arXiv:2607.08851v1 Announce Type: cross
Abstract: A pair of parallel polarizable planar walls at distance d is considered. The walls are symmetrically charged with a uniform surface charge density, neutralized by mobile point counterions moving between them. The case of repulsive particle images is studied in the strong-coupling (SC) regime. Of interest is the dependence of the effective inter-wall interaction (pressure), mediated by the mobile counterions, as a function of the distance d. It is shown that previous virial SC single-particle theories work well at small d when the dielectric jump is small; for intermediate and large dielectric jumps they are inadequate even in the SC region. Here, we propose a Wigner-type SC theory based on harmonic deviations of particles from their ground-state monolayer or bilayer Wigner structures formed inside the space between the dielectric walls. Our Monte-Carlo simulations are in very good agreement with the Wigner SC predictions, even down to moderate coupling constants ($\Xi > 10$).
Science Journals
arXiv:2505.24631v2 Announce Type: replace-cross
Abstract: We consider a version of the Watts threshold model on directed multiplex configuration model networks, and present a detailed analysis of the cascade size, single-seed cascade probability and cascade condition. We then introduce a smaller class of network models that we call "constrained multiplex networks", which is designed to represent networks with so-called "functional" or "complementary" structure. We find that the particular choice of functional structure affects the phase transitions of the cascade model in a variety of ways.
arXiv:2607.08908v1 Announce Type: cross
Abstract: In a binary polynomial optimization problem (BPO, in short) we are maximizing a multilinear polynomial expression depending on n binary variables. This is a hard optimization class, containing many NP-hard problems, including unconstrained quadratic binary optimization. Several tractable special classes were considered in the literature, including problems with bounded tree-width (Crama, Hansen, Jaumard, 1990), Berge-acyclic problems (Buchheim, Crama, and Heck, 2019), $\beta$-acyclic problems (Del Pia and Di Gregorio, 2022, 2023), limited reach problems (Clausen, Crama, Lusby, Rodr\'iguez, and Ropke, 2024), and $\alpha$-acyclic problems with bounded rank (Del Pia and Khajavirad, 2025). We focus on a general variable elimination scheme for BPO, and develop the unique explicit multi-linear polynomial form for the equivalent BPO problem obtained after the elimination of a given subset of the variables. The obtained closed form representation of such an equivalent BPO problem allows us to characterize new special classes for which this elimination method, when applied recursively, provides a computationally efficient solution. Our approach is elementary1, algebraic, and provides efficient solution to a wide problem class that properly generalizes all of the above mentioned tractable special cases.
arXiv:2603.15855v3 Announce Type: replace
Abstract: The dominant programming languages support nothing but linear text to express domain-specific geometric ideas. What is needed are hybrid languages that allow developers to create visual syntactic constructs so that they can express their ideas with a mix of textual and visual syntax tailored to an application domain. This mix must put the two kinds of syntax on equal footing and, just as importantly, the extended language must not disrupt a programmer's typical workflow. This means that any new visual syntax should be a proper language extension that is composable with other language features. Furthermore, the extensions should also preserve static reasoning about the program. This paper presents Hybrid ClojureScript the first such hybrid programming language. Hybrid ClojureScript allows programmers to add visual interactive syntax and to embed instances of this syntax within a program's text. An enhanced hybrid IDE can then display these embedded instances as mini-GUIs that programmers interact with, while other IDEs will show a textual representation of the syntax. The paper argues the necessity of such an extensibility mechanism, demonstrates the adoptability of the design, and discusses what might be needed to use the design in other languages.
