Papers

Frontier benchmarks need tasks that current models cannot solve. But a task that no model solves is not automatically a hard task. The same zero pass rate can come from a real capability gap, but it can also come from missing context, a broken reference solution, infrastructure failure, or a verifier that can be bypassed. In this paper, we study this issue using a frozen Terminal-Bench 3 / Frontier-Bench 0.1 production record with 1,081 pull requests, 639 scored tasks, 28,801 trials, and $105,933 in logged agent spend. We ask what an all-fail task actually certifies. For the 125 tasks with no honest pass, we combine task artifacts, reference-solution runs, empty-solution controls, adversarial trials, trajectories, telemetry, and review records, and apply an ordered validity screen. Only 78 of the 125 tasks survive as certified-unsolved candidates. The remaining tasks include 14 with broken oracles, 8 dominated by infrastructure failures, 4 that are only passable through verifier bypasses, and 21 whose solvability is not certified by the available evidence. Thus, lack of saturation and genuine difficulty are not the same thing. The certified-unsolved label is also narrow: it means that the authored route passed, infrastructure did not dominate, no strict bypass was observed, and all evaluated agents failed. It does not prove intrinsic hardness, verifier completeness, or failure at the intended capability. We further analyze rejected submissions and passing tasks to show that pass rate alone cannot explain why a task is difficult. Overall, our results suggest that frontier benchmarks should report the evidence behind their all-fail tasks before using them as capability claims.

An Aubry-André-Harper (AAH) quantum reservoir classifies strange nonchaotic attractors (SNAs) against chaos, substantially outperforming reservoirs built from dense random matrices on the full Fock space. Ablations and controlled interventions identify free-fermion one-body transition sparsity, rather than proximity to a quantum phase transition, as the dominant factor under our controls, since $H_0$ is quadratic in fermion operators and only $N(N-1)2^{N-2}=3584$ of the $65{,}280$ Fock-space transitions carry weight. Random on-site disorder, which preserves this quadratic structure, matches AAH accuracy, whereas full-Hilbert-space random matrices and eigenvector permutations, which break it, collapse to the random baseline. We characterize the resulting frequency-selective filtering with a Hamiltonian transition kernel, validate it to $N=8$ qubits, and reproduce it in a second dynamical system. We also use the reservoir as a training-free screen for strange-nonchaotic structure in Kepler RR Lyrae light curves.

The growing adoption of dataflow accelerators for neural network inference introduces new attack surfaces that existing verification methodologies fail to address. Inference ac- celeration frameworks such as FINN, which transform quantized neural networks into FPGA-deployable dataflow architectures, implicitly assume semantic equivalence between the software model and the synthesized hardware. In this work, we in- troduce the FINN-Tro attack, which identifies and exploits a critical verification gap in the FINN compilation pipeline that enables stealthy hardware Trojan insertion without modifying the original quantized model. The Trojan is placed in the last Matrix-Vector Activation Unit (MVAU) layer and supports two counter-based trigger modes, periodic and persistent, and three payload types: bias addition, logit swapping, and bias subtraction, resulting in six different configurations. FINN-Tro is evaluated on an MNIST feed-forward network and a CIFAR-10 convolutional neural network deployed on a PYNQ-Z1 board. Across the evaluated configurations, accuracy reductions range from 0.90% to 82.84%, while throughput and runtime remain close to the corresponding baseline designs. The most severe configuration, persistent Bias Addition, reduces accuracy from 92.96% to 10.12% on MNIST and from 84.19% to 10.00% on CIFAR-10. The inserted logic introduces modest implementation overhead, with maximum LUT and FF increases of 6.71% and 7.49% for MNIST, and 2.50% and 3.98% for CIFAR-10, respectively. Our findings reveal that widely used pre- and post- compilation verification flows are insufficient for detecting such temporally delayed hardware manipulations, motivating the need for stronger verification mechanisms in accelerator toolchains.

Text-output scores alone do not show whether quantization preserves performance on speech tasks whose target labels cannot be recovered from the transcript. We evaluate fixed mixed 4/8-bit Qwen2-Audio-7B-Instruct allocations averaging 6 and 7 bits per parameter on 508 English-to-German FLEURS utterances and on 512 RAVDESS emotion clips from 16 speakers. The BLEU and chrF differences from half precision (FP16) have intervals that include zero for both allocations. On RAVDESS, the same two sentences occur equally often with every emotion label. The absolute accuracy differences from FP16 are -3.71% for 6 bit and -1.17% for 7 bit. The 6-bit speaker interval excludes zero and an exact two-sided sign-flip test gives p=0.0148; the 7-bit interval includes zero. Same-budget controls do not identify either selected allocation as best. This case study shows why translation scores and performance on tasks beyond the transcript need separate evaluation.

