Papers

Historical post-16 data for UK A-Level Physics, Maths and Further Maths are analysed to determine the relative popularity of A-Level exam boards. A curriculum mapping of the exam board specifications is implemented and compared against first year syllabi of undergraduate physics courses at high-ranked UK universities. Gaps in curricula are identified and recommendations are made to both university module designers and A-level exam board curriculum setters, with regards to remedial action and a reconsideration of included content.

Breast cancer is a significant contributor to female mortality across the world, displaying one of the highest oc currence rates among the various cancer types. In response to the need for early breast cancer detection, researchers have increasingly turned to association rule-based classification as a favored method. Association Rule mining is a data mining approach which offers the benefit of yielding results that are readily understandable for medical professionals. This paper introduces a novel association rule-based data mining technique for breast cancer classification based on a weighted classification approach. This implementation employs three core algorithms: Rule Generation, Rule Pruning, and Rule Prediction. Rule Generation identifies frequent itemsets and creates association rules. Rule Pruning eliminates rules using specific criteria and separates them into major and minor groups based on their influence on training data. Rule Prediction applies the pruned rules to classify test data. The final prediction algorithm was tested on several testing samples to show the feasibility and performance of the approach.

This paper studies price discovery around contractual decidability rather than an arbitrary venue label. Its upstream lifecycle and decidability clocks are specified in Papers 7.1 and 7.3. Historical venue endpoints remain useful background: 152,694 ordinary markets form the retrospective feasibility denominator, 71,657 have an exact public endpoint, and 70,979 have an exact determination-to-endpoint pair. Those fields do not supply a contractual-decidability clock. The completed historical recovery produced no historically admissible contractual-decidability cohort. The prospective infrastructure shakedown has passed and evidence enrollment is active, but production price extraction has not started. The primary binary cohort will be drawn from the prospectively enrolled and blind-adjudicated contractual-decidability frame, with an accepted exact or interval first-decidability clock, exact terminal payoff, trading-availability classification, and admissible bounded non-block trade or real-candle coverage. Markets tradable after decidability enter a reaction cohort; markets closed before decidability enter a stale-terminal cohort. Closure is a competing event for convergence, not ordinary missingness. A 20-market price pilot may validate acquisition, block-trade treatment, synthetic-candle rejection, staleness, and clock alignment only after blind packet lock and only from accepted prospective clock candidates. It does not create price estimates. The paper specifies a prospective primary cohort and a targeted pilot protocol. Price estimation awaits independently reconstructed first/stable-decidability clocks and source-release clusters. No broad exchange-wide trade crawl or post hoc clock substitution is permitted.

We study the nonconvex trust-region subproblem by a certificate-coupled difference-of-convex algorithm that incorporates spectral information before exact first-order stationarity is attained. The method maintains a persistent randomized Krylov subspace together with the DCA iterates. Near stationarity, a sufficiently negative shifted Rayleigh quotient yields an explicit feasible correction with a quantitative decrease in the objective value; otherwise, completion of a prescribed Lanczos depth provides, with high probability, an approximate positive-semidefiniteness certificate. The same Krylov subspace also provides a certified upper bound on the largest eigenvalue for selecting the DC curvature parameter at subsequent accuracy stages. We prove a uniform negative-curvature correction result over the trust region, covering the near-orthogonal hard-case regime, together with finite-termination and work bounds at fixed tolerances and a quantitative objective-gap certificate. Under a progressive accuracy schedule, the certified objective values converge to the global optimum and the iterates converge in distance to the global solution set, while the Krylov subspace is retained across corrections and accuracy stages. Numerical experiments illustrate the phenomena established by the analysis: negative-curvature corrections can occur before the corresponding post-convergence spectral corrections, the quantitative decrease bound is satisfied in all tested near-orthogonal instances, and retaining the Krylov subspace reduces the median number of spectral matrix-vector products by approximately a factor of $2.6$ relative to restarting the spectral process in the controlled comparison.

