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arXiv2026

Supernovae Ia ejecta velocities and host galaxy environments: the role of survey-selection effects

The origin of the near-maximum-light Si II $λ$6355 velocity diversity among supernovae Ia (SNe Ia) remains uncertain. Previous studies have suggested that high-velocity (HV) and normal-velocity (NV) SNe Ia occupy systematically different host galaxy environments, implying differences in their progenitor populations. We re-examine this hypothesis using a sample of 354 nearby ($z\leq0.04$) spectroscopically normal SNe Ia, comprising 239 NV and 115 HV events, identified in targeted and untargeted surveys. For each SN, we determine the host galaxy morphology, galactocentric distance, and physical size, and obtain homogeneous stellar mass estimates while assessing the influence of survey-selection effects. The Si II velocity distribution is well described by two Gaussian components, confirming the NV and HV populations. We find no statistically significant differences between the galactocentric distance, host galaxy size, or stellar mass distributions of the two velocity subgroups. The environmental trends reported in previous studies are recovered only with marginal statistical significance in the targeted subsample, whereas they disappear almost entirely in the untargeted subsample, consistent with survey-selection effects playing a major role in the previously inferred environmental differences between the NV and HV events. Our results weaken the interpretation that the observed Si II velocity diversity is primarily driven by systematic differences in the global host properties examined here. Instead, they favour a scenario in which intrinsic explosion asymmetries and viewing-angle effects account for a substantial fraction of the observed velocity diversity, without excluding a possible contribution from local environmental conditions or progenitor properties.

astro-ph.GA↗

arXiv2026

Scalable Quantum Key Distribution via GHZ Entanglement and Qubit Reuse

Conventional Quantum Key Distribution (QKD) requires the transmission of qubits proportional to or exceeding the length of the key, as protocols such as BB84 transmit more qubits than the final key size due to basis sifting and privacy amplification. Since quantum networks are still in their infancy and have limited capacity, this overhead puts significant pressure on network resources. To address this issue, we propose a Multi-Qubit Greenberger--Horne--Zeilinger (GHZ) State-based QKD scheme that reduces the number of qubits transmitted over the quantum channel. The proposed method transmits one GHZ qubit between endpoints and reuses the resulting entanglement to convey multiple classical key bits with the help of Quantum Non-Demolition (QND) measurements. Under the stated assumptions on authenticated classical communication, local reset verification, and bounded-error QND discrimination, one can transfer $L$ classical bits by generating an (L+1)-qubit GHZ state and transferring one qubit to the remote party. We verify correctness using the NetSquid quantum network simulator: the protocol achieves 100\% raw-key fidelity for keys of length up to 12 bits under both ideal conditions and depolarizing noise up to p = 0.005 per round. We further show that the proposed QKD algorithm can be extended to multi-party QKD and server-client deployment. The proposed scheme offers a transmitted-qubit-efficient, noise-tolerant alternative for bandwidth-limited quantum networks.

quant-ph↗

arXiv2026

A Massively Parallel Three-Grid Preconditioner for the High-Frequency Helmholtz Equation

Accurate simulation of three-dimensional time-harmonic wave propagation over many wavelengths requires control of phase error and efficient solution of large indefinite systems. We develop a three-grid solver based on the compact 27-point interpolated optimized finite-difference (IOFD) discretization. Its wavenumber-dependent stencil supports a fine-grid resolution of six points per shortest wavelength and an unshifted physical correction on the $2h$ grid at only three points per shortest wavelength. The method retains unshifted IOFD operators on the $h$ and $2h$ grids, while a complex-shifted $2h$--$4h$ auxiliary cycle preconditions a factorization-free iterative approximation of the coarse inverse. Restricting the shift to this auxiliary cycle preserves the propagative character of the coarse correction. Comparison with the outgoing Green function confirms phase and relative-amplitude accuracy on a sequence of meshes up to \revision{$10240^3$}, \revision{exceeding one trillion unknowns,} with the largest problem spanning approximately \revision{1704} wavelengths per coordinate. The same fixed solver configuration retains robust convergence across smooth, discontinuous, high-contrast, and geophysical velocity models and exhibits scalable parallel performance. In particular, a \revision{$2560^3$} problem spanning approximately \revision{425} wavelengths in each coordinate direction is solved in \revision{43.8 seconds} on just 64 NVIDIA A100 GPUs.