Live financial forecasting must synchronize asynchronous bar completions across timeframes without using stale or unavailable information. We introduce HARN (Hierarchical Associative Resonance Network), an event-driven architecture that anchors each event to the finest configured timeframe and maintains persistent states and matrix-valued associative memories across temporal levels. Its timestamp-masked transition updates a level only when its completed-bar timestamp matches the current anchor, preserving inactive representations. HARN integrates causal multi-scale encoding, residual-driven gated associative writes, all-to-all cross-level resonance, and ordered bottom-up evidence aggregation to produce forecasts at each temporal level. Predictions are expressed as basis-point changes and reconstructed on the price scale for evaluation. We evaluate HARN on four assets spanning equities, foreign exchange, and gold (AAPL, EURUSD, USDCHF, and XAUUSD), using chronological 70/15/15 splits, 32-bar lookbacks, one-step horizons, and three random seeds. HARN obtains lower anchor-timeframe test mean absolute errors (MAEs) than the evaluated single-timeframe PatchTST and TimeXer baselines on all four assets. HARN's MAEs are 0.508, 0.000306, 0.000263, and 2.552, respectively; PatchTST records 2.074, 0.000759, 0.000638, and 9.563, while TimeXer records 2.882, 0.010838, 0.014144, and 15.297. These descriptive comparisons do not isolate architectural effects from differences in inputs, target formulations, or training procedures. Single-run component ablations on AAPL and EURUSD show small, non-monotonic differences. The results demonstrate HARN's feasibility for asynchronous multi-timeframe forecasting, while motivating controlled comparisons and broader ablations to establish its relative advantages and component contributions.

We develop a structural theory of the Gaussian mixed-norm Fock spaces $\mathcal F_{\alpha}^{p,q}$, where $\alpha>0$ and $0<p,q\leq\infty$, which separate angular $L^p$-means from radial Gaussian $L^q$-summability. We first prove the sharp circle-mean estimate $M_p(f,r)\leq C_{\alpha,q}(1+r)^{-\frac{1}{q}} e^{\frac{\alpha}{2}r^2}\lVert f\rVert_{\mathcal F_{\alpha}^{p,q}}$, $r\geq0$, where $M_p(f,r)$ denotes the angular $L^p$-mean of $f$ on the circle $\lvert z\rvert=r$ with the convention $\frac{1}{\infty}=0$, and show that the exponent $-\frac{1}{q}$ is optimal. The proof is based on a local mass principle for convex Laplace-type exponents, which also yields an annular discretization of the mixed Gaussian norm. Using this discretization, we characterize the continuous embeddings between mixed-norm Fock spaces and obtain an atomic decomposition in terms of normalized Fock kernels, with coefficients belonging to a corresponding annular mixed sequence space. We further characterize Carleson and vanishing Carleson measures and identify the continuous duals in the Banach, quasi-Banach, and endpoint regimes. For $p<1$, the atomic decomposition relies on a quantitative re-centering theorem that controls expansions of normalized Fock kernels under perturbations of their centers. This theorem is of independent interest even for the Hilbert Fock space $\mathcal F_{\alpha}^{2}$.

Physiological time series such as electrocardiograms (ECG) and electroencephalograms (EEG) exhibit complex temporal structure, substantial acquisition variability, and a strong need for transparent decision-making. Although deep models can achieve high detection performance, they often provide limited insight into why a segment is anomalous, how local anomalies relate over time, and whether a detection belongs to a broader recurring pattern. We propose Signal2Symbol, a neuro-symbolic framework for explainable biosignal anomaly detection. The method first converts ECG/EEG signals into symbolic sequences using either a learned VQ-VAE (Vector Quantized Variational Autoencoder) codebook or a SAX (Symbolic Aggregate approXimation) baseline. It then constructs bigram enriched token-window transactions and scores anomalies through rare itemset evidence derived from minimal rare itemset mining. Detected anomalous windows are merged into intervals and related using Allen interval algebra, enabling composite temporal explanations such as escalation chains, artifact overlap, and cross-channel synchrony. Finally, we introduce a rare temporal concept lattice based on Formal Concept Analysis (FCA), which groups anomalous intervals by shared rare symbolic evidence, Allen temporal relations, channel context, and robustness attributes. The resulting Galois lattice compresses many local detections into interpretable families of temporal-symbolic anomalies. We evaluate on three public benchmarks: MIT-BIH Arrhythmia (beat-level ECG), PTB-XL (record-level ECG), and the Bonn EEG dataset (segment-level EEG). We stress-test robustness under additive noise and baseline-wander perturbations. The results highlight the value of neuro-symbolic tokenization for temporal anomaly analysis and show that Allen/FCA reasoning provides compact, interpretable summaries of local detections.