arXiv:2607.09101v1 Announce Type: new
Abstract: Recently, the emergence of Large Language Models (LLMs) has spurred a surge of research into automated unit test generation, yielding impressive performance and reducing manual effort. However, existing LLM-based approaches still suffer from two major limitations: (1) they follow rigid, procedural workflows that underutilize the autonomous reasoning potential of LLMs, making it difficult to dynamically adapt testing strategies based on real-time feedback; and (2) they rely on rule-based context extraction that is not tailored to test generation, failing to capture fine-grained code dependencies and test-specific knowledge required for deriving test requirements. In this paper, we propose TestAgent, an LLM-based test generation approach that addresses the above limitations by emulating human testing practices via a multi-agent collaboration mechanism. Particularly, TestAgent designs three specialized agents, namely a requirement planner, a test generator, and a test reviewer, to simulate how developers understand, construct, and validate unit tests. To unleash the autonomous capabilities of LLMs, we equip TestAgent with a set of tool APIs that can be invoked dynamically in an on-demand and adaptive manner. To further support repository-level reasoning, TestAgent constructs a test-specialized knowledge graph via static analysis, which captures code entities and their dependencies across the project and persistently stores testing artifacts (e.g., test reports and failure analyses) produced during generation. Experimental results show that TestAgent achieves 97.46% execution rate, 92.34% line coverage, 90.24% branch coverage, and 83.69% mutation score on six Java projects, outperforming LLM-based baselines across all metrics and achieving substantially higher mutation scores than search-based tools.
arXiv:2607.09117v1 Announce Type: new
Abstract: The main focus of this paper is on the algebraic structure of two-dimensional $(\lambda,\mu)$-constacyclic codes of length $\ell\mathrm{m}$ over finite chain rings with residue field $\mathbb{F}_q$, where $q \equiv 1 \pmod{r\mathrm{m}}$ and $r$ denotes the multiplicative order of $\bar{\mu}$. In this paper, the structure of two-dimensional $(\lambda,\mu)$-constacyclic codes is obtained. Our approach relies on analysing primitive idempotents within the finite chain ring to determine the generators of these codes. We also find the condition under which two-dimensional constacyclic codes are maximum Hamming distance with respect to rank (MHDR) over finite chain rings.
arXiv:2603.27948v3 Announce Type: replace
Abstract: Although there has been significant progress in neural radiance fields, an issue on dynamic illumination changes still remains unsolved. Different from relevant works that parameterize time-variant/-invariant components in scenes, subjects' radiance is highly entangled with their own emitted radiance and lighting colors in spatio-temporal domain. In this paper, we present a new effective method to learn disentangled neural fields under the severe illumination changes, named RehearsalNeRF. Our key idea is to leverage scenes captured under stable lighting like rehearsal stages, easily taken before dynamic illumination occurs, to enforce geometric consistency between the different lighting conditions. In particular, RehearsalNeRF employs a learnable vector for lighting effects which represents illumination colors in a temporal dimension and is used to disentangle projected light colors from scene radiance. Furthermore, our RehearsalNeRF is also able to reconstruct the neural fields of dynamic objects by simply adopting off-the-shelf interactive masks. To decouple the dynamic objects, we propose a new regularization leveraging optical flow, which provides coarse supervision for the color disentanglement. We demonstrate the effectiveness of RehearsalNeRF by showing robust performances on novel view synthesis and scene editing under dynamic illumination conditions. Our source code and video datasets will be publicly available.
arXiv:2607.08774v1 Announce Type: new
Abstract: Reliability in large language model (LLM) systems is typically framed as a function of model capability. We challenge this by demonstrating that reliability is significantly influenced by \emph{inference-time control} -- the computational layer governing task framing and context selection. We introduce \emph{CogniConsole}, an architectural instantiation that externalizes this control into a structured interface combining programmatic coordination with bounded prompt-based reasoning. Through \emph{controllability-oriented probes} ($N=489$) in a multi-step interactive environment, we show that increasing structural scaffolding -- from unstructured to fully scaffolded -- \textbf{systematically reduces output variance and failure rates under a fixed model architecture}. Our results indicate that many observed failure modes, such as context drift and inconsistent constraint adherence, arise from under-specified control rather than insufficient capability. This work provides an empirical basis for treating inference-time control as a first-class abstraction, opening new directions for designing and evaluating LLM systems beyond scaling alone.
