Papers

Generative motion planners typically use learned trajectory priors for initial generation, while leaving test-time repair to local continuous refinement. We introduce Masked Generative Motion Planning (MGMP), which extends the learned prior from efficient parallel generation to structural repair. A masked generative transformer generates discrete trajectory candidates in parallel, and Geometry-Guided Token Search (GGTS) uses scene geometry to target where to edit and which prior-supported alternatives to evaluate. This turns refinement into an efficient search over discrete motion alternatives, enabling route-level restructuring beyond local trajectory deformation. MGMP achieves 96% success on Ring Maze and 82% repair success on Controlled Route Invalidation on Kuka, exceeding the strongest external baselines by 23 and 25 percentage points, respectively. It further generalizes to unseen layouts, additional obstacles, unseen geometries, single- and dual-arm planning, and real-world Baxter tasks.

A rigorous macroscopic analysis of classical thermodynamics reveals an overlooked contradiction at the foundations of ideal gas theory: the traditional volume dependent formula for entropy violates the fundamental axiom of thermal equilibrium during reversible isothermal processes. This paper resolves this inconsistency by establishing a strict operational distinction between strictly isothermal and quasi isothermal processes. We show that in order for the perfect gas to be strictly consistent with the laws of classical thermodynamics, the thermodynamic entropy of a perfect gas must be a function of temperature only. This independence of volume is also confirmed by a new analysis of the adiabatic free expansion of an ideal gas, which is found to be intrinsically reversible. To reconcile these results with standard thermodynamic practice, we introduce the concept of a pseudo isothermal process (a finite sequence of small adiabatic and isochoric steps) and show that the classical equations for work and heat apply rigorously to these real processes, as opposed to strictly isothermal ones. We conclude by discussing the profound implications of these findings for statistical mechanics, showing that while the corrected thermodynamic entropy is in perfect agreement with Maxwell's kinetic theory, it is essentially different from the Planck Boltzmann formula. Thus, thermodynamic entropy and statistical microstate counting are two different physical quantities, and the present analysis provides a simple way to free classical thermodynamics from the paradoxes of microscopic disorder.

The Common Criteria (CC; ISO/IEC 15408) is the principal international framework for evaluating the security of IT products, and its certificates gate procurement across government, defense, and regulated industry. Yet evaluations routinely stall, fail, or yield certificates whose assurances do not survive real-world deployment. Prior work has approached this from two directions: economic critiques of misaligned incentives and "security theatre"; and recent data-driven studies that quantify vulnerabilities in already-certified products. Comparatively little systematizes the problem from the evaluator's operational vantage - recurring, cross-vendor failures against the Common Criteria work units themselves. This paper presents a systematization of knowledge (SoK) of failure modes in Common Criteria product evaluation. Drawing on the standard, the Common Evaluation Methodology (ISO/IEC 18045), public NIAP Protection Profiles, and published Security Targets and Certification Reports, we organize recurring failures into a lifecycle taxonomy spanning Security Target scoping, Protection Profile conformance, assurance evidence, cryptographic requirements, functional testing, vulnerability analysis, operational guidance, and post-certification configuration drift. We analyze their root causes, derive a design-for-evaluability framework that product teams can apply before evaluation begins, and identify open problems for cloud, continuous-delivery, and AI-enabled systems.

Paulsen and West associate perfect cuboids with triples of rational points on a congruent-number elliptic curve and assert that the corresponding curve has rank at least two. The proof of their Theorem 4.2 contains a gap: translation of a generator by a point of order two interchanges only the odd-indexed terms of two coordinate sequences, rather than the entire sequences. We exhibit two explicit counterexamples to that intermediate assertion and give a complete proof of the rank obstruction. The division-polynomial argument reduces a hypothetical rank-one configuration to one remaining parity pattern. Ingram's primitive-divisor theorem then forces an additive relation among its indices, which is incompatible with a positivity lemma on the elliptic curve. More precisely, the three points of every positive cuboid configuration generate a subgroup of rank at least two, even when the ambient curve has larger rank. The proof is unconditional.

