Papers

We introduce a class of $2d$ quantum spin systems based on a unitary spherical fusion category with a chosen object. These models have frustration-free, reflection positive, but generally non-commuting local interactions, generalizing the Levin-Wen string-net models. Based on the theory developed in arXiv:2510.20662, we explicitly realize the Temperley-Lieb-Jones algebra, and more generally fusion spin chains as their boundary algebras.

We compare the superconformal index of three-dimensional ADHM theory in fixed monopole sectors with the index of the BMN matrix model around fuzzy-sphere vacua. The monopole charges determine the sizes of the fuzzy-sphere blocks, and their multiplicities determine how many identical blocks occur. At a fixed number of fundamental hypermultiplets, we increase all positive monopole charges by the same amount while keeping their differences and multiplicities fixed. After dividing the ADHM index by the contribution of the bare monopole, it agrees order by order with the BMN index in the corresponding limit of large blocks. Fundamental excitations move to arbitrarily high orders in the index expansion, while the upper angular-momentum cutoffs of the BMN harmonics diverge, leaving the same vector and adjoint contribution.

A proof of the cycle double cover conjecture was recently announced, yielding an $8$-cycle double cover for every bridgeless graph. The stronger $5$-cycle double cover conjecture, which is still open, is equivalent to the statement that the edge set of every bridgeless claw-free cubic graph can be covered by at most four perfect matchings. Perfect matchings in bridgeless cubic graphs have been studied extensively, with two of the main conjectures in this area being the Berge–Fulkerson and the Fan–Raspaud conjectures. The latter, a consequence of the former, states that every bridgeless cubic graph admits three perfect matchings $M_1, M_2, M_3$ such that $M_1\cap M_2\cap M_3=\emptyset$. Here we show that the Fan–Raspaud conjecture is true for bridgeless claw-free cubic graphs. This also gives further information on the interaction of perfect matchings in a class where the $5$-cycle double cover conjecture requires control of four of them.

In this paper, we introduce a gradient-based head attribution strategy where the Token-level Max-Margin loss is backpropagated to the attention maps. This framework enables a large-scale causal analysis of attention heads, making it suitable for LLMs. We evaluate our method on the task of disambiguation in Context-aware Machine Translation, where we analyze 50 phenomena across 4 models and 4 language directions. We empirically show the alignment of our method with the effects of increasing the attention scores of token-to-token relations on three models and two language directions, ensuring the robustness of our method. Our analysis reveals the presence of the "general-purpose" attention heads that improve the model's performance when attending to different relations. We find that the average attention a head assigns to a relation does not necessarily relate to the model's performance, which suggests that the models developed redundancies during training in terms of the head functions.

Fast surrogates for tokamak boundary-plasma simulation are typically deterministic regressors mapping a global operating point to a flattened vector of cell values. Near the divertor detachment transition the steady state is not reliably single-valued. A point estimate must average over qualitatively different plasma states, and it arrives with no statement of confidence. Moreover, the flattened vector representation discards the geometric structure of the SOLPS-ITER mesh. This work addresses both problems. We unroll the curvilinear mesh into three fixed-size image tensors whose layout preserves cell adjacency and inverts exactly, letting a convolutional network act on the geometry without loss of information. A conditional flow matching model, well suited to highly sensitive systems, is then trained on this representation. The result is an efficient, scalable surrogate that captures multiple plausible outcomes even at sensitive operating points. Along a gas-puff scan, the predictive distribution splits into a hot and a cold mode across an early regime transition. A further check on synthetic data with an injected bifurcation of known size confirms the model recovers both branches rather than their average.

