Papers

Self-evolving agents convert interaction feedback into persistent artifacts, such as memories or skills, which in turn guide subsequent decisions. As these artifacts are iteratively updated throughout an experience stream, the capabilities they support may evolve. Consequently, endpoint performance alone offers an incomplete view of self-evolution. Process-level evaluation is therefore essential to identify when a target capability emerges and whether later updates strengthen, preserve, or weaken it. Motivated by this, we propose EvoPathBench, a benchmark that tracks individual capabilities during artifact-level self-evolution. EvoPathBench fixes the base model, tools, freezes evolving artifacts at successive checkpoints, and evaluates the target capability on held-out episodes. This benchmark evaluates agent self-evolution using public trading data and calibrated trajectories. It tests three capabilities: generalization to unseen tasks, retention after unrelated learning, and rule adaptation to new evidence. Experimental results show that gains on similar unseen tasks often weaken under distribution shift, retention losses are concentrated in a minority of evolution paths, and no method achieves reliable rule adaptation. Moreover, while self-evolution enables agents to generate candidate artifacts with substantial held-out gains, the selected updates consistently fall short of realizing this potential. Together, these findings establish capability-level process evaluation as a foundation for analyzing self-evolution, identifying candidate evaluation and selection as key targets for improvement.

LLM-based agents increasingly operate in environments where they interact with users, tools, and external systems. Yet most security evaluations assume passive users and static control, ignoring the interactive dynamics that shape real agent behavior. We introduce DUMA-Bench, a benchmark and evaluation protocol for measuring agent security under dual-control interaction, where both the agent and the user can influence the shared environment state. DUMA-Bench extends $\tau^2$-bench ~\cite{barres2025tau} with adversarial environments covering eight vulnerability classes, including RAG poisoning, cross-agent manipulation, and unsafe output handling. We evaluate 14 models from five model families (OpenAI, Anthropic, DeepSeek, Qwen, and Z.ai) across eight domains and multiple user-behavior regimes. Across our experiments, introducing dual-control interaction increases the attack success rate from 26.9% to 41.1%. These results show that agent security is not solely a property of the model but emerges from the interaction between the model, the user, and the environment. DUMA-Bench provides a missing evaluation layer for studying security in realistic agent deployments.

Detecting hidden convexity is one of the tools to address nonconvex minimization problems, and find global minimizers. We introduce the notion of conditional infimum, develop the theory, and establish a tower property, relevant for minimization problems. Then, we illustrate how the conditional infimum is instrumental in revealing hidden convexity. Thus equipped, we provide a new sufficient condition for hidden convexity in nonconvex quadratic minimization problems, that encompasses and goes beyond known results (with the notion of block-signed pair matrix-vector). We also show how the conditional infimum is especially adapted to tackle the so-called S-procedure.

Human demonstrations offer a scalable way to collect manipulation data, but their contacts may be unstable or infeasible when transferred to a robot hand. Collecting demonstrations directly on the target robot avoids this mismatch but substantially increases the cost of data collection. To address this trade-off, we present Touch2Robot, a framework that lets humans collect demonstrations while seeing how the target robot hand would contact the object. We capture human hand motion, tactile-glove measurements, and object motion during human manipulation. These recordings guide object-specific RL policies to reproduce the demonstrated object motion while favoring contacts consistent with the recorded human touch. We distill the learned behaviors into a unified real-time retargeter that maps incoming human observations and object geometry to robot hand configurations. During collection, the predicted robot configuration is synchronized with the tracked object pose in simulation to reconstruct robot-object contacts, which are visualized to help the demonstrator adapt subsequent interactions to the target hand. Across four real-world tasks, Touch2Robot improves average real-robot replay completion from 37.9% to 72.1% over visual-only feedback, while reducing the collection time per replay-successful demonstration from 58.6s to 18.2s. Reconstructed target-hand contacts achieve 44.2% F1 against real-robot tactile measurements, and policies trained on Touch2Robot demonstrations improve downstream Diffusion Policy performance by 29.1 percentage points over visual-only feedback. These results show that bringing robot touch into the human demonstration loop improves both the quality and efficiency of scalable dexterous data collection. Project webpage: https://Touch2Robot.github.io/.

