Papers

Ghostline is a device-free motion tracking system built on six ESP32-S3 Wi-Fi boards and one consumer router. The boards' Wi-Fi driver reports channel state information (CSI) for every received frame with the sender's address, and a modified open-source firmware forwards both, so every board carries a CSI stream for the router and for each other board: seven radios give up to 36 directed Links over 21 Spans instead of a star of six. Each Link is compared with a self-forming quiet Baseline, disturbed Links vote on a floor grid, and the grid becomes anonymous Tracks. The system was built and run during a three-day hackathon in an ordinary room. We describe it in full and report a pilot evaluation with one walker: spoken cues at seven marked positions, a two-minute free walk and five minutes of empty room, synchronised to video within 0.18 s (median). Walking between marks, the Track lay a median 0.85 m from the straight path and 1.56 m (95% CI 1.29 to 2.83) from a cue-based reference trajectory (constant speed between cues, not measured positions), with 46% of walk updates within 2 m of it; the free walk was tracked in 94% of updates. The limits: a standing person is lost within seconds, a false Track appeared in 15.9% and 2.9% of updates in two empty-room periods, and informal runs that afternoon did not separate two walkers. Two offline replays through the same pipeline show where this comes from: with the node-to-node Links removed and settings unchanged, the tracked share of walk updates falls from 90% to 19% and the free walk from 96% to 60%; a plain radio tomographic image on the same per-Span evidence, at the same false rate, matches the grid and tracker at 2 m (48% against 47%) and is ahead at 1 m (36% against 21%). On this recording the Tracks depend on the Link set, and the imaging stage adds no measurable accuracy. We state what the pilot establishes and what it does not.

Online learning platforms are increasingly deploying AI assistants to provide personalized, on-demand tutoring. These can leverage infographics to communicate complex information and improve the learning experience. However, automating effective infographic generation remains a challenging task, requiring a combination of visual richness with precise typography, structured layouts, and continued editability. Existing representation methods satisfy these goals only in part: Scalable Vector Graphics (SVG) representations preserve geometry, hierarchy, and text but provide limited aesthetic flexibility, while raster diffusion models produce richer appearances by flattening content and layout into a single image. Conditioning a diffusion model on a rasterized SVG does not resolve this conflict because the raster preserves approximate placement but discards element ownership, occlusion relationships, and the structure needed to modify and recompose the result. We introduce LayerCanvas, a hybrid approach that retains SVG as the semantic, structural, and typographic program while using diffusion to aestheticize non-text content. Rather than generating one flattened raster, LayerCanvas partitions SVG elements into z-ordered sets of mutually non-overlapping elements and processes them through communicating parallel RGB generation streams. The resulting layers are independently editable and deterministically recomposed, while text is rendered from preserved vector metadata. Our approach combines rich visual synthesis with accurate typography and localized editing. LayerCanvas substantially improves text fidelity over state-of-the-art raster image generators while achieving the highest overall aesthetic quality. We further demonstrate non-destructive content editing, localization, asset reuse, and animation.

Evaluation for automatic crisis reporting should measure what practitioners need, not what is convenient to compare. Through LLM-assisted, author-approved content analysis, we derive a 15-slot information schema from professional humanitarian situation reports using qualitative content analysis, then evaluate 121 human and 261 LLM-generated reports across five disasters and three hazard types. Under google/gemini-3.7-flash on Cyclone Idai, the best machine arm is nominally above the empirical human ceiling (0.827 vs. 0.821), but the difference is statistically indistinguishable from zero (95% bootstrap CI $[-.049,.059]$; permutation $p=.852$), and the ordering does not replicate under openai/gpt-5.6-luna. On a blind 100-item Idai sample, the author agrees with the Gemini judge at 0.910 accuracy and unweighted Cohen's $\kappa=.799$. All four judges clear the plan's raw-agreement criterion of .7; only Gemini reaches .7 on chance-corrected $\kappa$. Across the three primary events, machine reports reproduce 5.4-11.0% of same-day official figures. Across those same events, raw exact-number matching links 14.3-19.6% of official figures and 85.4-90.1% of machine figures to the social stream; manual audit confirms 45/50 declared absences, 4/25 official matches, and 24/25 machine matches semantically. The issuing-provenance gap is positive in all 12 observed event-judge cells: report date, organisation, series, and authority were not supplied at professional-report coverage in any cell. On the three primary events, ROUGE-L is uninformative, BERTScore is negatively associated with completeness after multiplicity correction, and a generic LLM judge changes sign.