We study the one-parameter family of Hessian metrics $g_\alpha=\alpha h_++(1-\alpha)h_-$, $\alpha\in[0,1]$, formed by convexly combining the log-partition functions (not the densities) of the multinomial and negative multinomial Fisher information Hessians. Four results are proved in full. (1) $g_\alpha\succ0$ for all $\alpha\in[0,1]$; its Gaussian curvature ($n=2$) is $-\tfrac14$ at $\alpha=0$ and $+\tfrac14$ at $\alpha=1$, but non-constant for intermediate $\alpha$, changing sign at a closed-form critical value $\alpha^\ast(w)$, with an analytic uniqueness proof. (2) Viewing $g_\alpha$ as the spatial metric of a Kasner-type volume equation, positive-definiteness forces one conserved quantity $\beta\le0$, while a second, independent quantity $C=4\det K$ governs the equation's branch (bounded oscillatory, parabolic, or unbounded growth) and is not fixed by $\beta$ or positive-definiteness alone; we show this discriminant dictionary is a theorem about the abstract matrix equation, to which $g_\alpha$ supplies initial data of either sign of $C$ without the trajectories remaining on $\{g_\alpha(\theta)\}$ itself. (3) $\Psi_\alpha$ is identified as the log-partition function of a compound distribution: a negative-binomial latent count $M$ (parameter $r=1-\alpha$), augmented by a Bernoulli parity bit and split multinomially, with non-negative base measure for every $\alpha$. (4) The associated Bregman divergence obeys a generalised Pythagorean theorem whose projection onto the symmetric locus is the arithmetic mean, independent of $\alpha$; the endpoints' curvature sign matches the Gauss–Bonnet excess of genuine geodesic triangles. Numerical checks are kept separate from analytic proofs throughout.

Despite the remarkable progress of LLM-based and knowledge graph-augmented Radiology Report Generation (RRG) methods, existing techniques still suffer from inherent defects. Conventional LLM-only models lack structured medical prior knowledge, resulting in frequent medical hallucinations and low diagnostic interpretability. Current knowledge graph-enhanced schemes adopt static one-round knowledge fusion with single-source knowledge, incapable of dynamic knowledge updating according to generation feedback. This paper proposes a novel Multi-Agent Collaborative iterative framework for X-ray Radiology Report Generation, termed MAC-RRG. Inspired by multi-agent technology, our framework constructs a closed-loop optimization paradigm based on task decoupling and collaborative reasoning. Specifically, the framework first generates a preliminary radiology report from input X-ray images via a vision encoder and a basic LLM. Subsequently, a multimodal knowledge graph (MM-KG) agent mines structured disease correlation and anatomical knowledge from medical knowledge graphs, while an auxiliary knowledge agent extracts unstructured domain knowledge from public medical databases. The multi-source knowledge acquired by dual agents is fused and embedded to guide the LLM in iteratively refining the initial report. Extensive quantitative and qualitative experiments on mainstream X-ray RRG datasets, including IU X-ray, MIMIC, and CheXpert Plus, fully verify the superiority of our proposed method. The source code and pre-trained models have been released on https://github.com/Event-AHU/Medical_Image_Analysis

This paper presents a probabilistic perspective on large language models (LLMs), developed with the aim of bringing together, in a single self-contained account, tools that are usually treated separately across the literature. LLMs are described through probability measures on the set of sequences of tokens, specified via their autoregressive conditional distributions. Training is formulated as a maximum-likelihood estimation problem, addressed by stochastic gradient methods, while text generation is viewed as the sequential simulation of the resulting stochastic process. The role of the asymmetry of the Kullback–Leibler divergence in text generation is examined in relation with characteristic phenomena such as hallucination and the distinction between statistical plausibility and truth. As a complementary illustration of the same viewpoint, we also discuss diffusion models, built around the score function, which cast generation not as sequential token prediction but as the simulation of a reverse-time stochastic process transforming noise into data both in discrete and continuous time.