math.NA↗

arXiv2026

The Physical Crash Frontier: What Finite Option Quotes Can and Cannot Reveal

Physical crash probabilities recovered from option prices depend on a pricing kernel and on a risk-neutral distribution that finitely many bid and ask quotes do not identify. For a power utility investor, we characterize the pairs of physical crash probability and expected loss below the crash threshold that the quotes admit; the boundary of this set is the physical crash frontier. Both coordinates are ratios of moments, yet when the index is bounded above the closed set is convex, and under an interior regularity condition second-order cone programs compute it exactly at the benchmark risk aversion of two. In a decade of weekly S&P 500 cross sections, the quotes beyond the two puts nearest a 10 percent decline shrink the range of admissible crash probabilities by about 80 percent, yet its upper end remains two to three times its lower end. Under strict quote slack and the interior-mass condition stated below, removing the cap without further tail control drives the lower bounds on crash probability and unconditional shortfall to zero for risk aversion above one. A vanishing probability far in the right tail inflates the normalizing moment while every quote remains inside its spread. In this setting, a positive floor requires additional tail information, supplied here by the support cap.

q-fin.CP↗

arXiv2026

On a slight weakening of Kripke-Platek Set Theory

The weak set theory $\mathsf{ReR}$ is obtained from Kripke-Platek Set Theory ($\mathsf{KP}$) by replacing the bounded collection scheme with the bounded replacement scheme. We show that $\mathsf{ReR}$ proves $\mathsf{TCo}$, which asserts that every set is contained in a transitive set. This is used to show that the theories obtained by adding the negation of the axiom of infinity to $\mathsf{ReR}$ and $\mathsf{KP}$ have the same consequences. Our proof of $\mathsf{TCo}$ relies on the availability of a fragment of class foundation in $\mathsf{ReR}$. To demonstrate the necessity of this reliance, even in the presence of infinity, we build a model of a significant fragment of $\mathsf{ZF}$ that includes bounded separation and collection, infinity, powerset, regularity and the axiom of choice, in which $\mathsf{TCo}$ fails.

math.LO↗

arXiv2026

Energy of toroidal M2 brane in flat 11d background

The supermembrane action is non-linear and a priori non-renormalizable. Still, some quantities in this theory may be free of log UV divergences and thus defined unambiguously. To explore this possibility we compute the energy of an M2 brane wrapped on a 2-torus in flat 11d space to two loops in the inverse-tension expansion. The result is free of logarithmic divergences and the same should hold also at higher loop orders. For fermions periodic around both circles the quantum corrections cancel, consistent with the BPS nature of the wrapped M2 brane state. For fermions antiperiodic around one or both circles the energy is a non-trivial function of the radii given by infinite sums of modified Bessel functions. We also compute 3-loop correction to the energy of the bosonic membrane on $\mathbb R^2\times S^1$. In contrast to the string case, it contains, besides powers of the 1-loop $ζ(3)$ coefficient, a new term proportional to $ζ(9)$. Summing contributions of all-loop bubble graphs leads to a simple cubic equation for the membrane energy. The analogous resummation in the Nambu or GS string case reproduces the familiar exact square-root expression ${\mathcal E}=\sqrt{(2πR\,T_1)^2+m_0^2}$. We find that the bubble-graph part of the membrane energy does not vanish for any value of the radius $R_{11}$. If contributions of other non-trivial diagrams in the supermembrane case do not qualitatively change this conclusion, this would disfavour the conjectured relation between 11d theory on an antiperiodic circle and the strong-coupling limit of type 0A string theory.

hep-th↗

arXiv2026

Quantitative Links between Formation and Atmospheric Composition for Giant Planets

