Papers

We present an elementary recursive construction of Hermitian projectors on multi-quark ${\rm SU}(N)$ color states, based on the characterization of these states by their quadratic Casimir, and using the birdtrack pictorial technique.

Complete event generation on hardware accelerators such as GPUs requires vectorising the algorithms of components such as parton showers and hadronisation. To this end, I implemented a simplified cluster hadronisation and hadronic decay model in the GPU parton shower program GAPS, with one thread per event and each stage of the algorithm as a separate kernel. I compared simulation results for $e^+e^- \to \text{hadrons}$ at the $Z$ pole with the Herwig event generator and with ALEPH and L3 data, and measured execution times on an NVIDIA V100 GPU. The results agree well with Herwig, and GAPS generates one million hadron-level events (NLO hard process, shower, hadronisation and decays) in about four seconds on this GPU.

Extreme-mass-ratio inspirals are key gravitational-wave sources for testing strong gravity and the environments of massive black holes. While orbital motion in Kerr black hole spacetimes is integrable, realistic black holes may be surrounded by environments that break integrability. We investigate conservative orbital dynamics around rotating black holes surrounded by scalar clouds using fully nonlinear numerical solutions and an analytical post-Newtonian model. Poincaré sections and rotation curves reveal finite-width resonant islands, providing evidence for non-integrability even when the cloud carries only a small fraction of the black-hole mass. We show that the post-Newtonian description reproduces the dominant resonance and its island width for weak clouds, but underestimates the width in the configurations with stronger, more compact clouds examined here. Moreover, we find that for a scalar cloud as massive as the black hole, the phase space exhibits wider resonant islands as well as scattered layers indicative of chaotic motion. Together with earlier work, these results show that environmental effects can generically break the integrability of geodesic motion, motivating further study of resonance crossings and their gravitational-wave signatures once radiation reaction is included.

We develop a finite element method (FEM) for partial differential equation (PDE) solver based on the entanglement-basis representation introduced in our companion work. By lifting non-linear finite-element equations into an augmented coefficient space, the governing PDE together with boundary, initial, and inter-element constraints can be expressed through a unified quadratic residual minimization. Although this augmented space grows exponentially with the number of elements, its tensor-product structure allows it to be represented efficiently using tensor networks. Using the matrix product state (MPS) as a concrete example, we show that density matrix renormalization group (DMRG) sweeps enable element-by-element optimization without explicitly constructing the full augmented space. For bounded bond dimension, the resulting computational cost scales polynomially with the number of finite elements. We extend the framework to time-dependent problems through implicit temporal discretization and demonstrate convergence under both mesh and polynomial refinement using diffusion equations.

Different theories of dark matter predict different populations and morphologies of galactic subhaloes below about $10^8M_{\odot}$. The planned angular resolution and optical stability of the Habitable Worlds Observatory (HWO) should enable it to detect subtle subhalo perturbations in strongly lensed galaxy images. We simulate 2000-second exposures with its High Resolution Imager (HRI) under the fiducial Exploratory Analytic Case 1 (EAC1) design, assuming known source structure and omitting lens-galaxy light. Pre-selecting the top 50 of 965 lenses (5.2%) using only arc signal-to-noise and relative gradient power lowers the median mass threshold for 10% aperture coverage roughly tenfold relative to the full ensemble. The top 12 (1.2%) reach a median of $6.6\times10^7M_{\odot}$ for the same coverage. At their most sensitive positions, the top 50 and top 12 reach median thresholds of $3\times10^7M_{\odot}$ and $1.5\times10^7M_{\odot}$, respectively. Non-linear fits support the Fisher forecasts at the tested masses and positions. For these 12 lenses, increasing the physical wavefront error from 35 to 65 nm RMS raises the median thresholds by only 0.1 dex when the point spread function (PSF) is modelled correctly. Deliberately mismodelling the 35-nm reference PSF removes detectable positions, although false detections remain rare. Under our illustrative retention criteria, loss of sensitive area sets a median tolerated wavefront mismatch of 5 nm RMS (range 2–10 nm). Selective HWO follow-up of lenses discovered by Euclid or Roman could therefore transform our understanding of the nature of dark matter, provided that the PSF is characterized accurately enough to preserve this sensitivity.