Front-running has long plagued Ethereum's public mempool, earning it the nickname of a "dark forest", where predators lurk for profitable transactions. In response, Ethereum and other blockchain ecosystems increasingly rely on private RPCs and native protections to shield transactions from adversaries, which we refer to as protected order flow. Yet the effectiveness of these mechanisms in preventing front-running, and what trust assumptions they entail, remain poorly understood. In this work, we conduct the first longitudinal, three-year measurement study of sandwich attacks against protected order flow across six blockchains: Ethereum, Solana, Tron, Base, Arbitrum, and Monad. We introduce detection heuristics that capture wide attacks, both within and across blocks, and filter on bot behavior to distinguish sandwiches from legitimate trading activity. We identify 28.0 million sandwich attacks on Solana, 38,567 on Tron, 30,607 on Ethereum, and 1,889 on Base against transactions intended to be protected from front-running. Reorged blocks expose a further 2,875 Ethereum victims. Unlike conventional public-mempool sandwiches, these attacks rarely occur tightly around their victims and, outside Solana, are carried out by a small number of entities. Our analysis uncovers exposures at every layer: validator- and application-level exposure on Solana, order-flow auctions and reorged blocks on Ethereum, first-come-first-served ordering that fails to prevent latency-based front-running on Tron, and both an RPC bug that exposes pending transactions and predictable victim behavior on Base. These findings show that existing front-running protections can provide substantially weaker guarantees than users expect, highlighting the need for stronger end-to-end defenses against sandwich attacks.

The widespread use of social media, particularly image- and video-based platforms, has turned them into key sources of both normative and informational content related to health and diet. This may contribute to the development of disordered eating behaviors or, potentially, eating disorders. This study uses mixed-methods analysis applied to 3129 YouTube videos about diet and weight loss in order to quantify the level of risk of low-quality information and heightened focus on the body image. We adapt three quality measurement frameworks from the literature – PRHISM, HONcode and SMEC – to the online video context, perform manual annotation of a sample of the data, and design an LLM content characterization pipeline to score the videos on the quality of their content and the focus on the human body. Surprisingly, we find that videos around personal storytelling and mindset & motivation are associated with higher-quality content, whereas supplement reviews (arguably more medically sensitive ones) are not. Further, the body-related mentions of weight measurement and negative body image are associated with an increased viewership, whereas the mentions of positive body image are associated with an increased engagement rate in terms of likes and comments, but not viewership. Worryingly, we find a cluster of videos categorized as "music" which promote the dietary supplements Mitolyn and the injectable weight loss drug Mounjaro. As video-based platforms grow in popularity, particularly among younger audiences, studies such as the one presented here are essential for developing empirically grounded tools to enhance the detection of harmful content and inform more effective moderation practices.

The Generalized Langevin Equation (GLE) is an integro-differential equation of motion for a general observable of a many-body system and is rigorously derived using the projection operator formalism. In the standard derivation, a stationary canonical phase space distribution is used for the projection. Here, we derive a novel class of GLEs using a non-stationary projection distribution that constrains the initial ensemble to a hypersurface in phase space on which the observable has a fixed value $A_0$. As a result, all GLE parameters, and in particular the memory friction kernel, depend on $A_0$ and can be extracted from short simulations that do not sample the entire phase space. Applying this non-stationary GLE to protein folding trajectories, we find for villin and an $\alpha$-helical poly-alanine segment that the total friction is higher in the folded state. These results demonstrate that observable-dependent friction effects are non-negligible and can be accounted for using non-stationary GLEs derived by constrained projection schemes.