This paper studies the construction of an explanatory space for a weighted naive Bayes classifier from the supervised representation induced by the model. We start from the classical supervised distance based on conditional log-likelihoods and introduce a discriminative reformulation based on log-odds, which is more directly related to the classification decision. We then show that this representation induces a distance that exactly coincides with the $\ell_1$ distance between vectors of analytical Shapley values, thereby providing a formal explanatory interpretation of the geometry induced by the model. Finally, we empirically compare several supervised distances derived from these representations using a $k$-nearest neighbors classifier. This work highlights a close link between supervised distance, local explanation, and predictive behavior, from a primarily methodological perspective.

Large language models (LLMs) offer promising potential for next-visit diagnosis prediction, owing to their ability to integrate longitudinal clinical evidence and reason over it in natural language. However, reinforcement learning for LLM reasoning commonly rewards each trajectory according to the correctness of its final answer. In next-visit diagnosis prediction, multiple diagnoses can be simultaneously valid, but independently rewarding one diagnosis per trajectory does not distinguish repeated hits from coverage of different diagnoses. The policy can therefore concentrate on a few correct diagnoses, leaving others uncovered. Meanwhile, LLM tokenizers can split ICD codes into several generic tokens with limited clinical meaning, requiring multiple decoding steps to predict each diagnosis and hindering reasoning over a large disease vocabulary. To address both challenges, we propose CARing, a framework that represents diagnoses with compositional Semantic IDs (SIDs) and optimizes reasoning trajectories for multi-label coverage. Concretely, we first encode ontology-enriched disease semantics into compact SIDs through residual quantization, and ground the resulting SID tokens in natural language and longitudinal EHR contexts through multi-task alignment and reasoning-enriched training to unlock transferable LLM reasoning. CARing further improves unordered multi-label prediction through a coverage reward for reinforcement learning and multi-positive supervision. At inference time, the model supports both efficient direct constrained decoding and multi-chain reasoning with rank fusion. On MIMIC-III and MIMIC-IV, CARing exceeds all EHR-trained baselines in weighted F1 and attains the highest top-k recall at every reported cutoff, including R@30 of 46.04% and 46.52% in reasoning mode. Our codes and logs are available at https://github.com/zmlxzyh/CARing-Codes-Logs.

Diffusion samplers can reduce computation by generating selected spectral coordinates and filling the remaining directions with noise. How many directions must they retain? We study this question for data with power-law covariance spectra. For Gaussian data compared to a smoothed target, we prove matching bounds on the required number of retained directions, provided that the ambient dimension is sufficiently large. The truncation error depends on the combined Wiener gains of the omitted directions, regardless of the accuracy of the sampler on the retained coordinates. Keeping only directions whose signal exceeds the output noise level can therefore leave a non-vanishing error: many individually weak directions remain significant in aggregate. Combining this characterization with a diffusion convergence bound yields sufficient sampling-step complexity under exact scores. The upper bounds also extend to estimated principal components and, componentwise, to Gaussian mixtures. The practical prescription is to select the retained subspace using an aggregate spectral-tail error budget, then to choose the diffusion noise level accordingly.

Visible Chain-of-Thought (CoT) is often treated as a broadly useful reasoning instruction, yet analytics code generation combines natural-language ambiguity, schema grounding, target-language constraints, and model-specific inference behavior. Because the same analytics request can be expressed in two distinct target languages-SQL and Python (pandas)-this setting provides a natural test of a common but under-examined assumption: that visible reasoning is more effective when its representation matches the requested target, as in "think in SQL" or "think in Python." Together with generic instructions such as "think step-by-step," such recommendations remain insufficiently evaluated under controlled, execution-based comparisons. We study a query matched SQL-pandas benchmark that crosses persona phrasing, target language, visible-CoT format, control prefixes, direct generation, and internal-reasoning configurations. The results do not support either a universal accuracy advantage from visible CoT or a consistent benefit from matching the reasoning representation to the target language. Instead, the effects depend on the persona, target, model configuration, and internal-reasoning setting. The control ablations further distinguish effects of reasoning content from those of prompt format. These findings indicate that reasoning strategies should be selected jointly for the model, persona, target, and internal-reasoning configuration rather than adopted as universal defaults. More broadly, the study provides a controlled framework for identifying when visible reasoning improves executable generation, when it primarily perturbs model behavior, and when the internal-reasoning configuration is the more consequential factor.