We report certified computations on four no-three-in-line questions, two in the cube and two in the plane, by one method: exact decision procedures inside symmetry strata, every witness re-verified by a second program sharing no code, every number traced to a public journal. (I) Let a(n) be the largest number of points of {0,...,n-1}^3 with no three collinear (A399138). We determine a(1),...,a(6) = 1, 8, 16, 28, 40, 64 with DRAT-certified unsatisfiability proofs, give certified lower bounds a(7) >= 73, a(8) >= 94, a(9) >= 116, a(10) >= 138, a(11) >= 164, and prove a(p) >= p^2 for every prime p. The optima share a layer structure 2n^2 - 2n + 4 that provably fails at n = 5 and n = 7. (II) For b(n), the largest number with no four coplanar (A280537), nineteen public configurations give lower bounds for 9 <= n <= 29, four of which improve the known bounds and their monotone closure (b(12) >= 31, b(21) >= 47, b(22) >= 49, b(27) >= 56); the cyclically invariant subspace has maximum 23 at n = 9 and 26 at n = 10; four kinds of symmetry are incompatible with the problem; no upper bound beyond 3n is known. (III) The Guy-Kelly first-moment heuristic for the plane is audited against exact counts (A000755 to n = 20): its corrected constant comes out in closed form, pi/sqrt(3), the threshold crossing n = 493 is reproduced, and its error is shown to depend on the shape of the question rather than on n alone, with an unbounded multiplier; whether the residual error is Theta(n) or Theta(n ln n), which decides whether the constant survives, cannot be told by counting, and we measure how far from telling we are. (IV) The direction spectrum of the 2n-point solutions is measured, and a line model with no fitted parameter reproduces its shape (fifteen constants within 12%, seven predicted blind) but not its scale. Withdrawn claims are kept in the text; each part states what it does not establish.

We introduce several Ramsey-theoretic properties of 0-dimensional ambits and obtain their dynamical characterizations. In consequence, we obtain Ramsey-theoretic criteria for triviality and for profiniteness of some important invariants (in particular, of the Ellis groups) of the ambits in question. This yields a criterion for the structural property that each distal minimal factor of the given ambit is a profinite flow. Another result is a criterion for metrizability of the minimal left ideals in the Ellis semigroup. Then we study three specializations of the above abstract context: to first order theories, to definable groups, and to the classical Kechris-Pestov-Todorčević theory, recovering known and obtaining new results in each of these contexts.

Uniform discrete flow permits repeated updates at every generation position. While continued revision supports correction of wrong tokens, it also exposes correct intermediate predictions to later errors. An experiment on Sudoku puzzles shows that 9.4% of generated cells are correct at an intermediate step but incorrect in the final output. We introduce generation order into uniform discrete flow through selective absorption, which fixes chosen predictions while preserving the uniform flow velocity at active positions. To prioritize reliable predictions for absorption, we propose Low-Entropy Discrete Flow (LEDFlow), a training-free sampler that adaptively orders absorption by local entropy. By decomposing absorption error into joint dependence and conditional prediction terms, we show that, under entropy-error regularity, selecting the lowest-entropy positions under a fixed absorption count minimizes an upper bound on the conditional term. We further analyze sensitivity of global lookahead, whose worst-case decision-error bound grows with lookahead window under an imperfect denoiser. Across reasoning benchmarks, LEDFlow attains 0.845 Nikoli Sudoku solve accuracy, with largest gains on strongly constrained tasks. On a text-to-image generation benchmark it attains the best overall score among decode-time samplers, and on multimodal understanding it improves over the default sampler on all six benchmarks, at an inference cost comparable to standard flow sampling.

