Papers

Replica Symmetry Breaking (RSB) theory for spin glasses, which is exact in infinite dimensions, provides detailed predictions for the behavior of these systems. One of these predictions is that vanishing magnetic fields induce chaotic behavior. Here, vanishing has a precise meaning: we refer to an externally applied magnetic field with intensity scaling as $1/\sqrt{N}$, where $N$ is the number of spins in the system. RSB predicts that this chaotic behavior depends only on the probability density function of the overlap, $P(q)$, as computed at zero field. We proceed to test the RSB prediction in the 3D Edwards-Anderson model, by first computing the $P(q)$ numerically in the absence of a magnetic field. We then use this function as input to analytically compute the statistics of the states in the regime of a vanishing magnetic field, using a representation based on the Bolthausen-Sznitman coalescent process (which is exact for the mean-field Sherrington-Kirkpatrick model). This mixed numerical-analytical approach allows us to determine the prediction of RSB for the overlap distribution function measured in the presence of a small vanishing field, as well as the increase in chaoticity as the field strength grows. The above RSB predictions are quantitatively compared with the outcome of numerical simulations of the three-dimensional Edwards-Anderson in the presence of a small vanishing field, finding very good agreement. This agreement provides strong support for the idea that three-dimensional spin glass at zero magnetic field and low temperature is well described by RSB theory.

Certifiable optimization provides global optimality guarantees for non-convex state estimation in robotics. However, under severe physical sensing degeneracy, convex Semidefinite Programming relaxations solved via Interior-Point Methods suffer from rank expansion, rendering direct semidefinite solving and spectral rounding algebraically invalid. In this paper, we establish a universal candidate-driven dual certification framework that resolves this challenge without incurring rank expansion. First, from an epigraph perspective, we prove that while sensing degeneracy expands the primal optimal set into a flat equi-cost face, cost tightness and multiplier recovery remain strictly intact, enabling global verification without direct semidefinite solving. Second, we propose an observability-aware local search using solution remapping, coupled with a closed-form dual multiplier recovery scheme that executes in sub-microsecond latency. Third, we derive a model-specific adaptive dual safety threshold parameterized by the minimum non-zero eigenvalue of the observable Hessian and uneradicated residual leakage, preventing false rejections of optimal candidates under weak observability. We validate our universal framework with robust registration under degenerate measurements.

We prove that, for every real Lipschitz function $A$ and every integer $n\ge1$, $\|T_{A,n}\|_{L^2(\mathbb{R})\to L^2(\mathbb{R})}\le C\,\|A'\|_\infty^n$, where $T_{A,n}$ is the $n$-th Calderón commutator and $C$ is an absolute constant. The essential tool is the Coifman–McIntosh–Meyer theorem, applied to a holomorphic family of complex curves, together with the Cauchy integral formula on a contour surrounding the interval of secant slopes. We also include a simpler version of the argument that gives $O(\log n)$ and explains why the contour has the shape it has.

Anharmonic intensities reveal vibrational coupling that band positions alone cannot determine. We derive explicit second-order infrared transition moments in curvilinear normal coordinates, including kinetic metric derivatives and transport through variational resonance polyads. The vibrational perturbation-to-second-order-then-diagonalization (VP2TD) treatment covers fundamentals, overtones, three-quantum transitions, and hot bands. A general computational platform combines Extended Symmetry-Adapted Local Coordinates (ESALCs), using Cartesian (ESALC-C) or internal (ESALC-I) primitives, with interchangeable quantum-chemical programs and parallel finite differences. Independent oscillator matrices verify the intensity equations; a molecular water check reproduces second-order amplitudes within $8.4\times10^{-8}$ atomic units. Comparisons with established tools reproduce a formaldehyde Fermi polyad within 0.163 cm$^{-1}$ and 0.061 km mol$^{-1}$ and water Raman activities within $10^{-7}$ Angstrom$^6$. For 29 matched formaldehyde rotational line pairs, the predicted hot-to-fundamental intensity ratio, using the measured lower-state energy, is consistent with the nuclear-spin-corrected median: the differences are 3.9% (ESALC-I) and 3.8% (ESALC-C), compared with a 15% uncertainty estimate for individual measured line intensities. Common analytic reference derivatives ensure identical harmonic observables, while internal coordinates reduce and localize intermode anharmonic couplings. Rotation-vibration constants extend the same tensor treatment. An integrated adiabatic discrete-variable representation treats large-amplitude motions, and finite-level partition functions provide anharmonic thermochemistry.