Black-hole shadows and geometrothermodynamics (GTD) are defined in different spaces but depend on the same macroscopic black-hole parameters. We review their correspondence for Reissner–Nordström (RN), Kerr, and Kerr–AdS black holes. The three GTD metrics reveal complementary thermodynamic structures, including Davies instabilities, extremal and degenerate limits, and regular curvature zeros, which can be mapped to shadow configurations. Kerr–AdS extends this correspondence to asymmetric shadows and multidimensional equilibrium states. We formulate a local Jacobian-rank criterion for thermodynamic reconstruction from shadow observables and discuss shadow–microstructure (SM) diagrams as optical representations of GTD-classified equilibrium states. The application to Sagittarius A* illustrates the inverse problem: shadow observations constrain thermodynamic states and provide a basis for identifying additional metric-dependent observables that could distinguish among the GTD metric structures.

Hair stroking is common in daily grooming and personal care, and is also widely used in hair-product evaluation, motivating robots with similar physical interaction capabilities. Existing robotic hair-care and surface-following methods mainly rely on trajectory planning, compliance, force regulation, or tactile-conditioned policies, but deformable hair can remain in contact while gradually drifting across the end-effector, making local interaction difficult to regulate. We propose TacHair, a tactile contact-distribution guided online correction framework that represents high-resolution tactile observations as a spatial hair-contact distribution. A visuotactile imitation policy generates the nominal stroking motion, while a separately trained residual module corrects local contact deviations, separating task progression from contact recovery. We evaluate TacHair in 525 real-robot trials across five head geometries and three hair conditions. A successful stroke requires both sufficient task progression and contact maintenance; our method improves success from 42.9% to 62.3% and contact maintenance from 59.4% to 88.0% over the same visuotactile policy without correction. These results demonstrate spatial tactile contact distributions as an effective feedback representation for contact-preserving interaction with deformable and visually occluded surfaces. Demos, code, and datasets are available at https://tachair.github.io.

Compressing a matrix for reconstruction still defaults to the truncated SVD, approximating the data with a single low-rank structure. It is common to reduce the residual further by adding an overlapping row-sparse component, but methods that solve this joint problem often require iterative solvers and tuning of regularization parameters. We propose the Disjoint Row-Sparse plus Low-Rank (D-SLR) decomposition, a closed-form drop-in for the truncated SVD that improves or exactly matches it. D-SLR restricts rows to either being stored verbatim or approximated by the low-rank fit, never both. Under squared error this restriction costs nothing: the joint optimum is attainable disjointly with fewer parameters at every non-trivial rank and stored row count (shape). With zero stored rows D-SLR reduces to the truncated SVD, so it never does worse at equal cost. The algorithm scores the entire error-versus-parameters tradeoff, and the solution is chosen afterwards by a supplied error target or parameter count, or by a selection rule. The grid and solution together cost three SVDs, with no tuning or regularization. We derive an assumption-free, a-posteriori lower bound on the error at every shape, giving each solution a computable certificate on the potential gain of any other choice of rank and stored rows. Experiments on synthetic and real data (LLM embedding tables, network traffic, hyperspectral images) confirm the gains and quantify the certificate.

