Papers

Historical archives are an under-used source for extending the instrumental climate record backward in time, and LLMs offer a way to extract the indices climatologists derive by hand. Beyond measuring how well systems extract this signal, we check whether their errors are safe to use for cross-century comparison, since a good correlation score does not rule out systematic, era-linked bias. Comparing lexical baselines, fine-tuned historical transformers, and LLM prompting on the Pfister temperature index across five centuries of German text, lexical methods beat every fine-tuned transformer we test, including one pretrained from scratch on historical German (r=-0.016). All six LLMs we test (Gemini 2.5 Flash, GPT-5-mini, DeepSeek v4 Flash, Claude Sonnet 4.6, Qwen3.7-Plus, Kimi-K2.6-Fast) show a warm bias that grows with calendar year, with the same sign in every model (slopes +0.13 to +0.34/century, p<0.01). The effect is modest in size (r-squared approx equal to 0.01 to 0.05) but consistent across six independently developed models. The best-correlated of the six, Gemini 2.5 Flash, matches the best lexical correlation (r=0.32) at double the error. An ablation stripping explicit dates and calendar-era markers from the quotes leaves this trend essentially unchanged, favoring an anachronistic present-day prior over the model correctly inferring the quote's era. Correlation alone is thus insufficient for vetting an LLM as a historical-climate-index oracle.

Wikipedia aims to provide a unified, neutral record of history, yet its independent language editions often function as distinct epistemic communities, creating divergent narratives around contested events. This paper investigates cross-lingual historiographical bias by analyzing Wikipedia articles across five languages (Romanian, Hungarian, Russian, Turkish, and English) focusing on three contentious events in Romanian history: the Battle of Posada (1330), the Soviet occupation of Bessarabia (1940), and the Night Attack at Targoviste (1462). Using human annotators and Large Language Models (LLMs) to classify citation stance and quantify narrative evolution from 2005 to 2024, we identify a phenomenon of "citation isolation". In the case of the Battle of Posada, only 2 out of 119 citations were shared between language editions, with the Romanian edition exhibiting a 91% pro-national bias compared to the balanced Hungarian edition. Longitudinal analysis reveals that these narratives are volatile and responsive to contemporary geopolitics, evidenced by a significant shift in the Russian framing of Bessarabia in 2024. Finally, we propose a "Peace-Maker" pipeline to automate conflict reconciliation. We demonstrate that while standard prompting leads models to hallucinate consensus, "adversarial" prompting, which explicitly instructs the model to preserve and attribute disagreement, achieves near-perfect neutrality scores.

Modern transformer models excel at capturing semantic relationships through sentence embeddings, yet their ability to perform pragmatic reasoning remains understudied. This paper investigates whether encoder-based transformers such as DeBERTa employ the M-Heuristic (the neo-Gricean principle that marked linguistic forms implicate marked meanings). We test this hypothesis by contrasting lexical causatives (e.g., “Larry stopped the car”) with periphrastic causatives (e.g., “Larry caused the car to stop”) using a Natural Language Inference framework. Our experiments across 188 conditions with 15 ambitransitive verbs reveal that DeBERTa, RoBERTa, and BART show no evidence of capturing the pragmatic distinction between these forms, with DeBERTa predicting “Neutral” for 100% of cases. Probing analysis initially suggested a representation-use dissociation, but control experiments reveal the probe was tracking syntactic complexity, not causative pragmatics. Semantic similarity over 30 triplets places periphrastic causatives closer to unmediated manner descriptions in 29/30 cases, opposite to M-Heuristic predictions in the embedding space. Under explicit metalinguistic framing, Gemini Flash-Lite reaches 100% with item-specific traces, so the principle is available under instruction yet unused in default NLI.

Serving an answer from a large language model requires deciding when to abstain, yet a verifier's ranking accuracy alone does not determine the error rate among served answers. We introduce PriceCheck, which builds a compact family of decision rules from label-free checks such as re-solving a problem. Each check has a price: its agreement rates on correct and incorrect answers and its cost per run. Prices fitted on a small, class-enriched labelled set compose into predictions of a schedule's coverage and cost, guiding which checks to run and when to stop. A calibration test then selects a schedule at a stated selective-risk target. In mathematics, the selected schedules serve 76.1% of answers on average and keep held-out selective risk below 1.5% on all 15 splits. Under the shared testing protocol, PriceCheck serves more answers at that target than reward models, a prompted judge, the generator's confidence and a trained correctness classifier. At matched coverage, it keeps the fewest wrong answers among these scorers. Across 118 diagnostic schedules, price-based coverage predictions have a rank correlation of 0.97 with observed coverage. These results show that choosing how checks are combined and stopped matters alongside how well a verifier ranks answers. Code is available at https://github.com/js-lee-AI/PriceCheck.