Trapped-ion devices are being investigated for transportable applications, including the transfer of exotic charged particles between laboratories and the development of portable quantum technologies. To date, ion transport has been demonstrated only in magnetic (Penning) traps, whereas radiofrequency (Paul) traps are the predominant platform in quantum science. Here, we report the first transport of a few thousand ions confined in a linear Paul trap over distances of several kilometers, with transport durations of 15 and 45 min. These results establish a foundation for mobile trapped-ion quantum devices capable of operating while in motion and may enable the transport of exotic ions in Paul traps between experimental facilities.

In reinforcement learning, an agent must explore an unknown environment to learn how to make good decisions. Unlike methods that can freely sample any state–action pair, an agent learning from a single trajectory must spend additional time navigating between states. It is therefore natural to expect that learning from a single trajectory requires more experience. In this paper, we show that this additional cost is not always necessary. For average-reward reinforcement learning, we develop an algorithm that learns where to collect information while ensuring that the required samples can be obtained efficiently. We establish an upper bound on the number of interactions needed to identify a near-optimal policy. Furthermore, we prove a matching information theoretic lower bound, showing that, for a broad class of environments and at sufficiently high accuracy, learning from a single trajectory is no harder in the worst case than learning with unrestricted access to state action samples. Our results reveal that the additional complexity cost of navigation can be avoided by adapting information gathering requirements to how the environment provides information.

We prove a maximal diameter rigidity theorem for closed 3-dimensional Riemannian manifolds under a spectral lower bound for the Ricci curvature. We show that if $0<\gamma<2$, $K>0$ and $\lambda_1(-\gamma\Delta+\operatorname{Ric})\geq 2K$, then the optimal bound $\operatorname{diam}(M,g)\leq\frac{\pi}{\sqrt{K}}$ is attained if and only if (M,g) is isometric to the round 3-sphere of constant sectional curvature $K$.

This paper develops a framework for quantifying operational flexibility in radial electric distribution systems under coupled active- and reactive-load uncertainty. Flexibility is defined as the largest scaling of a prescribed uncertainty set that can be accommodated while satisfying network and actuator limits under a given control architecture. We consider a one-sided Euclidean set for robust demand-growth capability, with a direct extension to bidirectional variations. Under LinDistFlow, controllable distributed resources and feeder-head exchange with the upstream grid jointly balance active-power disturbances, while local Volt/VAR feedback regulates reactive power. The resulting affine closed-loop disturbance response admits exact second-order-cone robust counterparts. For fixed Volt/VAR gains, a convex reformulation jointly optimizes the flexibility margin and active-power participation factors, including feeder-head participation. A sparse load-to-generator feedforward map further captures communication constraints. Numerical studies on the Iowa-240 feeder demonstrate how the amount of control authority and communication structure shape the achievable flexibility margin.

We study how to improve LLM reasoning at inference time without updating model weights or using external reward models. Recent reward-free power-sampling methods define the sequence-level power target $\pi_\alpha(y\mid x)\propto p_0(y\mid x)^\alpha$, where $\alpha>1$, which increases the relative probability of completions that are already likely under the base model. Existing methods use Metropolis–Hastings or Sequential Monte Carlo (SMC) to approximately sample from this target. However, two challenges arise at different levels. At the target level, full-sequence sharpening can concentrate probability on a few exact reasoning–answer trajectories, suppressing alternative paths that support the same answer. At the sampler level, finite-particle SMC can suffer from path collapse when resampling repeatedly duplicates a few high-weight prefixes. To address these challenges, we propose Decoupled Marginal Sharpening (DMS), which separately controls how strongly the model favors particular reasoning paths and how strongly it favors final answers after aggregating support across those paths. At the target level, DMS first samples from a sharpened reasoning distribution, then marginalizes the model's answer probabilities over the resulting weighted reasoning population and sharpens the induced answer marginal. Separate exponents allow mild reasoning sharpening to encourage exploration of diverse paths, followed by stronger answer-marginal sharpening to concentrate probability on answers with greater aggregate support across those paths. At the sampler level, we develop Fully Adapted Annealed SMC, which combines an annealed sequence of power targets with locally fully adapted proposals and predictive ancestor resampling. Experiments on MATH500, GPQA-Diamond, HumanEval, and AIME24/25 across three base models show that DMS achieves the highest mean pass@1 among the compared methods in all tasks.