Recent advances have revealed an interplay between quantum computing and topological data analysis (TDA). Most quantum TDA has focused on Betti numbers, which characterize the connectivity and “holes” of a dataset. Homology, however, contains additional information in the form of torsion: a nontrivial cycle can become trivial after being repeated finitely, revealing global constraints on how cycles combine and wrap around one another. Beyond applications in biomolecular studies, torsion appears in physical settings including homological quantum rotor codes, discrete charges, and gauge sectors. We study torsion from both classical and quantum perspectives. Given a graph $G$ and its clique complex $K = \mathrm{Cl}(G)$, we first prove that, for fixed $r$ and prime $p$, deciding whether $H_r(K,\mathbb{Z})$ contains $p$-torsion is NP-hard. As a corollary, when a homological rotor code is specified by $G$, deciding whether the code has a finite-dimensional logical sector of a given order is NP-hard. We discuss related problems, including the Bockstein homomorphism, Smith normal form, lattice saturation, and cohomology. Second, for a finite set of primes $P$, we develop a quantum algorithm that serves as a one-sided torsion witness. For fixed $r$, it outputs WITNESS or INCONCLUSIVE, i.e. WITNESS certifies that either $H_r(K,\mathbb{Z})$ or $H_{r-1}(K,\mathbb{Z})$ contains $p$-torsion for some $p\in P$ while INCONCLUSIVE makes no claim about its presence or absence. We identify a regime in which the algorithm achieves a near-quadratic quantum speedup over the corresponding classical algorithm under the same input model. Our NP-hardness result complements recent hardness results for estimating Betti numbers, adding a complexity-theoretic perspective to quantum TDA. Together, these results demonstrate that integral homology, beyond its Betti numbers, can be computationally challenging.

Let {\Psi} be an Orlicz function, and let T denote any finite linear combination of composition operators. Motivated by the work of Choe, Koo, and Wang on the compactness of linear combinations of composition operators on weighted Bergman spaces, we completely characterize the compactness of T on the Bergman-Orlicz space A{\Psi}(D). Unlike the classical weighted Bergman space setting, the precise analysis on A{\Psi}(D) depends on the growth behavior of {\Psi} and the associated Luxemburg norm. Hence, the power-type estimates available in weighted Bergman spaces cannot be applied directly. To overcome this difficulty, under suitable growth assumptions on {\Psi} and using the Julia-Caratheodory type function theory and Carleson type measure technique, respectively, we establish two necessary and sufficient compactness characterizations for T on A{\Psi}(D).

Dental cone-beam computed tomography (CBCT) systems often employ detector configurations that provide a truncated field of view (FOV) that only captures a small part of the patient's anatomy. In this work, we aim to reconstruct an extended FOV using projections of truncated FOV scans. To this end, we propose a three-stage framework that consists of (1) an implicit neural representation (INR) for estimating missing parts of the truncated projection data, (2) an iterative reconstruction for generating a secondary volumetric image with improved anatomical consistency and (3) a fast diffusion model for image enhancement. The proposed approach combines the strengths of continuous representations, physics-based reconstruction and generative refinement within a unified pipeline for truncated CBCT imaging. Experimental results demonstrate that the method effectively reduces truncation artifacts, improves the reconstruction of structures extending beyond the original FOV and produces images with enhanced quality. Our code is publicly available at https://github.com/SusanneSchaub/CBCT-FOV-Extension.

We revisit the claimed converse theorem for mismatched decoding over binary-input discrete memoryless channels (Balakirsky, 1995) and the subsequent work refuting this converse via a numerical counter-example (Scarlett, Somekh-Baruch, Martinez, and Guillén i Fàbregas, 2015). A notable gap in the existing understanding is that no concrete flaw was identified in Balakirsky's analysis. In this paper, Balakirsky's proof is "diagnosed", and it is demonstrated that (i) his permutation lemma is flawed regardless of the correctness of his combinatorial approximation lemma; (ii) there are at least two specific incorrect steps regarding restricted codes and selector sequences, and these appear to be unlikely to admit a local repair; and (iii) the proposition in which these incorrect steps are used is false in general.

While hypergraph-based Retrieval-Augmented Generation (RAG) effectively captures higher-order multi-entity correlations, existing paradigms treat extracted hyperedges as isolated factual assertions. This structural fragmentation engenders rigid "knowledge islands" that bottleneck multi-hop causal inference, temporal tracking, and narrative synthesis. To systematically address these challenges, we introduce Dual-Hypergraph Indexing (DHI), a hierarchical representation framework that elevates discrete facts into structured analytical insights. DHI couples a foundational entity-relation factual hypergraph ($H_K$) with an elevated deep-insight hypergraph ($H_D$) via a dual-pathway aggregation algorithm. Specifically, DHI employs: (1) importance-driven hub aggregation via 5-metric topological profiling and adaptive thresholding to capture spatial semantic clusters; and (2) temporal chunk-chain progressive aggregation via sliding-window greedy exploration to track chronological evolutions. Across five benchmarks, DHI achieves state-of-the-art performance, boosting logical coherence by +1.53 on the multidisciplinary Mix benchmark and scoring 85.78% on complex medical pathology reasoning tasks. DHI provides a robust architecture for next-generation multi-hop RAG.