Memory systems for coding agents must decide, when a repository changes, which of their stored claims have become false. Content anchoring invalidates a claim whenever the artifact it came from changes, which fires constantly. Semantic-equivalence classification asks whether a diff preserves behavior, a question about the diff rather than about any stored claim. We show the second signal fails for a reason unrelated to model capability: asked whether a commit preserves behavior, five models spanning a 40x price range fire on 59-72% of real commits and reach precisions of only 0.291 to 0.329 against a 0.25 base rate. Asked instead whether one specific claim still holds, the same models on the same diffs reach 0.705 to 0.974. A control that hands the behavior-preservation judge the claim text, changing only the question, moves precision by 0.010 and 0.016; changing the question moves it by 0.49 and 0.65. We also compare against pytest-testmon, a deployed regression-test selector with coverage-derived dependency data: it reaches 0.868 recall at 0.415 precision, so near-complete knowledge of what a change can reach does not identify what it falsifies. Ground truth is execution, not annotation: a claim is a test function passing at commit t, and it has flipped if that same assertion text fails at t+1. Building this required an observation we did not find in prior work. On a CI-gated mainline a commit that leaves a pre-existing test failing cannot merge, so the naive construction has an empty positive class by design. We report 10,369 claims with 184 execution-verified flips mined from 23 Python libraries, splits held out by repository, a post-knowledge-cutoff split, a shuffled-diff null, a paraphrase control, and a leave-one-repository-out analysis over 17 repositories.

We obtain a strong decomposition theorem for invariant global types in a monadically NIP theory. From this, we prove that if an $n$-type $tp(\bar{a}/MC)$ does not fork over $M$ then $\bar{a}=(\bar{f},\bar{d})$ where $tp(\bar{d}/MC)$ is $M$-definable and $tp(\bar{f}/MC\bar{d})$ is finitely satisfied in $M$. Over arbitrary base sets $B$, we prove that an $n$-type $tp(\bar{a}/BC)$ does not fork over $B$ if and only if $tp(a_i/BC)$ does not fork over $B$ for each singleton $a_i\in\bar{a}$. We show that monadically NIP theories satisfy density of definable types among non-forking extensions.

A sub-quorum coloring is a partial vertex coloring in which every colored vertex sees at least half of its colored closed neighborhood in its own color. We study the maximum number of colors $\psq(G)$ from structural, algorithmic and extremal viewpoints. Every $2$-independent set yields a sub-quorum coloring, so $\psq(G)\ge\beta_2(G)$. We prove the degree bound $\psq(G)\le \Delta(G)|V(G)|/(\Delta(G)+\delta(G)-1)$ for $\delta(G)\ge2$, and obtain an exact matching characterization for graphs of maximum degree at most three. Consequently every cubic graph of order $n$ satisfies $n/2\le\psq(G)\le3n/5$, with a stability identity at the upper endpoint. For trees we give an edge representation and a linear-time dynamic program that computes both $\psq(T)$ and an optimal coloring; we also show on the double star $S_{2,2}$ that $\psq$ can exceed the dissociation number even on trees. We prove NP-completeness even for bipartite graphs and determine exact values for several classical families. For rectangular grids, we formulate the conjecture $\psq(G_{m,n})=\beta_2(G_{m,n})=F(m,n)$, recover the dissociation-number formula from known $3$-path vertex-cover results, prove the ladder case directly, and verify the conjecture for every fixed width $2\le m\le11$; widths $3$ through $11$ use exact transfer certificates. For hypercubes we prove $\psq(Q_n)=\beta_2(Q_n)=2^{n-1}$ for every $n\ge2$. Finally, a Nordhaus–Gaddum argument gives $\psq(G)+\psq(\overline G)>\log_2 |V(G)|$ and leads to a complementary upper-bound problem.

