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Explanations, Prompts, and Formalizations: Arguments for New Norms in LLM-Enabled Mathematical Research

As several mathematical conjectures have recently been settled using large language models (LLMs), the mathematical community has formulated norms and recommendations regarding the publishing of such results. These norms do not cover the disclosure of the prompts and precise software setup used to obtain those results, nor do they require that results be formalized in a manner that allows for machine verification. I argue that both of these are essential. In addition, since LLM-obtained results may be hard to understand, human authors have the responsibility to invent intuitive explanations.

math.HO

On systematicity of linear function-correcting codes

The standard formulation of function-correcting codes uses systematic encodings. We study the redundancy cost of this constraint when both the prescribed function and the encoding are linear. We introduce the function-separation distance and show that several classical unequal error protection parameters are special cases. For linear functions and encodings, this distance is the first relative generalized Hamming weight of the code relative to the encoded kernel. We formulate free and systematic linear separation problems. We prove that the optimal free redundancy depends only on the rank of the function, and determine the optimal systematic redundancy for prescribed separations $d\leq3$.

cs.IT

Fundamental Mathematics in the Age of AI -- The Residue, the Journey, and the Ecology

Large language models have begun refuting long-standing conjectures and solving long-open problems. The introspection this has prompted about the future of mathematical discovery is well under way, and the anxiety accompanying it legitimate -- but both, we claim, are attached to the wrong loss. What machines now produce is the countable part of mathematics -- theorems, proofs, refutations -- which was always the work's residue, not its product. The distinction is old, and not economic: a result can be taken in its finished essence, or in the operations that engendered it. The product is human understanding: not a stock of results but a collective, hard-won way of deciphering the world and acting upon it. The two are arcs of a single loop: understanding tells us where to look; looking produces the residue; and taking it up again, one journey at a time, rebuilds shared understanding. Machines are strong on the countable arc, absent from the one that feeds it. The peril is to leave the loop open. AI did not create the confusion between residue and product; it has called a bluff long on the books, driving the cost of the residue towards zero and making the scarce thing visible at last. A new instrument makes a new way of working before it makes a new result. The pressing questions are therefore institutional: who can check an announced result, whoever announces it; what work and training become for the next generation of researchers; and whether the one thing that cannot be mass-produced -- the journey that nourishes a shared understanding -- continues to be funded. Mathematics, we argue, is uniquely placed among the sciences on the first -- a proof answers to no one's permission -- and uniquely exposed on the other two: teaching cannot go on as before, and no collective position yet exists; and the journey has never had a price our institutions knew how to pay. The decision is ours.

math.HO

Dynamic Modeling of Target Cell Location for Mobility Robustness Analysis in Cellular Networks: Technical Report

Mobility robustness optimization (MRO) requires an appropriate selection of handover (HO) parameters such as the time-to-trigger (TTT) and offset margin to balance HO failures and ping-pong HOs. Existing stochastic geometry-based analyses for MRO have treated the angular position of the target base station (BS) as uniformly distributed over a feasible region. However, this treatment does not explicitly capture the spatial distribution of the target BS dynamically selected as a user equipment (UE) moves through the network. In this paper, we develop a stochastic geometry-based analytical framework for MRO in sub-6 GHz cellular networks. We derive the distribution of the HO triggering time and the spatial distribution of the dynamically selected target BS under straight-line UE mobility. Based on these distributions, we formulate too-late HO and ping-pong HO events as mutually exclusive events and analytically derive their probabilities. Numerical results validate the analysis, demonstrate improved accuracy over the conventional uniform-angle model, and reveal the tradeoff between the two HO events and the dependence of the optimal TTT on BS density.

cs.NI

PEARL: Front-Loading Relational Chains for Multi-Hop Table Retrieval

While large language models (LLMs) have shown strong capabilities in tabular reasoning, retrieving relevant tables remains challenging due to the fragmented and relational structure of real-world data. Existing work typically relies on whole table representations that overlook cross-table semantics induced by join relationships. We propose PEARL, a training-free framework that shifts the paradigm toward vertical partitioning-based sub-table encoding. PEARL augments the retrieval corpus offline by generating multi-hop queries over pre-identified join paths and reorganizing relevant columns into vertically partitioned corpus units, enabling effective multi-table retrieval without query-time LLM inference. Experiments show that PEARL consistently outperforms existing methods, with up to +30.05% gains in R@2 on 3-hop queries. The source code is available at https://github.com/SOOB2NHO/PEARL.