We demonstrate a general mechanism to generate scalable, metrologically useful entanglement in the form of generalized spin squeezing in multi-level (qudit) spin systems with power-law interactions. We demonstrate this for spin-changing dynamics, extending the physics of spin-nematic squeezing known from spinor BECs to spatially extended lattice geometries. In the absence of all-to-all connectivity, the dynamics generally suffers from leakage into non-collective finite-momentum modes, destroying Heisenberg scaling. We show that introducing local $\mathfrak{su}(D)$ exchange interactions establishes an energy gap that protects the fully symmetric collective manifold, suppressing non-collective excitations, and achieving Heisenberg scaling $\xi^2\propto1/N$ in one to three dimensions for any power-law exponent. We provide an analytical understanding of the mechanism via the analysis of the Bogoliubov excitation spectrum, and demonstrate its effectiveness via numerical simulations of the quantum many-body dynamics. Our findings more broadly apply to other spin-squeezing Hamiltonians, and directly generalize to larger internal spin dimensions. Our results provide a practical pathway towards scalable Heisenberg-limited qudit entanglement generation in experimental platforms such as arrays of (polar) molecules, magnetic atoms, and Rydberg atoms realizing multi-level spin systems.

We study how much quantum structure bottomonium retains during its evolution in the quark-gluon plasma. Within the open quantum system framework, we simulate the Lindblad equation obtained from potential nonrelativistic QCD in the quantum Brownian regime. From the resulting real-time evolution of the bottomonium density matrix, we compute the Wigner transform and study its negativity as a measure of nonclassicality and a test of a key condition underlying classical Langevin-type approximations. We find that the medium suppresses the negativity, which nevertheless approaches a finite plateau close to that of the $1\mathrm{S}$ state. The overlaps with the excited $2\mathrm{S}$ and $3\mathrm{S}$ states arise from near-canceling positive and negative phase-space contributions, driven by negative regions in the Wigner transforms of the bound-state projectors, while the $1\mathrm{S}$ overlap is insensitive to such contributions. We further show that the position-space coherence is similarly suppressed and plateaus close to the 1S value. We trace the finite residual quantum structure to conditional purification: the medium preferentially dissolves weakly bound and unbound modes with large $\langle r^2\rangle$, driving the surviving singlet $\mathrm{S}$-wave ensemble toward the $1\mathrm{S}$ state. More broadly, these results reveal that classicalization is partial and observable dependent, a feature that is relevant across applications of open quantum system methods in fundamental physics.

Counterdiabatic driving provides a universal route to fast quantum control, but its standard formulation presupposes a Hamiltonian generator. We develop a Hamiltonian-free theory of the adiabatic gauge potential (AGP) for parameter-dependent unitary operators $U_\lambda$. Exact and regularized versions of the AGP follow from a Hermitian, banded linear system at a cost comparable to the Lanczos construction in the Hermitian case, requiring neither diagonalization nor a matrix logarithm. We demonstrate rapid convergence of the truncated Krylov approximation for the kicked top and for an integrable brickwork circuit built from unitary $\check{R}$ matrices, a setting in which no local effective Hamiltonian is available. Our results extend shortcuts to adiabaticity, and AGP-based diagnostics of chaos, to Floquet systems and quantum circuits.

