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arXiv2026

L3M: A Verifiable Harness and Runtime for Self-Extending and Self-Improving Agents

The lasting gains in AI have come from methods that absorb more computation, and language models already scale computation within a call. Useful work, though, happens across calls: over hours or days, through tools and external systems, among many agents and the humans they work for, and increasingly through code the agents write themselves. Whether that work compounds is enabled by the harness around it, and the harness faces a constraint the model does not: of the three participants in such a computation, the human, the model and code, only the human's attention does not scale, so the computation can grow only if the human is not in every loop. L3M is a runtime built on that premise, written in Lean 4 so that one language implements the harness, states its invariants, and is the language agents extend it in. One computation spans humans, agents, models and code, and all of its state lives in Git: a rich state trajectory -- rather than a chat conversation -- is an object the runtime can resume, rewind, fork, compare and merge. Waiting, communication, delegation and undo are primitives, not patterns the model reasons through each time. When an agent works out a procedure, it can write it once as a sealed Lean program whose type is its permission request, and the harness offers it back as a tool -- machinery for the model to use. To take the human out of the loop, L3M uses reversibility to decide where that is safe: a tool's review tier follows from how far its effects can be undone, so agents act freely where the runtime can recover. Because the machinery can change, the properties that make this safe are stated as kernel-checked theorems about the code that runs. On Terminal-Bench, an untuned L3M reaches about two thirds of its (unsafe) shell-equipped pass rate using only safe (not needing human review) tools.

cs.AI↗
arXiv2026

InstructPro2: Natural Language and Biological Grounding Guided De Novo Protein Design

The ability to generate proteins with desired functions is a central goal of computational biology. Although natural language can express diverse design objectives, existing protein generation methods often support only narrow tasks or make limited use of biological constraints. We develop InstructPro2 to translate natural-language design objectives into protein sequences while incorporating task-specific biological context. A text encoder captures the design instructions, while dedicated ligand and antigen encoders provide biological context to the sequence-generating decoder. For pretraining, we assemble InstructPro2Bench, comprising 205.7 million pairs from UniProtKB. We subsequently adapt the model to ligand-binding protein and antibody design. On functional protein generation benchmarks, InstructPro2 outperforms Pinal, the strongest baseline, achieving a functional recovery F1 of 74.8 versus 62.2 and lowering global RMSD from 5.33A to 3.04A. For antibody design, the model obtains a DockQ score of 0.39, while ligand-binding protein design reaches a docking success rate of 72.6%. These findings highlight how integrating language-based instructions with biological conditioning can extend protein generation to distinct design settings.

cs.LG↗
arXiv2026

Complex pattern in periodically driven binary Quincke colloids

Binary active systems offer a minimal platform for understanding how component heterogeneity organizes non-equilibrium structures. Here we show that in a binary Quincke system driven by a periodic square-wave electric field, a dynamic square lattice in which small particles occupy the lattice-cell centers which are surrounded by large particles emerges spontaneously. Particle-resolved trajectories reveal that the size separation arises from the mobility difference of large particles and small particles. Increasing the driving frequency reduces the single-cycle path lengths of both species and simultaneously decreases the lattice constant. These results show how size-dependent activity,density redistribution, and periodic forcing cooperate to generate tunable complex active patterns.

cond-mat.soft↗
arXiv2026

RoboSpan: Learning Modular Coordination Policies for High-DoF Whole-Body Mobile Manipulation with Teleoperation

Whole-body mobile manipulation suffers from two fundamental challenges: inherent motion heterogeneity across locomotion, arm, and hand modules, and progressive error accumulation over long-horizon multi-stage tasks. Existing teleoperation platforms also lack integrated dexterous tactile sensing to support coordinated whole-body decision-making. This paper presents RoboSpan, a high-DoF whole-body teleoperation and demonstration platform, and the Hierarchical Modular Framework (HMF) for learning modular coordination policies. HMF functionally decouples the 29-DoF action space into fine hand manipulation, arm pose adjustment, and mobile-base spatial configuration branches, and introduces the Coordinated Modular Embodied Transformer (COMET) with inter-modular cross-attention to enable dynamic information exchange and action coordination. Vision-language model driven hierarchical task decomposition structurally suppresses temporal error propagation, while a full-palm 2D tactile representation encodes distributed contact signals for cross-module tactile empowerment. Experiments on a physical 29-DoF robot demonstrate that the proposed method achieves over 20\% higher task success rate than mainstream baselines across a range of long-horizon whole-body tasks, markedly improving stability and robustness in contact-rich manipulation.