In facility location problems, planners can reduce demand uncertainty by collecting data, but these actions are costly. In this paper, we ask how a planner should jointly decide where to open facilities and invest in demand learning, which comes with a cost. The challenge is that learning changes how future random costs should be evaluated, creating a model that is both endogenous and nonlinear in location decisions. We model this problem within a two-stage stochastic framework, where both location and learning decisions have to be made here-and-now. Under some mild assumptions, we obtain a closed-form reformulation, which further enables a theoretical analysis of the sensitivity of learning decisions to model parameters and design of convergent solution algorithms that alternate between updating location and learning decisions. Numerical experiments on benchmark instances show that learning is most valuable when initial demand uncertainty is high, learning is effective, and learning costs are low. Moreover, the proposed solution algorithms find high-quality solutions much faster than exhaustive search and a standard commercial nonlinear solver. These findings show how information-acquisition decisions can be built directly into strategic facility planning. They help decision makers target limited learning resources where better demand information has the greatest value.

Frozen multimodal large language models (MLLMs) now solve standard referring expression comprehension with a single prompted call, yet on adversarial benchmarks with same-category distractors and negation, even the largest models are confidently wrong, and resampling repeats the error. Models built from different data and architectures rarely fall for the same confounder, so their agreement is a strong label-free signal of the correct target. We present FORUM, a training-free test-time fusion of frozen MLLMs guided by two fixed geometric rules: agreement-based selection keeps the region supported by the most distinct models, and medoid localization returns an actual member box instead of a coordinate average, so one loose prediction cannot shift the answer. Fusing three open MLLMs, FORUM surpasses the 397B-parameter published reference by a relative 5% in mean accuracy on the adversarial Ref-Adv-s benchmark, and a plain averaging ensemble by 15%. The gains transfer to standard RefCOCO+, and a balanced lineup with no dominant member still surpasses the 397B model by 5%.

Precipitation nowcasting, generating future radar fields from past observations, is critical for flood warning and disaster response. It is also a demanding benchmark for spatiotemporal generative modeling, with chaotic dynamics, heavy-tailed intensities, and rare high-intensity structures that matter most. Deterministic models minimize a pixel loss and are driven toward the conditional mean, which blurs exactly those structures, while generative models that add a stochastic residual on top of a deterministic backbone inherit the same blur. We propose Physics-Guided Flow-Map Matching (PG-FMM), a conditional flow-map model that decouples predictable advection from uncertain small-scale detail. A frozen Lagrangian advection prior transports the radar field and supplies an explicit motion forecast, and a flow-map generative head, conditioned on the past frames and the prior rollout rather than summed onto it, produces sharp stochastic detail in four sampling steps. The prior serves only as guidance, so the head replaces blurred structure instead of inheriting it. Extensive experiments on four radar benchmarks show that PG-FMM outperforms state-of-the-art methods on 18 of 24 metrics, with the largest gains at heavy-rain thresholds, where the critical success index improves by up to 58.9%. The project page can be found at https://neurogica.github.io/PG-FMM.

We present an autonomous model to simulate the daytime variation of sub-ionospheric Very Low Frequency (VLF) signal amplitude, beginning with the computation of the D-region electron density by numerically solving the electron continuity equation (ECE). From the resulting altitude-dependent electron density profile (Ne), we extract Wait's ionospheric parameters (h' and beta) using a log-linear fitting method. The study focuses on two VLF propagation paths (one short and one medium in length) in India, originating from the VTX (18.2 kHz) transmitter. The model employs the Long Wave Propagation Capability (LWPC) framework to reproduce the daytime VLF signal amplitude profile. It accurately captures the daytime variations observed at the Bengaluru (BAN) station, where the ground-wave component is dominant, as well as at Khukurdaha, WB (KHK). A quantitative comparison between the simulated (Asim) and observed (Aobs) amplitudes shows good agreement, supporting the physical consistency and potential predictive capability of the proposed approach.