Line-intensity mapping (LIM) is an emerging technique for probing both the astrophysics of galaxy formation and the cosmological evolution of large-scale structure. We investigate, for the first time, its potential as a probe of dark matter-baryon (DM-$b$) interactions using the upcoming Carbon Monoxide Mapping Array Project (COMAP) surveys, COMAP-EoR (Epoch of Reionization) and COMAP-ERA (Expanded Reionization Array). Elastic scattering of dark matter (DM) with baryons, i.e., protons ($p$) and electrons ($e$), exchange momentum and heat with the DM, suppressing structure formation and leaving characteristic signatures in the linear matter power spectrum. These effects propagate to the LIM power spectrum (PS) and voxel intensity distribution (VID). We consider momentum-transfer cross sections $\sigma^{\chi b}_{T,n}=\sigma^{\chi b}_{n}v^n$, with $n=0,-2,$ and $-4$, corresponding to contact, electric dipole-moment-like, and Coulomb-like interactions, respectively. Using Fisher forecasts, we obtain the projected sensitivities to $\sigma^{\chi b}_{n}$ from the PS and VID. Our VID-only forecasts combining the 16 and 30 GHz observed bands yield stronger sensitivities than existing cosmological limits for $n=-2$ and $n=-4$ for sub-GeV DM masses. We also explore the potential of combining the PS and VID to probe these interactions. Our study highlights LIM as a complementary probe of DM models alongside other astrophysical, cosmological, and terrestrial searches.

Random projective measurements are an effective tool to model the interlinked phenomenology of monitoring, inferring, and decoding highly entangled states such as quantum error-correcting codes. At the same time, the study of such monitored dynamics has opened a new arena for critical phenomena, renewing longstanding questions in disordered statistical mechanics, including percolation, random-bond models, and Nishimori physics. Here we investigate the robustness of stabilizer quantum error-correcting codes under a single round of independently sampled single-qubit Pauli measurements and demonstrate that their threshold behavior falls into two broad categories - geometric and homological percolation transitions, with the toric code and color code being the principal examples for each class. We establish the distinct character of these two threshold theories by analyzing the logical-support criteria of these codes and by providing numerical estimates of their respective critical exponents obtained from optimized stabilizer simulations of large-scale systems with over one million qubits. Our framework extends to non-CSS, subsystem, higher-dimensional, and Floquet stabilizer codes and allows us to determine their respective threshold phase diagrams. We exemplify how the latter provide quantitative and qualitative guidance for the computationally more demanding problems of tunable learning and maximum-likelihood decoding. As a practical application of our framework, we discuss the robustness of the gross code.

We conjecture that the universal logarithmic coefficient for capacity of entanglement $c_{\mathrm{cap}}$ is bounded below by the corresponding entropy coefficient $c_{\mathrm{eff}}$ at conformal interfaces. We prove the bound in free boson and fermion CFTs and in holographic models with interface branes, and establish it using defect perturbation theory. Numerical calculations at interacting interfaces between the tricritical Ising and Ising CFTs further support the bound. Despite this constraint, capacity provides independent interface data. We construct interfaces with identical entropy and energy transmission coefficients but different capacity coefficients, and show that capacity can even increase as entropy decreases.

Galactic magnetic fields are thought to be seeded by microscopic processes such as the Biermann battery and are primarily amplified to observed microgauss strengths by dynamo processes. Much of this amplification likely occurs within proto-galaxies, where turbulent and rotational kinetic energy is converted into magnetic energy via dynamo action. However, two aspects of this process remain poorly constrained in simulations: the saturation level of the amplified field and the timescale on which it is reached. In particular, different numerical methods, resolution strategies, and subgrid prescriptions have not converged to similar results, making it difficult to establish robust, code-independent conclusions about dynamo amplification in galaxies. In this work, we present the first systematic comparison of both Eulerian and Lagrangian codes that employ diverse MHD schemes, including ART, RAMSES, AREPO, and SWIFT. Using identical initial conditions for Milky Way-type galaxies and without including star formation and stellar feedback, we find that the amplification history of the magnetic field within the galactic disk depends strongly on the choice of hydrodynamical scheme, with orders-of-magnitude differences between Eulerian and Lagrangian approaches. We further demonstrate that reducing the mesh velocity in the moving-mesh code AREPO leads to results consistent with those obtained using the static grid codes ART and RAMSES. These results highlight the importance of carefully assessing numerical effects when interpreting magnetic field amplification in galaxy simulations.