cs.IR

On Synthesis of Metric Interval Temporal Logics

Automated mining of formal specifications is vital for verifying real-time systems. However, existing passive learning approaches remain restricted to deterministic specifications or limited fragments of Timed Regular Expressions (TRE). To our knowledge, this paper presents the first framework to tackle \emph{precise} passive learning for an expressive timed logic, \emph{Metric Interval Temporal Logic} (MITL) without relying on predefined templates or restricted logic fragments. Our approach formally reduces the timed learning problem into a scalable untimed one. By identifying quantitative timing differences between positive and negative traces, we synthesise precise timed constraints and inject them as new Boolean atomic propositions. This embeds timing into the alphabet, delegating the complex formula evaluation to highly optimised, off-the-shelf untimed LTL tools. Crucially, our framework is complete, guaranteeing a separating specification can always be found. We evaluate our implementation across several benchmarks, demonstrating the effectiveness of our approach.

cs.LO

Oculi: A Conversational Agentic Platform for Automated Credit Risk Analysis

Credit risk analysis in financial institutions traditionally requires analysts to manually write SQL queries, run statistical computations, and build visualization dashboards. This is a time-consuming workflow that limits exploration to familiar segments. We introduce \textbf{Oculi}, a conversational platform that transforms natural language questions into comprehensive credit risk analyses, complete with data queries, statistical testing, and interactive visualizations. Oculi employs a three-layer architecture that separates reasoning (LLM-powered agent), execution (Model Context Protocol tool servers), and presentation (agentic UI), enabling analysts to discover high-risk portfolio segments. Within Oculi, a new segment discovery pipeline is proposed that combines deterministic statistical methods with LLM-guided feature selection, leveraging LLM semantic domain knowledge alongside data-driven metrics to identify meaningful, actionable portfolio segments. Evaluated on a mortgage portfolio with 200+ features, Oculi demonstrates effectiveness in discovering material risk segments previously intractable through manual exploration, reducing time-to-insight significantly while maintaining auditability and statistical rigor.

cs.AI

GazeTune: Facilitating Precise Gaze-Driven Interactions with Cascaded Touch Input

Eye gaze has become an essential input for spatial computing, but its coarse targeting and saccadic nature limit precision and complicate continuous interactions such as dragging, especially under user motion. Gaze+pinch has also become standard in XR for its convenience, yet mid-air gestures remain imprecise, fatiguing, and socially unacceptable. These limitations underscore the need for an approach that preserves the speed of gaze while enabling stable, fine control. We present GazeTune, a cascaded multimodal interaction technique combining gaze and touch to refine gaze-based selection and manipulation. Touch serves as a refinement channel within gaze pointing, allowing precise cursor and target control. Our work investigates how gaze-and-touch enhances dragging and mitigates Motion-Induced instability. In a study (N=20), we compared GazeTune against gaze-only and gaze-pinch methods in 2D dragging. Results show that GazeTune achieves significantly lower error with comparable execution time, validating its effectiveness and balanced trade-off between time and accuracy.

cs.HC

UniScale: Exploring Unimanual Gesture Mapping Strategies for Gaze+Pinch-based Scaling Interaction

Object scaling serves as a fundamental spatial manipulation that enables complex and productive tasks in XR environments. This paper investigates unimanual scaling techniques for XR using gaze and hand interactions. We propose UniScale, a set of unimanual alternatives to the standard bimanual pinch, allowing users to scale objects while preserving hand availability for concurrent spatial manipulations. We design five distinct mapping strategies based on physical metaphors, exploring unimanual control that varies depth, angle, micro-gestures, and finger-distance input. We then compare these techniques against a standard bimanual baseline, in which users adjust the inter-hand distance via a bimanual pinch gesture. In a user study, we evaluate their effectiveness in a 3D object scaling task under both clutching and clutching-free conditions. The results indicate that while bimanual scaling relies on clutching for stable control, unimanual techniques excel in clutching-free conditions, significantly reducing physical hand movement. From the results, we derive valuable design implications for developing efficient 3D multimodal interactions in XR.