The mkFit algorithm provides an implementation of the Kalman filter-based track reconstruction algorithm that exploits both thread- and data-level parallelism. It has been adopted by the CMS Collaboration as the primary track building algorithm during the Run 3 of the LHC for both the online and offline track reconstruction sequences. Thanks to mkFit, an average speedup of a factor 3.5 is achieved in track building while retaining or improving physics performance. As a consequence of the speedup provided by mkFit in track building, track fitting has become a comparably significant component of the overall tracking time. Given the increased demands of the High-Luminosity Large Hadron Collider, further speedup can be achieved by extending mkFit to the track fitting task. We present preliminary results for track fitting in the CMS High-Level Trigger using mkFit, covering both the physics and the computational performance, based on realistic Phase-2 simulations.

InvestorNerd is a web-based platform (investornerd.org) designed to educate and democratize financial understanding by providing accessible, AI-powered investment and personal finance insights tailored to potential user profiles. The system addresses a key challenge in helping everyday individuals, especially those without formal financial education, make sense of investment options and personal financial decisions. The platform offers three interactive tools: Stock Insights - Allows users to input any Stock, Mutual Fund, or Exchange Traded Fund (ETF) ticker to receive a summary of relevant news sentiment and quantitative metrics. Stock Insights Questionnaire - Builds on stock insights by letting users specify a preferred risk tolerance and sector interest. It returns categorized investment tables based on volatility and sector, sortable by dividend yield, return percentages, and others. General Insights Questionnaire - Provides users with personalized insights based on answers to an age-income-expenditure-savings questionnaire. Outputs include possible actions regarding savings strategies, account types (e.g., Roth IRA, UTMA), and potential loan options (e.g., FHA). The output is designed to be clear, unbiased, and educational, empowering novice investors with practical insights. This paper details the design, implementation, and evaluation of InvestorNerd, demonstrating how generative AI and open financial data can be integrated to create scalable, insight-rich tools for financial literacy.

Language models can be adapted by changing the computations applied to individual tokens. Quantum circuits offer one such approach, but evaluating wider circuits inside a large model can be computationally demanding. Here we introduce HyperQ, which adds token-conditioned quantum residual branches to a frozen masked-diffusion language model. A quantum residual branch is a module in each transformer block that reads a token's hidden state, emits the coordinates of that token's circuit, executes it, and adds the measured values back through a residual connection. The backbone remains frozen, and only the added branches are trained. Within each branch, a lightweight circuit hypernetwork emits token-specific rotation angles, coupling strengths, and measurement axes in a shared sparse circuit structure. The required expectation values have an exact classical expression whose evaluation cost grows linearly with the qubit count, enabling circuits from 16 to 64 qubits to be trained within a 1.1-billion-parameter backbone. Across downstream benchmarks, increasing circuit width raises the average score from 47.65 to 54.30. At 64 qubits, HyperQ exceeds the backbone and its low-rank-adapted counterpart by 4.71 and 3.67 points, respectively. HyperQ is fine-tuned on 20,000 prompt-response pairs, compared with 200,000 for the classical baselines. These findings support token-conditioned circuit emission as a tractable architectural approach to quantum-augmented language modelling.

The fifth generation of mobile networks was standardised with an explicit mandate to close long-standing privacy and security gaps, mandating the concealment of the subscriber's permanent identity, resistance to generational downgrade, and protection against location tracking. Assessing whether these guarantees hold in operational networks, however, requires separating two sources of residual exposure that prior studies do not distinguish and do not evaluate in the wild: protocol-design limitations, which remain exploitable even against a fully specification-compliant deployment, and implementation gaps, which arise from incomplete or non-compliant implementations. We present 5G-Shark, a security assessment tool and methodology that turns a legitimate mobility procedure against the subscriber. Rather than relying on active jamming or malformed-packet injection, 5G-Shark manipulates the standardised cell-reselection criterion to pull a target User Equipment onto a self-created rogue cell, establishing an attack vantage with minimal service disruption. Then, the proposed methodology effectively performs the required interactions to expose the security risks of the system under test, classifying them into the aforementioned categories. Built solely from open-source stacks and Software Defined Radio hardware and evaluated against commercial 5G Standalone deployments, 5G-Shark requests subscriber identifiers, forces Radio Access Technology downgrade via crafted Registration Reject codes, and induces denial-of-service states. For each vector, we attribute the root cause to protocol design or deployment non-compliance. We further provide empirical evidence that in several commercial deployments, temporary identifiers are re-allocated in near-sequential steps that keep successive values linkable, a weakness that enables persistent user tracking despite correct subscriber ID concealment.