We study the entanglement structure of partially entangled thermal states in double-scaled SYK , allowing flavor degrees of freedom carried by matter insertions to be in an arbitrary mixed state. In the semiclassical limit, followed by the heavy-probe limit, our replica calculation gives a Faulkner–Lewkowycz–Maldacena formula: the boundary entropy decomposes into an `area' term (independent of the flavor state) and the bulk matter entropy in a corresponding entanglement wedge. Varying the Euclidean locations of the operator insertions produces sharp transitions in the boundary entropy, which we interpret as individual matter excitations crossing the boundary of the wedge and hence as evidence for a sharply defined entanglement wedge. To derive this result, we analyze the semiclassical behavior of general Euclidean $2n$-point functions and give a probabilistic proof of their factorization into sums over products of two-point functions. We also give a complementary derivation from exact spectral representations, using the semiclassical behavior of the quantum $6j$-symbol.

The supersymmetric index, which gives a signed count of the microstates of black holes, can be computed directly from a gravitational path integral with appropriate boundary conditions. From general arguments based on the supersymmetry algebra, the index is expected to be independent of the temperature and, away from walls of marginal stability, of the asymptotic values of the scalar moduli. On the gravity side, this has been verified by explicit computations in many examples, but a general proof is lacking even at the classical level. We fill this gap by showing that in any four-dimensional supergravity theory with $\mathcal{N} \geq 2$ supersymmetry in asymptotically flat space-time, the classical contribution to the index from each supersymmetric saddle is independent of both. The argument uses only the behavior of the solution and of the Killing spinor equations near infinity. The result therefore holds in the presence of arbitrary higher-derivative corrections and for multi-centered black hole configurations. In particular, moduli independence follows without appeal to the attractor mechanism, which relies on the near-horizon geometry.

We study the thermodynamics of the BMN matrix model at large $N$ and strong coupling, using its dual black holes in eleven-dimensional supergravity. Within the consistent truncation to two-dimensional $SO(9)$ gauged supergravity, the static $SO(3)\times SO(6)$-invariant black holes solve ordinary differential equations, which we solve to high precision. We formulate holographic renormalisation for this truncation and fix the finite counterterms using a supersymmetric solution. This gives the energy, the entropy and the response to the BMN mass independently, and we verify the first law and the Smarr relation along the branch. The thermal branch ends at a critical value of $\mu/T$, which power-law fits place at $4\pi$ with an estimated uncertainty below $10^{-10}$. The first-order transition inferred in earlier work, where the free energy was reconstructed from the entropy, does not survive, and an independent eleven-dimensional calculation agrees with ours over the range it covers. Instead, the free energy, the entropy and the mass response approach their values in the confined phase continuously at the end of the branch, where the solutions become singular. If this branch remains the dominant one up to its end point, the transition therefore coincides with the singularity. Near the end of the branch, the scalar fields follow a solution of the supersymmetric first-order equations, while the metric carries a nontrivial blackening factor. The horizon develops a neck whose profile is universal, with radii growing as the $2/5$ power of the distance from the pinch. Within the range we resolve, the geometry is not that of the Ricci-flat double cone which governs mergers of vacuum black holes.