Bi-temporal change understanding, which localizes and characterizes what changed between two satellite images, is central to disaster response and environmental monitoring, spanning change detection, building localization, and damage assessment. Strong vision-language models address these tasks, but adapting them typically requires full fine-tuning or reinforcement learning, which is costly and unstable. We propose PoE-Fuse, a parameter-efficient framework that instead composes frozen foundation experts for geometry, grounding, and language, resampling their features onto a shared spatial grid and training only a lightweight fusion trunk. PoE-Fuse treats the aligned features as Gaussian observations of a latent scene state and fuses them by learned per-cell precision. This product-of-experts estimator strictly generalizes uniform summation and scalar gating, and extends to change fields by composing the precisions of the two timestamps. A single shared trunk solves the three tasks at once, reaching a mean F1 of 59.2%, compared with 40.7% for an instruction-tuned temporal vision-language assistant, and surpassing dedicated change-detection models retrained under the same protocol and training budget.

Jananthan and Simpson showed that special $\Pi^0_1$ classes exist in three of the four possible cases determined by whether the Join Property and the Pseudojump Inversion Property hold, leaving open the existence of a special $\Pi^0_1$ class with the Join Property but not the Pseudojump Inversion Property. We construct such a class, thereby answering their question affirmatively and completing the four-way existence pattern. Moreover, the class can be chosen to consist entirely of generalized low reals, with the Join Property holding locally on every nonempty relatively basic open subclass. More generally, every special $\Pi^0_1$ class contained in $\mathrm{GL}_1$ has a special $\Pi^0_1$ extension, still contained in $\mathrm{GL}_1$, on which the Join Property holds locally. We also show that no class contained in $\mathrm{GL}_1$ has the Pseudojump Inversion Property. An independent appendix proves that, for any class with the Join Property, every jump-inversion fibre above $0'$ is countably infinite.

Jananthan and Simpson asked in Conjecture~4.5 whether every pseudo-hyperjump $\operatorname{HJ}_e(X)=X\oplus V_e^X$, with $V_e^X$ uniformly $\Pi^1_1(X)$, admits Turing-degree inversion above Kleene's $\mathcal{O}$. We settle their conjecture in the negative. We construct one index $e_*$ such that $X<_{\mathrm T}\operatorname{HJ}_{e_*}(X)$ for every real $X$, while the range of $\operatorname{HJ}_{e_*}$ omits every Turing degree $\mathbf d$ such that $\deg_{\mathrm T}(\mathcal{O})\leq\mathbf d<\deg_{\mathrm T}(\mathcal{O}^{\mathcal{O}})$. Thus Conjecture~4.5 fails even for an operator which strictly raises the Turing degree of every input. Each of Properties~4.6–4.8 implies Conjecture~4.5; consequently, the accompanying class-characterisation problems collapse: no class of reals, even without a definability assumption, satisfies any one of these properties.

We test whether a multivariate vector X conforms to a specified distribution F, as in copula modelling and density forecasting. The Rosenblatt transform reduces this to testing uniformity, but its arbitrary coordinate ordering affects power under dependence. We study order randomization: transforming under many random orderings and merging evidence with dependence-robust rules. Reordering only redistributes the Mahalanobis signal energy, so one ordering is a lucky or unlucky draw, and pooling raises calibrated power. We compare against two order-invariant baselines, the chi-squared energy test and the symmetric-root test. With F known, the e-value average over orderings is at least as powerful as the symmetric-root test in every setting we ran, and as the chi-squared test on concentrated and fully diffuse departures. With Gaussian mean and covariance estimated, the classical conditional probability integral transform keeps each ordering's p-values exact and e-values valid, a parametric bootstrap calibrates the pooled tests, and the comparisons hold except for deficits of at most 0.02 against the symmetric-root test on single-coordinate departures. Validating a Gaussian risk model for nine currencies, the test flags Brexit, COVID and other episodes; it extends to any null with computable, simulable conditionals.