Precise atmospheric abundances of giant exoplanets are becoming increasingly prevalent and there is a need to systematically convert these measurements into metrics that inform us about the planets' accretion history. We present a quantitative framework for relating atmospheric composition to the accretion of metals and primordial gas. This includes i) new relations that simplify and generalize the connection between atmospheric metallicity and metal mass fraction, ii) methods for inferring the source of the metals and quantifying the quantity of metals accreted via different sources, and iii) relating the derived quantities to expectations from formation models. We also derive a new estimate of the minimum disk mass needed to form a planetary system based on the amount of excess metals accreted by a planet, assuming that this excess originates from the drift and evaporation of pebbles at condensation fronts. This paper is accompanied by an open-source code that implements the methods presented herein.

astro-ph.EP↗

arXiv2026

EXAM2: Extending Audio Understanding in Multilingual and Multimodal Analysis

Recent large audio language models (LALMs) have achieved impressive progress in audio understanding. However, existing evaluations remain largely constrained to English and narrow audio domains. Prior benchmarks typically focus on a single audio modality, i.e., speech, sound, or music, limiting the systematic investigation into how these models generalize across diverse visual scenarios. In this paper, we introduce EXAM$^2$, a benchmark for multilingual and multimodal audio understanding spanning six languages and multiple modalities, including speech, sound, music, mixed-audio settings, and visual images. By incorporating visual information alongside heterogeneous audio inputs, EXAM$^2$ enables more realistic evaluation of scene-aware audio reasoning and cross-modal comprehension. EXAM$^2$ comprises $5,667$ multiple-choice questions, $22,614$ image instances, and $135,684$ multilingual translations. We evaluate state-of-the-art open-source and proprietary LALMs as well as multimodal LLMs, revealing substantial performance gaps in multilingual and cross-modal understanding. Furthermore, we propose Gemma3n-EXAM$^2$, a lightweight fusion-model fine-tuned on EXAM$^2$-train, achieves up to $15.8\%$ improvement in multilingual settings and $16.5\%$ gains in multimodal evaluation over a strong baseline. Empirical results establish EXAM$^2$ as a challenging benchmark and pioneer future multilingual and multimodal audio intelligence research.

cs.SD↗

arXiv2026

Steering Recurrent Reasoners at Inference Time with Readout Feedback

Recurrent models, which repeatedly update latent states with shared computation blocks, have emerged as powerful architectures for solving complex reasoning tasks. Existing inference-time methods scale computation by running more steps or sampling more trajectories, but ignore information revealed within each trajectory. Here we show that recurrent models can be improved at inference time by using their own readout probabilities to steer latent dynamics without retraining. We introduce Readout Feedback (RoFB), a test-time intervention that converts intermediate predictions into token-wise pairwise coupling forces injected into the latent dynamics. Across three recurrent models (AKOrN, ItrSA++, TRM) on Sudoku and Maze, RoFB yields clear gains in four of six model-task pairs and a small gain in one. The four positive pairs achieve performance unattainable by merely running more steps or selecting from multiple trajectories, at comparable or lower computational cost. These results suggest that closed-loop steering of latent dynamics can serve as a complementary inference-time control mechanism for recurrent reasoning models.

cs.LG↗

arXiv2026

Linear maps preserving families of C-symmetric operators

Let $\cH$ be a separable complex Hilbert space with $\dim\cH\ge3$. We characterize the bounded bijective complex-linear maps $T$ on $\BH$ for which there exists a bijection $ψ$ of the set of conjugations,preserving commutativity in both directions, such that $T$ maps the space of $C$-symmetric operators onto the space of $ψ(C)$-symmetric operators for every conjugation $C$. We show that this condition is equivalent to the existence of a bijection $φ$ of the set of all orthonormal bases such that $T$ maps the set of all $(e_n)$-diagonal operators onto the set of all $φ((e_n))$-diagonal operators. We also characterize the corresponding preservers in dimension two using Pauli coordinates, without assuming the commutativity condition on $ψ$.

