requirement generally cannot be expressed by standard LTL specifications. Furthermore, we develop a planning approach that synthesizes an LTL-satisfying path whose long-run visit proportion remains within a prescribed tolerance of a desired value while satisfying an overall cost constraint. By adjusting the desired proportion, the synthesized path can allocate more or less long-run attention to the atomic proposition sequence of interest, thereby improving the flexibility and efficiency of the task execution. Finally, experiments on a quadruped robot demonstrate the practical significance of the proposed long-run visit proportion and the effectiveness of the proposed planning approach.

eess.SY↗
arXiv2026

Heat flow and repeated differentiation of polynomials with i.i.d. roots

How do the zeros of a polynomial evolve under the holomorphic heat flow or repeated differentiation? In this work, we develop a unified probabilistic proof to three conjectures on the evolution of polynomial zeros under holomorphic heat flow and repeated differentiation. We study these two evolutions for random polynomials with i.i.d.~roots $z_1,\dots,z_n\simμ_0$, where $μ_0$ on $\mathbb C$ satisfies suitable $2+δ$ logarithmic moment conditions. For the heat flow of small time $t>0$ and Lipschitz continuous Stieltjes transform of $μ_0$, we identify the limit distribution $μ_t$ as explicit push-forward of $μ_0$ under a transport map. For rotationally invariant $μ_0$, we characterize the limit after $\lfloor tn\rfloor$ differentiations through its radial quantiles. For instance, the heat flow evolves the circular law into the elliptic and semicircle law, while differentiation moves surviving mass towards the origin. We also show that $o(n)$ derivatives preserve the initial distribution $μ_0$. In fact, all convergences hold almost surely. The common proof strategy crucially relies on recursion identities from leaving out a root, and concentration inequalities, which lead to self-consistent equations for Stieltjes transforms. This brings a method familiar from random matrix theory to polynomial evolutions. Moreover, it allows for generalizations beyond rotational symmetric distributions and quantitative stability estimates for $o(n)$ differentiations and vanishing heat-flow times.

math.PR↗
arXiv2026

Mitigating LLM Over-Refusal via Dynamic Semantic Routing Calibration

Large language models (LLMs) aligned for safety often suffer from over-refusal, incorrectly rejecting benign yet safety-related instructions. Prior studies primarily attribute this to static representation overlap, largely overlooking the underlying dynamic mechanisms. In this paper, we present the mechanistic analysis of over-refusal through the lens of internal routing conflicts within transformer attention. We discover that a sparse subset of Hypersensitive Safety Heads misfires on Hard-Safe prompts, exhibiting abnormal attention entanglement that forcefully binds harmless target entities to refusal semantics. This triggers a severe, high-entropy routing conflict that deprives target entities of necessary attention. To counteract this, we propose Semantic Routing Calibration (SRC), a lightweight, training-free inference framework. SRC precisely localizes and dynamically suppresses these hypersensitive safety heads at the inference stage. Coupled with a dual-branch logits fusion that acts as a safety regularizer during subsequent decoding, SRC seamlessly restores trustworthy reasoning. Extensive experiments demonstrate that SRC alleviates over-refusal, with intrinsic safety performance preserved as much as feasible.

cs.CL↗
arXiv2026

JAMB: Joint Action-Motion Diffusion for Bimanual Manipulation

Coordinated bimanual manipulation is challenging because the motion of either arm can alter the shared 3D scene and thereby affect the other arm. Yet most diffusion policies generate actions without explicitly modeling these future geometric consequences, while predictive variants typically use future state only as auxiliary supervision or fixed conditioning. We address this limitation by proposing JAMB, a diffusion policy that jointly denoises bimanual actions and future 3D point tracks. By allowing action and track hypotheses to evolve together within a shared Transformer, each can inform and refine the other throughout denoising. We further ground multimodal representations in a shared spatiotemporal coordinate system to facilitate geometry-aware interaction during joint denoising. We evaluate JAMB on diverse bimanual manipulation tasks in RoboTwin 2.0 and on a real-world robot, comparing it with action-only policies and alternative future-prediction approaches spanning different state representations and learning objectives. Across 16 simulation tasks, JAMB achieves an average success rate of 83.4%, outperforming the strongest baseline by 23.9 percentage points. On three real-world tasks, it outperforms the action-only and auxiliary geometry prediction methods by 50.0 and 21.2 percentage points, respectively. Beyond these performance gains, JAMB shows stronger generalization to cluttered scenes and out-of-distribution backgrounds than the evaluated baselines. Together, these results demonstrate the effectiveness of our joint action-motion modeling framework for coordinated bimanual manipulation. Our project website is available at https://jam-bimanual.github.io/