Advances in generative modeling have recently been extensively employed in robotics for policy learning. In particular, Conditional Flow Matching (CFM) trained with expert demonstrations has been shown to outperform existing methods on robot manipulation benchmarks. While prior work has mainly focused on single-task settings, we study the problem from a multi-task perspective, as training independent models for each task is computationally expensive. Multi-Task policy learning comes with its own set of challenges, as naively training on a concatenated dataset of demonstrations would either require increased model capacity to accommodate the added complexity or result in drops in performance. We propose to distill knowledge from single-task CFM experts into a shared multi-task policy by transferring their learned velocity fields. We combine this distillation signal with the original CFM objective to retain fidelity to the demonstrations. Experiments on RLBench show that our approach improves multi-task policy performance over naive training while maintaining a fixed model size.

This paper presents the realization and performance of the CBM T0 detector system. Built upon an approximately 70 {\mu}m thin polycrystalline CVD (pcCVD) diamond sensor with pad metallization, the detector is mounted on a flexible vacuum manipulator and operates entirely under passive cooling. Interfaced with the DOGMA readout architecture, the system successfully meets all operational requirements for CBM. It demonstrates a high detection efficiency (near 100%) and a timing precision below 50 ps RMS across a broad range of beam species, from light ions (such as Carbon) to heavy ions (such as Gold). The DOGMA readout features two distinct data paths: a high-precision TDC path routing data directly to the global CBM DAQ, and a secondary path deliver in real-time rate measurements crucial for online beam quality monitoring and fast beam abort logic. Finally, detailed performance studies conducted with light-ion beams at EBG MedAustron are discussed.

Multi-center clinical studies and biomedical research collaborations increasingly seek to utilize data across centers to build models that generalize beyond any single center. This creates two distinct challenges: data protection regulations may restrict the sharing of raw patient data across institutions, while centers may collect only partially overlapping sets of features under different protocols. Federated learning enables collaborative model training without centralizing raw data. However, existing federated imputation methods rarely evaluate feature-level missingness, in which entire features are unobserved at some centers. To address this setting, we adapt the ReMasker masked autoencoder to federated learning (Fed-ReMasker), enabling centers to impute features never observed locally by leveraging knowledge learned across collaborating centers. We evaluate Fed-ReMasker in a benchmark spanning synthetic datasets with linear and nonlinear relationships and real-world tabular datasets, including clinical data. The benchmark varies the number of centers, the missingness ratios, and client heterogeneity. Fed-ReMasker achieves the lowest imputation error in 93.2% of value-level and 96.7% of feature-level scenarios in the homogeneous benchmark. It also remains robust to client heterogeneity using simple federated averaging, outperforming all baselines in all 36 value-level scenarios and each baseline in at least 35 of 36 feature-level scenarios, and comes within 3.0% on average of a centralized model trained on the pooled data.

A class of models which does not require additional operators on the language of classical sentential calculi to capture some notion of necessity, possibility, and impossibility is introduced and investigated.

In this paper, we establish local and global Schauder estimates for classical solutions of a class of fully nonlinear elliptic partial differential equations, which are not necessarily convex or concave, under suitable Hölder continuity assumptions on the data. Our approach is based on a robust blow-up argument, combined with geometric tangential analysis and compactness techniques. This strategy is strongly influenced by methodologies developed in the contemporary theory of nonlinear elliptic PDEs.