We develop a Banach-valued lateral Stieltjes calculus adapted to linear evolution equations on a Gelfand triple \[ V\hookrightarrow H\simeq H^*\hookrightarrow V^*. \] The evolution problem is formulated with the posterior state, \[ D_g u(t)+A(t) S_g u(t)=f(t),\qquad u(a)=u_0. \] This choice is decisive at atoms of the Stieltjes measure: if $\delta=\Delta_g(r)>0$, the equation yields the implicit variational resolvent \[ (I+\delta A(r))u(r^+)=u(r)+\delta f(r). \] We prove a Banach-valued lateral product formula, a weak–strong reconstruction theorem, and a Stieltjes analogue of the Lions–Magenes energy identity. In the separable Hilbert setting considered here, the stable projection chain used in the proof is shown to exist automatically by a spectral-band construction. The latter contains the exact positive jump contribution \[ \frac12\sum_r\|u(r^+)-u(r)\|_H^2. \] Existence is constructed independently by Galerkin approximation and by a Rothe scheme adapted to the Stieltjes mass and its atoms. The Rothe construction does not use spatial projections. We also explain why the available Aubin–Lions theorem for anterior Stieltjes–Bochner evolution graphs is not automatically applicable to the posterior energy space and, in the present linear coercive setting, is not needed. A heat equation with Stieltjes time is included as a model application. The claims are positioned relative to earlier Stieltjes parabolic equations, general measure-driven evolution, and operator-valued-measure parabolic systems; no priority is claimed for measure-driven parabolic theory or Galerkin approximation in general.

We study commercial intent inference that runs entirely on the user's device, under three constraints frozen before the work began: the downloaded payload under 3 MiB, Tier-0 inference under 20 ms at p95, and no raw text, content embedding, or stable identifier leaving the device. Under them we build a retrieval path over a 6,020-leaf commercial taxonomy: a static embedding table distilled from a Korean sentence transformer, quantized to 4 bits, no inference runtime. Our main result is where that constraint costs accuracy. On real Korean commerce text labelled by others (22,900 AI-Hub shopping reviews), mid-category top-5 on real product names is 75.0% against an 18.4% permutation baseline, but splits on one observable: a query containing some leaf name as a substring scores 83.5%, one containing none 45.2%. A generic 196.6x larger teacher seemed to localize the gap (+20.1 pp without an anchor, +0.1 with). That null was two effects cancelling: the same teacher fine-tuned on the student's own contrastive pairs reaches 0.8586 and beats the pure-encoder student by +10.6 pp with an anchor and +20.9 pp without. The cost is not uniform, but it is not free anywhere; where the anchor is absent, task adaptation buys the teacher nothing, so what the constrained encoder lacks there is capacity. The expensive regime is detectable on-device from the ranker's own score margin: declining the least confident fifth lifts the rest to 0.8296. A second axis we first reported, a manufacturer model code, does not survive source-category fixed effects (-4.0 pp, p=0.51); the anchor does (+13.0 pp). Payload is 2,942,652 bytes, all three library links measured. Tier-0 p95 is 4.431 and 3.670 ms on two iPhones (A14, A16) and 5.080 ms on a budget Android tablet (Snapdragon 695), all slower than three server CPUs on the same code. Taxonomy supervision is mostly synthetic Korean utterances.

Natural turn-taking in full-duplex voice interaction requires determining from partial speech whether a pause reflects hesitation or a completed conversational intent. Acoustic voice activity detection lacks this semantic information, while cascaded ASR-based endpointing introduces transcription dependence and additional processing stages. We formulate semantic endpoint detection as a causal audio-language reasoning task and introduce FD-VAD, an ASR-free streaming endpointer that maps bounded causal audio windows directly to Continue/Stop decisions. FD-VAD combines a frozen speech encoder with a lightweight modality adapter and a parameter-efficiently adapted language model, using a last-chunk training objective for streaming inference. We further introduce confidence-gated endpoint commitment to control interruption versus delay and boundary-focused hard-negative sampling to improve decisions around ambiguous turn boundaries. Across in-domain and conversational evaluations, FD-VAD outperforms strong streaming and non-streaming semantic turn classifiers, and achieves the highest EOT recall among qualifying systems on TurnBench dev set $0.853$ (at FP<=0.10) in a zero-shot setting. These results show that semantic endpointing can be performed directly from streaming audio without intermediate ASR or dialogue state tracking.