Equivalent probability requests can lead to different decisions even when both reports are valid. We introduce probability contracts, a benchmark that connects exact finite-world posteriors, validated event alignment, interface coherence, and failure-aware decision evaluation. Across four model-interface configurations on 1,000 worlds, Kev has lower aggregate canonical posterior error than Jev but larger complement and coarsening residuals; accuracy ordering varies by stratum. Jev's Event and Choice interfaces change the binary action on 32.8% of valid pairs at defer cost 0.10. Post-hoc analyses show that disagreement certifies only 11-52% of mean binary pair error and does not consistently outperform confidence for selection. An action-region characterization and a standard scoring-rule identity explain averaging's expected Brier guarantee relative to random interface selection, but not a decision-loss guarantee at each cost. The loss contrast takes both signs on a 99-cost grid for every configuration; small penalties where both policies beat deferral have pointwise intervals containing zero. Secondary checks specified before collection include a separate 400-root cohort, where Event/Choice effects remain configuration-dependent. A joint surface-order and answer-ID intervention shifts posttrained probabilities. Both bounded reasoning arms yield no valid probability reports, leaving their probability accuracy undefined. Probability contracts make these distinctions measurable by evaluating event semantics, posterior error, coverage, and decision cost together.

Retrieval-augmented generation (RAG) grounds large language models in external sources, but retrieved passages often name the right entities without providing the facts needed to answer. Even when instructed to abstain, 12 generators answer 40.0-99.3% of insufficient-evidence questions. Training generators to abstain ties the decision to model weights, may reward answers recalled from parametric knowledge, and still requires a full generator call. Can sufficiency be judged from the question and evidence alone, before any answer exists? We identify pitfalls in constructing insufficient-evidence tests: removing relevant evidence or pairing evidence with unrelated questions can reveal labels through lexical overlap or evidence position. We build a paired benchmark using substitution, deletion, and question-swap constructions that vary answer support while controlling selected surface features, such as word use. Sufficiency can be judged without generating an answer, but no single signal works across all datasets. We introduce RINSE (Relevance Is Not Sufficient Evidence), which combines three signals: whether every part of the question is covered, whether any passage offers an answer, and whether a small language model reading the passages together judges them sufficient. Across six datasets, RINSE ranks sufficient above insufficient evidence with a score of 0.837 (chance 0.5), exceeding the best of 10 prior methods (0.746) and a frontier model queried through an API (0.784). Its weakest dataset scores higher than any other method's weakest (0.684 vs. 0.676). RINSE runs locally before generation, taking 36.5 ms per question on a single GPU.

Counting completed wingbeats requires identifying individual cycles, including during frequency changes and pauses; estimating a dominant frequency alone is insufficient. Camera motion further mixes target and background brightness changes in event observations. We present a controlled MuJoCo benchmark that separates motion training from event-only image translation compensation. The acquisition contains 324 streams from 24 independent scenes, three flapping geometries, two distances (1.5 and 3.0 m), and static, moderate-motion and stronger-motion views. Fifteen scenes are used for fitting, three for validation and six for held-out testing. A fixed causal temporal convolutional network is evaluated in a matched 2 x 2 ablation with three initialization seeds and compared with ridge, Fourier, autocorrelation and an adapted EEPPR baseline. Under moderate motion, paired motion training reduces count mean absolute error from 31.130 to 3.185 cycles at 1.5 m and from 42.019 to 5.444 at 3.0 m. Adding the tested compensation increases these errors to 4.630 and 10.185, respectively. A Fourier baseline achieves 0.944 cycles at 1.5 m under moderate motion, showing that the neural model is not uniformly best. We report exact-count accuracy and temporally matched cycle F1 alongside count error. These findings support motion-aware training in this small synthetic benchmark, while exposing limits of simple event-background stabilization. They do not establish real-sensor performance, aerodynamic flight, or generalization to unseen vehicle types.

The honeybee waggle dance motivates a communication mechanism in which one agent's motion guides the subsequent work of other agents. For aerial robots, realizing this mechanism requires a link from observed movement to a complete message, local task selection, and execution. This paper presents a MuJoCo system for comparing RGB and synthetic event vision within that link. One performer broadcasts six-bit task offers to one to three observers, each of which independently decodes both offers before selecting a task. The RGB receiver extracts trajectories using sparse optical flow; the event receiver uses only local event support and packet timing. Both use a common motion alphabet and explicit null delimiters. Because event silence does not establish target visibility, the event version includes a physical acquisition motion and continuity-qualified null confirmation. In the nominal three-observer case, each version produced 12 complete message receptions, six completed work units, and reassignment after withdrawal of a depleted task. Six paired functional cases produced the same message and work counts; an additional event-stream dropout case preserved inactivity of the affected observer. Replaying 42,060,633 recorded synthetic events reproduced all 12 event-message payloads and completion timestamps. Total nominal mission time was 493.80 s for RGB and 517.40 s for events, with the difference dominated by the event acquisition schedule. These fixed simulation results establish functional feasibility across two receiver implementations, rather than a sensor-performance advantage or hardware validation.