cs.RO↗
arXiv2026

A possible evolutionary connection between high-mass X-ray binary pulsars and isolated rotation-powered pulsars

We investigate the long-term spin evolution of high-mass X-ray binary (HMXB) pulsars in the Small Magellanic Cloud (SMC) using archival measurements of spin periods and period derivatives from XMM-Newton, Chandra, and RXTE. In the P-|dP/dt| plane, the HMXB pulsars follow an approximately linear relation in log-log space with a slope of 1.02 +/- 0.11, similar to the trend shown by the youngest isolated rotation-powered pulsars (RPPs; e.g., Manchester et al., 2005; Lorimer and Kramer, 2005). For comparison, young RPPs from the ATNF Pulsar Catalogue give slopes that depend strongly on the characteristic-age cut: 1.10 +/- 0.16 for characteristic ages below 10,000 years and 0.72 +/- 0.08 for characteristic ages below 100,000 years. The full non-recycled population shows no significant correlation. The HMXB pulsars lie in the same characteristic-age range (approximately 1,000-10,000 years) as the youngest RPPs, but at spin periods two to three orders of magnitude longer. Reference characteristic-age contours in the HMXB P-|dP/dt| plane are roughly parallel to this relation, consistent with a continuous evolutionary sequence.

astro-ph.HE↗
arXiv2026

JevCoder: When Does Decision Delegation Pay Off in Code Repair?

A coding agent repeatedly makes decisions as it repairs code. These decisions shape repair trajectories and affect the token cost of successive model requests. We ask which repair decisions can be delegated to a low-cost probabilistic judge to reduce token use while maintaining repair quality. The judges answer questions with probabilities over predefined answers, without generating explanations. We evaluate judgment quality across repair stages and test how individual interventions change subsequent repair work. We compare these interventions with unguided repair, which uses no judge, and with the same workflow using the repair model itself as the judge. The benefit depends on the work an intervention changes, rather than the cost of the judgment alone. Based on these studies, we propose JevCoder, a workflow built around Jev, a low-cost probabilistic judge. It combines code-snippet recommendations with action-type guidance and uses judgments to determine when to submit. We evaluate three repair models, each on the same 400 tasks: 200 from SWE-bench Verified and 200 from SWE-Bench Pro Verified. Compared to unguided repair, JevCoder reduces mean repair-model token use by 21.6%-50.6%, with higher observed repair rates across all three models.

cs.SE↗
arXiv2026

On the Erdős--Odlyzko--Sárközy conjecture for prime-power moduli

Erdős, Odlyzko and Sárközy conjectured that every reduced residue class modulo $q$ contains a product of two primes not exceeding $q$. O. Klurman, A. P. Mangerel and J. Teräväinen (2023) have shown that three primes suffice when $q$ is sufficiently smooth. We study the moduli $q=p^γ$ that are powers of a fixed prime $p$ and we show that the third prime can be taken subpolynomially small. For any $q_\bullet\le q$ for which $q_\bullet\ge\exp\bigl(C(\log q)^{2/3}(\log\log q)^{4/3}\bigr)$, we give an asymptotic formula for the weighted number of representations of each reduced class as a product of two primes not exceeding $q$ and a third not exceeding~$q_\bullet$. We also show that the conjecture holds for all but a proportion $\exp\bigl(-c(\log q)^{1/3}(\log\log q)^{-1/3}\bigr)$ of the reduced classes. Here $C$ and $c$ are positive constants that depend only on $p$. Both results are unconditional and they rely on a wide zero-free region with no exceptional zeros for the Dirichlet $L$-functions attached to characters modulo $p^γ$.We also present conditional versions of these results for arbitrary $q$ under a quasi-Riemann hypothesis.