We consider relatively prime integer numbers $m$ and $n$ such that each group of order $mn$ has a normal subgroup of order $m$. We prove that any skew brace of size $mn$ has an ideal of size $m$ and, if the subgroup of order $m$ of its additive group is abelian, a subbrace of size $n$. We give a method to classify skew braces of size $mn$, such that the subgroup of order $m$ of their additive group is abelian, from the classification of braces of size $m$ and the classification of skew braces of size $n$. We apply this result to determine all skew braces of size $p^2q^2$ of non-abelian type, for $p$ and $q$ odd primes, $p<q$, such that their ideal of order $q^2$ is cyclic.

A mobile is a rooted full binary tree whose leaves carry positive integer weights. The imbalance of an internal node is the absolute difference between the total weights of its two child subtrees, and the cost of the mobile is the sum of these imbalances. In the unrestricted Balanced Mobiles problem, only the multiset of leaf weights is given: both the tree topology and the placement of the weights must be chosen so as to minimize the cost. The computational complexity of this unrestricted variant has remained open, although the variant with a prescribed topology is strongly NP-hard. We close this gap by proving that the decision version of unrestricted Balanced Mobiles is strongly NP-complete. Our reduction from Numerical 3-Dimensional Matching with Distinct Integers uses three widely separated numerical scales. Tight telescoping bounds force every threshold-achieving mobile into a canonical hierarchy, after which pairwise distinctness of the source integers collapses the hierarchy to single triples from which a valid numerical matching can be recovered.

In this paper, we prove that there exist a symmetric quantum Latin square with maximal cardinality of order $n$ for all $n\geq 6$, and a symmetric idempotent quantum Latin square with maximal cardinality of order $4k+2$ for all $k\geq 1$.

We study randomized stopping times for a Markov process, described by a progressively measurable intensity $\alpha_t(\omega)$. We prove that every admissible intensity has a Markovian representative $\lambda(t,X_t)$, explicitly obtained from the observed measure and the surviving occupation measure. This representative preserves both the family of surviving mass measures and the joint distribution of the stopping time and the state at stopping. Whenever the relative entropy with respect to a reference intensity $r(t,x)$ is finite, we prove an exact decomposition showing that Markovization does not increase the entropy. As a consequence, variational problems in which a randomized stopping time enters only through its observed measure and an entropy penalty can be reduced to optimization over Markovian intensities $\lambda(t,x)$. For every observed measure admitting a finite-entropy representative, there is a unique minimum-entropy randomized stopping time, and it is Markovian. We discuss the connection with optimal Skorokhod embedding and prove a finite-constraint realization result for Brownian stopping. We also approximate arbitrary observed measures by those generated by bounded Markovian intensities.

Diffusion and flow models, as promising generative paradigms for speech enhancement, face a training–inference mismatch: training uses analytical path states, whereas inference recursively evaluates models on self-generated rollout states along discretized sampling trajectories. This mismatch causes prediction and discretization errors to accumulate. To address it, we introduce Corrective Forcing (CoF), a post-training paradigm that forces diffusion and flow models to learn from self-generated rollouts and correct their predictions. CoF corrects clean-speech predictions on rollout states toward the ground truth under dynamic sampling schedules, exposing the model to varying inference conditions. It further regularizes local evolution using locally corrected counterfactual transitions as references for factual transitions. By expressing model outputs through a shared clean-speech prediction parameterization, CoF applies the same post-training objective across diffusion and flow formulations. Experiments with SB-VE and OT-CFM demonstrate improvements in perceptual quality and reconstruction fidelity, together with robust performance across different numbers of sampling steps.