For a fixed modulus h and residue class c, we study the logarithmic mass of primes p in a fixed power band for which the exponent of p in n! is congruent to c modulo h. We establish the asymptotic ((b-a)/h + o(1)) log(n!) for primes satisfying n^a < p <= n^b, where 0 <= a < b <= 1. The argument combines a fixed-order derivative estimate, Vaughan's identity, and finite Fourier approximation of a discontinuous valuation function. We also derive a necessary capacity condition for infinite families of solutions to polynomial-factorial equations P(x) = n!.

Robotic ultrasound commonly targets standardized views, predefined scanning protocols, or expert-scan reproduction. We target a different role: while a clinician performs the primary procedure, a robotic assistant maintains a clinician-selected view so that changing tissue remains observable. We present contact-adaptive robotic ultrasound monitoring derived from robot-free demonstrations. Sonologger clamps a six-axis inertial sensor to the clinician-operated probe and records synchronized ultrasound and probe-frame relative rotations without a robot, camera, or tracker. Rather than imitating trajectories, the recordings measure which probe axis and sign the clinician uses to correct an image offset. A measured image latency is removed before still-move-still segmentation yields relative-rotation labels; translation is excluded from control because of inertial drift. These measurements parameterize the Demonstration-Informed Image-Motion Controller (DIMC), an interpretable, non-learned controller combined with beam-axis force regulation and an independent safety supervisor with 5 N forced retreat. On a dynamic bladder phantom, DIMC acquired and held a task-relevant view in 7 of 7 blind, pose-paired trials versus 1 of 7 for a static hold (McNemar p = 0.031), and retained the view during syringe-driven hydro-distension while the supervisor bounded the force excursion. The framework offers an operational representation of ultrasound context for contact-adaptive intraoperative monitoring; clinical validation remains future work.

High-performance surgical master consoles offer intuitive articulated manipulation but are expensive and difficult to reproduce, while accessible commercial haptic devices lack built-in interfaces for surgical wrist articulation and continuous grasp. We present a laparoscopic master in which general-purpose robot manipulators provide the programmable base and surgical-specific interaction is concentrated in a separable distal adapter. Each 6-DoF arm carries a custom 2-DoF direct-drive wrist, continuous grasp sensing, and clutch-based workspace management; the complete bimanual hardware costs approximately US$5,500, below common bimanual commercial haptic references. To support sustained hand-guided use, we characterize current scaling, gravity, and break-away friction and use them for posture-dependent gravity compensation and motion-gated assistance, reducing continuous actuation and thermal loading. A common master state drives either Isaac Sim or an RCM-constrained dual-FR3 platform. Master-state publication to FR3 target update adds at most 8 ms, and tip tracking shows 0.31-0.66 mm mean delay-aligned residuals. In a porcine cholecystectomy experiment, five common operator-side metrics and hand/tip-speed distributions were compared descriptively with human in-vivo telemetry from 120 clinical Versius recordings of 99 cholecystectomy procedures; no interruption originated from the master console, and no abnormal clinical signs were recorded during the 7-day postoperative observation period. These results demonstrate a surgical master built from general-purpose robot arms with surgical-specific interaction concentrated in a separable distal interface.