math.NT↗
arXiv2026

Cosmology with strong gravitational lenses

Three of the most pressing open questions in cosmology -- the nature of dark energy and dark matter, and the growing tension in the value of the Hubble constant H$_0$ -- call for cosmological probes that are independent of, and complementary to, traditional methods. Strong gravitational lensing offers exactly that: a purely gravitational probe of the universe's expansion history and matter distribution, sensitive to dark matter's presence regardless of whether it interacts with light. Time-delay lenses and multiplane lenses can measure H$_0$ and the dark energy equation of state directly, while the distortion of lensed images can reveal the abundance and internal structure of dark matter subhalos. After a brief theoretical and historical introduction, I review recent breakthroughs enabled by JWST and by advances in lens modeling and stellar dynamics. Examples include the recent measurement of H$_0$ with 3\% precision in flat $Λ$ cold dark matter cosmology, and a tentative detection of dark matter self-interaction. Strong lensing is entering a pivotal era: wide-field surveys with Euclid, Rubin, and Roman, and radio surveys with the Square Kilometer Array, are poised to increase the number of known strong lenses by orders of magnitude, positioning strong lensing to play a central role in answering these open questions in the decade ahead.

astro-ph.CO↗
arXiv2026

Cracking Mobile Manipulation: From Failure Diagnosis to Agentic Robot System

Recent vision-language-action (VLA) models have shown strong performance on local robot manipulation, yet their success does not readily translate to long-horizon mobile manipulation. In our experiments, a pretrained subtask VLA achieves 80% success rate on atomic manipulation tasks but only 19% when these skills are composed into mobile manipulation. We argue that this gap stems from failures across the execution process rather than from local manipulation capability alone. To uncover these bottlenecks, we systematically diagnose failures in long-horizon mobile manipulation and identify three dominant regimes: task planning, navigation and base positioning, and local manipulation. Based on this diagnosis, we develop failure-guided agentic intervention that augments a fixed subtask VLA with demonstration-based planning guidance, adaptive visual memory, accessibility-aware base adjustment, and local end-effector adjustment. On RoboCasa365, these interventions progressively improve task success from 19% to 47%, with the finalized system reaching 49% on held-out episode seeds, compared with 18% for the baseline. The same design improves performance from 14% to 37% on BEHAVIOR-1K and from 5/20 to 13/20 on real-robot tasks. These results suggest that reliable mobile manipulation can be advanced by diagnosing and intervening on the current bottleneck, rather than uniformly scaling the underlying policy. Our code will be released at https://github.com/PKU-VaLuE-Lab/Cracking-Mobile-Manipulation.git.

cs.RO↗
arXiv2026

PA1-OPD: One-Step Prefix-Augmented On-Policy Distillation for Language Model Pretraining

Knowledge distillation (KD) improves language-model pretraining by matching teacher distributions at corpus prefixes, but provides no direct supervision at contexts induced by student predictions. We introduce PA1-OPD, which augments corpus-path distillation with teacher feedback after one student-sampled transition per selected prefix. This expands the supervised states while retaining next-token prediction and corpus-path KD. Data-anchored roots support parallel sampling, and differentiable tree attention shares prefix computation without changing inference. In two continued-pretraining settings, full coverage improves held-out cross-entropy over KD across C4, PG-19, and Pile at every evaluated checkpoint. In Stage2, selecting the 10% of roots with highest student surprisal adds 48.85% to KD's Macro cross-entropy gain over next-token training. Gains remain when branch supervision excludes successor states already on the corpus path, supporting the value of feedback beyond observed contexts. Additional depth or breadth improves aggregate results at unchanged per-term supervision weight, with benefits varying by corpus. These findings support local student-induced supervision as a complement to pretraining distillation.

cs.CL↗
arXiv2026

Seismology of Glasses

Aging and relaxation of glasses proceed through localized rearrangements that also generate long-ranged mechanical responses in their surroundings. We develop a theory that treats these rearrangements as internal microseismic sources, and thereby separates the direct effects emerging from an event from the effects from the far-field displacements it generates. These far-field disturbances propagate and relax through the viscoelastic medium through which they move, producing a stochastic background of weak but numerous perturbations at any given location. Combining the description of local events from the Random First Order Transition theory with this propagating background, we derive a unified equation for the dynamical structure factor of a relaxing glass. The theory identifies a finite wave-vector and time window in which the growing viscoelastic far-field disturbances can produce compressed exponential relaxation, which has been observed using X-ray photon correlation spectroscopy. At higher wave vectors that resolve local jumps, heterogeneity of the local event dynamics instead produces stretched exponential relaxation. The crossover between these behaviors depends on the event statistics and the scattering phase accumulated across the region reached through viscoelastic propagation from the numerous distant sources.