math.FA↗

arXiv2026

No Free Compression in Quantum Relaxations for Optimization

Qubit-efficient quantum relaxations compress classical decision variables into expectation values on substantially fewer qubits. We ask what resource tradeoffs this compression entails for quantum optimization. For the complete quadratic-Majorana encoding of $m=Θ(n^2)$ binary variables on~$n$ qubits, we define the universal margin as the smallest correlator magnitude that can be guaranteed with prescribed signs for every target sign (bit) assignment. We show that it is exactly $Δ_{\rm Maj}(n)=\tan\!\left(\fracπ{4n}\right)=Θ(1/n)$, whereas uniformly random sign assignments retain $Θ(1/\sqrt n)$ target-specific margins. Arbitrary density operators and mixed fermionic Gaussian states generate the same quadratic-Majorana covariance body, so non-Gaussian state resources cannot enlarge this two-point relaxation. More generally, standard quantum random access code bounds provide general information-theoretic baselines. For any fixed family of $m$ designated binary observables on~$n$ qubits, the universal margin is at most $\sqrt{(2\ln2\,n/m)}$, and random access decoding from $N$ copies with constant success probability above $1/2$ requires $nN=Ω(m)$. For a fixed Pauli correlation encoding required to work uniformly over all targets, maintaining a fixed nonzero decoded magnitude under smooth sign decoding therefore requires a rescaling parameter that grows as the available margin shrinks. Thus, while providing substantial qubit savings, compression can shift cost into restricted expectation value geometry, smaller expectation value magnitudes, or more demanding information recovery rather than eliminate it.

quant-ph↗

arXiv2026

ConfAL-WM: Confidence-Guided Active Learning for Action-Conditioned World Models

Action-conditioned world models have become an important foundation for embodied prediction, planning, and synthetic data generation, but their errors under new task and scene distributions are often concentrated in localized spatiotemporal regions such as robot arms, manipulated objects, contact areas, and occluded objects. This paper presents ConfAL-WM, a confidence-guided active learning framework for post-training embodied world models. Building upon EnerVerse-AC (EVAC), we attach a lightweight confidence probe to UNet decoder features and predict dense confidence maps in the latent space. These maps are aggregated into task-, frame-, and patch-level scores, enabling data-budget allocation and localized training enhancement. Our pipeline trains the probe and warms up EVAC on a small target-domain subset. EVAC-v1 then supplies task-level acquisition and optional frame/patch weighting signals; all selected-data models are initialized from the original pretrained EVAC checkpoint for retraining. Experiments on RoboTwin2.0 at the default 40% data budget show that confidence-guided selection improves post-training quality, while dense frame and patch weighting offers complementary reconstruction and semantic gains compared with scalar reward, progress, and judge-based scoring baselines. A quick visual overview of this work is available at https://ConfAL-WM.github.io.

cs.RO↗

arXiv2026

The bursting of hollow droplets

A bubble bursting from a drop of finite size (a hollow droplet) is the generic bursting event in a breaking wave, yet it has been studied almost exclusively at unbounded baths. We follow it from the puncture of the film to the spectrum of a spray, in axisymmetric simulations over liquid-to-gas volume ratios $Λ$ from $1/16$ to $512$ and Ohnesorge numbers from $0.005$ to $0.11$. Ejection ceases at $\mathit{Oh}_1=\mathit{Oh}_c(1+2β/λ)$, with $β\simeq0.83$ and $λ=(1+Λ)^{1/3}$: confinement extends ejection to bubbles too small to eject at a flat surface, and the distance $δ=1-\mathit{Oh}/\mathit{Oh}_1$ to that boundary organizes everything that follows. The collapse, driven by capillary waves, is that of a gas thread pinching next to its mouth, whether the liquid shell is punctured once or twice. The ejected volume is $M_e=C\,δ\,V_{\rm red}$, with $C\simeq0.013$ and $V_{\rm red}=V_{\rm gas}V_{\rm liq}/(V_{\rm gas}+V_{\rm liq})$ a reduced volume. Whatever the confinement, the first droplet is smallest at $δ\simeq0.2$ in units of the viscocapillary length $\ell_μ=μ^2/(ρσ)$ and at $δ\simeq0.3$ in units of the bubble radius $R_0$, where the unbounded bath also places its optimum. The largest reaches a tenth of $R_0$. Between them the census is exponential, with a scale set by $R_0$ and no lower cut-off: the smallest droplet a simulation records is set by its resolution, not by $\ell_μ$, which belongs to the pinch singularity rather than to the droplets. Mixed over bubble populations, the census gives spray spectra in closed form, whose shape measures the population. The bursting also produces hollow droplets, each a potential new generator.