In this paper, we determine the precise asymptotics of the number of parts of stable regularity equipartitions in terms of the Littlestone dimension: every graph $G$ of Littlestone dimension $\operatorname{Lit}(G)\leq\ell$ has a regular equipartition into excellent sets with $(1 + o_{\epsilon\to 0,\ell}(1))\cdot\epsilon^{-\ell-1}$ parts and in the other direction, for every $\ell\in\mathbb{N}_+$, there is an infinite family of graphs, all of Littlestone dimension $\ell$, whose equipartitions into good sets must have size at least $(1 + o_{\epsilon\to 0,\ell}(1))\cdot\epsilon^{-\ell-1}$. Dropping the equitability condition, we determine the asymptotics of non-equitable partitions up to a multiplicative $\log(1/\epsilon)$: every graph $G$ with $\operatorname{Lit}(G)\leq\ell$ has a regular partition into excellent sets with $(1 + o_{\epsilon\to 0,\ell}(1))\cdot\epsilon^{-\ell}\cdot\ln(1/\epsilon)$ parts and in the other direction, for every $\ell\in\mathbb{N}_+$, there is an infinite family of graphs, all of Littlestone dimension $\ell$, whose partitions into good sets must have size at least $(1 + o_{\epsilon\to 0,\ell}(1))\cdot\epsilon^{-\ell}$. We also show that such partition can be obtained algorithmically efficiently in an approximation scheme fashion: replacing the $o_{\epsilon\to 0,\ell}(1)$ term above by a constant $c > 0$, we obtain randomized $O_{c,\epsilon,\ell}(n\cdot\log(n))$-time algorithms for partitions/equipartitions into good sets, a deterministic $O_{c,\epsilon,\ell}(n^2)$-time algorithm for partitions into good sets, a deterministic $O_{c,\epsilon,\ell}(n^6)$-time algorithm for equipartitions into good sets, a deterministic $O_{c,\ell,\epsilon}(1)\cdot n^{O(\ell\cdot 2^{2\cdot\ell+4})}$-time algorithm for partitions/equipartitions into excellent sets, and $O_{c,\epsilon,\ell}(\log(n+1))$-space algorithms for partitions/equipartitions into good/excellent sets.

We construct a measurable aggregator for the value processes associated with stochastic control problems, where the criterion to optimise is given by solutions to semi-martingale backward stochastic differential equations (BSDEs) with jumps. The results can be applied to control problems where the triplet of semi-martingale characteristics is controlled in a possibly non-dominated case or where uncertainty about the characteristics is present in the optimisation. The construction also provides a time-consistent system of fully nonlinear conditional expectations on the Skorokhod space. We also construct an appropriate path-regularisation of the value function and prove a corresponding dynamic programming principle. The generality we seek allows for the treatment of controlled diffusions, pure-jump processes, and discrete-time processes in a unified setting.

We establish the Margulis-Soifer dichotomy for one-relator groups: every one-relator group is either virtually solvable or has a maximal subgroup of infinite index. We also present examples of one-relator groups with and without free maximal subgroups of infinite index, as well as examples that possess both free and non-free infinite index maximal subgroups. Triviality of the Frattini subgroup is also shown for all non-solvable one-relator groups. We close the paper with a short list of questions.

We show that the $ \mathrm{K}_1 $-functor modeled on simple reductive groups over semilocal rings is solvable if the isotropic rank is at least $ 2 $ and that the Tits index is neither $ {}^{2} \mathsf{E}_{6, 2}^{16'} $ nor $ \mathsf{E}_{8, 2}^{78} $. For these two Tits indices the result is already known, but assuming that the base ring contains a field. Our result implies that the elementary subgroup (or its derived subgroup) is the maximal perfect subgroup of the reductive group.

Pathologists examine tissue sections across multiple magnifications and slides, integrating morphological information to establish a diagnosis. In contrast, most pathology foundation models encode thousands of image patches from a single representative ("best") slide and aggregate their features, limiting multiscale and patient-level contextual integration. Here we introduce WILSON, a vision-language foundation model that represents whole-slide images and multi-slide cases through multi-magnification composites. Trained on approximately 189,000 slides spanning 42 organs and 838 diagnostic entities, WILSON enables patient-level analysis, multimodal retrieval and diagnostic text generation. Without task-specific training, WILSON outperformed a dedicated case-level model (macro-F1, 0.52 versus 0.38) and matched substantially larger slide-level models while requiring 400-1,350 times fewer computational operations. End-to-end fine-tuning improved breast cancer subtyping and stromal lymphocyte grading. WILSON also surpassed PRISM in image-text retrieval (recall@1, 75.6% versus 58.1%) and generated diagnostic descriptions that received higher ratings from five board-certified pathologists than competing models. These findings demonstrate that compact, multiscale representations can support computationally efficient, clinically grounded pathology foundation models.

The rare type match problem is a challenging situation faced by a forensic statistician who aims at providing the value of a match between some characteristic of a crime stain and the corresponding characteristic of a suspect's stain when this characteristic has not been observed before. Several methods have been designed in the literature to assess likelihood ratios for the rare type match case when evidence consists of a Y-STR profile found on the crime scene matching the Y-STR profile of a designated suspect. We develop a general Bayesian decision-theoretic framework for quantifying the expected cost of alternative approaches using the logarithmic scoring rule. The framework provides a novel formalization of the posterior cross-entropy, which explicitly enhances the contribution of the method-specific strategy used to extract information from the data. We revisit existing decompositions of posterior cross-entropy and introduce a new complementary decomposition that provides a more interpretable characterization of this contribution. This work compares nine different methods by assessing their performance using empirical validation experiments. Its ultimate goal is to provide forensic experts and triers of fact with methodological insight and a pre-experimental guide to these alternative approaches.