We associate each h-convex body in hyperbolic space $\mathbb{H}^{n+1}(n\geq 2)$ with a Radon measure valued $(0,2)$-tensor on the sphere $\mathbb{S}^n$ through its horospherical function. Using spherical convolution, we prove that any h-convex body can be approximated by a sequence of smooth strictly h-convex bodies in the Hausdorff sense. This approximation result extends the inequality parts of the Alexandrov-Fenchel inequality and the modified Alexandrov-Fenchel inequality to general h-convex bodies, but equality rigidity cannot be obtained directly. We prove that the equality holds in the Alexandrov-Fenchel inequality and the modified Alexandrov-Fenchel inequality if and only if the h-convex bodies are geodesic balls. For the Alexandrov-Fenchel inequality, we establish the Hausdorff stability independent of curvature bounds described by the Alexandrov-Fenchel deficits for h-convex bodies, which implies the equality rigidity of the Alexandrov-Fenchel inequality. For the modified Alexandrov-Fenchel inequality, we introduce a class of globally constrained $k$-th modified quermassintegrals preserving flows with general h-convex initial hypersurfaces to obtain the equality rigidity. Moreover, we prove the flows above preserve h-convexity, make the $(k+1)$-th modified quermassintegrals non-increasing and converge to geodesic spheres. We prove a rigidity theorem for modified area measures for h-convex bodies and use this rigidity theorem to characterize the geodesic balls via modified support measures for h-convex bodies, from which we prove that the $(k+1)$-th modified quermassintegrals strictly decrease in a short time along the flows with non-spherical initial hypersurfaces. Then we obtain the equality rigidity of the modified Alexandrov-Fenchel inequality.

Test-time scaling for large language models (LLMs) can involve generating multiple candidate solutions for selection or revising an earlier attempt. To guide selection and revision, we need a verifier that can estimate candidate correctness and provide evidence of failure. In competitive programming, however, official judging systems provide authoritative verdicts under finite submission budgets, without revealing failure explanations or failing inputs. To provide informative feedback without consuming official submissions, we formulate a task in which a model judges and diagnoses a candidate program using only the problem statement and source code, with generated counterexamples serving as checkable evidence. To evaluate this task, we build USACO-JUDGE from the USACO 2026 contests, using accepted and unaccepted programs written by human experts and multiple LLMs. We then train ARBITER, a 35B mixture-of-experts (MoE) agentic verifier, with reinforcement learning in a generic execution sandbox. Training raises counterexample success on incorrect programs from 40.61% to 62.67% and mean binary verdict accuracy on USACO-JUDGE from 71.41% to 87.41%, approaching frontier verification performance. Beyond verification, ARBITER outperforms baselines in both code selection and refinement. In an IOI 2026 case study, ARBITER-guided refinement raises GPT-OSS-120B's expected score above the gold-medal threshold under the official submission limit.

Coloring building-integrated photovoltaics poses a dilemma: absorptive pigments cost photocurrent, while ordered photonic structures are iridescent. Amorphous photonic glasses, disordered packings of high-index nanospheres, are proposed to avoid both, yet their angle-independent color has rarely been quantified on a realistic module stack. A non-absorbing scatterer needs a high index with visible transparency, which the Moss rule caps near 2.35. Coupling Mie scattering, the Percus-Yevick structure factor, the exact phase function, and two-flux transfer with absorption and refraction at the front glass, we fix four target colors that a crowd-sourced naming survey calls unambiguously blue, green, gold, and terracotta, and map the recipes reaching them across four metal oxides, four encapsulants, two cell technologies, and wide ranges of particle size, packing fraction, and layer number. All four are reached in a laminated three-layer coating, to within DeltaE00 of 0.8 to 2.5, but not from one oxide: transparent TiO2 renders the blue and only pale warm tones; the green, gold, and terracotta require the blue-band absorption of V2O5, and the low-contrast oxides turn grey at the warm end. The encapsulant governs the color, and the cell technology does not. Disorder does not confer angle independence: the colors hold for an observer moving under a fixed sun but drift by DeltaE00 of 5 to 18 over the day, terracotta least, and a facade lit from above and viewed from below shifts every color towards the blue. Oxide, layer number, and facade geometry must therefore be designed together.