physics.flu-dyn↗

arXiv2026

Resultants of dynatomic polynomials of $x^d$

Let $K$ be a field of characteristic zero, and let $ϕ(x)\in K[x]$ be a polynomial of degree at least 2. Denote the $n$-th iterate of $ϕ$ by $ϕ^n$. The $n$-th dynatomic polynomial of $ϕ$ is defined by $$Φ_{ϕ,n}(x) := \prod_{k\mid n}(ϕ^k(x)-x)^{μ(n/k)}.$$ In this paper, we specialize to the case $ϕ(x) = x^d$. We first establish several properties of $Φ_{ϕ,n}$ that are analogous to those of cyclotomic polynomials. We then combine these properties with known results on resultants of cyclotomic polynomials to determine the resultants of dynatomic polynomials. In particular, for $1\leq n< m$, we show that $\operatorname{Res}(Φ_{ϕ,n},Φ_{ϕ,m}) = 1$ if and only if $n\nmid m$. When $n\mid m$, we obtain the explicit formula $$\operatorname{Res}(Φ_{ϕ,n},Φ_{ϕ,m}) = Φ_{m/n}(d^n)^{ν_d(n)},$$ where $Φ_j$ is the $j$-th cyclotomic polynomial, $ν_d(1) = d-1$, and $ν_d(n) = \operatorname{deg}Φ_{ϕ,n}$ for $n>1$.

math.NT↗

arXiv2026

Discovering Substellar Dark Matter Halos with Astrometric Weak Lensing of Multiply Imaged Quasars

We propose time-domain astrometric weak lensing of multiply imaged quasars as a probe of substellar dark matter (DM) halos. In $Λ$CDM, each macro-image's light traverses many microhalos, producing a stochastic centroid motion with a calculable red power spectrum. Halos with crossing times longer than the survey impart a relative angular acceleration between image pairs. The response peaks at subhalo scale radii 0.005-2 pc and masses $3\times10^{-6}$-$10^2\,M_\odot$, 12-14 orders of magnitude below the smallest detected DM structures, down to the damping cutoffs of a 100 GeV thermal relic. We forecast the sensitivity of ten-year campaigns with 300 epochs for two benchmark systems: the galaxy-lensed quadruple B1422+231 at a 0.1 $μ$as per-epoch precision forecast for extended-path intensity correlation, and the cluster-lensed triple SDSS J1029+2623 at 1 $μ$as. The angular-acceleration channel reaches the standard $Λ$CDM microhalo population with a variance signal-to-noise ratio of order ten for the galaxy lens (order unity after stellar microlensing subtraction) and 0.35 for the cluster under the optimistic assumption that 10% of the projected mass density at the image positions resides in surviving microhalos. A positive detection would: raise universal lower bounds on the DM particle mass to $\gtrsim400$ keV for fermions and $\gtrsim10^{-12}$ eV for bosons; constrain the DM kinetic decoupling temperature to $\gtrsim 10$ MeV; and be sensitive to the running of the spectral tilt at the 0.01 level over 15-20 e-folds of the primordial curvature power spectrum. A robust null result across well-characterized lenses would constrain microhalo survival and/or imply violations of the above inequalities. These signatures motivate differential astrometric observations with extreme 0.1-1 $μ$as light-centroiding precision on multiply imaged quasars. [Abridged]