Readability assessment is essential for tailoring texts to intended audiences across educational, healthcare, and information retrieval domains. However, traditional readability formulas struggle to generalize across genres and languages, while supervised machine learning models rely on scarce, domain-specific annotated corpora, limiting their applicability–particularly for less-resourced languages. Large Language Models (LLMs) offer a highly scalable, multilingual alternative that requires no task-specific training, yet the impact of advanced prompting strategies on their performance remains underexplored. In this paper, we conduct a systematic benchmark of diverse open-source LLMs for multilingual readability assessment, focusing on the prediction of discrete readability levels required by educational frameworks. In addition to English, we evaluate our approach on a less-resourced language, Slovenian, to establish whether LLMs remain effective in low-resource settings. Specifically, we investigate the influence of explicit reasoning, demonstrating that Chain-of-Thought (CoT) prompting and reasoning-oriented models yield significant improvements over direct answering. Furthermore, our exploration of few-shot in-context learning reveals that providing just one labelled example per category (1-shot) substantially enhances prediction quality compared to zero-shot settings, with additional examples offering diminishing returns. By comprehensively comparing these approaches against traditional unsupervised metrics and state-of-the-art supervised baselines, we establish the viability of out-of-the-box LLMs as robust, cross-lingual readability assessors.

We study a double scale limit of $U(N)_k\times U(N)_{-k}$ ABJM theory, with $N,k\to\infty$ and $N/k^2\to\nu\in(0,\infty)$, at fixed positive total monopole charge $q$. In this limit, the Penrose geometry retains a compact null circle of finite radius, and the sector of monopole charge $q$ carries $q$ units of longitudinal momentum. It is therefore naturally associated with the rank-$q$ BMN matrix model, while $\nu$ fixes its dimensionless coupling. We establish this relation from both gravity and the supersymmetric index. On the gravity side, we take the double scale limit of Hopf quotients of the Donos–Simón half-BPS geometries. The disk carrying the growing background flux becomes an infinite conducting plane, while the remaining finite disks reproduce the Lin–Maldacena electrostatic problem. Their quantized fluxes map directly to the partition data labeling BMN vacua. On the field-theory side, starting from the finite-$N$, finite-$k$ ABJM localization formula, we prove that, at fixed positive monopole charge $q$, the ABJM superconformal index factorizes coefficientwise in the transverse fugacities into a universal neutral contribution and the refined Witten index of the rank-$q$ BMN matrix model, together with the longitudinal momentum weight. The neutral contribution is precisely the limiting zero-monopole-charge index. Dividing by this universal factor therefore isolates the BMN index summed over all its supersymmetric vacua.

The black hole zeroth law asserts the thermal equilibrium of a stationary Killing horizon, yet its status beyond general relativity remains limited. We demonstrate that its validity is not governed by a universal mechanism: distinct gravitational theories enforce constancy of the surface gravity through different horizon-projections of their field equations. In general relativity, $f(R)$-gravity, and Lovelock theories, the zeroth law is known to follow from the mixed (null-transverse) horizon equations. By contrast, we show that in non-Lovelock theories the zeroth law is enforced by qualitatively different mechanisms. In generalized quadratic gravity, for instance, the null-null component of the field equations dictates its validity. Exploiting this novel diagnostic, we obtain the first exact proof of the zeroth law in the broader landscape of higher-curvature gravity, without relying on a perturbative expansion around general relativity. Our result establishes the zeroth law as a sharp probe of the underlying thermodynamic structure of gravity, and points toward a classification of modified theories according to the mechanism responsible for its validity.

We compare the performance of the RPA and CHIRRUP decoding algorithms for second-order Reed–Muller codes. The RPA algorithm recovers a binary quadratic form associated with a skew-symmetric matrix $M$, whereas CHIRRUP recovers a $\mathbb{Z}_4$-valued quadratic form associated with a symmetric matrix $P$. We describe how the Gray map connects the evaluation vectors of these forms, inducing a rank-preserving correspondence between $M$ and $P$. We analyze how Euclidean distance between evaluation vectors is governed by matrix rank differences using Delsarte–Goethals sets $DG(m,r)$. We demonstrate that CHIRRUP uses repeated measurements more effectively than RPA on these ensembles. While a kernel-aware variant of RPA improves performance on singular quadratic forms by aggregating projection directions across cosets of $\ker M$, CHIRRUP's tree search combines multiple row estimates more efficiently on $DG(m,r)$ when $r < \frac{m-1}{2}$, outperforming vanilla RPA.