Sensitivity analysis of coupled systems typically propagates derivatives of single-valued maps, whereas multiobjective optimization generally treats sensitivity at the system level rather than through interconnected subsystems. We develop a mathematical framework for compositional sensitivity analysis in multiobjective system design, building on monotone co-design. Subsystems are represented as design problems (DPs), interconnected through series, parallel, union, intersection, and feedback composition. We introduce tangential DPs (TDPs) to describe first-order variations around an operating point, show that they preserve the structure of DPs, and characterize their queries through graphical derivatives. To account for multiple internal realizations of a system-level operating point, tangential co-design problems compose families of local TDPs by taking a union over these realizations while retaining the original interconnection structure. We show that these compositions yield families of TDPs and establish conditions under which sensitivity analysis commutes with individual composition operations. Beyond infinitesimal sensitivity, we show that bounded tangential models of convex DPs provide tighter outer approximations of feasible finite changes, which can be propagated through co-design problems without union compositions. We conclude with several convex and nonconvex numerical examples that showcase the framework's accuracy and computational benefits.

Gravitational tail-of-tail corrections arise when radiation scatters twice from the mass-monopole field of its source. In the multipolar effective field theory, one of the two-loop topologies contributing to this process involves genuinely coupled loop momenta, preventing its evaluation through nested one-loop integrations. After tensor reduction, this nonfactorizing structure leads to a particularly challenging family of scalar integrals with unbounded numerator powers as the multipole rank increases. We derive exact closed-form expressions for the entire relevant integer numerator domain, valid in generic dimension and accommodating Feynman, retarded, and advanced prescriptions through consistent analytic continuation. Near $d=3+\epsilon$, we also obtain explicit Laurent expansions through $O(\epsilon)$, retaining the subleading information needed in higher-order radiative calculations. While these expansions determine the dimensional poles, identifying their ultraviolet (UV) or infrared (IR) origin requires a separate analysis of momentum regions. We carry out this analysis throughout the integral domain and apply it directly to the coupled tail-of-tail emission diagram for arbitrary electric and magnetic multipoles. In this way, we independently determine the UV and IR residues, and explicitly verify that the complete infrared pole structure, including both double and simple poles, agrees with the exponentiation of the one-loop gravitational tail. The UV residues, calculated directly from hard-momentum regions, reproduce the established multipole anomalous dimensions when combined with the known contributions of the remaining diagrams.

We study optimal transport with a non-convex polyhedral target in $\mathbb{R}^n$. The closure of the singular set is locally a smooth hypersurface outside a relatively closed set of Hausdorff dimension at most $n-2$. For partial transport between domains separated by a hyperplane, the source free boundary has the same regularity.

Reinforcement learning (RL) from unit tests is the common recipe for post-training code models, but a unit test only asks whether the final program passes. We analyze what this unit-test-only reward teaches a model during debugging and find that, while it raises pass rates, it also teaches the model to edit more and to hallucinate bugs in code that is already correct. We introduce PreciseCoder, a training algorithm that augments the unit-test reward with a signal for semantically verified, localized edits, which correlates with smaller edits and higher pass rates. On 4B, 9B, and 27B models, PreciseCoder reduces the average number of edit lines from 7-15to 3 at a pass rate on par with unit-test-only training. Trained only on single-line bugs, PreciseCoder can generalize to repository-level program repair, where it resolves more issues with smaller patches. Its precision also transfers from weaker to stronger models: given the reasoning trace of a 9B PreciseCoder model, frontier models such as GPT-5.6 Sol and Qwen3.8-Max gain 4.6-12.4 points in edit precision with no additional training. Linguistic analysis of the thinking traces shows that our reward encourages the model to reason about individual lines, name the buggy ones, and form consistent bug hypotheses.

We propose a of definition conjugate stack for a class of suitable $\mathbb{E}_3$-$\mathrm{MU}$-algebras that includes the truncated Brown-Peterson spectra $\mathrm{BP}\langle n \rangle$ for all heights $n$. Then we calculate part of $\mathrm{BP}\langle n \rangle^{\mathrm{conj}}$ as a quotient stack in terms of Witt vectors. To perform this computation we study generalized Thom spectra and their relative Topological Hochschild Homology. We exhibit the Eilenberg-Mac Lane spectrum $\mathrm{H}\mathbb{F}_2$ as a $\mathbb{E}_3$-$\mathrm{MU}$-Thom spectrum, the $p$-local Eilenberg-Mac Lane spectra $\mathrm{H}\mathbb{Z}/p^n$ (except for $\mathrm{H}\mathbb{Z}/4$) and $\mathrm{H}\mathbb{Z}_{(p)}$ as $\mathbb{E}_3$-$\mathrm{MU}_{(p)}$-Thom spectra, and the connective complex K-theory spectrum $ku$ as $\mathbb{E}_1$-$\mathrm{MU}$-Thom spectra. We accompany these “go" results with “no-go" results that show these “go" results do not admit $\mathbb{E}_{\infty}$-refinements.