cs.RO↗
arXiv2026

Density of large holes among power-free lattice points

For fixed integers $d,r\ge1$ with $dr\ge2$, the $r$-free points of $\mathbb{Z}^d$ are those whose coordinate gcd is not divisible by the $r$th power of any prime. Fix $1\le q\le \infty$. A lattice point is $R$-deep if every lattice point in the closed $\ell_q$-ball of radius $R$ centred there is non-$r$-free. We mark each finite nearest-neighbour component of non-$r$-free points containing an $R$-deep point by its lexicographically least such point. Uniformly for $1\le q\le\infty$, the densities of $R$-deep points and of these representatives both have the asymptotic form $\exp\left\{-\frac{v_{d,q}R^d}{ζ(dr)}\left[d(dr-1)\log R+dr\log\log R-Υ_{d,r,q}+r\frac{\log\log R}{\log R}-\frac{Λ_{d,r,q}}{\log R}+O_{d,r}\left(\frac{(\log\log R)^2}{(\log R)^2}\right)\right]\right\}$ as $R\to\infty$, where $v_{d,q}$ is the volume of the unit $\ell_q$-ball and $Υ_{d,r,q},Λ_{d,r,q}$ are explicit constants. For deep points, this sharpens the positive-density hole constructions of Baake, Moody, and Pleasants and of Pleasants and Huck, and the latter authors' upper bounds for sparse-pattern frequencies. For $d=1$, consider the densities of $r$-free integers followed by at least $g-1$ consecutive non-$r$-free integers, or by exactly $g-1$ such integers and then another $r$-free integer. Both have the asymptotics $\exp\left\{-\frac{g}{ζ(r)}\left[(r-1)\log g+r\log\log g-\widehatΥ_r+r\frac{\log\log g}{\log g}-\frac{\widehatΛ_r}{\log g}+O_r\left(\frac{(\log\log g)^2}{(\log g)^2}\right)\right]\right\}$ as $g\to\infty$, where $\widehatΥ_r=Υ_{1,r,1}+(r-1)\log2$ and $\widehatΛ_r=Λ_{1,r,1}+r\log2$. The exact-gap expansion improves Grimmett's leading asymptotic and refines the formula in Jiang's recent preprint. For fixed $r$, we also obtain estimates uniform in growing dimensions $d=O_r((\log R)^r)$.

math.NT↗
arXiv2026

Pointwise provable equality and the failure of composition

In their studies of pathologies in recursion categories, Montagna (1989) and Di Paola--Montagna (1991) introduce the algebraic systems $S'$ and $S'_T$, respectively, and claim that they are categories. We show that the proposed composition is not independent of the choice of representatives. For every consistent recursively enumerable extension $T$ of Peano arithmetic ($\mathrm{PA}$), we exhibit two unary programs whose partial functions are provably equal in $T$, separately at each standard input. Composing each after a program that searches for a $T$-proof of contradiction and returns its code yields programs that are not equivalent in this sense. An alternative proof uses the productivity of the complement of the diagonal halting set. Montagna's $S'$ is the case $T=\mathrm{PA}$. More generally, for consistent $T\supseteq\mathrm{PA}$, pointwise provable equality is a composition congruence exactly when $T$ proves every true $Π^0_1$ sentence, in which case it is extensional equality. This completeness condition fails for every consistent recursively enumerable $T\supseteq\mathrm{PA}$ by Gödel's second incompleteness theorem. For every extension $T\supseteq\mathrm{PA}$, the least composition congruence containing pointwise provable equality is extensional equality if $T$ is $Σ^0_1$-sound and the universal relation otherwise.

math.LO↗
arXiv2026

Leader-follower Attitude Synchronization of Rigid-body Systems on SO(3)