On-policy self-distillation fine-tuning (SDFT) learns new skills from demonstrations while reducing forgetting, but it always distils toward the full demonstration-conditioned teacher. This fixes teacher influence at the full-teacher endpoint, providing no control over how much demonstration information should be transferred at each prediction state. We introduce Information-Proximal SDFT (iSDFT), which instead treats the teacher as a budgeted source of information. At each token, iSDFT selects the distribution closest to the current student that satisfies a prescribed teacher-information constraint, yielding a closed-form exponential target with a locally determined tilt. To control cumulative drift, we further anchor the student to its frozen base policy. Across four heterogeneous LLM backbones and two specialisation tasks, iSDFT improves vanilla SDFT in 7 of 8 model-task settings and matches it in the remaining one. It also provides tighter retention on the original SDFT benchmark suite, with 73% of evaluations remaining within 0.5 points of the base model versus 52% for the strongest baseline, while achieving the largest mean improvement on all ten additional mathematics, coding, and competition-mathematics benchmarks. These results show that controlling how much and when teacher information is introduced improves specialisation while preserving broader capability.

The transit timing variation (TTV) method is a key approach to the confirmation, detection, and characterisation of exoplanetary systems. This review discusses the detection of TTVs from transit observations and the origins of TTVs, mainly due to gravitational interactions with perturbing planets, whether transiting or not. Additionally, this work details methodologies for deriving planetary parameters, employing quasi-global and local optimisation algorithms within a Bayesian framework. By analysing TTVs, planetary orbital parameters and dynamical properties can be inferred, providing valuable insights into system formation and evolution. The role of resonances and stability in shaping these systems is reviewed, along with sensitivity biases that influence mass determination. Comparative analyses highlight the unique demographic contributions of TTV systems. TTVs offer a window into the dynamical and physical properties of planetary systems, advancing our understanding of their diversity and stability.

As people turn to generative AI for financial advice, these systems can personalize how they communicate and what they say. Whether these forms of personalization shape decisions differently remains unclear. We conducted a preregistered 2 x 2 between-subjects factorial experiment (N=240): participants ranked three comparably viable stocks, discussed them with an AI, and reranked them. Participants perceived both forms of personalization, but only context-based personalization reliably changed ranking behavior: it increased reconsideration and moved rankings toward the AI's assigned recommendation. Participants felt more influenced without judging the AI as more correct, trustworthy, intelligent, likeable, or high-quality. Those initially farther from its recommendation moved more toward it while judging its advice less correct; exploratory analyses suggest greater susceptibility among lower-expertise participants. These findings show how personalized AI can steer decisions among defensible options with only a minimal evaluative trace, raising concerns for the design and governance of personalized decision support.

Recent observations of replica symmetry breaking (RSB) in ytterbium-based mode-locked fiber lasers have revealed glassy behavior in the quasi-mode-locked (QML) regime. Here, we investigate whether this behavior is restricted to a specific laser implementation or represents a more general feature of mode-locked systems. By analyzing statistical correlations of spectral intensity fluctuations through the Parisi overlap and Pearson correlation parameters, we study two Titanium:sapphire laser systems: a homemade cavity and a commercial laser. In both cases, clear signatures of RSB are observed in the QML regime, while replica-symmetric behavior is recovered in the amplified spontaneous emission (ASE) and standard mode-locked (SML) regimes. These results demonstrate the occurrence of RSB in Titanium:sapphire lasers and support the interpretation of the QML regime as a photonic glassy phase. Together with previous observations in ytterbium-based fiber lasers, these findings suggest that the connection between QML dynamics and RSB may be a general feature of mode-locked laser systems.

We continue to develop a theory of Besov and Triebel-Lizorkin spaces associated with weighted subcoercive operators on a real connected Lie group, specializing to the case of groups with polynomial volume growth. We consider the full scale of spaces and consider interpolation, localization, and pointwise multiplication.