We study quantum spectrum and eigenstate property estimation using multiple initial states and generalized Hadamard tests. Building on the QFAMES (quantum filtering and analysis of multiplicities in eigenvalue spectra) framework, we introduce a new method that samples evolution times independently for each initial-state pair. Under the stated assumptions, when statistical error determines the sampling cost, the total Hamiltonian simulation cost required for fixed-accuracy eigenvalue and observable estimation is independent of the number of initial states, up to logarithmic factors. This improves scalability when many initial states are needed to explore the target eigenspaces. The method also reduces the cost of multiplicity recovery and retains Heisenberg-limited scaling for eigenvalue estimation. Numerical experiments support the predicted statistical error scalings.

Stochastic physical computers use random transitions between states to process inputs. We quantify their ability to solve distinct tasks as the control parameters of a device vary. For Markov jump devices, we bound the number of classification tasks attainable at a prescribed output margin, with each task defined as a binary labeling of fixed inputs. Combining geometric packing with fluctuation-response inequalities, we bound this number in terms of the control range and dimension, rate sensitivities, output fluctuations, and entropy production. For state and net-current observables, when controls change kinetics without changing thermodynamic forces and energies, the number of tasks is shaped by entropy production and output fluctuations. If the product of their maximum values over the allowed control settings and inputs is too small, the device can perform at most one task. An exactly solvable two-state switch illustrates how sufficient driving and observation time enable barrier tuning to select copying or inversion.

In this article, we study the fractal refinement of the Carleson's problem: (1) We introduce an equivalence relation on linear dispersive PDEs on $\mathbb{R}^{n}$ based on the high-frequency oscillation of their Fourier multipliers, proving that equations in the same class share the same Hausdorff dimension of divergence sets. As applications, we estimate these dimensions for abstract dispersive families. Consequently, we recover known $1$-dimensional results for linearized Boussinesq and Beam propagations, while establishing new results for both in higher dimensions and for Klein-Gordon propagations in all dimensions. (2) Next, we study the effect of radial symmetry by obtaining dimension estimates for fractional Schrödinger equations with concave phase and radial initial data. Applying a transference principle, dimension estimates are extended to families of abstract dispersive equations. As special cases, we recover the known result for the Beam propagation and also obtain new results for the linearized Boussinesq and the Klein-Gordon propagations in the radial setting. (3) We study analogues of (2) for the $3$-dimensional real hyperbolic space by obtaining dimension estimates for a wide class of dispersive propagations: the Schrödinger, fractional Schrödinger (with convex and concave phases), Beam, linearized Boussinesq, Wave and Klein-Gordon equations. This is the first result of its kind, outside the setting of flat Euclidean geometry. Our arguments are based on an inter-spatial transference principle of geometric-analytic flavour. In the process, we also obtain a quantitative result on the singular sets of Sobolev functions, in the spirit of Žubrinić, which may be of independent interest.

Bias audits of multilingual language models usually compare a model's average stereotype score in English with its average in another language and read the difference as a difference in fairness. We ask how much of that difference is noise. Auditing ten open models in eight languages, we measure how far scores move when English test items are merely reworded, test every language shift item by item, and check that the test catches shifts we inject on purpose. In all 70 model-language pairs the stereotype score falls below its English level, and for Hindi, Korean and Swahili the drop clearly exceeds what rewording English produces; most of it comes from StereoSet items. Judging every translation, we find that imperfect ones drop more, but faithful translations alone drop nearly as much. Still, a lower average does not show that a model is fairer. An item's English score predicts its translated score far less well than its reworded score (correlation 0.23, 0.27 on faithful translations, vs. 0.48), while scores stay as far from neutral, models agree on translated items, and within Hindi or Spanish a translated item's score correlates with its own rewording at 0.84 and 0.82. The average cannot distinguish lower bias from a different pattern of item-level scores. We also document three common pipeline errors that silently erase bias signal, and release our code.