This paper addresses the leader-follower attitude synchronization problem on $\mathrm{SO}(3)$ for a group of heterogeneous rigid body systems. The reference attitude, represented by a virtual leader, is accessible only to a subset of agents in the network. The follower communication graph is assumed to be undirected and acyclic, and every agent is connected to the virtual leader through a path in the corresponding augmented graph (including the virtual leader). An observer-based distributed control strategy, endowed with almost global asymptotic stability guarantees, is proposed to synchronize all rigid-body attitudes with a desired time-varying reference attitude. An observer-based distributed control, with reduced complexity, as well an observerless distributed control strategy are also developed for the constant-reference case, with almost global asymptotic stability guarantees. Numerical simulations are presented to demonstrate the effectiveness and performance of the proposed distributed control strategies.

eess.SY↗
arXiv2026

Signed Graph Pre-Training and Prompt Learning

Signed graphs arise in trust--distrust networks, financial correlation systems, biological interaction graphs, and many other domains in which edges can be positive or negative and may also be directed. While signed graph neural networks have improved task-specific learning, graph transfer learning on signed graphs remains underdeveloped. In this paper, we introduce TopoSIGN, a pioneer topology-guided graph pre-training and prompt learning framework for signed graphs. TopoSIGN combines a structural encoder built on the magnetic signed Laplacian with a novel persistent-homology branch that summarizes signed topology through Dowker-complex persistence images. The fused embeddings are then transferred to a prompt learning function. Experimental results on synthetic and real-world datasets demonstrate the efficacy of TopoSIGN in extracting useful structural information in signed graphs, as well as the adaptability and flexibility of the proposed general framework.

cs.LG↗
arXiv2026

Constant Chern Holomorphic Sectional Curvature: Rigidity and Counterexamples to the Flatness Conjecture

We prove rigidity results for Hermitian metrics of constant Chern holomorphic sectional curvature and construct counterexamples to the flatness conjecture. On a compact complex manifold in Fujiki's class $\mathcal C$ of dimension $n\ge2$, every such metric with nonpositive curvature is Kähler; its universal cover is complex hyperbolic in the negative case and Euclidean in the zero case. On an arbitrary compact complex threefold, nonzero constant curvature forces Kählerness, while zero curvature forces Chern flatness. For every complex dimension $n\ge7$, we construct compact Hermitian manifolds carrying balanced metrics with zero Chern holomorphic sectional curvature, vanishing first and second Chern--Ricci tensors, and nonzero full Chern curvature. The rigidity proofs use weighted integral comparison, differential compatibility in complex dimension three, and compactness obstructions from common kernels and null foliations. The counterexamples arise from a positive invariant Hermitian metric on a seven-dimensional complex quadric. Its Chern curvature is expressed by the octonion associator, whose alternating four-tensor makes holomorphic sectional curvature and both Ricci contractions vanish while retaining nonzero curvature. The metric descends to compact quotients; products with flat complex tori give the higher-dimensional counterexamples.

math.DG↗
arXiv2026

Propagation electrodynamics differential conduction of action potentials in geometrically branched squid giant axons

Classical cable theory neglects magnetic induction, Lorentz forces, and transient electromagnetic (EM) currents, limiting its accuracy for action potential propagation in branched neuronal geometries. We develop a coupled Maxwell-cable framework that integrates finite-difference time-domain (FDTD) solutions of Maxwell's equations with extended Hodgkin-Huxley and Fitzhugh-Nagumo dynamics, including magnetic gating, EM transmembrane currents $I_{\text{EM}}$, and quantum corrections for thin segments. Controlled simulations in asymmetric and symmetric axonal bifurcations show that inductive effects lower the critical branch radius for conduction failure and break symmetry in identical daughter branches under transverse magnetic fields. We introduce an EM-corrected geometric ratio $GR_{\text{EM}}$ that revises branch-point impedance matching and captures size-dependent axial current imbalances. Parent axon conduction velocity deviates significantly from the $\sqrt{d}$ scaling law when EM feedback and quantum effects are included, leading to early blockage at large diameters. Overall, quasi-static models underestimate EM corrections to speed, waveform, and transmission fidelity; our framework offers a multi-physics tool for electrodynamic signaling in complex neuronal architectures.