We continue the study of beautiful pairs of henselian valued fields, initiated in joint work of the second author with Cubides Kovacsics and Ye. As our main result, we show that separably closed non-trivially valued fields of arbitrary imperfection degree admit beautiful pairs which are elementary pairs satisfying certain natural axioms. They satisfy beauty transfer, i.e., saturated models of their theory are again beautiful. The same holds for beautiful pairs associated to natural subclasses of all definable types, most notably for all definable types orthogonal to the value group and for all bounded definable types. This yields strict pro-definability of the space of the definable types from any of these classes, in the theory SCVF of separably closed non-trivially valued fields. We also show a separable analog of a classical result of Keisler's, namely that the first order theory of an infinite separable extension $L/K$ of fields - considered in the pairs language and where the large field $L$ is separably closed, is determined by the theory of the small field $K$ together with the imperfection degree of $L$ over $K$.

We constructed a (2+1)-dimensional gravastar whose interior region was characterized by a noncommutative geometry with Gauss-Bonnet corrections, while the exterior region was described by a Gauss-Bonnet-modified BTZ solution. The two geometries were joined across a thin shell using the generalized junction formalism, from which we derived the surface equations of state. We investigated the energy conditions at the shell, determining the parameter regimes under which the null, weak, and strong energy conditions were satisfied. We also analyzed the thermodynamic properties of the noncommutative interior region, including the temperature, entropy, and heat capacity.

In [1], we surveyed classical and recent results on the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We also constructed well-conditioned exponential bases on certain planar sets that multi-tile the plane. In this revision, we identify an error in the choice of basis used in the proof of Theorem 3.11 and we provide a new proof using a simpler exponential basis.

We study the long-time, large-distance asymptotics of finite-temperature dynamical Fredholm determinants using effective form factors. The method expresses these asymptotics as a functional of an effective phase shift. We determine its two branches on either side of a quadratic stationary point and the transition profile joining them. The profile is expressed through parabolic-cylinder functions. Its connection to the high-temperature Gaussian $\beta$ ensemble fixes the finite normalization, in agreement with an independent Riemann–Hilbert analysis. We also show that the leading exponential asymptotics suffice to recover the Euler-scale prediction of generalized hydrodynamics for the dynamical structure factor of hard rods.

We investigate dilepton production via virtual quark bremsstrahlung in a hot, magnetized quark-gluon plasma (QGP), extending the Landau-Pomeranchuk-Migdal (LPM) framework to account for a background magnetic field and for Fermi-Dirac quark statistics. An external electromagnetic field drives the quark distribution out of equilibrium, and this off-equilibrium correction, obtained from the Boltzmann equation in the relaxation-time approximation, is in principle explicit in the electric and magnetic field strengths. We argue that this correction, being linear in the electric field, vanishes identically upon integration over the full dilepton solid angle and therefore does not contribute to the dilepton production rate (DPR). The leading magnetic-field signature in the rate instead enters entirely through the equilibrium sector: the medium density and Debye screening mass, computed from the Landau-level structure of the magnetized QGP, modifying the LPM suppression parameter. Working in the regime relevant to the hydrodynamic phase of heavy-ion collisions, we present the LPM-induced DPR for quark scatterers and establish, for the first time, a nonzero magnetic-field imprint on this observable through the LPM mechanism.