astro-ph.CO↗

arXiv2026

Exact Risk Ratios for Weighted Data Selection in Linear Regression

How much data must a fixed learner retain? Hanneke, Moran, Shlimovich and Yehudayoff (COLT 2025) posed this question for linear regression with the minimum-norm empirical risk minimizer. A selector sees a finite dataset $D\subseteq R^d\times R$, keeps at most $n$ examples with nonnegative weights, and $F_w(d,n)$ is the worst-case ratio between the full-data loss of the trained predictor and the optimal loss. The value is $\infty$ for $n<d$, $d+1$ at $n=d$ and $1$ for $n\ge2d$, and the regime $d<n<2d$ was left open. We settle several cases. For every $d$ we prove $F_w(d,2d-1)=1+1/d$, which confirms a claim stated without proof in the original note. We also prove $F_w(3,4)=5/3$, $F_w(4,5)=2$ and $F_w(4,6)=3/2$, the three smallest cells not covered by that formula. For every intermediate budget $n=d+k$ we prove the lower bound $F_w(d,d+k)\ge1+Γ_{d,k}$, where $Γ_{d,k}$ is an explicit harmonic quantity over balanced partitions of $d$. This bound is the exact minimax value on the class of datasets whose whitened systems split into orthogonal circuit blocks. All proved values equal $1+Γ_{d,k}$, and we conjecture that this holds throughout the open regime. Our upper bounds combine a rigidity theorem for positive spanning configurations of loss gradients with normal forms of the small positive bases in $R^3$ and $R^4$. These forms are special cases of the classification of Cornaz, Kerleau and Royer; we also control all gradients outside the basis. A dimension-free extremal-basis argument converts sign-cone geometry into selections of $d+1$ points. Explicit counterexamples rule out several shorter routes. Every upper bound is constructive, with selection procedures polynomial in the number of points for fixed dimension. Every numerical claim about a specific instance is an exact rational or algebraic identity, recomputed in exact arithmetic in the supplementary material.

cs.LG↗

arXiv2026

Reassessing the contribution of long-GRB high-energy afterglows to the isotropic gamma-ray background after GRB 221009A

Very-high-energy photons from gamma-ray bursts (GRBs) are absorbed by the extragalactic background light and partly reprocessed into the GeV band. We update previous estimates of the long-GRB contribution to the Fermi-LAT isotropic gamma-ray background (IGRB), using a time-integrated high-energy afterglow template of GRB 221009A, anchored by GeV-TeV data, together with an explicitly specified scaling with prompt energy and beaming. Despite the observed multi-TeV afterglow, the cascade component reaches only 1.6e-4 of the IGRB. Including direct GeV emission raises the maximum fraction to 1.1e-3, but makes the result more dependent on the population-averaged broadband template. Variations of the extragalactic background light, propagation implementation, intrinsic spectral cutoff, and population prescription do not change the conclusion: the multi-TeV detection of GRB 221009A does not make long GRBs a significant source of the IGRB.

astro-ph.HE↗

arXiv2026

Talked Out of the Truth: Sycophancy in the Reasoning Chains of Multimodal Models

Large multimodal reasoning models (LMRMs) are increasingly capable, largely through generating explicit chain-of-thought reasoning before answering, but in language models this often comes with sycophancy, the tendency to agree with the user over the evidence, and no reliable method to measure it in LMRMs yet exists. We bridge this gap with a benchmark and dataset for LMRM sycophancy when a user asserts a wrong answer, pairing four visually grounded datasets spanning mathematical, clinical, temporal, and demographic reasoning with five pressure conditions in single-turn and multi-turn settings, scored both in the final answer and within the reasoning chain. Sycophancy is prevalent under pressure: Statement pressure elicits the highest rates and Conviction among the lowest for all models except Mistral-Small-4, and under multi-turn pressure reasoning-level sycophancy intensifies sharply in PathVQA, reaching 95.7% for the most affected model. We further introduce a failure taxonomy separating reasoning-chain from answer-level sycophancy, and an exploratory sentence-level taxonomy locating where drift first emerges. A targeted intervention that restores a model's own correct reasoning recovers 79.2% of sycophantic answers on reasoning-heavy tasks, showing the answer follows the sycophantic reasoning rather than merely co-occurring with it. Thus, sycophancy corrupts not just the answer but the reasoning that produces it, so the chain itself is what we must measure.

cs.CL↗