physics.comp-ph↗
arXiv2026

Gödel's and Scott's Variants of the Ontological Argument in Lean 4 and TPTP THF

The Isabelle/HOL dataset of Benzmüller and Scott's study of Gödel's ontological argument and Scott's variant (Monatshefte für Mathematik, 2025) is carried to Lean 4 and from there back to the automated provers, as a benchmark independent of either proof assistant. The port covers all thirty theories, structure and names preserved: 548 statements compare identical as parsed, every named result is proved again, and five results the original reports without replaying them are proved here. For every theorem, #print axioms gives the postulates its proof consumes: Scott's necessary existence and modal collapse need only a symmetric frame, confirming that KB suffices. The benchmark, in TPTP THF and SMT-LIB, turns the steps of an argument debated in philosophy into 294 theorems, alongside 45 statements the original refutes or leaves open, ten left open there. Five THF provers, and cvc5 on SMT-LIB, prove 227 theorems within ten seconds on one core and 232 within sixty, and none proves any of the 45. E and Leo-II solve the most, although Leo-II's calculus has been unchanged for about a decade and was only repaired and modernised here, as release 2.2. Vampire, whose later version won the higher-order division of CASC-30, solves the most in no configuration. Only E and Leo-II are measured in their own automatic mode: Zipperposition proves 101 in a single mode and 213 with its developers' portfolio, Vampire 174 without options and 209 with a higher-order schedule that its CASC mode does not select, and Leo-III 159 alone and 177 with E as partner.

cs.LO↗
arXiv2026

Quantum Chemistry in a Novel Hybrid Dipolar Atom-Ion Mixture

Merging trapped ions with cold atomic clouds offers intriguing prospects for quantum chemistry and many-body quantum simulations. Especially when going beyond the standard alkali atomic baths by using lanthanide atoms, opportunities arise to study the interplay between the intermediate-range atom-ion interaction and the tunable long-range dipolar atom-atom interactions. However, the high total angular momentum of the ground-state of open-shell lanthanides, e.g. $^{5}I_{8}$ for dysprosium, affects the atom-ion potential. Here, we discuss the implications for long- and short-range atom-ion interactions and present a novel apparatus which combines an ytterbium ion (Yb$^{+}$) with dipolar dysprosium (Dy) atoms. We highlight the consequences of this novel Dy-Yb$^{+}$ mixture for observing buffer gas cooling, (non-) radiative charge transfer, and three-body recombination. While the energy-averaged rates are dominated by radiative charge transfer, particularly radiative association, we find that three-body recombination can compete with molecular-ion formation at Dy densities $n\gtrsim 10^{12}$ cm$^{-3}$. This competition is further enhanced by the expected non-thermal distribution of ion energies. These processes could be experimentally characterised through controlled variation of the atom-ion interaction parameters, providing a direct test of our theoretical predictions.

physics.atom-ph↗
arXiv2026

Transfer Learning with Conformalized Quantile Regression for Solar PV Forecasting Under Load-Shedding-Driven Data Scarcity

Solar photovoltaic (PV) forecasting in regions affected by load shedding is challenging because reliable historical observations are scarce. This study proposes a transfer learning framework combined with Conformalized Quantile Regression (CQR) to improve PV power forecasting and provide reliable uncertainty estimates under severe data scarcity. A source-domain PV dataset from Alice Springs, Australia, is used to pretrain a temporal forecasting model, which is then adapted to simulated Bangladesh PV data representing different levels of historical availability. Experimental results show that transfer learning reduces RMSE by up to 23.7% when only one month of target-domain data is available and by 13.7% with three months of data. The proposed Transfer Learning plus CQR framework achieves 94.3% empirical coverage with three months of target data while producing prediction intervals that are 14% narrower than those obtained without transfer learning. These results demonstrate that combining transfer learning with conformal uncertainty quantification can improve both point forecasting accuracy and uncertainty reliability when target-domain PV data are severely limited.

cs.LG↗
arXiv2026

Pheno-GS: Phenoscape-scale Geodesic Sinkhorn

High-throughput single-cell data is now collected across large patient cohorts. Understanding patient-level heterogeneity from cellular-level data motivates phenoscaping: embedding each single-cell distribution as a "datapoint," with distances given by optimal transport (OT). Computing geometry-aware OT at this scale, between all pairs of patient datasets, remains an open challenge, since existing methods either rely on Euclidean ground metrics that distort manifold structure or fail under sparse, unevenly sampled, or large-scale data. We present \textbf{Pheno-GS} (Phenoscape-scale Geodesic Sinkhorn), which computes accurate, scalable geodesic transport distances under noisy, unbalanced, large-scale settings via three components: ($1$) graph connectivity regularization for well-defined geodesics on sparse/disconnected manifolds; ($2$) an unbalanced OT formulation via KL marginal penalties; and ($3$) a batched matrix algorithm computing all pairwise distances in one heat diffusion (over $200 \times$ faster than Geodesic Sinkhorn for $500$ distributions). We validate Pheno-GS on synthetic benchmarks and a CyTOF perturbation dataset.