Current and upcoming galaxy-redshift surveys offer a promising path for constraining inflationary physics. These constraints are often imposed by relating correlations of the primordial curvature perturbation to the late-time galaxy correlation functions. The primordial correlators can either be computed analytically, or via realizations of the primordial curvature perturbations that are initialized on a grid and evolved numerically according to the classical equations of motion. In this work we take a hybrid approach, initializing the fields in the Bunch-Davies vacuum; and then imposing time evolution through direct numerical integration. Our method efficiently generates realizations of the inverse decay primordial curvature perturbations for axion inflation—an inflationary model in which a pseudoscalar inflaton field couples to a $U(1)$ gauge field via a Chern-Simons interaction. Depending on the choice of parameter $\xi\in\{2, 2.5, 3\}$, which controls gauge field particle production in this model, our method generates realizations with an average runtime of a few hours on 1 CPU core. We compute the power spectrum and bispectrum from these realizations and find a surprisingly large discrepancy between our result and previous work that used an approximation for the gauge field mode functions—up to a factor of $\sim4$ difference for the bispectrum in the case of $\xi=2$. This new method enables not only rapid computation of higher order polyspectra, but also generation of initial conditions for large-scale structure analyses.

We investigate how the long-range tail of dipole-dipole interactions modifies the dynamics of strongly interacting hard-core bosons in a one-dimensional lattice. In the nearest-neighbour model, large interactions generate an emergent Hilbert-space fragmentation into manifolds labelled by the number of nearest-neighbour bonds \(N_{\mathrm{NN}}\). The dipolar tail has a non-monotonic effect on this fragmented dynamics as the interaction-to-tunnelling ratio \(V/t\) is increased. At intermediate \(V/t\), it enhances delocalisation relative to the nearest-neighbour model by reducing the energetic detuning between neighbouring \(N_{\mathrm{NN}}\) manifolds and sustaining their hybridisation by hopping. At larger \(V/t\), the same tail lifts degeneracies within each manifold, beginning with the splitting associated with the next-nearest-neighbour bond number \(N_{\mathrm{NNN}}\), and promotes intra-manifold localisation and Hilbert-space shattering. The competition between these two effects produces a crossover from a delocalising to a localising role of the dipolar tail, visible in the late-time spatial inhomogeneity. This crossover occurs for nearly all initial states considered and persists at different fillings. Transverse confinement strengthens the short-range part of the dipolar tail and shifts the crossover to lower \(V/t\), bringing it into the regime relevant to current experiments with magnetic atoms and polar molecules.

Electrotactile stimulation, as a haptic feedback method, often struggles to evoke high-quality natural sensations. Consequently, despite its practical advantages, it is generally less preferred in human-machine systems than mechanical approaches. In this paper, we propose a bio-inspired stimulation framework that generates signals modelled on afferent neural activity derived from a touch model. By producing more biologically plausible spiking patterns, the proposed approach aims to enhance the realism of perceived tactile sensations. To evaluate these stimulation patterns in a realistic task context and to quantify the influence of visual and movement cues, we conducted a series of subjective experiments under three conditions. The results indicate that bio-inspired modulation was effective: in particular, bio-inspired co-modulation of amplitude and frequency achieved a favourable pressure-irritation trade-off, increasing the probability of perceiving pressure while maintaining low irritation (pressure: 0.78; irritation: 0.24) relative to the other patterns. Visual cues and hand movement further improved feedback quality by significantly increasing the probability of reporting pressure (p$<$0.001) without a corresponding increase in irritation, and by increasing mean naturalness ratings. Overall, these findings demonstrate the potential of bio-inspired electrotactile patterns to improve haptic feedback quality, and highlight the importance of evaluating such methods under realistic, multimodal interaction scenarios.

Large language models increasingly generate Solidity smart contracts that, once deployed, can never be patched, making a single latent fault permanent and exploitable. Yet current evaluations mostly ask only whether generated code compiles. We introduce SolBehave, a benchmark for evaluating the correctness of model-generated contracts at scale, moving beyond ad hoc unit tests. Across 250 real, reproducible Ethereum contracts, we apply three complementary tests of behavioural fidelity: differential fuzzing, historical-transaction replay, and, as our core contribution, synthetic-transaction replay guided by a Dynamic Condition Response (DCR) graph that enumerates the space of legitimate function-call sequences. Differential fuzzing compares each generated function with the original on automatically generated inputs; historical replay compares the whole contract on the transactions it actually received on-chain; DCR-guided replay compares it on sequences of calls that follow its intended usage, including orderings that never occurred on-chain. We evaluate seven state-of-the-art open-weight models after one round of automated repair. Compilation success ranges from 26.4% to 92.7%, but under differential fuzzing only 31.4% of all generated function bodies that compile, pooled over models and samples, are equivalent to the original. Divergence at the contract level is the norm rather than the exception: for six of the seven models, between 13% and 31% of the generated contracts that compile diverge from the original under historical replay, and between 13% and 44% under DCR-guided replay; only Gemma-4-31B stays below 3% on both. Compilation is therefore a necessary condition for correctness and far from a sufficient one.