Existing Simulink benchmarks mainly evaluate whether generated models compile, execute, or resemble a reference model. These criteria do not establish whether a model satisfies its engineering requirements. We introduce SimuVerity, a benchmark of 101 text-to-executable Simulink model-generation tasks across ten engineering domains. For each task, executable-system profiles ground the engineering specification and four families of native simulation scenarios. A hierarchical evaluator first checks artifact delivery, native executability, and engineering qualification, then scores qualified models across six dimensions covering accuracy, output quality, mechanistic fidelity, control and causal integrity, operating-domain robustness, and dynamic response. We evaluate six agent systems with SimuVerity. The best system achieves an overall score of only 42.86. The results show that structural similarity is a poor proxy for engineering performance: capability bottlenecks arise both in producing qualified implementations and in satisfying multidimensional requirements after qualification. Meanwhile, some high-scoring models still exhibit severe visual-layout disorder. SimuVerity provides a systematic basis for assessing agents' engineering capabilities and diagnosing failures in executable Simulink model generation.

Language models increasingly assist people with power-related requests, so systematic differences in whom they help could shift the distribution of power at scale, or be exploited by users who learn which identities are refused less. We introduce PowerBench, an evaluation of power-shifting requests that distinguishes self-empowerment, disempowerment, and power grabbing, plus a control of refusal-inducing requests that shift no power. We build, curate, and open-source a dataset of such requests varying the power domain, the context, the scale of the affected party, and the prior power standing of the user, and evaluate 24 models (12 from US and 12 from Chinese developers) under three experimental conditions: reciprocal nationalities of user and affected party, an AI agent as the user, and 8 request languages. Models refuse power grabbing more than disempowerment, and disempowerment more than self-empowerment. Refusal of power grabbing rises with the scale of the affected party, from an individual to a society. Models are biased toward helping others take power from the US and against helping US users take power from others, but favor the US when it gains power and nobody loses it. When the user is an AI agent, refusal of power-shifting requests increases, especially in power grabbing against an individual. Finally, language biases refusal, but in model-specific ways that largely cancel on average. We release PowerBench to make these asymmetries measurable in current and future models.

Recent work has shown that large language models (LLMs) can be vulnerable to jailbreak attacks in which harmful intent is obscured through composition with benign tasks. A harmful request refused in isolation may elicit a different response when embedded within a larger, seemingly benign query. We study these compositional intent-hiding jailbreaks from an information-theoretic perspective. Our formulation associates each task with an estimated probability of being judged harmful: the average over the full task collection defines the prior probability of harmful intent, while the average over a selected bundle containing the target defines the posterior. Selecting auxiliary tasks so that these averages agree, which we call prior-posterior matching, leaves the estimated intent unchanged even though the harmful target remains in the bundle. We study two settings that differ in whether query construction is part of the optimization. In the query-independent setting, tasks are selected without regard to how they will be expressed in the final query. We show that exact prior-posterior matching under a bundle-size constraint is computationally hard, derive an optimal water-filling solution for fractional weights, and characterize the smallest bundle satisfying a prescribed safety threshold. In the query-dependent setting, task selection and query construction are considered jointly, and intent concealment and target preservation are evaluated on the resulting query. We evaluate jailbreak effectiveness and preservation of the target behavior across bundle sizes, query generators, and several open-source models. These results show that compositional queries can elicit target behaviors beyond the direct-request baseline under the evaluated search budgets, while revealing a trade-off: as bundle size increases, response-level target preservation tends to decrease for several models.

The measurement of primordial CMB B-mode polarization is fundamentally limited by our ability to separate this faint signal from bright and complex Galactic foregrounds. Spectral Matching Independent Component Analysis (SMICA) offers a flexible, semi-blind approach to this foreground-cleaning problem. However, its standard implementation relies on a physically unrealistic assumption of non-spatially varying foreground emission, reducing the efficiency of the method. In this work, we develop two complementary strategies to address this limitation at the component-separation level. First, we augment SMICA with effective foreground components beyond the physical dust and synchrotron degrees of freedom. Second, we extend SMICA to operate independently on subsets of the sky, better capturing local variations in the foreground emission. Beyond component separation, we further explore a likelihood-level marginalization procedure using internally reconstructed foreground templates. We demonstrate the performance of the pipeline on simulated LiteBIRD-like observations, using foreground models of increasing complexity based on $\texttt{d1s1}$ and $\texttt{d10s5}$. Combining our component-separation improvements with template marginalization brings the recovered tensor-to-scalar ratio $r$ to effectively unbiased levels, with statistical uncertainties on the order of $10^{-3}$ or below.