cs.HC

CoCoA: Context-Conditional Cultural Alignment for Large Language Models

Large Language Models (LLMs) often favor Western-associated entities across cultural contexts. Conventional debiasing methods aim for uniform neutrality, but cultural bias mitigation demands context-conditional behavior, preferring culturally appropriate entities when cultural cues are present and remaining neutral when they are absent. We propose CoCoA (Context-Conditional Cultural Alignment), a framework that learns this behavior through dual-context training on the same entity pairs under contexts with and without cultural cues. CoCoA combines a contrastive alignment objective with calibration and drift regularization, optimized through goal-aware gradient reconciliation. We evaluate CoCoA on CAMeL and Camellia, two entity-centric cultural bias benchmarks, across ten language settings and four LLMs. CoCoA reduces the Cultural Bias Score from 43 to 24 on average while maintaining near-neutral preferences at 50.2, with minimal impact on general performance across five standard benchmarks. These findings highlight that effective cultural alignment requires context-conditional modeling rather than uniform debiasing, and establish a new direction for mitigating entity-centric cultural bias in LLMs.

cs.CL

CARA: Concept-Aware Risk Attention for Interpretable Collision Anticipation

Collision anticipation in autonomous driving requires not only accurate early warnings but also interpretable reasoning about what risk factors are being tracked and how risk evolves over time. Existing methods fall short in this regard: feature-driven models are opaque, post-hoc explanations often lack fidelity, and concept-based methods are mostly designed for static recognition rather than dynamic driving scenes. We propose CARA (Concept-Aware Risk Attention), an intrinsically interpretable spatio-temporal framework for collision anticipation. CARA derives domain-grounded risk concepts from accident narratives, aligns them with video frames via vision-language similarity, and organizes them into evolving concept trajectories. These trajectories provide explicit risk evidence that guides spatial attention, temporal attention, and anticipation, allowing semantic concepts to directly influence both where the model attends and how it predicts risk over time. By treating semantic risk factors as dynamic intermediate evidence rather than auxiliary post-hoc explanations, CARA tightly couples interpretability with the predictive process. Extensive experiments on three benchmarks show that CARA consistently improves anticipation accuracy and warning earliness over strong baselines, while providing sparse and semantically grounded concept evidence.

cs.MM

DOBI: Dynamic Opportunistic Body Input via Spare Joint Recruitment for Hands-Free XR

Extended Reality (XR) systems are often most useful when users are engaged in ongoing physical tasks, yet current interaction techniques still largely assume the hands are available. We present opportunistic body input, an interaction paradigm that redirects continuous XR control to whichever available body region remains free in the moment. To investigate how users naturally coordinate these spare-body movements, we conducted an elicitation study across six hand-busy scenarios. We found that while users' preferred spare body regions shift dynamically based on physical constraints, the resulting spontaneous movements share a consistent, low-dimensional kinematic structure organized around a dominant principal axis. Building on these findings, we present DOBI (Dynamic Opportunistic Body Input), a real-time XR technique that uses gaze to target a UI element, a brief trigger gesture to identify the recruited spare body region, and the region's subsequent motion to drive continuous 1D control. A 1D Fitts' law study establishes the baseline motor performance of this paradigm across four distinct body regions, achieving throughputs up to 2.62 bits/s with an overall 5.0% error rate, and a dual-task usability study shows that DOBI supports reliable, low-effort control (SUS = 84.2) while users remain engaged in realistic hand-busy activities.

cs.HC

Self-Geometry: GT-Free and Plug-and-Play Test-Time Adaptation for Geometrically Consistent 3D Vision Foundation Models