While neural theorem provers have achieved impressive milestones in formal mathematics, they largely operate on the assumption that faithful Lean 4 formal statements are already provided. Translating informal natural language into a formal language is a critical data bottleneck plagued by an "illusion of rigor": standard type-checkers accept statements that compile but drop hypotheses, introduce vacuous truths, or subtly alter mathematical bounds. To resolve this, we introduce Sage (Semantic Agent-Guided Formalization Engine), an agentic framework that replaces monolithic translation with a four-stage decomposed generation pipeline coupled with a dual-signal semantic correction loop. By pairing Lean 4 compiler diagnostics with multi-dimensional semantic feedback, our correction loop enforces mathematical fidelity alongside syntactic validity. By explicitly accounting for the gap between open-ended queries and declarative formal targets, our pipeline prevents models from achieving high formalization rates by guessing unverified answers (exhibiting a 70.9% answer leakage rate in monolithic baselines). Consequently, Sage suppresses leakage to 2.7% while achieving 73.3% pass@4 joint compilation and semantic fidelity on the Omni-MATH without proofs (compared to 42.0% for a fine-tuned Goedel-Formalizer-V2 baseline). Finally, on IMO-Unformalized, a novel frontier of 175 unformalized International Mathematical Olympiad problems, Sage demonstrates effective zero-shot generalization with 87.4% pass@4 verified fidelity compared to just 19.4% for the baseline, winning over 79% of blind pairwise evaluations.

We prove that every equal-weight spherical $4$-design on $\mathbb{S}^2$ has at least twelve points. Since the regular icosahedron is a spherical $5$-design, this determines the exact minimum$$N_4(\mathbb{S}^2)=12;$$equivalently, no such design has $9$, $10$ or $11$ points.The proof is part of a finite-defect theory. If a spherical $2m$-design has corank $c=N-\dim P_m$, its Naimark complement consists of unit vectors $u_x\in\mathbb{S}^{c-1}$ forming a spherical $2$-design and satisfying the exact coupling$$u_x\cdot u_y=-\frac{K_m^{(d)}(x\cdot y)}{c}\qquad(x\ne y).$$This gives a pairwise kernel bound, an antipodal lower bound, Cayley-Bacharach information, and uniform lower bounds for multiplicative-relation spaces. In corank one the design splits into two equal spherical $m$-designs. We derive a residue formula for its signed Schoenberg coefficients; the coefficient of degree $m+3$ is negative exactly when $3\le d\le m+1$, excluding corank one throughout that range. At strengths four and six the only examples in any dimension are the regular hexagon and octagon, respectively.In corank two the complement is a circle Gale frame. Multiplication by its phase forces at least $d-1$ linear-quadratic aliases and yields exact norm and socle identities in every dimension. For eleven nodes on $\mathbb{S}^2$, two aliases produce a real harmonic cubic and a Hermitian quartic matrix. A matrix-valued Cayley-Bacharach argument eliminates the generic branch; the exceptional branch reduces to a Pauli normal form and contradicts the second moments. In dimensions $d\ge4$ the corank-two problem remains open; we identify a forced quadratic socle as the obstruction to extending the present argument.

In verifiable domains such as math and coding, finding one correct solution among many attempts can matter more than the pass rate of each attempt. Post-training can concentrate large language model outputs around a few modes, while increasing sampling temperature has limited effectiveness. We introduce Don't Repeat Yourself Supervised Fine-Tuning (DRY-SFT), a post-training method that increases output diversity and coverage: the probability of at least one correct solution among many attempts. DRY-SFT has two stages. First, for each problem, sequentially generate K solutions, showing the model all prior attempts and asking for a different solution. Second, fine-tune on each attempt independently, removing prior attempts from the context. The process uses no reward, verifier, or correctness filter. On HumanEval+, MBPP+, and DS-1000, DRY-SFT raises pass@100 by 10.8, 12.5, and 12.4 percentage points, respectively, at a small cost to pass@1. Structural diversity, measured by abstract syntax tree edit distance among passing solutions, rises significantly on all three benchmarks. DRY-SFT also solves 244 of 600 problems that the base model did not solve in the same 200 attempts. Across nine open-weight models, lower structural diversity of the base model significantly predicts larger DRY-SFT gains, indicating that the method is especially effective on more mode-collapsed models.