We simplify algorithms for Knapsack, output-sensitive Subset Sum, and near-convex min-plus convolution. For bounded Knapsack, we give a deterministic algorithm using $O(N+W^2\log^3(W+2))$ arithmetic and comparison operations, where $W$ is the maximum item weight and $N$ counts input records with binary-encoded multiplicities. Following Bringmann's approach, we partition the items and bound the weight added or removed within each part when correcting a greedy solution to an optimum. These bounds keep the dynamic-programming tables small. The same analysis gives the corresponding bound with maximum profit in place of weight. For multiple-choice Knapsack, we give a randomized $\widetilde O(N+w^2\min\{r,w\})$ algorithm, where $N$ counts alternatives, $r$ counts classes, and $w$ is the maximum within-class weight range. Randomly grouping classes exploits cancellation between positive and negative weight changes. For Subset Sum of $n$ nonnegative integer vectors in any fixed dimension $d$, we obtain expected time $\widetilde O(n+s\sqrt n)$, where $s$ counts attainable sums in the target box. With high probability, all sums are returned within the same bound. This improves the $\widetilde O(n+s n^{d/(d+1)})$ bound of Bringmann, Fischer, and Nakos for $d>1$. The key step computes a sumset inside a box without generating the potentially much larger unrestricted sumset. Finally, we simplify the $\widetilde O(N(D+1))$ algorithm for min-plus convolution of integer arrays of total length $N$, where $D$ is the sum of their maximum deviations above convex arrays. The deviations can change the minimizing pairs substantially, but restrict relevant candidate values to short intervals.

How strong can an AlphaZero-style chess system become under limited training compute when its entire learning loop is engineered for efficiency? We train from random initialization through searched self-play on a single eight-GPU node for 2.5 days. The resulting 6.32-million-parameter model reaches 3,251 benchmark Elo [3,206, 3,297] at 100,000 searches per move (estimated at under five seconds of thinking time) against a fixed-node Stockfish 13 ladder. The run ingests 3.25 million completed games, involves an estimated 100 billion search simulations, and makes 836.6 million training presentations. We investigate search allocation, replay and restart-state selection, policy representation, progressive model sizing, quantized inference, and throughput engineering. Alongside the retained design, we document plausible alternatives that failed to improve the complete learning loop or did not justify their cost. The reported strength is a result of the integrated system, not an isolated Elo gain attributable to any single choice.

This paper proposes Wasserstein Causal Forests (WCF) for settings in which each unit's outcome is itself a probability distribution. This study also defines finite-grid transformed average and conditional average treatment effects, including a reference-distance contrast that asks whether treatment moves unit-level distributions toward a prespecified benchmark. Simulations cover null effects, location and shape changes, limited overlap, equal-mean but different laws, heterogeneous effects, multimodality, and structural zeros. WCF is most accurate on the conditional-law metric in most reported designs and sharply improves reference-effect estimation in the principal location-and-shape settings, but it is less accurate than the forest baselines for multimodal settings. WCF is applied to the famous Project STAR \citep{word1990state}, revealing that small classes alter more than the mean: they raise within-grade mathematics achievement by $0.161$ standard deviations on average (SE $0.028$); but the gain is not a uniform location shift, it is larger in the upper part of the classroom score distribution ($+0.179$ at the ninetieth percentile versus $+0.091$ at the tenth) and, in descriptive stratum estimates, largest in the schools serving the most economically disadvantaged students (highest free-lunch quartile, $+0.262$, versus $+0.092$ to $+0.164$ elsewhere), while overall dispersion is essentially unchanged.

The pursuit of recursive self-improvement (RSI) toward general intelligence is divided between macro-level language model scaling and the interaction-driven principles of "Era of Experience". Yet, any self-improving architecture ultimately rests upon its underlying optimization engine: if general intelligence requires learning from grounded interaction, the reinforcement learning (RL) update rule itself must be capable of cumulative adaptation. While algorithm self-discovery has produced Disco103 that surpassed PPO to achieve SOTA benchmark performance – its internal update machinery remains an uninspected black box. We present the first causal mechanistic audit of a self-discovered RL rule, structured directly around the five pillars of the Era of Experience: extended horizon, grounded reward scales, continuing streams, within-lifetime change, and exploration depth. By surgically pinning, freezing, and transplanting recurrent states while holding meta-parameters fixed, we test when learning history acts as an asset or a burden. Three findings organize the audit: (1) Recurrent history actively expands usable reward scales, sustaining a six-decade window versus three under zero-pinning. (2) Decoupling historical content from its maintenance reveals that the penalty of mismatched history stems from perpetual clamping; allowing imported state to evolve naturally attenuates this burden. (3) Under environmental change, controlling replay retention reverses the apparent adaptation advantage over DQN, demonstrating that external data turnover can confound internal plasticity. Validated through capability thresholds and ported to a second rule (OPEN), this work grounds macro-RSI ambitions in micro-level learning dynamics, establishing a foundational audit standard for next-generation, self-evolving RL algorithms.