A graph is biplanar if it is the union of two planar graphs on the same vertex set. The largest chromatic number of a biplanar graph is known to lie between 9 and 12. The lower bound comes from Sulanke's graph, which has independence number 2, and a biplanar graph on 19 vertices with independence number 2 would have chromatic number at least 10. Gethner and Sulanke asked in 2009 whether such a graph exists. We show that it does not, and more generally that every biplanar graph with independence number at most 2 is 9-colorable. The proof embeds a hypothetical counterexample in the union of two sphere triangulations, enumerates with SAT modulo symmetries the 3271 graphs that pass a necessary filter for the complement of such a union, and shows with a SAT solver that none of them is such a complement; a matching argument reduces the general statement to this computation and one further case on 18 vertices. The computational part of the proof, including the completeness of the enumeration and every refutation, is checked in Lean 4, assuming three classical facts about planar graphs. The Lean development, the SAT instances, and the enumeration certificates are available on Zenodo.

We introduce a notion of strict stability for the ADM mass on asymptotically flat manifolds with boundary and establish several of its fundamental properties. In particular, we show that a strictly stable static vacuum metric is a strict local ADM mass minimizer, thus proving a local version of Bartnik's Mass Minimizer Conjecture near Euclidean exterior regions. Our approach also gives a new proof of the existence of static vacuum extensions for nearby Bartnik boundary data on arbitrary exterior regions of Euclidean space.

Introductory physics students benefit from learning to integrate new physics knowledge with prior knowledge related to their interests. Writing assignments that offer high epistemic agency can foster this integration, and provide rich artifacts for qualitative analysis. Physics education researchers are increasingly interested in studying such artifacts using computer-based textual analysis. In this paper, we use lexical methods to look for evidence of knowledge integration in written assignments from a Physics of Music course. These assignments require students to communicate to an external audience a clear and cohesive narrative that synthesizes concepts from music and physics. To apply this methodology, we first establish a lexicon of music, physics, and integrated keywords that 10 students used across 6 writing assignments. Then, we visualize this word usage in a series of network diagrams based on which keywords were used in proximity to each other in each assignment. We find that students most strongly connected ideas from music and physics using keywords related to the physical structure of sound (sound, frequency, and wave). Applying these methods to each assignment prompt and its resulting student submissions, we find that, in assignments with a lower degree of epistemic agency (assessed qualitatively by our experience teaching the course), students primarily followed the example of integration modeled by the assignment prompt, but in assignments with a higher degree of epistemic agency, they explored music-physics integration to a greater degree. We use this analysis to offer a pedagogical contribution to introductory physics courses centered around students' interests, a theoretical contribution by illustrating a means of quantifying epistemic agency, and a methodological contribution that complements textual analysis and offers the scalability sought in such approaches.

Deep vision systems remain vulnerable to corruption, occlusion, and distribution shift despite strong benchmark performance. Existing reliability methods typically evaluate uncertainty at individual time steps and do not explicitly model how a system progresses toward failure. We introduce Visual Tripwires, a predictive reliability framework that uses temporal instability in model behaviour to anticipate impending failure. Our central hypothesis is that predictive degradation develops progressively through measurable changes in latent representations, prediction trajectories, and attention structure. Visual Tripwires captures these changes using representation drift, prediction oscillation, trajectory curvature, and attention entropy. A lightweight tripwire predictor aggregates these signals over a temporal window to estimate the probability of failure within a future prediction horizon. Experiments across multiple datasets, architectures, and progressive perturbation settings show that the proposed instability signals emerge before predictive degradation and provide earlier and more accurate failure warnings than conventional uncertainty estimation methods. These results demonstrate that temporal instability contains useful information about future model reliability and provides a practical basis for early warning in deep vision systems.