Aerial vision-and-language navigation (VLN) agents are typically trained on detail-rich, trajectory-aligned commands, whereas users issue short, intent-driven instructions; on a frozen OpenFly navigator, this instruction gap drops success rate (SR) from $31.03\%$ to $11.33\%$. To scale translator training, we prompt a language model with human-written style examples to convert original commands into paired, intent-centered Weak commands, which yield $15.27\%$ SR. We introduce the Trajectory-Grounded Instruction Translator (TGIT), a front-end that keeps the navigator frozen and translates Weak inputs into agent-executable commands by learning from its trajectory outcomes. The resulting Weak-trained translator raises Weak-input SR to $37.93\%$ and transfers zero-shot to real human instructions ($11.33\%{\rightarrow}32.51\%$); it also improves held-out OpenFly ($4.95\%{\rightarrow}20.79\%$) and yields recovery on CityNav and AirVLN.

A $\lambda$-self-expander $F: M^n\to \mathbb{R}^{n+1}$ is the solution of the isoperimetric problem of weight $e^{\frac{|x|^2}{4}}$. In this paper, for sufficiently large $\lambda$, we construct an immersed non-embedded spherical $\lambda$-self-expander in $\mathbb{R}^{n+1}$ with the mean curvature $H>0$. Moreover, we obtain the explicit solution for $n=2$.

Screening in systematic reviews (SRs) is manual and time-consuming. Prior work has explored large language models (LLMs) for automating this step, but LLMs are evolving rapidly, so earlier performance claims may no longer accurately reflect their screening performance. We used an existing software engineering SR screening benchmark (SESR-Eval) as our data. We also power-sampled a new, smaller dataset (SESR-Eval-Mini) that allows evaluation at lower costs. Using this data, we evaluated eight new LLMs for screening performance. Additionally, we tested different prompts, analyzed LLM agreement in screening decisions and criteria, and examined the effect of refining the inclusion and exclusion criteria on screening performance. The eight new LLMs performed marginally better than the seven old ones: avg. MCC across secondary studies rose from 0.347 to 0.365. Differences between secondary studies are still bigger than between LLMs. Computing the overall screening decision from criterion-level decisions degraded screening performance only slightly. LLMs generally agree with each other in their corresponding screening decisions (mean Gwet's AC1 = 0.830), though certain inclusion and exclusion criteria showed larger disagreement than others. Refining the inclusion and exclusion criteria slightly improved recall and made decisions easier for some LLMs, but overall impacts of criteria refinement were modest. LLMs are not yet ready to replace humans in paper screening and the advantages new, more costly models bring, appear to be very limited. Agent-based approaches, prompt engineering, and further criteria refinement are three potential future research avenues.

This is a Corrigendum and Addendum to Algorithmica paper (2026) 88:51.

Digital twins (DTs) can be thought of as digital counterparts of physical objects, or more generally, twinning targets (TTs). To enact changes on and optimize for properties of their TTs, DTs use an element of decision-making. Traditionally, many domains, such as home automation, utilize rule-based decision-making models to imperatively define DT actions based on desired TT conditions. With evolving user specifications, rule-based models have become increasingly complex to develop and maintain, particularly in scenarios involving optimizations under dynamically changing systems, such as those affected by weather or dynamic energy pricing. We present an alternative in the form of ruleless digital twins (RDTs) that automatically produce optimal decisions with respect to purely declarative user specifications, similarly to the well-established ruleless approach of model predictive control. They do so through a combination of a semantic knowledge base, logical inference, simulation models, and an autonomic computing architecture, each exclusively based on a widely-used standard or technology. We evaluate our proof of concept through an incubator case study and experiments against a rule-based bang-bang controller in the context of a virtual office room environment. Results show core that RDT functionality performs better than the control in terms of maintaining desired room temperatures and minimizing energy costs under dynamically changing spot pricing. Additionally, due to combinatorial decision tree construction, RDTs require considerable computational power for longer prediction horizons, although their applicability to specific problem domains (and use of shorter horizons) ultimately falls on their users.