Parallel numerical libraries such as PETSc are widely used in science and engineering applications where wrong results can have costly consequences. Despite this, numerical libraries are rarely formally verified. One of the challenges is the need for an expert to hand-write a specification and manually apply a verification tool, often requiring the development of a harness or driver, all of which can contain additional bugs that lead to false positives or false negatives during verification. With recent advancements in large language models (LLMs), it is tempting to generate such drivers and reference models automatically, but one-shot generation based on a simple prompt is brittle and leads to additional unverified code that needs to be audited. In this paper, we present an approach to use LLMs in a limited setting to generate a small, human-certifiable ACSL contract from the function's documentation, combined with a deterministic toolchain that supports a restricted ACSL profile and generates a driver that uses the CIVL verifier to check the implementation against the contract and, when available, an existing reference model. We demonstrate the pipeline end-to-end on three PETSc functions: MatAXPY (reference model already exists), MatAYPX (no reference model, so the certified contract is the sole oracle), and the non-compressing mode of MatFilter (no reference model, with more complex, conditional behavior). With this pipeline, we were able to discover a bug in PETSc's MatAYPX function that was previously undiscovered and had been present in the code since 1997.

Existing aviation emissions inventories lack accurate trajectory data for high-resolution social cost and health impact assessment. This paper develops a 3-D emissions map by reconstructing flight trajectories for US west coast hubs to estimate regional environmental and near-airport health impacts. A physics-informed autoencoder (AE) is applied to ADS-B trajectory records for January 2025 covering US west coast hubs. The encoder combines a Convolutional Neural Network (CNN), a Bi-GRU, and a 3-D CNN with skip connection; the decoder is a Temporal Convolutional Network (TCN). It is benchmarked against a baseline-AE and cubic spline interpolation. Emissions are mapped via EUROCONTROL Base of Aircraft Data (BADA) performance tables and ICAO Engine Emissions Databank (EEDB) emission indices, with altitude corrections via Boeing Fuel Flow Method 2 (BFFM2). Social costs are quantified for all flight phases, with health impacts assessed for Landing and Takeoff cycles within 50 km of each hub. The proposed AE model outperforms both a TCN-AE and cubic spline interpolation across 5% to 50% missing rates. Monetizing the emissions inventory shows NOx produces a small net cooling effect in direct climate forcing, while accounting for 99.7% of monetized air-quality and health cost despite being under 0.4% of CO2 by mass, making it the dominant health-cost driver. To our knowledge, this is among the first studies combining AE-based trajectory reconstruction with separate spatial-temporal feature encoding and altitude-based emissions modeling to produce a regional aviation emissions inventory for air quality, climate impact and population exposure. The resulting emissions map and social cost estimates provide quantitative context for environmental impact assessment and near-airport health policy evaluation for US domestic aviation.

Diffusion language models (DLMs) enable flexible, parallel generation, but their iterative denoising remains computationally expensive, motivating increasingly aggressive compression. Existing compression objectives largely measure how well compressed computation approximates the original locally, but local error does not reveal which removed computations actually matter to the downstream denoising trajectory. We introduce Same-State Causal Restoration (SSR), which restores the original FFN on the exact current input reached by the compressed model and measures how the resulting trajectory changes. To our knowledge, this is the first direct measurement of the same-current-input closed-loop effect of removed FFN computation in DLM compression. Across LLaDA-8B-Instruct and Dream-v0-Instruct-7B, compressed-side state ranks this downstream effect substantially better than local NMSE at fixed denoising phase, while controlled interventions show that correction structure matters beyond magnitude. Using task-label-free calibration, SSR freezes a single restoration window for held-out inference. Under aggressive LLaDA compression, restoring only four transitions recovers 89.9% of the lost accuracy while retaining an estimated 36.8% whole-model MAC saving and outperforming an equal-budget local-error baseline. Dream further shows that restoring dense behavior and repairing the final task are distinct outcomes.