With the rapid development of technology, interval data have been increasingly widely used in various fields, as they can effectively carry information on measurement uncertainty and original variability. Reasonable ranking and outlier screening of interval data are crucial for exploring their value, and statistical depth theory is an important tool to achieve this goal. Existing statistical depth methods are mostly defined for ordinary point-valued data, which are difficult to adapt to the characteristics of interval data and cannot meet the needs of their ranking and outlier detection. Therefore, this paper proposes a statistical depth suitable for interval data and conducts relevant application verification.

Finite simple skew braces with non-abelian additive group remain largely unexplored. In particular, to the best of our knowledge, no finite simple skew brace with non-abelian nilpotent additive group had previously been constructed. We introduce an inverse Baer deformation which produces skew braces of additive nilpotency class at most two from braces of abelian type. Starting from a finite left brace $C=(A,\oplus,\circ)$ of odd order and a suitable biadditive alternating map $\kappa:A\times A\to A$, we define \[ x+y=x\oplus y\oplus\frac12\kappa(x,y). \] The resulting skew brace $\IB_\kappa(C)$ satisfies $\Br(\IB_\kappa(C))=C$ and $[x,y]_+=\kappa(x,y)$, and simplicity passes from $C$ to $\IB_\kappa(C)$. Applying this construction to simple left braces arising from asymmetric products, for every pair of odd primes $p,q$ with $p\mid(q-1)$ and every $m\ge1$ we construct a finite simple skew brace $X_{p,q}^{(m)}$ of order $p^{2m(q-1)+1}q$ such that \[ (X_{p,q}^{(m)},+)\cong E_{p,q}^{(m)}\times C_q, \] where $E_{p,q}^{(m)}$ is an extraspecial $p$-group of order $p^{2m(q-1)+1}$ and exponent $p$. Thus every fixed admissible pair $(p,q)$ yields infinitely many pairwise non-isomorphic finite simple skew braces with non-abelian nilpotent additive group of class two.

Power availability increasingly constrains the operation of AI inference fleets, creating a need for provisioning methods that jointly consider serving capacity and power consumption. Prefill–decode (PD) disaggregation has emerged as a prevalent architecture for large-scale inference serving. However, determining the appropriate numbers of prefill and decode instances is challenging because serving capacity depends jointly on workload characteristics, hardware constraints, queueing, and KV-cache reservations. Existing approaches largely rely on profiling and simulation, providing limited analytical insight into how provisioning decisions shape the tradeoff between serving capacity and power consumption. This paper develops an analytical framework for power-aware provisioning of PD-disaggregated AI inference. Given an inference workload and hardware, the framework models the serving capacity and average power consumption of a provisioned deployment. The serving-capacity model is derived from the joint distribution of input–output lengths and hardware compute and memory limits. In particular, it explicitly captures the coupling between prefill and decode induced by KV-cache reservations, as well as the impact of request queueing. On this basis, the power model determines per-instance power consumption as a function of normalized serving throughput. Together, the models determine the serving capacity–power Pareto front among candidate provisioned deployments, enabling the service provider to choose a provisioned deployment as the workload or available power changes.

Katz centrality is a well-established measure to identify and rank the most important nodes in complex networks by means of a linear system solve. Recent works have developed notions of Katz centrality for temporal, i.e., time-evolving networks. Their drawback is that small changes in the network structure may drastically change centralities across large parts of the network. Moreover, an unproportional effort in the network science community has been devoted to the study of node-based quantities while edge-based measures are far less explored. In this manuscript, we introduce a novel failure-aware temporal multiplex network model for computing edge-based Katz centralities for spatial networks. This class of networks admits the use of the line graph as network representation. We use a block-triangular and -banded supra-adjacency matrix representation, modeling inter-layer connections as low-rank matrices, which assigns a spatially constrained emphasis on up- or downdated edges. These could represent, e.g., breakages of water/gas pipes or obstructions in street networks in real-time infrastructure monitoring applications. We analyze the structure of the of the block matrix inverse with respect to entry decay in the blocks above the block-diagonal. This gives rise to two truncation approaches that allow drastic computational runtime reductions at the cost of introducing a controlled truncation error. Numerical experiments on a range of real-world spatio-temporal networks of size up to $2\cdot 10^8$ illustrate accuracy and efficiency with runtime gains of up to a factor of $679$.