arXiv:2607.08781v1 Announce Type: new
Abstract: The coupling in flow matching -- the rule pairing noise vectors with data points -- is typically treated as a computational choice. We show that this coupling can instead serve as an alignment interface: by matching noise and data according to a target molecular property, it embeds controllable structure directly into the learned flow field. Building on this view, we introduce Reward Transport, which uses optimal transport coupling at training time to align a scalar noise-space coordinate with molecular rewards; at inference, varying this coordinate steers the generated distribution without requiring an oracle, reward model, gradient guidance, or additional computation. In the coupling-preserving limit, thresholding this coordinate recovers the Cross-Entropy Method's truncated reward distribution, providing a principled, continuously adjustable distribution-level control knob. Empirically, on ZINC-250K and GuacaMol, sweeping the scalar induces monotone control of logP and consistent QED control over its operating range; most tellingly, the same knob produces opposite structural responses for different targets, growing molecules for logP but shrinking them for QED, which rules out a generic size bias. The interface is complementary to classifier-free guidance and conditional flow matching, while a negative result under epsilon-prediction diffusion clarifies where coupling-level alignment is structurally absent. Code: https://github.com/KehanGuo2/reward-transport
arXiv:2607.08782v1 Announce Type: new
Abstract: Expert parallelism has become the prevailing paradigm to serve Mixture-of-Experts (MoE) models. Its efficiency depends on the communication and computation latencies of the GPUs, which are linked to the placement of experts in the GPUs. Existing works for optimizing expert placement focus on leveraging past requests' expert activation patterns. However, they demonstrate deficiencies facing diverse and rapidly changing request patterns, calling for an online, proactive approach. Implementing such an approach requires addressing several challenges: the uncertainty associated with incoming requests' expert activation, the cost of expert migration, and the NP-hard complexity in optimization. Therefore, we present Director, a new distributed MoE serving system that minimizes end-to-end latency via prediction-driven, online expert placement. Director uses either a lightweight cascaded predictor or a low-bit quantized replica for expert activation patterns of incoming requests. An online migration module then enacts the changes with near-zero downtime by executing migrations in compute-bound phases, keeping disruption bounded. At its core, a relaxation-based expert placement optimizer operates under capacity constraints, runs in polynomial time, and achieves a $(1+\epsilon)$ approximation ratio. Finally, we implement a prototype and demonstrate, through extensive experiments, a reduction in end-to-end latency of $11\sim55\%$ for popular MoE models (e.g., Mistral, DeepSeek and Qwen) compared to existing work.
arXiv:2607.09207v1 Announce Type: new
Abstract: It is well established that the reasoning capabilities of large language models (LLMs) can be improved by applying reinforcement learning (RL) in a post-training stage. In a standard RL iteration, the current model (the policy) generates experience through rollouts, and the resulting data is then used to update the policy during training. High-performance RL frameworks such as StreamRL and AReaL employ a disaggregated architecture and asynchronous rollouts to better exploit both rollout and training resources, thereby increasing overall system throughput.
Nonetheless, across varying RL setups (e.g., hardware configurations, model scales, staleness levels, and hyperparameters) and under changing workloads, it remains common for both rollout and training resources to experience idle periods.
In this paper, we present BiDiRL, a hybrid time-space multiplexing architecture for asynchronous, disaggregated RL designed to reduce resource idleness. First, we develop a hot-switch runtime that enables rapid switching between rollout and training resources with negligible overhead. Second, we propose a static, scheduling-aware planner based on time-performance modeling that chooses a hot-switch-friendly resource partition, so that rollout and training durations are roughly balanced at a coarse level. Third, at execution time, we introduce a bidirectional scheduler that further exploits runtime bubbles through fine-grained resource switching, allowing the bottleneck stage to temporarily borrow idle resources from the other pool. Across a wide range of workloads, datasets, and models on two 32-GPU testbeds, BiDiRL increases RL training throughput by up to 1.94x compared with RL systems including veRL, AReaL, and ROLL, without affecting convergence behavior.