Training a compact model often needs far more memory than storing it, because the optimizer keeps its own records of past gradients. For a hyperdimensional classifier whose learned parameters are low-bit angles, which we call a phase memory, these records take several times more memory than the model itself. We ask whether such a model can be trained while storing nothing but the model. The proposed method, Phase-HDC, turns each stored angle by at most one step per update, against the sign of its current gradient, and only when that gradient is large enough. We show that this simple rule is the exact solution of a first-order loss model in which every changed parameter pays a fixed cost. When everything except the update rule is held fixed, Phase-HDC matches the accuracy of Adam with 6-bit moments while storing three times less. Across eleven image, tabular, and text datasets, it stores 16–23$\times$ less than standard float32 Adam and 4–6$\times$ less than 8-bit Adam. The price is an average loss of about five accuracy points against float32 Adam, while Phase-HDC is more accurate than 8-bit Adam on six of the eleven datasets, including byte-level text prediction, where 8-bit Adam collapses. Instrumented training runs explain these outcomes. Once parameters must sit on a discrete grid, Adam's moments mainly decide whether a parameter moves at all, a decision that a threshold on the current gradient can make without memory, and coarse quantization of the moments breaks this decision for inputs that the data rarely contain. The storage savings are logical state rather than measured hardware memory.

Self-improving LLM agents can adapt a credit pipeline to a changed rule, but an agent that rewrites itself destroys the artefact a supervisor reviews: a named change, a recorded test, an approval. We argue that self-evolution is reviewable only if it is confined to the runtime harness (instruction text, tool-call logic and primitive composition) while model weights stay fixed, so that every adaptation is a diff with a cause and a test attached. We give a dual-loop engine built on that bound, with one admission gate that writes a hash-chained record before deployment, and we measure the gate in simulation, with a simulated agent and a seeded-search proposer rather than language models. Across three families of supervisory re-interpretation at three severities, 10 seeds each, the gated loop admitted 144 of 7,449 candidate changes, none of which worsened error on held-out history, and restored the false-positive rate to the oracle level without raising missed flags in every low- and mid-severity cell. With the gate replaced by the check an unbounded system applies (fewer errors visible in recent traces), the same loops admitted 309 harmful changes and left missed flags above 10% in 49 of 90 runs: false positives fell because the screen was loosened. Evaluated on pre-shift labels, the gate rejected every candidate, so a re-interpretation must be encoded as a rule that relabels history. Parametric and scope shifts were repaired locally, a structural one only by primitive replacement; at the highest structural severity the gate's fixed tolerance blocked the correct replacement in half the seeds. We map the mechanisms to the EU AI Act's provisions for high-risk credit scoring and note that the April 2026 US model-risk guidance excludes agentic AI from its scope.

Existing LLM-based approaches for software Requirements Engineering (RE) typically rely on basic prompting strategies or rudimentary agent collaboration, under-utilizing the full potential of multi-agent systems. Meanwhile, available datasets focus on isolated subtasks, such as requirements extraction, classification, and completeness detection, leaving the absence of an end-to-end RE benchmark that spans from requirements elicitation to generation. We present Agent4RE - a self-refining multi-agent RE system that orchestrates specialized agents and incorporates two iterative improvement loops. To support evaluation, we construct RE-E2E - a real-world dataset built from human-written requirement specifications, enabling end-to-end assessment of RE workflows. Building on this foundation, we further propose two enhanced Agent4RE versions that incorporate either autonomous self-refinement or structured human feedback, and analyze their strengths and limitations across different scenarios. Evaluation on 8 Large Language Models (LLMs) demonstrates that all three Agent4RE variants consistently outperform a domain-context-augmented prompting baseline by average 8% in text-based metrics. The two enhanced variants achieve the highest LLM-as-a-judge and human ratings, surpassing two RE baselines by approximately 0.8 points on a four-point scale. This consistent performance establishes Agent4RE as a practical end-to-end RE solution for industrial environments.