Training-free safeguards for text-to-image generation often rely on a reusable safety signal, such as an unsafe direction or global toxic subspace, applied broadly across prompts. We provide a controlled geometric analysis of this global-unsafety assumption and reveal a consistent coverage-selectivity trade-off: compact unsafe subspaces fail to cover heterogeneous unsafe semantics, whereas broader aggregation increasingly distorts safety-adjacent benign prompts. Motivated by this finding, we propose CALM (Counterfactual Adaptive Local Modulation), a training-free safeguard that replaces uniform global removal with prompt-local counterfactual correction. Using matched unsafe-benign anchors, CALM routes each prompt to active unsafe categories, minimally edits only violating token representations toward the safe side, and suppresses positively aligned unsafe residual components. Across broad evaluation, CALM significantly improves unsafe content suppression while preserving benign utility, demonstrating that local counterfactual correction provides a more selective alternative to global unsafe signal removal.

We introduce $\Psi$-Resilience, a model-free feature importance method that derives explanations directly from the data itself via 1D topological signals. Our method constructs a class-disagreement landscape by estimating class-conditional densities and taking their pointwise absolute difference along the feature axis. Then, the 0-dimensional persistence of this 1D signal defines a resilience functional that aggregates only those topological features that survive perturbations up to a robustness scale which is set by the user. This gives us a context-robust importance score that is inherently auditable via the underlying 1D landscapes and their persistence. We evaluate our method on both synthetic and real datasets. On synthetic generators with specified ground-truth importance, $\Psi$-Resilience recovers the ranking of features with high fidelity, achieving Spearman rank correlations up to 0.8 and performing competitively with multiple feature importance methods, including SHAP and mutual information. On real datasets with no known ground truth, our technique agrees with these methods, with correlations up to 0.9. These results show that $\Psi$-Resilience is a stable explanation method that enables rigorous, distribution-level auditing of feature importance without relying on a predictive model.

3D editing methods are usually tested on a single edit, yet an asset is built through a long sequence of revisions, each of which must implement the requested change while leaving everything else unchanged. We introduce EditHero, to our knowledge the first benchmark for long-horizon, part-level 3D editing, with natural-language instructions and target images for both geometry and texture. A deterministic assembly engine produces the exact target after every edit, and every sequence is reviewed by hand. We use EditHero to compare 2 opposite approaches to 3D editing. Non-agentic methods operate top down, regenerating the object from a learned 3D representation and inferring what to keep. In contrast, LLM/VLM agents operate bottom up, editing through code that inspects the mesh and rewrites only the parts required by instructions. The non-agentic methods often miss the requested change and disturb regions that should stay fixed. Most LLMs follow instructions more closely, and all of them preserve the unedited parts better, but each of their edits takes minutes. We will release the engine and the edit sequences to support research on reliable iterative 3D editing.

Commercial observability platforms rely on domain artifacts like distributed traces, topology maps, and baseline metrics. However, when troubleshooting proprietary software, enterprise operators are left with only raw, unannotated text logs. We explore the extreme boundary of log-only diagnosis: To what extent can we isolate failure propagation using strictly raw text logs? We present LOGOS, an unsupervised system that exploits entity-event co-occurrence and temporal precedence to collapse millions of raw log lines into a compact precedence forest. Evaluated across 25 production enterprise outages and 12 open-source issues, LOGOS operates with zero prior knowledge—requiring no seed queries, observed symptoms, or pre-defined incident boundaries. In a median wall-time of 4.5 minutes, LOGOS eliminates a median 99.8% of background noise, achieves 0.76 mean recall, and detects failure cascades with a 16-hour median diagnosis-verified lead time—consolidating alert floods 124x to enable 80% enterprise (100% open-source) zero-shot LLM root-cause accuracy.