Memory-safety vulnerabilities remain a persistent source of security risk in critical software, much of which is implemented in memory-unsafe languages such as C and C++. Recent advances in programming languages, program analysis, and artificial intelligence have created new opportunities to modernize these legacy systems through automated translation to memory-safe languages such as Rust. The DARPA Translating All C to Rust (TRACTOR) program seeks to develop scalable techniques for translating large C codebases into safe, performant, and maintainable Rust. MIT Lincoln Laboratory serves as the program's independent test and evaluation organization and has developed a standardized benchmark for systematically assessing C-to-Rust translation tools. This report describes the TRACTOR benchmark, including progressively challenging test batteries and larger milestone projects, as well as the supporting evaluation infrastructure and metrics for assessing correctness, safety, idiomaticity, and performance. The benchmark and associated evaluation infrastructure are publicly available to support the broader development and evaluation of C-to-Rust translation technologies.

We prove that every Voronoi cell of a unit-ball packing of $\mathbb{R}^4$ has volume at least $8$, with equality only at the $D_4$ configuration, so that the twenty-four-cell conjecture holds and the density of a sphere packing in four dimensions is at most $\pi^2/16$. The proof runs through the number of contacts of a cell. Up to twenty-two a covering estimate suffices; at twenty-three the cell is bounded through an exact volume identity inside a ball and a semidefinite certificate for one inequality between pair angles; at twenty-four the configuration is the root system, which we prove from the second level of the semidefinite hierarchy with its equality case, the positive kernel verified in exact arithmetic.

We consider the three-dimensional incompressible Navier–Stokes–Cahn–Hilliard (NSCH) system in domains perforated by no-slip obstacles of diameter of order \(\varepsilon^3\) separated by distances of order \(\varepsilon\). Both viscosity and mobility may depend on the phase variable. At this critical Stokes-capacity scale, the limiting velocity \(\boldsymbol u\) and phase field \(\phi\) satisfy an NSCH system with the additional Brinkman resistance \(\nu(\phi)\mathbf B\boldsymbol u\), where \(\mathbf B\) is determined by the exterior Stokes capacity of the reference obstacle. The principal analytical difficulty is the interaction between the phase-dependent viscosity and the order-one energy concentration of the critical Stokes correctors. The variational chemical-potential identity yields, after scalar extension, strong convergence of the phase in \(L^2(0,T;H^1(\Omega))\), and hence strong convergence of the phase-dependent viscosity in the same topology. Combined with a cellwise Hardy multiplier estimate, this compactness can be transferred through the concentrated corrector layer. The resulting weighted-capacity statement applies to uniformly positive and bounded coefficient sequences converging strongly in \(L^2(0,T;H^1(\Omega))\) and simultaneously identifies the effective Brinkman force and the corresponding viscous dissipation lower bound. We also investigate a vanishing capillary coefficient \(\lambda_\varepsilon\to0\). After the natural velocity scaling, the limit is an unsteady Stokes–Brinkman equation coupled to an unadvected Cahn–Hilliard equation.

Retrosynthetic planning advances through decisions that reshape the remaining chemical problem: a locally plausible disconnection can leave precursors whose chemoselectivity constraints complicate the rest of the route. Existing planners often channel model proposals through search or template procedures, leaving open whether a general-purpose large language model (LLM) can itself sustain and revise route strategy. We developed Rachel, a stateful environment that executes and checks LLM-directed chemistry but prescribes neither a search policy nor a stopping rule. Without supplied reference routes or route-level solutions, GPT-5.5 achieved strict closure for 111 of 120 PaRoutes120 targets and 24 of 25 targets in the separate RF25 difficult-target cohort. RF25 was drawn largely from studies published after GPT-5.5's reported knowledge cutoff. Closure required complete routes and independent source resolution of every terminal precursor after planning. On a shared PaRoutes subset, forward-model support exceeded that of most comparator methods, and Rachel received the highest mean overall route score from both method-blinded LLM evaluators. Recorded trajectories showed continued model-proposed chemistry, with revised strategies carried into subsequent steps. Replacing LLM route decisions with fixed policies reduced strict closure to 6-15/120 despite continued local chemical execution; restricting planning support also reduced closure in RF25. Within Rachel, a general-purpose LLM coordinated successive chemical choices and revised its strategy as earlier decisions reshaped the remaining problems.