We establish weighted bilinear summation identities for two families of Apéry-like polynomials $g_n(x)$ and $v_n(x)$. The identities express weighted sums in terms of consecutive endpoint values and, when necessary, lower moments. For $g_n(x)^2$ we obtain identities with weights $(2n+1)^r$ for $1\le r\le4$; for $v_n(x)^2$ we treat the cubic and quintic weights. Combining these formulas with congruences for the endpoint values gives supercongruences modulo $p^3$ and $p^4$, together with special evaluations modulo $p^5$ and $p^7$, where $p$ is a prime greater than $3$. In particular, $$\sum_{n=0}^{p-1}(2n+1)^3v_n\!\left(\frac52\right)^2 \equiv 6p^4-\frac{143}{3}p^6\pmod {p^7},$$ confirming a congruence conjectured by Sun. The proofs use explicit quadratic telescoping identities and $p$-adic endpoint expansions.

This text is a self-contained expository survey of the Lagrange and Markov spectra, centered on a comprehensive exposition of Markov's theorem and its generalizations. Its purpose is to provide a systematic text for learning the theory, with detailed proofs and explanations of the connections among its arithmetic, combinatorial, and geometric descriptions. The necessary background in continued fractions, quadratic irrationals, binary quadratic forms, and bi-infinite sequences is developed step by step, followed by an exposition of generalized Markov numbers, fence posets, curve lengths, and generalized Cohn matrices. One goal of this exposition is to explain the formula connecting generalized Markov numbers with the two spectra. For nonnegative integer parameters $(k_1,k_2,k_3)$, a permutation $\sigma\in\mathfrak S_3$, and a fraction label $t\in\mathbb Q_{\geq0}\cup\{\infty\}$, let $m_t$ be the associated generalized Markov number and let $k_t=k_{i_t}$ be the parameter assigned to its position $i_t\in\{1,2,3\}$. The text explains the construction of an associated finite sequence $S(t)$ of positive integers and the identity \[ \mathcal L(\alpha_{S(t)}) =\mathcal M(Q_{S(t)}) =\frac{\sqrt{((3+k_1+k_2+k_3)m_t-k_t)^2-4}}{m_t}, \] where $\alpha_{S(t)}=[\overline{S(t)}]$ and $Q_{S(t)}=(x-\alpha_{S(t)}y)(x-\alpha'_{S(t)}y)$, with the prime denoting quadratic conjugation. Here $\mathcal L$ and $\mathcal M$ denote the Lagrange and Markov constants, respectively. The survey explains how this identity relates generalized discrete Markov spectra to the classical theory and how Markov's theorem is recovered when the parameters vanish. The account also includes boundary values arising from irrational slopes and generalizations of Frobenius's uniqueness conjecture, providing a unified perspective on the classical theorem and its extensions.

Atomic-resolution micrographs remain limited in application due to small field of view and low numbers of recorded defects. Defect imaging with reliable statistics in transmission electron microscopy (TEM) relies heavily on diffraction contrast. However, with 200-300 kV electrons, low-curvature Ewald sphere limits diffraction resolution at ~5 nm. Here, we imaged defects with a forbidden condition in TEM and improved the resolution in diffraction contrast from 5 to 0.5 nm. The superiority of our equal-s method is demonstrated by the discovery of a novel phase and dislocation loop structure in steels, which have not been previously reported experimentally or theoretically. Our equal-s can largely replace the classical two-beam condition for defect study.

Recent advances in text-to-video generation have enabled high-fidelity visual synthesis, yet realistic motion remains challenging. Generated videos may exhibit temporal discontinuities, inconsistent action progression, and structural distortions during complex movements. Even when individual frames appear realistic, the underlying motion may evolve in inconsistent or implausible ways. Standard generative objectives provide limited motion-specific supervision, leaving motion evolution insufficiently constrained. In this paper, we propose MotionSpec, a motion supervision framework centered on Spectral Trajectory Consistency (STC). STC constructs dense anchor-relative motion trajectories and transforms them into motion spectral volumes via a temporal Fourier transform. By aligning the spectral amplitude and phase of predicted and target trajectories, STC constrains both motion strength across temporal frequencies and the temporal organization of motion. To complement this trajectory-level supervision, we introduce Local Flow Consistency (LFC), which aligns consecutive-frame optical flow between predicted and target videos to stabilize local motion transitions. Experiments demonstrate that MotionSpec consistently improves motion consistency, temporal coherence, and plausibility while preserving visual fidelity.