The User Plane Function (UPF) of a 5G Standalone core terminates every GPRS Tunnelling Protocol user-plane (GTP-U) packet arriving from the radio access network, which makes its N3 interface both the busiest and the most exposed point of the mobile data path. As operators migrate the core onto Kubernetes and public cloud, the UPF increasingly shares a general-purpose Linux kernel with other workloads, and kernel-bypass frameworks such as DPDK become harder to operate. This paper presents GTP-Guard, a design for line-rate GTP-U admission control built on the eXpress Data Path (XDP) hook of the Linux kernel. GTP-Guard drops illegitimate tunnel traffic in the network driver, before socket-buffer allocation, using six ordered stages: peer allow-listing, GTP-U header validation, Tunnel Endpoint Identifier (TEID) admission against session state derived from the Packet Forwarding Control Protocol (PFCP), bounded extension-header parsing, inner-packet anti-spoofing with GTP-in-GTP detection, and per-session policing. We formalize stage ordering as a cost-minimization problem and show that sorting stages by the ratio of per-packet cost to rejection probability minimizes expected per-packet work, which motivates run-time reordering through tail-call program arrays when traffic mix shifts under attack. We further describe a Kubernetes deployment model based on a node-level DaemonSet with pinned eBPF maps that survive agent upgrades, discuss constraints specific to public-cloud virtual NICs, and define a reproducible evaluation methodology, with explicit hypotheses, for throughput, latency, CPU efficiency and attack resilience. This paper presents the design and methodology; experimental results will be reported in a subsequent version.

The union-closed sets conjecture asks whether every finite union-closed family containing a nonempty set has an element contained in at least half of its members. Let $c_{\mathrm{UC}}$ denote the largest universal lower bound on this proportion. The best previously proved lower bound is due to Liu and is above $0.3823455$; his own numerical optimization suggested a stronger threshold $c_{\mathrm L}>0.382709087918735$. The main argument of this paper is to use different protocols (suitable families of probability measures) within Liu's framework. In particular, we combine the independent protocol with Liu's Example 5 to prove the conjectured bound $c_{\mathrm{UC}}\ge c_{\mathrm L}$. We then vary the parameter in Example 5 and optimize the choice of the two coefficients in the combination to obtain $c_{\mathrm{UC}}\ge 0.3828852549667978$. We also show that the inequality used in this proof cannot give a threshold larger than $0.3828852599667\ldots$.

Unital quantum channels are the noncommutative analogues of doubly stochastic matrices. In 1959, Marcus and Ree showed that the squared Frobenius norm of a doubly stochastic matrix is at most its maximal diagonal sum. We prove a quantum version of this inequality for mixed unitary channels on $\mathbb{M}_d$ and give an example showing that it fails for general unital channels. As in the classical case, we call the channels attaining equality as Erdős channels. We show that the trace-preserving conditional expectation onto any unital $C^*$-subalgebra of $\mathbb{M}_d$ is an Erdős channel. It is also locally isolated among channels of the same Choi rank. Next, we introduce quantum RCDS channels. These are the noncommutative analogue of doubly stochastic matrices whose supported permutations all have the same diagonal sum. We prove a structure theorem for them and use it to characterize the quantum RCDS Erdős channels. We give an explicit form, up to unitary equivalence, for the Erdős channels of Choi rank $2$, and further show that there are uncountably many unitary equivalence classes of Erdős channels unlike the classical case. We also characterize the Erdős channels among mixed Weyl-unitary channels of any Choi rank. For qubits, we prove that there are exactly four unitary equivalence classes of Erdős channels and they are represented by the identity channel and uniform averages of Pauli channels. Finally, restricting to the diagonal channels, our results recover the Marcus–Ree inequality, the structure of RCDS doubly stochastic matrices, and the characterization of Erdős.