arXiv:2607.09058v1 Announce Type: new
Abstract: Reliable fault recovery of grid-forming (GFM) converters under current-limited conditions is increasingly important as inverter-based resources replace synchronous generation. Existing current-limiting strategies primarily focus on current-angle regulation and synchronization trajectory shaping, while the interaction between the current limiter and the voltage control structure remains insufficiently understood. Consequently, post-fault recovery may exhibit converter trapping in current-limited control (CLC) or oscillatory transitions between CLC and constant voltage control (CVC). This paper shows that, under conventional PI-based voltage control, the interaction between the voltage controller and the current limiter creates a moving recovery boundary that contributes to these recovery failures. To address this issue, a post-fault recovery framework is proposed that combines structurally decoupled virtual admittance voltage control with current-angle steering. The proposed framework simultaneously improves synchronization trajectory evolution and stabilizes the recovery boundary during fault recovery. Experimental validation on a 3-kVA GFM inverter prototype confirms reliable post-fault synchronization recovery under both symmetrical and unsymmetrical voltage sag conditions, with trapping and oscillatory CLC-CVC transitions eliminated.
arXiv:2604.11398v2 Announce Type: replace
Abstract: Software deployment suffers from numerous problems pertaining, for example, to reproducibility and dependency resolution. Many of these problems have been successfully solved by the purely functional approach to package management implemented in the Nix project. However, Nix does not solve all issues, and it does introduce some novel problems of its own. Therefore, the aim of this thesis is to conduct a literature review on the current state of research on Nix and to determine the direction of future research.
The first part of this paper explores the problems historically faced in different areas of software deployment, e.g., irreproducibility and dependency resolution issues. The main four categories of software deployment tools analyzed are build systems, package managers, configuration management, and development environments. Popular software from each category serve as case studies to illustrate the problems. The second part introduces Nix and explains the methods utilized to solve some of the problems introduced in the earlier part.
Because Nix is the first large project to utilize the purely functional approach, it is far from a perfect solution. Thus, the third part is dedicated to analyzing the new problems that Nix introduces, as well as old problems, which Nix has been unable to solve, such as trust and granular incremental builds. Furthermore, some proposed state of the art solutions put forth by the Nix community are discussed.
arXiv:2607.09528v1 Announce Type: new
Abstract: The emergence of metaverse platforms has created virtual economies that introduce new challenges related to fraud, bot activity, and illicit financial behavior. Despite growing interest in trustworthy metaverse analytics, existing datasets typically focus on user behavior, authentication, or financial transactions in isolation, limiting the development and reproducible evaluation of multimodal fraud detection methods. To address this gap, we present TSAI-MetaFraud, a multimodal, multi-task benchmark dataset for fraud analytics in virtual economies. TSAI-MetaFraud integrates behavioral, transactional, and graph-structured information while incorporating realistic fraud and automated bot scenarios. We define benchmark tasks including transaction fraud detection, cross-modal node classification, temporal link prediction, and weakly supervised fraud detection, and provide baseline evaluations using machine learning models and graph neural networks. By jointly capturing behavioral activity, financial interactions, and relational structure within a unified virtual economy, TSAI-MetaFraud provides a benchmark for advancing multimodal learning, graph mining, fraud analytics, and trustworthy AI in emerging metaverse ecosystems.
arXiv:2607.09211v1 Announce Type: new
Abstract: While traditional evolutionary algorithms hard-code reproduction, self-replication can emerge spontaneously within digital ``primordial soups''. This paper investigates the co-evolution of this emergent self-replication alongside problem-solving capabilities. We initialize a population of random 32-byte Z80 assembly programs, requiring self-replication to arise purely through random assembly-level mutations and pairwise program interactions. To link these behaviors, we introduce a task-based validation step: correctly evaluating a polynomial raises a program's interaction probability above a baseline rate. Our experiments yield four primary findings. First, self-replication and mathematical problem-solving successfully co-evolve from initial randomness. Second, the pressure to compute accelerates the emergence of compact, robust reproductive architectures that preserve memory for task execution. Third, applying metabolic constraints increases the likelihood that programs evolve conditional halting, terminating early during validation while bypassing the halt during interaction to execute block-copy replication. Finally, when programs are partitioned into spatial task niches, spontaneous self-replication generates an emergent learning curriculum, utilizing simple solutions as stepping stones toward complex polynomials. Altogether, these results demonstrate an interactive feedback loop: environmental task demands actively shape the physical architecture of self-replication, while spontaneous replication alters the evolutionary trajectory of functional problem-solving.