cs.LG↗
arXiv2026

The winner's curse in hardware VQE: drift-differenced remeasurement of finite-shot selection bias

Finite-shot optimization can make noisy variational quantum eigensolver energies look artificially accurate. We studied six hardware-tractable molecular active spaces on two IBM Heron r3 processors. Seven optimizer-selected values fell below the exact active-space eigenvalue by up to 17.36 mHa. The cell-balanced fraction of the source-observed best-final advantage not retained on later fixed-parameter measurement was 0.989 (approximate 95% session-level interval [0.906, 1.072]); alternative aggregations span 0.892-0.989. Thus little of the selected advantage remained on average. Measurements occurred 5.6-38.4 days later, so parameter-dependent drift remains a competing explanation. Best-observed hardware VQE values require prompt independent confirmation before supporting accuracy claims.

quant-ph↗
arXiv2026

The Lasserre Rank of the Cropped Hypercube

In an $n$-dimensional cropped hypercube each of the $2^n$ cropping inequalities chops off a single corner of the $0$--$1$ hypercube by an $\ell_1$-distance $ρ$. The case $ρ= 1/2$ has been extensively studied in the literature. This paper shows that the Lasserre rank of the $n$-dimensional cropped hypercube where $ρ= 1/2$, $n \geq 2$, is the smallest integer $0\leq t \leq n$ such that $Δ_t < 0$ in the recurrence $Δ_{-1} = 1$, $Δ_{0} = n-1$, $Δ_t = (n-1)Δ_{t-1} - t(n-t+1)Δ_{t-2}$. It follows that the Lasserre rank can be computed in time $O(n^2 \log^2 n)$. Asymptotically, the rank is $\frac{n}{2} + c_{1/2}\sqrt{n} + o(\sqrt{n})$, where $c_{1/2}$ is the unique zero of a given function. Numerically, $c_{1/2} \approx 0.3825$. In fact, we prove such results for any fixed $0 < ρ< 1$.

math.CO↗
arXiv2026

Locally computable error estimators for conforming approximations of interface problems cannot be robust

We prove an impossibility result for finite-range locally computable a posteriori error estimators for the conforming finite element discretization of an elliptic interface problem. For a class of interface problems with a checkerboard cross-point and $\{1,M\}$-valued coefficients, we construct two problem instances on the same interface-fitted mesh. The two instances share a piecewise-constant load for which the finite element solution and the data oscillation both vanish. The ratio of their exact energy errors grows at least proportionally to $M^{1/4}$. Locality together with efficiency forces identical estimator values for these instances. The product of reliability and efficiency constants is therefore bounded below by a constant multiple of $M^{1/4}$. Consequently, any locally computable error estimator for interface problems, whether of residual, equilibrated, or recovery type, cannot be simultaneously reliable and efficient with contrast-independent constants.

math.NA↗
arXiv2026

Randomized Spectral Inference for Hyperuniformity

We test hyperuniformity from one large realization of a stationary point process. Hyperuniformity is equivalent to the average $A_r$ of the structure factor over $B_r$ vanishing as $r\downarrow0$, so the target is a low-frequency average rather than the value of the structure factor at the origin, which need not exist. We estimate $A_r$ from squared Fourier coefficients at frequencies drawn uniformly from $B_r$; if these coefficients are asymptotically Gaussian at almost every fixed frequency, the squared coefficients converge to independent variables with mean $A_r$. Assuming $A_r=s+c r^α+\varepsilon_r$ with $|\varepsilon_r|\leq Lr^β$ and given exponents $0<α<β$, a two-radius extrapolation removes the $r^α$ term and estimates $s$ with deterministic error of order $r^β$. This gives confidence bounds and a one-sided test of $H_0:s=0$ with asymptotic level at most $γ$, consistent against every fixed $s>0$ as $R\to\infty$, then the number of sampled frequencies tends to infinity, and then $r\downarrow0$. Essentially free translation actions with completely positive entropy satisfy the Fourier assumption.

math.ST↗