Retrieval-Augmented Generation (RAG) introduces a specific failure mode in discrete diffusion language models: when retrieved context contradicts parametric knowledge, the iterative denoising process becomes a visible battleground between competing knowledge sources. We identify temporal semantic divergence as an observable for detecting these conflicts and introduce the Trajectory Variance Score (TVS), a simple and interpretable measure of this divergence. TVS computes the mean pairwise cosine distance of answer embeddings across independent stochastic denoising trajectories, capturing the temporal tug of war between parametric and contextual attractors. Requiring as few as two parallel inference runs, TVS is computationally lightweight. Across four diverse datasets (Synthetic, SciQ, PopQA, and CounterFact), a simple Logistic Regression classifier using TVS achieves $70.10\%$ accuracy and $0.7647$ AUROC on LLaDA. On Dream 7B, increasing the number of trajectories from two to five improves accuracy from $63.91\%$ to $69.62\%$. More complex sequential models provide only marginal improvements over the linear classifier. Evaluation across LLaDA and Dream 7B demonstrates that conflict-induced trajectory dynamics and their key properties transfer across distinct diffusion architectures.

This work presents an end-to-end demonstration of autonomous machine learning research conducted by an agent skill on consumer hardware. The demonstration evaluates an FFT-based Kernel Ridge Regression (KRR) solver for regular spatial grids using 2005 monthly NOAA Kaplan SST v2 anomaly fields on a $36 \times 72$ grid. This was autonomously executed by DeepSeek V4 Flash, orchestrated by our agent skill suite within DeepSeek Harness (DSH). Experiments were executed on CPU-only hardware (Apple M2 Pro; 78.7 s solver time, 1.57 GB peak RSS). Long-horizon state was decoupled into a file-based epic- and issue-tracking substrate. Across 74 sub-agent sessions, the agent demonstrated closed-loop scientific resilience: routing two failed hypothesis review gates back to literature retrieval, patching bootstrap indexing bugs, and executing with only four discrete human steering events. Finally, we reflect on autonomous research governance, arguing that scientific credibility requires inspectable state, falsifiable review gates, and transparent reporting of negative results, urging the machine learning community to favour agent-accessible structured formats over static PDF manuscripts.

More than 80 countries have reported malaria cases with 610 thousand deaths and are projected to increase. Identifying malaria early and accurately helps save lives and effective way to diagnose malaria is through microscopic methods that are labor intensive and require experts with special equipment. Deep learning (DL) has shown promising results in medical diagnosis. Here, we explored various DL models: ResNet18, MobileNetV2, EfficientNet-B2, VGG19 and proposed model ResNet18+TTA (ResNet18 backbone with modified classification head and test time augmentation) for detecting malaria presence using blood smears taken from the NIH Malaria dataset. Our experiment shows MobileNetV2 achieved 96.85 % accuracy with smallest model size (8.49 MB) and fastest inference (1.35 ms). The ResNet18+TTA model achieved 97.96 % accuracy, 0.996 AUC with longest inference time (13.32 ms). Larger architecture outputs a larger model size with moderate accuracy. Upon further pruning, ResNet18+TTA model gained a slight improvement in accuracy and reduced inference time. GRAD-CAM, SHAP and LIME provide explainable AI (XAI) insights into model predictions, using explanation agreement and divergence to evaluate predictive reliability.

Devnagari is a one of the ancient language of the Indian subcontinent consisting of 36 vowels, 14 consonants and 10 numerals. The accurate recognition of handwritten Devnagari characters is challenging due to high complexity of Devnagari scripts. This paper presents a method to fine tune the pre trained TrOCR model to accurately recognize Devanagari handwritten characters. The Methodology consists of a preprocessing mechanism where input images are standardized into RGB format, tokenized in batches and integrated with Hugging Face Dataset. The pre-trained microsoft/trocr-base-handwritten model is fine-tuned over a dataset of nearly 5000 character images that are uniformly partitioned in the ratio 8:1:1 for training, evaluation and testing. Further optimization is done is the training process through mixed precision training, gradient checkpointing, and early stopping mechanism. The model achieves a character error rate (CER) of 3.95% and a character-level accuracy of 96.05%, outperforming the previous CNN based models. A scalable web application is developed using Vite.js, Golang, and FastAPI which practically deploys the OCR model and serves character recognition task with a latency less than 5 seconds per request. This study demonstrates the use of TrOCR model to build a scalable handwritten Devnagari character recognition system and also a foundation to future research on Devnagari Script Recognition using Transformers.