arXiv:2607.09626v1 Announce Type: new
Abstract: Local Computation Algorithms (LCAs), introduced by Rubinfeld, Tamir, Vardi, and Xie (2011), are a special type of sublinear algorithms that, given probing access to a possibly massive input, are required to provide query access to a consistent solution, without maintaining a state between different queries. In this paper, we try to understand LCA through the lens of complexity classifications, described by the following question: Given a target complexity function $f(n)$, is there a problem whose local computation complexity is $f(n)$, up to polylogarithmic factors?
We restrict our focus to Locally Checkable Labeling (LCL) problems, which can be seen as constant-degree constraint satisfaction problems. Possible complexity classes of this problem family have been extensively studied in various distributed computation models, including the $\mathrm{VOLUME}$ model proposed by Rosenbaum and Suomela (2020), which is an invariant of local computation algorithms with additional locality requirements.
In this paper, we provide new LCL complexity constructions in the $\mathrm{VOLUME}$ model, and generalize the results to LCAs. Specifically, we show that there are LCLs whose probe complexities in the $\mathrm{VOLUME}$ and LCA models are $\Theta(\log^k n)$ and $\tilde \Theta(n^{p/q})$ for any positive integer $k \ge 1$ and rational $p/q \in (0,1]$. Our approach, completely different from the approach to a similar result in the distributed $\mathrm{LOCAL}$ model by Balliu et al. (2018), is to stack instances of complexity $\Theta(\log n)$ and $\tilde \Theta(n^{1/k})$ in the $\mathrm{VOLUME}$ model constructed by Rosenbaum and Suomela (2020).
arXiv:2607.09628v1 Announce Type: new
Abstract: Problem posing is a valuable learning activity in computing education, encouraging learners to actively construct, refine, and reflect on problems rather than simply solving them. This experience report presents the design and pilot deployment of two LLM-powered scaffolding systems for supporting problem posing across two computational scenarios with different levels of task openness. Both systems assessed student-generated problems using Bloom's Taxonomy-based criteria and applied the same assessment framework, differing only in output modality: one provided guiding questions (Indirect scaffolding), while the other offered worked examples (Direct scaffolding). We conducted a within-subjects, counterbalanced pilot study with 20 graduate students and collected problem-quality ratings, user-experience surveys, and post-session interviews. Our deployment showed that both systems supported problem refinement in complementary ways, each offering distinct benefits. Direct scaffolding produced greater immediate improvements, while interviews showed that participants valued Indirect scaffolding for promoting deeper reflection on their own problem design. Based on these findings, we suggest sequencing the two modalities by beginning with Indirect scaffolding to promote reflection, then shifting to Direct scaffolding when learners become stuck. These lessons offer an initial practical strategy for integrating LLM-based scaffolding into computing classrooms.
arXiv:2607.09566v1 Announce Type: new
Abstract: Decision-making is posing an increasingly formidable challenge to investors because of the growing number of alternatives available in financial markets. A hot area of research over the past few decades has been portfolio optimization that seeks to determine how much an investor should invest in which asset. Introducing real-world conditions to the optimization model turns the problem into an NP-hard one for whose solution exact methods become inefficient; hence, researchers have turned to evolutionary algorithms to approximate solutions. In this paper, strengthening strategies are presented for multi-objective evolutionary algorithms that can provide a faster convergence rate and extensive search ability in the portfolio optimization problem under the cardinality constraint. To implement those features, a unique solution representation, a novel operator, and new repair mechanisms are introduced for solving the aforementioned problem in which lower and upper limits are set on the number of assets in the portfolio. For this purpose, new mating strategies along with the aforesaid package are implemented in well-known multi-objective evolutionary algorithms to solve the problem. The customized algorithms are subsequently tested against traditional ones using well-known market indices as benchmarks. Results indicate that the proposed strategy not only provides better approximations but also converges faster as well at no loss of performance with an increasing number of assets in the market.