We consider vector mean-field spin glass models with independent and identically distributed spins without assuming the covariance function is convex. We identify the limit free energy as the minimum of a functional that can be written as the sum of a relative entropy and the solution of a Hamilton–Jacobi equation. The proof of this result relies on the observation that when the spin configurations of the system are constrained to have a given empirical measure, the corresponding free energy approximately satisfies a Hamilton–Jacobi equation with a uniformly bounded error.

Fewest-switches surface hopping (FSSH) is a popular and versatile approach for performing dynamical simulations beyond the Born-Oppenheimer approximation, in which nonadiabatic effects are incorporated through stochastic hops of the active potential energy surface. However, the FSSH algorithm does not ensure that hops are completely consistent with the underlying electronic wavefunction dynamics. This can lead to significant errors as well as requiring small propagation time steps, which can significantly compromise the computational efficiency of the method. These problems are known to be particularly severe at so-called trivial crossings, for which the nonadiabatic coupling is entirely localized at the crossing point. Here, we solve the trivial-crossing problem by developing a fully-consistent hopping-probability formula, which generates attempted hops that match the time-evolution of the wavefunction across any size time step by construction. A state-tracking algorithm is also utilized to ensure that attempted hops are always accepted at trivial crossings. Through application to systems that contain extremely challenging trivial crossings, we demonstrate that this hopping scheme is capable of obtaining highly accurate results, even when large propagation time steps are used.

Gauge-equivariant graph neural networks generate ordered products of gauge links through local message passing, but the geometry of these internal structures is not captured by the receptive field alone. We investigate the statistical ensemble of closed lattice walks generated by recursive node- and edge-feature operations, independently of network training. Analytical and numerical results reveal a separation between rapid growth of contour length and much slower spatial expansion: deeper compositions generate increasingly long paths through repeated traversal of relatively compact regions. Loop expansions of fermionic observables provide a physical interpretation of this hierarchy, showing how spatial locality remains compatible with high-order dependence on nearby gauge fields. These findings identify complementary roles of network depth in extending spatial reach and enriching the representations constructed within that reach, providing a geometrical perspective on learning lattice gauge observables.

Reliable detection of pedestrians and road users is essential for the safe operation of autonomous vehicles. However, this task becomes increasingly challenging under adverse environmental conditions, such as poor weather and low lighting, where the performance of state-of-the-art pre-trained object detectors and on-board sensors tends to degrade, which limits their effectiveness and reliability. Moreover, retraining models for each operating context imposes significant constraints due to high data requirements, computational resources, and time. Considering this, we propose a novel context-aware multimodal late fusion approach that integrates a lightweight gating network within our probabilistic calibration framework. The gating network extracts environmental context and dynamically modulates the detection outputs of pre-trained object detectors based on the inferred context, without retraining of the detectors. Our methodology is evaluated on a modified KITTI dataset, in which the camera images and lidar pointclouds are augmented for varying fog levels. Experimental results show that our approach yields an approximately 14% relative improvement over non-adaptive late fusion baselines, achieving a consistent average precision of 56% across different fog levels.

Let $V_i(n)$ denote the minimum worst-case number of comparisons needed to find the $i$-th smallest of $n$ distinct elements. We construct algorithms showing $V_7(16)\le28$ and $V_8(16)\le29$, improving the previously reported upper bounds of 30 and 31. Together with known lower bounds, these results establish $V_7(16)=28$ and leave $V_8(16)\in\{28,29\}$. For 17 elements, we establish $V_5(17)=27$ and improve the upper bounds for ranks 6 through 9 to 29, 30, 31, and 31, respectively. Every new upper bound has an explicit decision-graph certificate verified by a static checker developed independently of the search. We also derive a lower bound for selection from a partially ordered state by combining the Fussenegger-Gabow weight with its order-reversed counterpart. All new upper bounds and this lower bound are formally verified in Lean 4. For $V_8(16)$, we show that a lower bound based solely on the total number of decision-tree leaves cannot establish $V_8(16)\ge29$. The algorithms were found using fixed-budget search, information-guided comparison ordering, and proof-number search. Proof-number search was decisive in finding the 28-comparison algorithm; in our experiments, refuting a comparison budget remained substantially more expensive than finding an algorithm within it.