Joint-embedding predictive architectures (JEPA) have emerged as a promising self-supervised pretraining paradigm for time series, learning representations by predicting target embeddings in latent space rather than reconstructing raw signals. Yet evidence on their benefits remains mixed, and most studies test only a single backbone or a narrow set of architectures, leaving unclear whether JEPA pretraining is a reliable improvement or one that depends heavily on the downstream model. We address this gap through a large scale evaluation of one JEPA instantiation across nine backbones and eleven benchmarks spanning temporal and spatio-temporal forecasting, the most extensive cross architecture assessment of JEPA for time series to date. We find that the benefit of this instantiation varies sharply across backbones, producing consistent gains for some architectures and consistent degradation for others, even on the same dataset. This pattern holds across both task families, indicating the variability is a general property of this instantiation rather than a dataset specific artifact worth accounting for when choosing a backbone in practice.

Coccidiosis caused by Eimeria parasites is a major economic burden in poultry production, and effective control depends on accurate species-level diagnosis. This study evaluates whether a general-purpose multimodal large language model can support such diagnosis. Google Gemini was assessed on 4,225 mi- croscopy images covering the seven fowl-infecting Eimeria species under two prompting conditions, one without candidate labels and one with a predefined class list, and was further tested for pathology-report generation, while BiomedParse was examined for parasite segmentation. Without candidate labels, the model produced broad and taxonomically inconsistent outputs. With candidate labels, overall accuracy reached only 14.9%, with a strong bias toward E. tenella at 74% and no correct classifications for E. acervulina, E. mitis and E. praecox. Generated treatment reports were coherent but unverified, and segmentation was only partial. Current multimodal models are therefore not yet reliable for standalone Eimeria diagnosis without domain-specific fine- tuning and expert validation.

KV cache compression is widely used for long context LLM inference under memory constraints, while deployed systems typically score refusals after generation with keyword filters or learned classifiers. Such monitors are intended to indicate whether a model declined a harmful request under the serving regime actually used. However, it remains unclear whether matched compression that preserves task accuracy also preserves agreement between lightweight lexical monitors and stronger refusal classifiers. We study this with a paired protocol on n=200 harmful prompts with a long filler context: each prompt is answered once under full retention and once under matched eviction after a shared prefill, and the same replies are scored by keyword heuristics, the HarmBench Llama-2-13B classifier, an auxiliary LLM judge, and humans on disagreements. On Qwen2.5-3B, keyword refusal falls from 98.0% to 80.5% (McNemar p~1e-8) while classifier refusal stays near ceiling (99.0%-99.5%) and MMLU accuracy is unchanged (50.0%); human labels predominantly follow the classifier, consistent with soft refusals. The gap is not universal and weakens under short fillers and paired SnapKV, so safety auditing under compression should rely on several judges matched to the serving context rather than on keyword rates alone.

Face recognition is widely deployed in surveillance, access control, and forensic workflows, yet accuracy degrades sharply once the face is occluded by accessories, foreground objects, or the frame edge. Because most faces in the wild are partial, robust partial face recognition (PFR) remains open. This paper compares three pretrained convolutional backbones, ResNet-50, VGG-16, and FaceNet, fine-tuned for PFR by transfer learning under identical preprocessing, splitting, and optimization protocols on the Specs-on-Faces (SoF) dataset. All three arms use a common 160x160 input and a frozen backbone with a trainable head under a fixed epoch budget and no per-backbone hyperparameter search. The FaceNet configuration, denoted PFN (Partial FaceNet), substantially outperforms the other two, reaching 97.4% test accuracy with macro-averaged 87.04% precision, 84.61% recall, and 84.17% F1 over the 112 identity classes, the highest accuracy and recall reported on SoF.

Public speaking is an essential skill in academic and professional contexts, but it often causes anxiety. Although several AI-based speech coaching tools exist, they typically provide generic feedback and lack model speeches for learning. This study addresses these gaps by developing a system that incorporates speech context into evaluation criteria, enabling more tailored feedback. It also generates improved model speeches in both text and audio formats to support example-based learning. The system was evaluated in a pilot study with seven undergraduate students over one to three weeks. Participants used the system repeatedly and practiced the same speech at least three times. Results showed improvements in public speaking performance for all participants. Filler word usage decreased, and anxiety levels dropped by 15.3% to 34.4%. Participants found the context-aware feedback and revised speeches useful and confidence-building. These findings suggest that context-aware feedback and model speeches can enhance public speaking skills and reduce anxiety. Future studies could explore video-based analysis of physical behavior during speeches.