arXiv:2607.09578v1 Announce Type: new
Abstract: Pre-demolition assessment, the regulated audit process at the heart of urban mining, is an information process in which AI support must serve qualified auditors who remain accountable for the decisions taken. The relevant unit of value is not prediction accuracy alone, but the defensibility of the supported decisions: their legibility, plausibility, sourcing, and contestability. Explainable AI techniques and domain knowledge graphs each address parts of this requirement, and existing taxonomies have catalogued their integration. The literature is descriptively rich but structurally under-specified: what remains less developed is a structural account of why specific integrations produce artefacts neither resource can provide alone. This paper offers a complementarity-theoretic interpretation grounded in the IS resource-based tradition. We propose four consolidated KG-XAI integration modes (Lifting, Constraining, Typing, and Revising), each defined as a typed operation over XAI artefacts and knowledge-graph substrate structures. Each mode unlocks a distinct property of defensibility and contributes to the kind of regulatory artefact pre-demolition assessment demands. A fire-door example from the urban-mining process illustrates the modes using the W3C Linked Building Data stack and valuation extensions.
arXiv:2603.21141v2 Announce Type: replace
Abstract: Learning derivative-accurate surrogates for implicit simulators is a key challenge in scientific machine learning. High-order Taylor surrogates have long been considered intractable in high dimensions, because the derivative tensors are enormous and accessible only through probes. We make such surrogates tractable with the Tucker tensor train Taylor series (T4S), a local surrogate that represents each derivative tensor of a truncated Taylor expansion as a Tucker tensor train. T4S targets a different learning problem than global operator learning: rather than training from input-output pairs at many parameter values, it is trained from random directionally symmetric derivative probes at a single expansion point. Computing $m$ probes of the $k$th derivative requires only $O(mk)$ linearized solves sharing one operator, cheaper than the $O(m)$ nonlinear solves for function evaluations or $O(m\,2^k)$ linearized solves for asymmetric probes. We develop derivative-informed dimension reduction, Riemannian Gauss-Newton and Cauchy SGD fitting algorithms with rank continuation, requiring little hyperparameter tuning, and fast sweeping routines for the Riemannian Jacobian. We prove representational guarantees under spectral decay of the input covariance. Experiments show that our methods match quasi-optimal T3-SVD accuracy on random tensors from probes alone, up to data-limited ranks, and recover high-order Taylor structure in Poisson PDE examples.
arXiv:2408.03118v4 Announce Type: replace-cross
Abstract: We propose a MFG model with quadratic Hamiltonian involving $N$ populations. This results in a system of $N$ Hamilton-Jacobi-Bellman and $N$ Fokker-Planck equations with non-local interactions. As in the classical case we introduce an Eulerian variational formulation which, despite the non convexity of the interaction, still gives a weak solution to the MFG model. The problem can be reformulated in Lagrangian terms and solved numerically by a Sinkhorn-like scheme. We present numerical results based on this approach, these simulations exhibit different behaviours depending on the nature (repulsive or attractive) of the non-local interaction.