cond-mat.dis-nn↗
arXiv2026

Beyond Static Positional Encoding: Bayesian Time-aware Attention for Non-Stationary Long-term Time Series Forecasting

Transformers have demonstrated strong performance in long-term time series forecasting (LTSF), yet modeling non-stationary temporal dependencies remains challenging. In this paper, we interpret self-attention as a Bayesian posterior over attended positions, combining a content-based prior induced by scaled dot-product similarity with a temporal-evidence likelihood induced by positional encoding. This formulation provides a probabilistic interpretation of how positional encoding shapes the temporal dependencies captured by self-attention. Building on this perspective, we derive a population-level evidence lower bound (ELBO) that characterizes the role of positional encoding in forecasting weakly stationary time series. Our analysis further highlights a limitation of static positional encoding: when temporal dependence structures vary across input windows, a fixed temporal bias must accommodate heterogeneous dynamics and can therefore be suboptimal for non-stationary forecasting. Motivated by this analysis, we propose Bayesian Time-aware Attention (BTA), which employs a mixture-of-experts (MoE) router to adaptively combine temporal kernels and generate input-conditioned, head-specific positional biases. Extensive experiments on standard LTSF benchmarks demonstrate that BTA consistently improves forecasting performance across multiple Transformer backbones and achieves competitive overall performance with modest computational overhead and stable training.

cs.LG↗
arXiv2026

ForceBench: Benchmarking Force Integration for Robotic Manipulation

Force feedback provides vision-language-action (VLA) policies with physical observations that can guide action selection and execution. However, differences in tasks, demonstrations, and control settings across existing systems hinder reliable comparisons of force integration designs. We introduce ForceBench, a simulation benchmark for evaluating six-axis wrist-force integration under a unified protocol. ForceBench combines eight tasks spanning physical-property inference, resistance-dependent interaction, and contact-rich assembly with 1,600 synchronized demonstrations and task-specific success criteria. We compare one no-force baseline and six force integration designs on a shared $π_{0.5}$ backbone. Prompt Fusion achieves the highest observed mean simulation success of 35.31%, compared with 23.25% for the baseline, and improves success rates across all three task categories. Predictive and temporal gains in simulation concentrate on physical-property inference, while both temporal designs underperform the baseline on assembly. Real-world evaluation of eight systems across five tasks supports the main qualitative trends: Prompt Fusion and Dual-Path Fusion achieve 63.00% mean success, compared with 40.00% for the baseline, but only Prompt Fusion improves every task. These findings support ForceBench's practical value for identifying the benefits and limitations of force integration across manipulation demands. The project page is available at https://forcebench-platform.github.io/.

cs.RO↗
arXiv2026

PN-Mix: Pair-Norm Guided Mixed-Precision Key Cache Quantization for Efficient Long-Output LLM Inference

Long-output inference in large language models suffers from severe KV cache memory and bandwidth bottlenecks. While KV cache quantization alleviates this issue, low-bit quantization (e.g., 2-bit) severely degrades model accuracy. Recent mixed-precision key-cache quantization methods mitigate this degradation by allocating higher precision to important key channels, but estimate channel saliency using only key statistics. Through attention logit perturbation analysis at the RoPE channel-pair level, we show that quantization errors in channel pairs with large query--key pair-norm products contribute significantly to logit variation. Based on this insight, we propose PN-Mix, a mixed-precision key-cache quantization method for RoPE-based decoder-only LLMs, which allocates higher precision to salient channel pairs identified once during the prefill stage and reused throughout decoding. Across standard reasoning, code-generation, and AIME benchmarks, PN-Mix with 2.26-bit average precision achieves comparable or better average accuracy than prior mixed-precision methods using 2.32--2.39 bits. Furthermore, in our Pareto sweep, PN-Mix degrades gracefully down to 1.5 bits, whereas the compared baselines exhibit sharper performance drops below 2.25 bits.