Recent Vision Foundation Models (VFMs) predict depth, camera pose, and pointmap in a single forward pass without per-scene optimization, achieving strong generalization. However, enforcing explicit multi-view geometric consistency, e.g., through bundle adjustment, is computationally costly and is thus not imposed during VFM pretraining, so such inconsistency can arise. To address this, implicit self-consistency derived from model outputs (e.g., pointmaps, features), though enforced at test-time in prior work, delivers inherently limited performance gain, especially on scenes where the pretrained VFM is highly inaccurate. In contrast to this implicit signal, we propose Self-Geometry, a plug-and-play test-time adaptation pipeline that directly imposes explicit multi-view geometric constraints using 2D pixel correspondences as pseudo ground-truth. Our proposed Self-Geometry consists of Geometric Disentanglement Optimization, which combines Multi-View Consistency and Epipolar Consistency losses with Gradient Disentanglement to prevent gradient conflict; Frame Angular-Neighbor, a view sampler based on SO(3) geodesic distances for lightly imposing these constraints; and Lightweight TTA, which adapts VFMs via LoRA. Our method achieves consistent improvements in both pose and geometry estimation across six VFMs (VGGT, $π^3$, DA3-Giant/Large/Base/Small) and four benchmarks (7Scenes, ETH3D, ScanNet++, HiRoom).

cs.CV

GadIR: A Spatial-Topology Preserving Compiler for Quantum Many-Body Systems Simulation

Simulating quantum many-body systems has been one of the most important applications of quantum computation. For simulation, the Hamiltonian of a physical system is compiled into quantum programs with native instructions for quantum hardware. In previous works, the Hamiltonian is represented as Pauli strings, then compiled and optimized based on the quantum circuit model. Such representation paradigm neglects the spatial topology of original physical models, which is vital information to reducing the overhead of compiling many-body systems Hamiltonians. To address such neglect, we introduce a spatial-topology preserving compiler for quantum many-body simulation. Using Pauli gadgets as the representations of the Hamiltonian, we introduce our intermediate representation -- GadIR, to preserve the spatial-topology information of original physical models. Our compiler frontend performs the group reduction algorithm based on Pauli gadget model, which is a hardware-independent optimization. Our compiler backend performs trotterization and scheduling on Pauli gadgets, then synthesizes the Pauli gadgets into hardware-native quantum programs. We evaluate our compiler on all the canonical quantum many-body system models, while achieving a significant reduction on compilation overhead regarding four major quantum architectures. Overall, our spatial-topology preserving IR exploits the compilation optimization space for quantum many-body systems Hamiltonian.

quant-ph

Sharing Roughness with Hand-Outline Visualization to Reduce Sensory Asymmetry in VR Collaboration

In collaborative VR, asymmetric access to haptic hardware creates a critical information gap: tactile evidence remains private to the haptic user, hindering the shared understanding needed for joint decision-making. While prior work has explored crossmodal sensory cues in virtual environments, it remains unclear how such cues should be designed for asymmetric collaboration, where collaborators receive information through different modalities. In our setting, the haptic user feels roughness through fingertip vibration, whereas the non-haptic user relies on vision alone. To reduce this asymmetry, we propose externalizing an object's tactile state through a glanceable hand-outline visual proxy. Specifically, we examine whether abstract visual roughness cues based on line shape and motion can encode three discrete roughness levels for both haptic and non-haptic users. Two preliminary studies establish a shared visual semantics by identifying visually distinguishable cues for non-haptic users and validating their visuo-haptic correspondence for haptic users. In a main study of a collaborative sorting task, showing this visualization on both users' hands significantly reduced completion time relative to a no-visualization baseline. Moreover, NU-side cue visibility was associated with higher confidence and perceived contribution for the non-haptic user. These findings show that hand-anchored abstract visual cues provide a lightweight means of externalizing object tactile state, reducing information asymmetry without compromising social presence.