Deep reinforcement learning has achieved substantial performance gains over classical control approaches. Yet, a central challenge to learning in real-world applications is acquiring costly samples. Kolmogorov-Arnold Networks are a recently proposed architecture that can learn physical relationships in control problems effectively, with significantly higher parameter efficiency and interpretability when compared to Multi-Layer-Perceptron architectures. In this work, we systematically study sample-efficiency using computational experiments, covering the Feynman dataset and the Gymnasium RL benchmark. The results show that similar performance can be achieved with 40% fewer samples using the Kolmogorov-Arnold architecture, and that relative performance improvements up to 50% occur during the training process. The observed gains are robust to varying levels of noise in rewards. These results highlight the potential of the Kolmogorov-Arnold architectures for more sample-efficient reinforcement learning. Code: https://github.com/DerKevinRiehl/neurips26_kan_training

Neural surrogates for vector-valued partial differential equations can fit training data yet change their predictions when the same physical state is expressed in a rotated coordinate frame. We study this failure on three-dimensional Navier–Stokes dynamics observed at irregularly placed points. We introduce the Invariant-Conditioned Isotropic Kernel Neural Operator (IKNO), a compact graph model that builds local interactions from scalar quantities unchanged by rotation and vector directions that rotate with the data. Consequently, rotating the positions and velocities rotates the predicted velocity change in exactly the same way. On a held-out test set fixed after model design, training unconstrained graph models on randomly rotated examples reduces but does not eliminate their coordinate dependence. In contrast, IKNO is consistent to numerical precision, matches the forecasting accuracy of a general rotation-aware Tensor Field Network with $5.6$ times fewer parameters, and outperforms a parameter-matched graph simulator. These results show that a compact, PDE-specialized model can remove coordinate dependence without sacrificing forecasting accuracy.

Looped Language Models (LoopLMs) provide a parameter efficient approach to scaling model capabilities through repeated use of shared parameters across recurrent steps. Since each recurrent depth can be read out independently, a single LoopLM exposes a broader output space across inference depths, raising an important question: whether safety is preserved throughout recurrent computation. Prior evaluations suggest that deeper recurrence can improve safety on harmful queries, but robustness under jailbreak attacks remains unclear. We therefore conduct a comprehensive safety evaluation of LoopLMs under jailbreak attacks targeting different recurrent depths. We find that attack success can increase at deeper inference depths, the same query can elicit different safety behaviors across depths, and attacks constructed against one depth can transfer to others. Moreover, SFT and preference alignment do not eliminate these safety gaps, motivating an alignment method designed for LoopLMs. We introduce SafeBridge, which combines lightweight depth specific control of shared recurrent layers, selective state bridging, and joint safety supervision across recurrent depths. Across model scales, multiple attack methods, and safety benchmarks, SafeBridge substantially reduces attack success for both matched-depth and cross-depth attacks. It also improves general utility over the vanilla models while maintaining comparable over-refusal behavior. Our results show that the safety of a LoopLM cannot be inferred from a single recurrent depth, motivating safety alignment across recurrent computation. Our code and model checkpoints will be released upon acceptance.

Spatial audio-visual understanding requires models to recognize not only what is present, but also where events occur and how they relate across modalities. Existing benchmarks often rely on simulated scenes, evaluate isolated spatial skills, and provide limited diagnostic insight into failure modes. We introduce SAVU-Bench, a real-world benchmark that systematically evaluates spatial audio-visual understanding across three capability levels and seven evaluation tasks. We further introduce SAVU-Diag, a scene-linked diagnostic set that decomposes reasoning questions into their prerequisite grounding and alignment sub-tasks. Evaluation of 12 representative models on SAVU-Bench reveals that while visual spatial grounding is relatively mature, spatial perception involving audio remains a primary bottleneck. SAVU-Diag further demonstrates that most reasoning errors co-occur with failures on these prerequisite tasks, though reasoning gaps persist even when prerequisites are correctly resolved. Motivated by these findings, we introduce SAVU-EA, a training-free evidence-augmented baseline that makes spatial cues more explicit. While SAVU-EA substantially improves spatial grounding and joint matching, high-level spatial reasoning remains challenging. Our findings highlight the urgent need for both robust spatial audio perception and deeper integration of cross-modal spatial relations.