We prove the Kazhdan-Lusztig correspondence for the Lie superalgebra $\mathfrak{osp}_{1|2n}$ at irrational levels, that is, we show the category $\mathrm{KL}_k^{\rm ev}(\mathfrak{osp}_{1|2n})$ of finite-length even ordinary modules for the affine vertex operator superalgebra of $\mathfrak{osp}_{1|2n}$ at level $k \in \mathbb{C} \setminus \mathbb{Q}$ is braided tensor equivalent to the category of finite-dimensional even weight modules for the quantum group of $\mathfrak{osp}_{1|2n}$ at parameter $q = e^{\pi i/(2k+2n+1)}$. We also prove that ${\rm KL}_k^{\rm ev}(\mathfrak{osp}_{1|2n})$ is braided tensor equivalent to the category ${\rm KL}_\ell^{\rm ns}(\mathfrak{so}_{2n+1})$ of finite-length ordinary modules with non-spinorial top level for the affine vertex operator algebra of $\mathfrak{so}_{2n+1}$ at level $\ell$ such that $ \frac{1}{\ell+ 2n-1} = \frac{1}{2k+2n+1} + 1 \ \ ({\rm mod}\ 2\mathbb Z).$ Consequently, by gluing vertex operator (super)algebras via tensor categories, we construct a few new families of simple conformal vertex (super)algebras, including the mixed kernel VOAs that were the missing ingredient for proving certain Feigin-Frenkel type dualities in previous work of the first-named author with Linshaw, Nakatsuka, and Sato.

We prove a long time well-posedness result for a quadratic non-linear Schrödinger equation with random well prepared initial conditions in dimension d $\ge$ 1. In some regimes, we derive the Wave Kinetic equation associated with the equation in dimension d $\ge$ 5, almost up to the kinetic time to the power d/(d + 1). Our analysis relies on the ideas introduced by Deng and Hani.

Strong magnetic fields allow accreting neutron stars to form magnetically controlled funnel flows. At sufficiently high accretion rates, such flows become radiation-pressure-supported. In the conventional picture, the magnetospheric flow contains a nearly free-falling transonic outer region, a radiation-mediated shock, and a subsonic accretion column. We investigate the regime in which the height of the column is expected to exceed the magnetospheric radius. In this case a self-consistent transonic solution with a standing shock is no longer possible, and the entire magnetospheric flow remains subsonic. We construct a semi-analytical hydrodynamical solution for a fully subsonic, radiation-supported magnetospheric flow in the low-Mach-number limit. The magnetic field is treated in the force-free approximation, while the flow structure is determined by mass conservation, energy conservation, and the momentum equation along the field lines. We test the solution using one-dimensional time-dependent simulations with the code HACol. The shock-free solution is highly advective. Its enthalpy profile is close to the adiabatic limit, while the energy density is regulated by leakage of mass and heat through the sides of the accretion channel. Most of the observable power is expected to be released by plasma leaving the magnetospheric flow above the neutron-star surface. Such systems should be associated with super-Eddington accretion discs and low pulse fractions due to visibility selection and scattering in the disc wind. We suggest that many non-pulsating ultraluminous X-ray sources containing neutron stars may accrete in this shock-free regime.

For the sinh-Gordon model (without external mass term), we show that the log-Sobolev inequality holds uniformly in the lattice and volume regularisations for all parameters in the regime in which the Gaussian multiplicative chaos has second moments. This implies that infinite-volume “massless” sinh-Gordon measures on $\mathbb{R}^2$ satisfying all Osterwalder–Schrader axioms exist and that they have exponential decay of correlations (are “massive”). The proof uses the Polchinski equation method for log-Sobolev inequalities. The required estimates on the renormalised potential are established using simple perturbation theoretic bounds, valid for absolutely monotone potentials, and an extension of the correlation inequality of Ding–Song–Sun to potentials in the GHS class. This inequality is proved also by using a variant of the Polchinski equation through the maximum principle.