cs.HC

SIR: Self-improving Red-teaming for Compute Use Agents

Computer use agents (CUAs) are vision-language models that perceive a screen and act on a real operating system through mouse, keyboard, and terminal, and they are increasingly deployed to automate everyday digital tasks. Because they can be exposed to untrusted content while operating, they are vulnerable to indirect prompt injection (IPI), in which an adversary plants instructions in content the agent will read and redirects it toward actions that violate the user's intent. Existing CUA safety benchmarks evaluate fixed injections written by hand, which may underestimate the risk posed by an adaptive adversary. We present SIR, a black box IPI attack that (i) composes stealthy injections from a small library of reusable principles stated in plain language and (ii) wraps composition in an iterative feedback loop that diagnoses the victim's failed trajectories and distills the bypasses into new, named strategies that are reapplied across tasks. Unlike prior red teaming of web agents, we target CUAs at the operating system level and score attacks with a fully deterministic oracle, using checks on filesystem, service, and permission state rather than an LLM judge. On experiment, we evaluate three frontier CUAs. Composing principles with feedback raises the attack success rate over a baseline written by hand, for example from 4% to 24% on Claude Opus 4.8 and from 0% to 28% on Gemini 3.5 Flash, while the benign task still completes. Principles discovered against one model further transfer to a different architecture with no additional feedback.

cs.CR

Verification-Time Dependency on a Disappearing Evaluator

AI governance and assurance often assume that a consequential model-mediated decision can be reconstructed or tested after the fact. That assumption may fail when the evaluator that produced the decision is no longer accessible in the same version and execution context. This paper develops three verification-time constructs derived from Execution Governance (EG) 3.0: Decision-State Commitment, Independent Verifiability, and Counterfactual Auditability. Independent reprocessing of released Study 2 artifacts reproduces two original within-family behavioural comparisons: 52.0% modal-decision reversal for Llama 3.1 8B versus Llama 3.3 70B (26/50) and 30.0% for GPT-OSS 20B versus GPT-OSS 120B (15/50). The corrected baseline establishes that these are within-family comparisons, not provider-established succession. Post-hoc re-pairing against Groq-designated migration paths yields 64.0% and 38.0% reversal, but these figures remain descriptive because the cross-family invocation parameters were asymmetric. A 22-event retirement census independently recomputes to median 16.45 months, mean 18.72 months, range 3.9-40.3 months, with 17/22 intervals below 24 months, while also showing that evaluator availability can differ by service surface. The joint contribution is an operational verification-time protocol and optional Verification-Time Preservation Package (VTPP) specifying what evidence to bind at authorization time, what a separately trusted verifier can substantiate later, how stability and paired counterfactual tests should be calibrated, and which semantic checks remain beyond JSON Schema validity. The protocol is downstream and non-authorizing: it does not alter the EG Core Formula, add a seventh live condition, or state jurisdiction-specific legal admissibility.

cs.CY

The Brand War: A Gamified AI-Feedback System for Time-Limited EFL Writing

Writing is cognitively demanding and anxiety-provoking for English as a Foreign Language (EFL) learners, especially under time pressure. This paper presents The Brand War, a web-based gamified writing application combining competitive game mechanics with iterative GPT-4.1-powered formative feedback for undergraduate EFL learners completing a timed narrative writing task. Students role-play as marketing interns competing for a job offer, using review passes to receive AI feedback, attack opponents, or shield their own passes while drafting a 500-word brand story. We conducted an exploratory single-session classroom study with 29 university EFL students in Taiwan to examine engagement patterns, whether iterative AI feedback improved writing performance across revisions, and how AI and human scores related to overall outcomes. Students wrote within 60 minutes, using up to five AI feedback passes before a final human-graded submission. Most (65.5%) used the AI feedback system, and within-student AI scores improved modestly across revisions (M = +3.7, SD = 7.4), with larger gains among students completing more cycles and significantly higher final- versus first-review scores among multi-cycle completers (p = .032). AI-assessed and human final scores showed strong convergent validity (r = 0.722, p < .001), and AI-feedback users scored descriptively, though not significantly, higher than non-users. Students maintained a high mean focus ratio (82.4%), and competitive mechanics were used sparingly, suggesting most prioritized writing over social interference even when available. Findings suggest embedding iterative AI scoring within a competitive game context is feasible and may scaffold writing improvement, with implications for EFL writing pedagogy and AI-mediated gamified learning design.

cs.CY