Looped Language Models (LoopLMs) offer a parameter efficient approach to scaling reasoning by reusing shared parameters across recurrent computation steps. Despite their promise, effective post-training of LoopLMs remains challenging. Existing approaches either provide reward based supervision that is sparse or costly to extend across loops, or rely on external teachers or privileged information, leading to limited teacher availability or teacher-student context mismatch. To address these limitations, we introduce LoopOPD, a cross-loop on-policy distillation framework that uses additional recurrent computation within a LoopLM as its own source of supervision. LoopOPD uses a frozen terminal loop policy as a compute privileged teacher for an intermediate loop student on student generated rollouts, providing dense supervision without an external teacher or privileged information. We further propose Dynamic LoopOPD (D-LoopOPD), which continually refreshes the terminal loop teacher as the shared model parameters are updated, enabling recurrent self-improvement. We characterize how distillation updates propagate across loop depths and derive sufficient conditions under which a single update yields simultaneous local improvement at both loop depths. Experiments on Ouro-Thinking models show that LoopOPD improves mathematical reasoning, while D-LoopOPD yields further gains through dynamic teacher updates. Despite being trained only on mathematical data, the resulting models also improve on general reasoning and code generation benchmarks, demonstrating that recurrent computation can serve as an effective source of supervision for LoopLMs. Our code and model checkpoints will be released upon acceptance.

Large language models can now write complete, interactive 3D worlds as code, but grading those worlds automatically is unreliable. Existing judges take one view of the output: a vision-language model scores a few rendered snapshots, or a language model reads the source. On worlds written by five frontier models we find that the two views disagree on 32% of required items, mostly code that no frame shows, and that fixed views miss small close-up contents. We present WorldBench, a benchmark and judge for open-ended, LLM-generated Three.js worlds. From one prompt describing a floating voxel island with ten biomes, physics, and day/night and seasonal cycles, the judge explores the running world, controlling its clock, orbiting it, and sending a navigator agent to frame each biome, and reads the code for what it sees. Neither channel is trusted on its own: a code quote counts only if it is text the source contains, and visual claims are checked against measured pixels where the property is measurable. A mutation test, in which we remove features by construction, shows that code-only judging gives full credit to four of five removed features, because their code remains in the file. Our judge cuts the points kept on removed features by a third (5.44 to 3.55 of 7.11), and what it still credits is mostly code that exists but never runs. We evaluate five frontier models: Claude Fable 5.1, GPT-6 Astra, Kimi K3, Grok 4.7 and Gemini 3.1 Pro. Code, prompt, tests and judge configuration are available at https://github.com/KrishBakshi/worldbench

How does dynamic order emerge spontaneously in closed systems without external driving? Existing paradigms all require external energy flows, temperature quenching, or slow driving. Here we report constraint-induced self-organization via geometric radiation in coupled metric evolution systems. Simulations reveal a universal four-stage cycle: stress accumulation, super-exponential radiation, chaotic collapse, and convergence to a fractal limit cycle, a novel attractor topology we term the wedge-shaped attractor, with five quantized curvature states and fractal micro-fluctuations. We identify four jointly sufficient conditions: an irreversible geometric horizon, persistent stress injection from quantum coherence, endogenous geometric tension between incompatible curvatures, and effective fluctuations. Their synergy triggers a critical avalanche at the horizon boundary. We prove three theorems: the Geometric Horizon Theorem, the Geometric Energy Dissipation Theorem (implying wave-like entropy evolution in closed systems), and the Radiation as Phase Transition Channel Theorem. We further establish the Constraint-Induced Self-Organization Theorem: these conditions guarantee the complete cycle with probability one. Systematic scans reveal a critical noise threshold and power-law scaling of radiation onset. We verify universality across 12 configurations, multiple noise types, and three geometric flows. This work establishes a new paradigm for closed-system self-organization, forging an exact mathematical duality between classical nonlinear constraints and gravitational horizons.