For $n\geq3$, let $\overline B_n=B_n/[P_n,P_n]$ be the crystallographic quotient of the Artin braid group, with translation subgroup $\overline P_n=P_n/[P_n,P_n]\cong\mathbb Z^N$, where $N=\binom n2$. We prove that every compact connected flat $3$-manifold $M$, considered up to affine equivalence, is the base of a geometric torus bundle whose total space is a compact flat manifold with fundamental group a Bieberbach subgroup of some $\overline B_n$. More precisely, for every $n\geq n_M$, where $n_M\in\{3,4,5\}$ is an explicit optimal threshold depending on $M$, we construct a Bieberbach subgroup $\Gamma_n(M)\leq\overline B_n$ of dimension $N$ and a complete normal subgroup $K_n(M)\cong\mathbb Z^{N-3}$ consisting of translations such that $$ \Gamma_n(M)/K_n(M)\cong\pi_1(M). $$ We also determine which of the associated torus-bundle group extensions split: for the realizations constructed here, splitting occurs for exactly four of the ten affine-equivalence classes of compact flat $3$-manifolds.

Recent LHAASO observations indicate that microquasars and massive star clusters contribute to Galactic cosmic rays, and likely also to the pre-knee spectral hardening. Their markedly different astrophysical environments, compared with supernova remnants (SNRs), may imprint distinct cosmic-ray abundances. We investigate the spectra and composition of new-source cosmic rays under two abundance scenarios: Case-1, the SNR-like composition with enhanced heavy nuclei, and Case-2, the surface abundances of microquasar companion stars. We constrain injection spectral indices using LHAASO proton, helium, and all-particle spectra, and use their <lnA> data for model discrimination. Under the assumption of a unified heavy-element injection spectrum, Case-2 fits the <lnA> data significantly better than Case-1, but at the cost of large, physically unmotivated differences between heavy-element and He injection indices. This suggests the need to either relax the unified heavy-element injection-index assumption or explore alternative abundance patterns. We predict that if the new-source composition follows Case-1, the individual elemental spectral indices before the knee should remain nearly consistent; if it follows Case-2, the Mg, Si, and Fe spectra will be significantly softer than those of He, C, and O. Future element-resolved energy-spectrum measurements by HERD and LHAASO will provide a decisive test of this discriminating feature.

Real-time volumetric mapping for a planning robot is dominated by the cost of integrating and storing information at the finest resolution, yet only a small fraction of any map ever lies on or near a path the planner actually considers. We exploit this with a tiered-resolution mapping mechanism that integrates LiDAR into a single map structure at two resolutions simultaneously: fine inside a corridor around the robot's current plan, and coarse everywhere else. As opposed to traditional navigation pipelines where path planning uses the mapping result and provides no feedback, we propose a feedback loop where planning also informs mapping to dynamically integrate information at different leaf resolutions. Across two real-world teleoperated datasets, replayed and scored offline against an independent full-resolution map, the tiered maps are 13-15x smaller and require 6-8x less integration CPU time than a uniform fine map, while producing paths at a similar cost per meter as the ones generated from fine resolution maps on both scenarios. A uniform coarse map reaches the same size savings but its path quality collapses (+210% cost per meter) on the harder scenario, because it over-discretizes terrain the robot must traverse. Tiering approximates the coarse map's cheapness without its failure mode.