Let $m,n \geq 3$. A set of vertices $S$ of the rectangular grid graph $P_m \square P_n$ is resolving if the taxicab distance vectors of the vertices of $P_m \square P_n$ with respect to $S$ are pairwise distinct. A resolving set $S$ is minimal if no proper subset of $S$ is resolving, and a minimal resolving set of cardinality $k$ is called a $k$-minimal. We extend the work of Andersen et al., who characterized $3$-minimals, established the maximum cardinality $2\min(m,n)-2$, and posed the complete characterization and enumeration of minimal resolving sets for grids as an open problem, and Adar and Epstein, who showed that $3$ is the only possible odd cardinality and that every minimal resolving set of cardinality at least $4$ can be ordered to form a sequence corresponding to a zigzag sequence. We provide a recursive construction that generates exactly the minimal resolving sets of cardinality at least $4$ for grids. We derive from the construction closed-form formulas to enumerate the $k$-minimals for all even $4 \leq k \leq 2\min(m,n) -2$. Together with the known characterizations for cardinalities $2$ and $3$ and a direct enumeration of the $3$-minimals, this yields a complete characterization and enumeration of the minimal resolving sets of rectangular grid graphs of every possible cardinality.

We study the monic recurrence coefficients of the generalized Charlier polynomials associated with the discrete weight \[ \rho_\mu(k) = \frac{\mu^k}{(k!)^2}, \qquad k\in\mathbb N_0, \qquad \mu>0. \] The coefficients $\beta_n$ and $\gamma_n$ in the recurrence relation \[ P_{n+1}(x) = (x-\beta_n)P_n(x)-\gamma_nP_{n-1}(x) \] are described through complementary moment, determinant, discrete dynamical, and continuous integrable formulations. We give a consistent normalization of the Markov function and its Jacobi continued fraction, and express the recurrence coefficients in terms of Hankel determinants, using a bordered determinant for the diagonal coefficient $\beta_n$. Starting from the original Laguerre–Freud equations, we derive the local recursive system used for computation and relate it to the Toda deformation. We also recall the known Painlevé~V representations associated with the two-parameter generalized Charlier family, in a normalization consistent with the present specialization. Moment/Hankelconstructions provide complementary moment-theoretic realizations of the recurrence coefficients, while the local Laguerre–Freud recursion provides an independent dynamical construction. Their comparison is used for numerical cross-validation. The numerical results are consistent with the leading large-degree behavior \[ \beta_n\sim n, \qquad \gamma_n\sim\mu. \]

The wave-particle decomposition of kinetic relaxation equations is extended to the full Boltzmann equation. An identity transformation writes the collision term as a relaxation toward the local Maxwellian plus a conservative remainder. Along characteristics, the equilibrium integral over a local kinetic horizon defines the wave, and its exact complement, the particle, carries the remainder. The moments of the wave and particle equations are extended Navier-Stokes equations, and the total conservation law and the particle equation form the wave-particle multiscale equations, a closed system, exact for every horizon, that spans a continuous spectrum from the Boltzmann equation to Navier-Stokes hydrodynamics, parametrized by the horizon-to-relaxation ratio. A coupled implicit wave-particle iteration solves this system, updating the conservative variables with the particle fixed and the particle with the predicted wave and an endpoint traction from the macroscopic prediction. Under discrete compatibility assumptions the iteration preserves the discrete Boltzmann solution as its fixed point, and its near-continuum convergence factor is bounded by a particle transport share decaying exponentially with this ratio. Tests on a normal shock, Couette and cavity flows, and hypersonic cylinder and Apollo flows agree with the conventional iterative scheme in rarefied and transition regimes and with Navier-Stokes solutions near the continuum limit. There the wave-particle iteration needs about three to more than four orders of magnitude fewer iterations than this scheme or, where it did not converge, its Shakhov version, and the Boltzmann solution costs one to four times the wall time of a Navier-Stokes solver on the same mesh.