HakemBench is a Turkish benchmark of typed decisions, in which the model under test reads a text, a question and a fixed set of options and returns a probability for every option. Version 1.0 is released fully open under CC BY 4.0, with 2,346 items and 4,275 choice, yes/no and score questions in seven tracks (fact-check triage, education, guardrails, legal routing, moderation, spam and phishing, and customer support). One harness scores decision quality (macro F1), calibration (from the normalised Brier score) and selective automation (from the normalised area under the generalised risk-coverage curve), combines them by a geometric mean and reports intervals from 2,000 bootstrap draws; probes for option order, paraphrase, English translation and substituted names are reported alongside. Most gold labels come from blind passes of one AI model family compared with the votes of a panel of large language models from other model families; they are not human-verified. On a board of 16 rows the leader scores a composite of 0.888 and the lab's own model is 7th at 0.660. Its numbers are not blind. Earlier runs' test results shaped its training data, so its guardrail, moderation and customer support numbers are flagged; with every model scored on the other four tracks only, its composite is 0.678, 6th of 16.

Human activity recognition (HAR) is increasingly important for healthcare, well-being, and daily monitoring ap- plications, for which detecting alimentary activities such as eating and drinking can provide actionable insight into dietary habits and chronic disease management. HAR systems, however, often underperform on subtle and underrepresented classes, limiting their utility in real-world dietary monitoring. This work builds upon CABiGRU, a convolutional architecture with Bidirectional GRU layers, multi-head attention, and residual connections, designed to capture discriminative temporal patterns from smart- watch accelerometer, gyroscope, and magnetometer data. To improve CaBiGRU's generalization and reduce underfitting in the minority class, we leverage synthetic sensor data windows using a diffusion model and adopt a two-stage training strategy: pre-training CABiGRU on synthetic data, followed by fine-tuning on the real-world data. On the DEO (drinking/eating/other) dataset, the proposed pipeline achieves a balanced accuracy of 90.6%, improving over a strong supervised baseline and showing the benefits of diffusion-based synthetic pre-training for recognizing alimentary activities and representing a step forward dealing with unbalanced classes. These results suggest that combining diffusion-generated data with targeted fine-tuning enhances robust recognition of dietary behaviors, supporting more reliable deployment in healthcare and nutrition-monitoring settings.

Rotational variations in pulsars reflect either internal angular momentum exchange via equal and opposite torques (stationary spin noise) or independent torques causing diffusive changes in total angular momentum (nonstationary spin noise). We compare two models of a radio-emitting crust and interior superfluid to test the stationarity of angular velocity fluctuations through observed pulsar phases. We present results for three isolated pulsars with measurable timing noise, demonstrating distinct inference outcomes. For PSR J1359-6038, the data mildly favor independent torques over equal-and-opposite torques, with an odds ratio of seven hundred to one. For PSR B1937+21, the analysis shows no clear preference between the models. For Vela in a pre-glitch interval, excess scatter and unexplained residual structure limit the interpretation.

This study considers the problem of portfolio choice, where we recommend a portfolio to an investor to maximize the expected utility of their wealth. Our goal is to construct an asymptotically optimal portfolio choice rule in terms of expected utility regret, the difference between the expected utility of an oracle investor and that achieved by a portfolio chosen from data. We propose the Expected Utility Regret (EUR) rule, which jointly selects a portfolio class and estimates its weights. In a regular parametric return model, a single EUR rule attains both the minimax and the Bayes lower bounds, including their leading constants, without using the prior distribution that defines the Bayes criterion. We then derive the mean–variance and risk-parity portfolios as special cases of this framework. Under smooth increasing and concave utility, the EUR rule and the sample mean–variance portfolio attain the same leading expected regret when expected excess returns approach zero sufficiently fast. When the returns divided by their volatilities have a joint distribution that does not depend on the order of the assets, the EUR rule and the risk-parity portfolio coincide.