cs.LG↗
arXiv2026

The $RO(C_2)$-graded Hurewicz image of Atiyah's Real K-theory

We determine the $RO(C_2)$-graded $k\mathbb R$-Hurewicz image, where $k \mathbb R$ denotes the connective Atiyah's Real $K$-theory spectrum. As a consequence, we obtain four infinite families in the $RO(C_2)$-graded equivariant stable stems that are $C_2$-equivariant refinements of the classical $μ$-families. Using a $C_2$-equivariant $v_{1,0}$-self map, we explicitly construct an equivariant Adams periodicity operator $P_{C_2}$ that captures these $v_1$-periodicity phenomena in the $C_2$-stable stems.

math.AT↗
arXiv2026

A Graph-Based Analysis of Comparability, Scale, and Attribution in Private Transformer Inference

Rising privacy concerns around large language models have accelerated research in private Transformer inference (PTI). Synthesizing the empirical claims in this line of research, however, is hindered by multi-dimensional cryptographic progress and inconsistent evaluation contracts. In this work, we systematize the field by constructing an empirical graph of 62 PTI systems, mapping system attributes to node features and evaluation compatibility to edges. A three-tiered analysis of this graph illuminates the state of private inference. Node-level attribution shows that cryptographic progress drives performance gains across most systems, yet always co-occurs with other factors (model fidelity, hardware, cost accounting). Edge-level auditing shows that only 1 of 1891 candidate system pairs is directly comparable under shared assumptions. Finally, graph-level analysis shows that the scaling frontier of private inference has plateaued at 13B parameters and projects the cost of deploying current PTI techniques on production-scale Transformers. Overall, this graph-based framework equips the community to evaluate PTI claims transparently and channel technical speedups into deployment-scale private inference.

cs.CR↗
arXiv2026

Twenty Days Later: A Pre-Registered Test of History-Based Forecasts of Brand Mentions in Gemini Answers

Counts of which brands a large language model names are useful only if they hold long enough to act on. We test this with a pre-registered replication. The same 162 requests (54 questions in English, Estonian and Finnish about three software categories, four of twelve candidate brands per question, three repeats) were sent to gemini-3.1-pro-preview in three waves within about ten hours on 22 and 23 September 2026, and again on 13 October 2026, 20.3 days after the third wave, with identical request bodies. The plan and its decision rule were frozen, hashed and registered on OSF before the first call. The outcome is a lexical mention label per answer and brand, 648 per wave. The primary forecast, each brand-and-question cell's mention rate over the nine earlier answers, scored Brier 0.0281 and log loss 0.126, against Brier 0.0259 for the six-answer forecast of the 8-hour wave and a registered ceiling of 0.0559. It beat brand history (0.104), the overall rate (0.234) and a constant 0.5 (0.250) on both scores and in all nine question families (exact sign-flip p = 0.0039), so durability holds under the registered rule. A forecast frozen from the first wave alone scored 0.0599, 0.0587 and 0.0604 at horizons of 1.5 hours, 9.6 hours and 20.7 days. Of the 202 cells unanimous in the 8-hour wave, 194 were unchanged at D1 and none reversed. The latest wave alone was nearly as accurate as the pooled history (Brier 0.0292; pooled lower in 5 of 9 families, p = 0.28). Every answer reported the requested model version, and none issued a search query although search was enabled. A blind human check of 96 labels agreed with the rule on 94; both disagreements were adjudicated as rater omissions, so after adjudication the rule matched on 96 of 96. The test covers one model, one interval and twelve known brands, and estimates no decay rate.

cs.IR↗
arXiv2026

Sharp Constants, Threshold, and Failure of Uncertainty Principles on Non-trivial Flat Finsler Manifolds

By uncertainty principles we mean the generalized Caffarelli--Kohn--Nirenberg (CKN) inequality and the Heisenberg--Pauli--Weyl (HPW) uncertainty principle, with the latter being an endpoint case and the Hardy inequality a further limiting case. We study these \(L^p\)-type inequalities \((1 2\) but fail completely for \(s\le2\). When the generating Minkowski norm is reversible (while the Finsler metric itself remains irreversible with infinite reversibility), we determine the sharp constants for \(s>2\), which were previously unknown. These constants are approached in the limit by compactly supported radial functions. As a corollary, our results cover Berwald's metric space and resolve the open questions on its sharp constants. These findings reveal that the threshold phenomenon is structural for the entire class and is a genuinely non-Riemannian feature with no analogue in the Riemannian flat case.

math.FA↗