We introduce the Active Causal Discovery Benchmark (ACDB), an SCM-grounded environment for evaluating whether LLM agents recover causal graph structure from observations and budget-constrained hard interventions. ACDB pairs a linear-Gaussian world generator with a fixed observe-intervene-submit API and a three-layer scoring contract that separates skeleton recovery, DAG recovery, and intervention efficiency. On the current six-level ladder, PC with a greedy active orientation heuristic is the strongest non-oracle method (directed F1 42.7%, SHD 4.79), ahead of Claude Sonnet 4.6 raw active (31.7%, 7.25) and GPT-5.4 raw active (22.9%, 9.27). The most informative diagnostic is the precision-recall decomposition: PC under-commits with high precision, LLMs over-commit with lower precision, and statistical-tool access often increases abstention rather than useful intervention. A structure-blind random DAG baseline reaches 23.6% directed F1 on this dense v0 ladder; a density probe lowers this floor to 16.9%, motivating the v1 calibration pass. The current results should therefore be read as a benchmark audit and calibration report, not as evidence that current LLMs solve active causal discovery.

A majority C-colouring partitions a graph into classes in which every vertex has at least half of its neighbours. Write $M(G)$ for the maximum number of classes. We determine $M(K_q^{\square(2k+1)})=\left\lfloor\frac{q^{k+1}}{\lfloor q/2\rfloor+1}\right\rfloor\qquad(q\ge3,\ k\ge0).$ The lower bound follows from explicit rectangular partitions and a uniform three-dimensional bridge. A punctured-rectangle construction supplies both the bridge and a partition in the intermediate dimension. The upper bound is a classical consequence of Hamming edge isoperimetry; an elementary proof is included. We also prove $M(C_m\square P_n)=\frac n2\lfloor m/2\rfloor$ for $m\ge4$ and even $n\ge2$, contradicting the cylinder assertion of Conjecture 4 in arXiv:2608.27669v1 for odd $m\ge7$ and even $n\ge6$. Further layer bounds determine additional cylinder and torus families.

Agentic speech systems must exchange more than text, including speaker identity, timing, phonetic information, and behavioral annotations. Yet these signals are often produced in incompatible tool-specific formats, making agent-to-agent handoff fragile. We present OneVoice, a lightweight, JSON-native intermediate representation that provides a shared semantic structure for speech pipelines. OneVoice organizes heterogeneous speech evidence into validated session records with stable identifiers, layered transcripts, explicit timing relationships, and provenance information. We evaluate OneVoice in two complementary multi-agent workflows covering event aggregation and acoustic-phonetic temporal linking across three language models. Compared with implicit agent-defined handoffs, OneVoice substantially improves aggregation reliability and the preservation of temporal relationships, demonstrating the value of an explicit speech-specific representation for agent communication.

Systematic reviews (SR) are essential for evidence-based research, but their screening phase is highly time-consuming and labor-intensive. Large language models (LLMs) offer a promising opportunity to reduce this workload by assisting with article relevance classification. However, existing evaluation approaches often rely on traditional metrics that may be misleading for highly imbalanced SR screening datasets. This paper presents a benchmark dataset of $45\,064$ labeled entries for evaluating LLM performance in SR screening across 32 curated secondary studies. It proposes an evaluation framework that accounts for class imbalance, i.e., the natural prevalence of excluded articles relative to included articles in SRs. It also introduces PromptSR, a tool designed to support prompt experimentation, experiment management, and result analysis for LLM-based screening. We also present a use case demonstrating the application of SRBench and PromptSR.

Conversational recommendation agents are a new paradigm for content discovery, enabling users to express complex intents through natural language (e.g., "recommend Italian indie artists I haven't heard before"). A central challenge in building such agents is optimizing agent planning – deciding how to select, sequence, and invoke tools – particularly in cold-start settings where real user interactions are not yet available. We introduce a pipeline for multi-turn synthetic data generation and a self-improvement loop to address this challenge. The synthetic data pipeline transforms single-turn prompts into realistic multi-turn conversations, enabling systematic evaluation before launch. The self-improvement loop combines variance-based contrastive optimization with iterative refinement through a coding agent, automatically identifying and fixing planning and tool-use errors. Our approach improves quality by +8% on top of a highly optimized manual prompt. The system has been productionized and significantly accelerated iteration cycles for the launch of a conversational recommendation agent at Spotify. Online A/B tests demonstrate its effectiveness, with +14% user listening, +5% increase in weekly active users, and a 5% reduction in skip rate compared to a prior experience supporting only session refinement. This work provides a practical framework for accelerating the development of conversational recommendation agents in industry.