When an assistant encounters a message for another AI, does it tell its user? Four fixed model-provider deployments perform simulated source tasks in 1,280 ordinary-note and 128 enhanced-note sessions. Harmless and harmful messages have matched plaintext and ROT13 versions, with no-message controls. Observers receive no decoder or decoded meaning; a requested reference code incentivizes inspection. Asking for reports increases rule-detected notifications identifying another AI as recipient by 53.1 percentage points for harmless ROT13 messages and 54.7 for harmful ones. This is a joint inspection, recognition, and notification effect; missing-response bounds are 38.3–77.3 and 36.7–78.1 points. Model-based trace checks identify eleven ordinary plaintext cases where agents interpret the message but do not notify their user. Seven encoded omissions are verified with enhanced notes; ordinary encoded omissions remain unverified. Seven simulated filename disclosures coexist with accurate review-status answers, and two answers use a planted false count. Interpretation, notification, and authorized task performance are distinct outcomes.

Large language model (LLM) agents are rapidly reshaping software engineering, accompanied by an explosion of new code benchmarks. Yet nearly all existing benchmarks still rely on the same decades-old criterion: a solution is correct if it passes a fixed set of unit tests. Such tests are often insufficient: they check only part of what the task requires, so agents can reward hack them or silently miss required behavior while still passing every test. As a result, higher benchmark scores may partly reflect better adaptation to the evaluator rather than better problem solving. Existing works focus on static test augmentation: they strengthen each task's tests once, before any trial is seen, and thus overlook how real trials actually fail. We introduce TestJack, a scalable framework for evaluating patches beyond fixed tests. For each trial, TestJack generates tests targeting prompt requirements the patch may violate, retains only tests passed by the ground-truth patch, and re-examines any trial failures. Each confirmed failure is thus supported by a replayable test. To reduce evaluation cost, we also introduce a lightweight variant which audits a random sample of trials in depth and reuses the resulting tests across all trials for the same task. Across 6 frontier model backends and 5 benchmarks such as DeepSWE and SWE Marathon, we find that about 34.4% of the model trials currently judged correct violate the task requirements, lowering the overall resolution rate from 50.6% to 33.2%. Our results reveal a fundamental limitation of current coding-agent evaluation: as LLMs become better at optimizing against fixed evaluators, those evaluators themselves must become more adaptive.

The balanced Hellinger conjecture compares the overlap of two output laws induced by a Boolean decision under binary symmetric noise. We prove that a single input coordinate minimizes this overlap among antipodal decisions, whose values reverse when all input signs are reversed, throughout the noise interval. The proof uses a normalized nuclear norm of the cross-class block of the Gram matrix of square-root channel densities. Multiplication by an antipodal decision exchanges the even and odd Fourier spaces preserved by the Gram matrix. A coordinate exchange attains the minimum cost of matching their spectra. A matrix contraction extends the sharp bound to arbitrary independent binary-input channels. Fixed coordinate flips and randomized decisions follow from the same argument and concavity. These extensions give bounds for information and testing, including linear Gaussian observations, and a weighted edge-boundary inequality.

In post-deployment time, inputs to deep learning models may or may not be adversarially patched. Patch robustness certification on such inputs within a patch bound can verify their label benignity and should retain high prediction accuracy. However, existing smoothing-based and masking-based recovery defenders cannot achieve both simultaneously: they degrade the prediction accuracy much and cannot verify the benignity of the returned label of an adversarially patched input, respectively. We propose MRCert, the first masking-based certified recovery defender that shows the feasibility of achieving both. Unlike all existing works to apply a common condition across both types of input (benign and adversarially patched samples) for certification, MRCert infers type-specific necessary properties of deep learning models for both types in post-deployment time and formally relates them to verify the label benignity through a novel type-oriented design of label recovery and certification function pair. Without incurring the degradation in clean accuracy caused by smoothing, experimental results confirm that MRCert achieves 35.1% adversarial certified accuracy on ImageNet at patch size 16 pixels, whereas the SOTA PatchCURE fails completely.