We develop a rate-transfer method that converts finite-time Lyapunov estimates for an associated stochastic differential equation (SDE) into finite-time convergence bounds for stochastic gradient algorithms. Under generic moment and smoothness conditions, the convergence analysis of the stochastic gradient method reduces to a calculus argument verifying a Lyapunov generator inequality for the SDE. The method recovers established rates for classical stochastic gradient methods and provides a way to establish convergence rates for new optimization algorithms through calculus arguments applied to their associated SDEs.

Off-policy data in reinforcement learning with verifiable rewards (RLVR) can arise from asynchronous generation, rollout-training mismatch, and response reuse. Token-wise importance weighting avoids multiplying likelihood ratios across a response but generally biases policy gradients. We prove that, under coverage and local expressiveness conditions, full future KL credit makes the exact proximal optimizer the update's unique stationary policy, even for mixtures of older policies, without full-response weights or a fitted critic. We further establish convergence of continuous-time tabular population updates under persistent coverage and time-varying behavior policies, and a finite-sample reward guarantee for linear logistic models under additional assumptions. These results motivate Proximal KL, a practical off-policy RLVR method that separates the proximal reference from the sampling policy and replaces PPO clipping with bounded future KL credit. Across all seven matched off-policy comparisons on Qwen3-1.7B and Qwen3-4B, spanning two learning rates, response reuse, and rollout staleness, Proximal KL outperforms GRPO in micro-averaged accuracy over eight math benchmarks by up to 2.58%. A separate on-policy comparison yields comparable aggregate accuracy. In periodic-refresh experiments, Proximal KL avoids the collapses observed in PG and CISPO, exceeds GRPO's training accuracy, and reaches higher accuracy in fewer policy updates. Ablations show that token-wise correction outperforms sequence-level and unweighted controls. With token-wise correction retained, future KL feedback reduces sensitivity to the tested baseline perturbation relative to PPO clipping. A finite future horizon improves AIME24 mean@16 and pass@16 over the full tail, while fixed-policy measurements show that truncation reduces correction variance over the tested horizons.

We establish bounds on the norm of signed indecomposable integers in totally real number fields, via a geometric argument. We also improve the bound on the norm of totally positive indecomposable integers in real quadratic fields by Tinková and Voutier.

While conventional camera-based surveillance systems and metal detectors can provide a sufficient level of security when used appropriately, they have fundamental limitations that reduce their applicability. Camera-based systems are unable to detect occluded or concealed threats and metal detectors require each person to enter through a narrow opening one at a time, leading to congestion issues and limited use in large crowds. A WiFi-based security system has the potential to be a complementary modality that is able to handle occlusions or concealment and is not hindered by strict spatial configurations. In this paper, we propose use Channel State Information estimated from WiFi-signals to detect concealed handguns. To this end we collect a dataset of aligned WiFi signals and RGB images that we call the WiFire dataset. We also propose a deep learning model called WiFireNet tailored to detect concealed handguns in WiFi signals using vision-based supervision signals. Our results show that concealed handgun detection is possible in WiFi and has promise as a complementary modality to surveillance cameras and metal detectors. We release the dataset, model and code to facilitate the further research into WiFi-based handgun detection.

Speculative Decoding (SD) has demonstrated its efficacy in accelerating large language model inference, but for Vision-Language Models (VLMs), the diverse input modalities make it difficult for a small trained drafter to achieve consistently high throughput. Self-speculative decoding reuses parts of the target model as a drafter which retains the multi-modal capability of the VLMs, yet its efficiency depends on choosing a suitable draft configuration for each prompt. We propose Single-Peak SPeculative decoding (SP$^2$ec), a training-free bandit algorithm that adapts the draft configuration during generation. SP$^2$ec exploits the single-peak throughput pattern observed in existing self-speculative methods, including SWIFT, KnapSpec, SpecVLM, and our simple cosSim. Our algorithmic design explicitly minimizes a novel notion of wall-time regret for each given query, corresponding to the empirical wall-time latency. Theoretical guarantees on the wall-time regret show that SP$^2$ec can exploit the optimal draft configuration, with negligible exploration cost. Extensive experiments on Qwen2.5-VL-7B-Instruct and LLaVA-NeXT-Mistral-7B across visual and textual tasks show consistent improvements of up to 11% over the original self-speculative methods, demonstrating the wide applicability of the proposed SP$^2$ec algorithm.