We show that exact self-testing of a quantum correlation does not imply robust self-testing. Mančinska and Schmidt previously established such a separation for non-local games, but their obstruction to robustness arises from two distinct optimal correlations, with the self-tested one remaining robust. We establish the separation for a single correlation. Our proof is operator-algebraic. The main technical contribution is a general construction that associates a synchronous binary correlation to any finitely presented C*-algebra with unitary generators and real-coefficient relations. The implementing states of the correlation correspond exactly to the tracial states on the algebra. We apply this construction to an algebra with a unique finite-dimensional tracial state and a distinct amenable tracial state. By a characterization established by Zhao and independently by Kar, the resulting correlation is a self-test but not a robust self-test.

We prove a PL bordism version of Gromov's linearity conjecture over a broad class of asphericalization groups for manifolds endowed with faithful representations in all dimensions. Since every group embeds into an asphericalization group, this bordism version of the conjecture holds after allowing the target group to be enlarged. Our results apply in both the oriented and unoriented settings. In the PL category, no bounded local geometry is required. As an application, we obtain improved linear bounds for the Cheeger–Gromov $L^2$ $\rho$-invariants of PL $(4k-1)$-manifolds associated with their universal covers, replacing the previous superfactorial growth in dimension by factorial growth. The proofs are based on a quantitative asphericalization method that provides explicit control of the complexity of the resulting bordisms.

Generalized covering radii measure how many columns of a parity-check matrix are needed to generate several syndromes simultaneously. Their finite-geometric counterparts are $(\rho,t)$-saturating sets, for which every $t$-dimensional subspace is contained in a subspace generated by at most $\rho$ prescribed vectors. We investigate this covering problem for the norm-one configurations associated with generalized Zetterberg codes. We establish the upper bound $2t+1$ over every nonbinary finite field and in an explicit binary range, together with complementary lower bounds obtained by counting subspaces and constructing subfield obstructions. For an explicit range of large $t$, these configurations are $t$-strong blocking sets, and the $t^{\rm th}$ generalized covering radius attains its minimum possible value $t$. For binary Zetterberg codes, we determine the second generalized covering radius in every extension degree and prove that the third radius is seven for an infinite subfamily.

The 2026 LUX-ZEPLIN search reports one nuclear recoil candidate at $248\pm23_{\rm stat}\pm23_{\rm sys}~\mathrm{keV}$ in an extended window reaching about $270~\mathrm{keV}$. We consider elastic scattering of neutral complex vector dark matter through its dimension-six toroidal electromagnetic moment and find appreciable spectral weight in this recoil region. The nonrelativistic reduction correlates $\mathcal O_{17}$ and $\mathcal O_{20}$, relating a coherent charge branch to a transverse spin tensor branch. For $m_X=1~\mathrm{TeV}$, natural xenon exhibits a broad high recoil maximum at $204.8$ to $206.6~\mathrm{keV}$ and retains $80.4$ to $85.4\%$ of this maximum at $248~\mathrm{keV}$. Resolving the interaction through a dark photon relates the high-to-low recoil ratio to the mediator mass. A renormalizable $SU(2)_X\times U(1)_D$ realization stabilizes the complex vector by a residual $Z_3$ gauge symmetry and generates the toroidal current through vectorlike messengers carrying a physical CP phase. For a benchmark with $m_X=0.998~\mathrm{TeV}$ and $m_{A'}=0.450~\mathrm{GeV}$, $R(248)/R(50)=1.43$ for GCN and $1.21$ for JJ55, while the odd $A$ xenon fraction remains above $99.9\%$. The response level ratio between the $350$ to $590~\mathrm{keV}$ and $100$ to $270~\mathrm{keV}$ intervals is about $0.46$ at this benchmark. The tensor branch is absent for spin zero argon, whereas annual modulation remains at the few percent level. The resulting spectral, isotope, target, timing, mediator, and high energy dependences give correlated tests of an elastic tensor interpretation of the LZ recoil.