The probability of interstellar contact depends not only on the abundance of technological civilizations but also on their spatial connectivity. Treating civilizations as nodes linked whenever their separation is smaller than the distance a signal travels within a communicative lifetime, we determine the radial structure of Galactic civilization networks. An exponential stellar disc replaces the uniform disc of earlier work, and the fraction of stars hosting civilizations may vary with radius as a Galactic Habitable Zone (GHZ). The isolation, contact and network transitions are frontiers several kiloparsecs wide, not boundaries: the contact frontier is set entirely by the disc scale length, and the network frontier, broadened by gradient percolation, stays near 1.5 scale lengths. The two frontiers overlap over a band containing the Sun, where both transitions proceed at once. Within this factorized GHZ model, the radius of peak civilization density depends only logarithmically on the strength of supernova sterilization, and the wide range of published peak radii, from the Galactic centre to 12 kpc, is reproduced primarily by varying that one parameter. Under the present normalization, the location of the zone has only a modest effect on the local contact probability, whereas the modelled Galactic connectivity is minimized when the civilization-density peak lies near the solar Galactocentric radius, where current determinations place the peak.

Pretrained vision-language-action models (VLAs) often fail midway through unseen long-horizon tasks. Recursive self-improvement (RSI) offers a remedy, but embodied RSI methods either refine the harness around a frozen executor and so cannot add a missing motion, or train the executor on persistent failures without asking whether a failure lies in how the executor is called or in what it can do. We ask when a self-improving embodied system should change the weights of its executor, and propose AdaRSI, an on-demand RSI framework for embodied agents. A coding agent first improves its skills and harness, then attributes persistent failures by retrying failing sub-steps from saved states, and fine-tunes only the sub-steps that remain unreliable, with demonstrations it collects itself and experience carried over from earlier tasks. On all 50 target tasks of RoboCasa365, with GR00T N1.5 as the executor and no human demonstrations, AdaRSI improves the VLA on all three suites and raises its success on unseen composite tasks from 4.6% to 13.8%. Compared with fine-tuning every sub-step, it reaches slightly higher success while using only 28% of the GPU time and 22% of the self-collected demonstrations, and fine-tuning without a harness trains more yet gains far less.

Opponent histories can mislead after behavioral shifts. SafeAdapt-Poker formulates budgeted adaptation under opponent shift as a dual-counterfactual sequential-control problem using only information available before each decision. At each decision the controller asks two distinct questions: what local downside a deviation from the frozen anchor would induce under matched legal continuations, and what future adaptation value would be lost by consuming part of the remaining deviation budget now. The first question is answered by a monotone strategic-risk model over deviation intensity; the second by a paired budget-state continuation model that prices current budget consumption. The controller selects among support-preserving candidate deviations by trading immediate adaptation value against these two quantities, a pathwise cumulative-KL ledger bounds total anchor-relative deviation, and a finite family of frozen controllers is screened on complete paired calibration sessions before held-out interaction. A finite-candidate perturbation bound shows that the allocation objective degrades continuously with continuation-value estimation error. Evaluation covers exact-game exploitation and safety, four opponent shifts, local-risk calibration, delayed-opportunity allocation, direct opportunity-value estimation, value-error robustness, factorial mechanism attribution, budget sensitivity, abstract-HUNL cross-play, and player/time-held-out public-history behavior. On exact Leduc the full controller attains a matched weak-pool gain of +0.0718 with a worst-opponent delta of -0.0126, raises delayed-opportunity capture from 0.6318 under myopic allocation to 0.7841 under the same session budget, and reaches +42.7 mbb/hand in abstract-HUNL cross-play; the retained public-history screen reports 0.5820 action accuracy and 0.9277 log loss versus 0.5039 and 0.9778 for a public prior.

Cultural attitudes and social norms evolve over time, yet most cultural benchmarks for large language models (LLMs) treat culture as a static attribute of a country or region. We introduce ChronoCulture, a benchmark of 10,360 temporal pairs built from longitudinal survey data across 72 countries. Each pair contains the same survey question asked in the same country in an older and a newer year, with full population response distributions as ground truth. Across six LLMs, we find that models can often predict a country's attitudes at one point in time but do not reliably capture how those attitudes change. Their predictions for different years tend to stay close together, failing to capture much of the observed change. Specifying the intended year in the prompt also offers little overall improvement in alignment with survey responses. These findings suggest that models often present a largely static picture of cultural attitudes, highlighting the need to evaluate cultural awareness across time.