arXiv:2607.07918v1 Announce Type: new
Abstract: Current safety methods for large language models are known to be vulnerable to adversarial attacks, motivating research into robust alternatives. Latent Adversarial Training (LAT) is among the most effective defenses, but can degrade utility and requires training on large datasets of harmful prompts. We introduce Latent Personality Alignment (LPA), which replaces explicit harm refusal with adversarial training on just 66 harm-agnostic statements drawn from psychometric personality literature. We hypothesize that personality-anchored representations share latent structure with harm avoidance, so adversarially stabilizing them implicitly constrains the subspace exploited by jailbreak attacks. LPA achieves near-zero attack success rates on HarmBench across direct requests and five jailbreak methods, despite never seeing harmful content during training and no loss of performance on standard benchmarks. Moreover, the training process is lightweight; the entire procedure completes in minutes on a single GPU and uses 75x fewer examples than standard LAT. Extensive ablations demonstrate the robustness, efficiency, and generalization of our method.
arXiv:2607.08572v1 Announce Type: new
Abstract: Multimodal Large Language Models (MLLMs) often follow a fixed Think-then-Answer paradigm, which is inefficient in heterogeneous multitask settings because simple inputs may not require explicit reasoning while difficult ones can benefit substantially from it. Learning when to think is also unstable during post-training, where imbalanced rollouts can drive the model toward always-thinking or always-direct behavior. We propose Switch-Reasoner, a GRPO-based framework that learns to adaptively select reasoning modes for MLLMs. It treats thinking as a virtual tool invocation and allows the model to either answer directly or invoke explicit reasoning before answering. To stabilize this decision, we introduce a dual-level regulation mechanism that balances the overall use of Thinking Mode and Direct Mode while providing sample-level supervision based on the relative benefit of the two choices. Experiments on 11 multimodal tasks show that Switch-Reasoner reduces unnecessary reasoning while maintaining strong performance, achieving a better accuracy-efficiency trade-off.
arXiv:2607.08239v1 Announce Type: cross
Abstract: Ferrers diagram rank-metric codes are rank-metric codes with prescribed support, and their dimension is bounded from above by the Etzion--Silberstein bound. In this paper, we study this problem for block Ferrers diagrams, namely Ferrers diagrams whose dots are grouped into square blocks of a fixed size. Motivated by the diagonal construction for MDS-constructible Ferrers diagrams, we introduce the notion of MSRD-constructibility, where MDS codes on diagonals are replaced by maximum sum-rank distance (MSRD) codes on block diagonals. We show that MSRD-constructible pairs yield optimal Ferrers diagram rank-metric codes over sufficiently large finite fields. We then relate MSRD-constructibility of a block Ferrers diagram to MDS-constructibility of its contraction, proving an equivalence when the distance is compatible with the block size and giving lifting criteria in the general case. As a consequence, we obtain MSRD-constructibility for strictly block-monotone and initially block-convex diagrams. Finally, we prove a reduction to block triangular diagrams and use it to obtain new arbitrary-field cases of the Etzion--Silberstein conjecture for MSRD-constructible block Ferrers diagrams.
arXiv:2607.08355v1 Announce Type: cross
Abstract: Magnetic van der Waals semiconductors such as CrSBr host an intricate exciton landscape whose physical interpretation has converged only recently. A many-body Feynman diagrammatic approach based on quasiparticle self-consistent GW with electron-hole ladder vertex corrections to the screened Coulomb interaction has established the electronic band gap, excitonic orbital character, real-space extent, binding energies, and bosonic-coupling signatures of the bright XA exciton near 1.34 eV and the higher XB manifold near 1.8 eV. These results agree well with ARPES and magneto-optical experiments and supersede the early Rydberg-like assignment of the excitons. What has remained unresolved is why these intense bright excitons coexist, within a few tens of meV, with companion states that are several orders of magnitude darker despite drawing from essentially the same single-particle transition manifold. Here we show that brightness is a band-coherent property of the excitonic eigenfunctions: bright and dark partners are sublattice-symmetric and sublattice-antisymmetric superpositions of the same ligand-field-like Bloch transitions across the two Cr atoms of the orthorhombic primitive cell. The commonly used Frenkel and Wannier-Mott labels describe what an exciton is made of, but brightness requires a symmetry-adapted interference rule between transition dipoles. Disentangling this bare excitonic structure is a prerequisite for interpreting the optical response of CrSBr once magnon, phonon, and photon couplings are included.