We investigate matter creation in the cosmological framework of unimodular gravity. We keep the energy density $\rho$, pressure $p$, particle number density $n$, and particle number $N=nV$ as the physical thermodynamic variables of the matter sector, and introduce particle creation directly through the balance equation $N^{\mu}{}_{;\mu}=n\Gamma$. Combining this open-system formulation with the unimodular diffusion term $Q$, we derive the exact identity $nT\dot\sigma=-3Hp_c-(\rho+p)\Gamma-\dot Q$, which shows that the creation pressure $p_c$, the creation rate $\Gamma$, and the diffusion term $Q$ are, in general, three independent sources of entropy production per particle. Adopting the standard postulate that particle creation is itself adiabatic, the first two terms cancel identically and the relation reduces to the particular case $nT\dot\sigma=-\dot Q$, so that the entropy per particle is constant only when $Q$ is constant. Thus, even when the creation process associated with $\Gamma$ is adiabatic in the usual Prigogine sense, the full matter evolution in unimodular gravity is non-adiabatic whenever $\dot Q\neq0$. The general identity, however, remains available as a starting point for relaxing this postulate in future work.

TW3Cast is a time-series forecasting system that reaches position 3 of 130 entries on the GIFT-Eval benchmark by mean MASE rank, as of 2026-09-14. The two entries above it belong to the leaderboard's agentic category, multi-step systems that use agents or language models to reason about, generate or select forecasts. TW3Cast runs no agent and no language model. Its selection is a table computed once on the training split and then frozen, and its experts are public foundation models lightly fine-tuned on those training splits. For each of the 97 dataset, frequency and horizon configurations, the table serves one of four modes: a specialist, which is a LoRA or full fine-tune of Chronos-2, TiRex or Toto whose training data was cleaned and enriched by explicit rules; a quantile blend that contains a specialist; a blend of base models; or a selection tournament played on a backtest carved from the training split. Every decision in the table was taken on that backtest. A specialist is admitted the moment it beats the tournament there, so a candidate costs a few megabytes and minutes of GPU time, and a failed candidate changes nothing. Three guarded mechanisms protect the selection from its own biases: a dual accuracy and calibration criterion, an asymmetric margin against candidates that saw the series during training, and conservative per-window gates. The selection rules themselves were chosen inside a temporal meta-backtest. The best base model served alone reaches a mean MASE rank of 33.8, the tournament served on every configuration reaches 38.0, and the full router reaches 19.4. The routing table, the expert index, the pinned base-model revisions, the submitted score file and the dated snapshot of the public scores are released, and every leaderboard number in this paper regenerates from them by one script.

Let $\mathbb{A}=\mathbb{R}1_{\mathbb{A}}\oplus\mathfrak{m}$ be a Weil algebra with $\mathfrak{m}^{N+1}=0$. We study the exponential geometry of the proper orthogonal group $\mathrm{SO}(3,\mathbb{A})$ through finite Weil prolongation. An exact Rodrigues formula is obtained for every element of $\mathfrak{so}(3,\mathbb{A})$, and the exponential map $\mathfrak{so}(3,\mathbb{A})\to\mathrm{SO}(3,\mathbb{A})$ is proved to be surjective. Although every proper orthogonal Weil tensor is therefore exponential and has an unnormalized Rodrigues representation, a factorization of a generator into one scalar angle and one unit axis may fail above the identity; the obstruction is established for every logarithmic branch, including scalar angles $2k\pi$. The analytic mechanism is an explicit finite-regularity rigidity theorem: an $\mathbb{A}$-holomorphic map on $U+\mathfrak{m}$ with scalar-valued real trace is uniquely its finite Weil jet. Together with functoriality, this yields exact transfer of functional, matrix, orthogonality, and composition identities. The results provide a rigorous basis for dual, multidual, hyper-dual, and hyper-multidual calculations in theoretical and computational kinematics.