We study rough differential equations driven by controlled rough paths with drift. By means of the canonical lift of the controlled driver, we establish pathwise well-posedness and continuity. Under compatible time-shift conditions, we construct differentiable solution cocycles for the associated dynamical system generated by the equations considered here. Furthermore, assuming the corresponding regularity, moment, and spectral hypotheses, we prove the invariance of the local stable, unstable, and center manifolds.

Dynamical quantum phase transitions (DQPT) are commonly defined either by the behavior of a late-time order parameter or by nonanalyticities in a quantum state's return rate. We show that discrete phase space fundamentally separates these two notions by the scale of information they require. An order parameter transition is determined by a local reduced state, requiring no quasiprobability negativity. In contrast, general global returns can contain information absent from every proper reduced state. For stabilizer returns, we derive an exact decomposition of the rate into distinct costs from loss of support and destructive quantum interference. Dynamics of a qutrit Potts chain show that selective cancellation can reverse the ranking of competing block returns and delay their exchange. An exact control also exhibits a thermodynamic return cusp with zero negativity at the crossing. The existence of a return singularity and the role of interference in selecting its branches are therefore distinct physical questions.

When a language model reads an operation such as "Swap the contents of Box F and Box B", its forward pass writes keys and values for those tokens into the KV cache. Prior work on entity tracking establishes what models use: bindings are resolved at query time rather than stored as explicit latent state. We ask what they write at the operation span and how it is accessed. We split a forward pass into a frozen writer and a reader: the writer's cache is recomputed without gradients, while the reader sees only the instruction and operation tokens, with all state descriptions hidden, and is trained in isolation. Anything the reader recovers was therefore already present in the unmodified cache. On a synthetic boxes task, a base reader recovers $\leq 0.06$ of queried bindings against $0.75$–$1.00$ after training, and recoverability tracks the operation's read/write footprint. We find two modes of access. Across Llama-3.1-8B and Mistral-7B, operation-span transplants causally redirect which visible state is read even when the two worlds hold identical values, revealing a routing record. Isolation training preserves routing and adds direct access to the payload, the value the operation read, from the single operand-name token in a narrow mid-depth band (layers 12–15 of 32 in Llama-3.1-8B, 14–17 in Mistral-7B) — the same site that holds the routing record. The same recipe extends to further operations, ToMi and GSM8K, but is bounded by training coverage and costs open-book accuracy. Operation tokens thus leave localized, causally recoverable records that support both routing and direct payload access, though the model that writes them reads mainly the address they carry and not the value.

Nitrogen dioxide (NO2) is a common air pollutant, released into the atmosphere through the incomplete burning of fossil fuels, and associated with respiratory and cardiovascular diseases in humans. Ambient NO2 concentrations are regulated through air-quality limits assessed with a sparse network of fixed monitors. The revised EU Ambient Air Quality Directive (2024/2881) introduces a daily NO2 limit to be met from 2030. At present, neither the regulatory monitoring network nor existing coarse, annual-mean models can resolve NO2 concentrations at the spatio-temporal resolutions necessary to assess compliance. Here we map NO2 across Europe at hourly and 10m resolution with a machine-learning model that combines ground monitors with satellite, reanalysis, land-use, traffic and emission data and returns a calibrated predictive distribution at every location. Validated against held-out regulatory monitors and independent citizen-science campaigns, the maps resolve high-resolution spatiotemporal NO2 gradients for 110 metropolitan areas in Europe. We reconstruct the daily compliance statistic across those regions and find limit breaches in 91 EU air quality zones deemed compliant by the regulatory monitoring network, covering a population of approximately 135M. Beyond air quality zones and monitor locations, an estimated 9-9.4% (20M) of the population in mapped regions lives in areas where the daily NO2 limit is breached. The high-resolution maps offer a route to population-scale assessment of compliance with the 2030 limits.