Bringmann, Han, Heim, and Kane recently investigated periodic sign patterns in the Fourier coefficients of weakly holomorphic modular forms arising from eta-quotients and posed numerous conjectures in the appendix to their work. Using classical theta-function identities, dissections, and coefficientwise positivity, we prove 72 of these conjectural sign patterns. The eta-quotients considered here have periods 2, 3, 4, 5, 6, 8, and 12. Our proofs are elementary at the level of $q$-series and yield explicit generating functions for the coefficients in each relevant residue class.

As adolescents increasingly use LLMs in everyday life, ensuring safe and developmentally appropriate responses has become essential. However, existing LLM guardrails primarily target explicit harmful content in isolated prompts or responses and are less effective at identifying implicit, context-dependent developmental risks. To address this limitation, we propose SaplingGuard, a plug-and-play, profile-aware and dialogue-aware guardrail that requires no modification to downstream model parameters. SaplingGuard decomposes adolescent safety intervention into three specialized agents for user profile construction, context-aware risk assessment, and intent-preserving prompt optimization. Together, these agents leverage the current prompt, preceding dialogue, and structured user characteristics to identify contextual risks and guide downstream response generation. We evaluate SaplingGuard on SaplingBench, which contains 276 three-turn dialogues spanning seven categories of developmental risk. Across ten adolescent profile conditions and nine open- and closed-source downstream LLMs, profile-aware retrieval improves the Major Hit rate from 50.8% to 63.7+/-1.1%. End-to-end intervention further reduces the average harmful response rate from 17.10% to 5.27% and increases the average safety score from 0.7017 to 1.0043. These results show that user-profile and dialogue context provide complementary signals for identifying implicit developmental risks, and that SaplingGuard can serve as an effective external safety layer for adolescent-LLM interaction.

Artifact promotion means building the software once and moving that same built copy through the test and production environments, instead of building it again on each server. A previous treatment by the first author presented it as a control model for cloud deployment in accessible engineering prose. Part I of this paper restates the model in stricter form: the release object, the control domains a deployment crosses, the artifact-versus-environment identity distinction, source-control compromise as a control-domain question, and the regulatory controls (FedRAMP/SI-7, SOX 404, FFIEC, DO-178C, FDA 21 CFR Part 11, HIPAA, DoD IL) whose integrity and change-control requirements the model's properties meet more directly than build-on-target does. The parts of the model are each in the literature already: the build-once principle, the build/release/run split, binary authorization, separation as a supply-chain property, NIST SP 800-204D. The paper assembles them as one model, whatever form the built copy takes; states that a secret injected at build time breaks artifact identity; restates why downloading libraries at deployment time is an attack surface that grows with their number; and derives that the releasing role needs no production password. Part II is an anonymized case study of a production web application on AWS in which a release is one command and the artifact's path from upload to running fleet is autonomous. It reports 31 production rollouts timed stage by stage from the platform's records (36 s per server inside a six-minute rollout), 22 releases in the first four weeks, the application's service levels, a control table stating which controls the implementation has and which it lacks (no signature, no scan, no approval record, no verification at deploy), and the two release units the pipeline did not cover. A closing table checks each claim of Part I against that record.

Sparse-autoencoder decomposability and concentrated feature attribution are increasingly treated as evidence that a model's computation is easier to reverse-engineer. Whether this representational and attributional cleanliness actually predicts a smaller or more tractable causal circuit remains an open question. We test this directly using adversarial training as a controlled instrument: it reliably reshapes internal representations, but this alone does not constitute a test of circuit size. We investigate this question through reverse-engineering complexity: the causal structure required to recover a model's behavior at a fixed level of faithfulness. To our knowledge, this is the first controlled empirical test of whether representational or attributional simplicity translates into causal simplicity at the circuit level. Starting from the same pretrained GPT-2 Small checkpoint, we apply matched standard and adversarial continual training, requiring both conditions to retain competence on indirect object identification and pass independent robustness verification before comparing mechanisms. We then compare the models along three complementary axes: sparse-autoencoder decomposability, SAE feature engagement in task attribution, and the size of faithful circuits recovered from the raw computational graph. The robust model is more SAE-decomposable and engages fewer SAE features in task attribution. Circuit size is regime-dependent: on competence-matched IOI, standard leads or ties below 85% faithfulness, but robust needs substantially fewer edges at high faithfulness (90%, 95%), a pattern established on the primary pair while representational trends generalize across a seven-point sweep and a second corpus.