Residual scalar quantization can produce highly dependent indices when successive stages reuse identical, unscaled grids. This case study examines that behavior in a frozen neural audio codec and develops an exact recoding procedure that reduces storage while preserving its decoder inputs. Analysis of the repeated-grid recurrence identifies predictable stage sequences; finite-precision checks motivate preserving every original index through explicit exception records. The model weights and reconstruction graph remain fixed. On the studied 62- and 512-file cohorts, a predictor, adaptive coding and explicit file selection reduce complete stored bytes. The final 512-file rate is 129.591 kbps including headers, 25.943% below an original-index XZ control. Original recorded CPU runs establish bitwise latent and waveform preservation; independent readers verify exact index and metadata recovery in subsequent saved-stream experiments. Later coding choices use previously studied cohorts, and fresh encoding requires generating three alternatives. The engineering result is implementation-specific storage reduction with exact index recovery; the underlying lossy reconstruction quality remains unchanged.

Lab-scale membrane distillation (MD) modules are commonly used for membrane characterization and developing empirical heat-transfer correlations. Entrance-induced flow structures can introduce geometry-specific effects into measured temperature polarization (TP) and heat transfer. However, the dependence of these effects on module geometry and flow condition remains unclear. We performed three-dimensional computational fluid dynamics (CFD) simulations of direct contact membrane distillation (DCMD) over inlet Reynolds numbers of $\Re_{\mathrm{in}}=10$-$1000$, focusing on side-chamber length and main-channel height. We discovered that counter-rotating streamwise vortices formed near the main-channel entrance across all geometries, but their downstream persistence increased with $\Re_{\mathrm{in}}$. At lower $\Re_{\mathrm{in}}$, the vortices mostly decayed before mid-channel, while at higher $\Re_{\mathrm{in}}$ they persisted farther downstream and produced pronounced spatial variations in TP. Increasing side-chamber length reduced the secondary-flow kinetic energy entering the main channel, and generally strengthened TP, whereas increasing main-channel height reduced the bulk velocity and streamwise kinetic energy, resulting in a thicker thermal boundary layer and stronger TP. For most geometries, the deviation from the straight-channel baseline changed from stronger TP at lower $\Re_{\mathrm{in}}$ to weaker TP at higher $\Re_{\mathrm{in}}$. Entrance effects therefore vary in both magnitude and direction with operating condition and cannot be represented by a constant correction across the Reynolds-number range.

We prove a new extension principle for the spherically symmetric Einstein–Maxwell–charged scalar field system. Rather than imposing conditions for mass ratio $2m/r$ as in Christodoulou's small-mass-ratio criterion or as in An–Chen–Singh's proof [1] with $2m/r<3/8$, here we work through a proposal by An-Tan [2] with finite Doppler exponent (blueshift). By conducting two successive blow-up analyses, followed by a stationary comparison and a rigidity argument, we establish the uniform boundness of $\alpha'$ with $\alpha'=\partial_v\alpha/\partial_vr$ and $\alpha=\partial_v(r\phi)/\partial_vr$. This provides the desired extension principle in An-Tan [2] and completes the picture of weak cosmic censorship developed therein. As we were about to release our preprint, Cicortas communicated to us that together with his collaborators, they concomitantly used a different approach to obtain the corresponding extension principle with finite blueshift (Doppler exponent) for the uncharged Einstein-scalar field system. Hence, we decided to put the current paper as an appendix to An-Tan [2], thereby completing the proof of the weak cosmic censorship for the Einstein-Maxwell-charged scalar field system. At the same time, we are working with Cicortas and his collaborators to write a new preprint containing both approaches for the Einstein-scalar field system.

We present a new quantitative, scale-critical $C^1$ extension principle for the spherically symmetric Einstein–scalar field system. We derive estimates for solutions in the causal past of a possibly singular endpoint $\mathcal{O}$ of the center. Assume that there is no trapped surface in this region and assume that the Doppler exponent (blue shift) along each incoming null cone is uniformly bounded. We then prove that the solution can extend regularly across $\mathcal{O}$ provided the mass ratio $\mu=2m/r$ satisfies $\sup\mu<\frac38$. This improves the small-mass-ratio condition in Christodoulou's extension principle by an explicit threshold of order one. Our proof has three new ingredients. First, we derive several new uniform scale-critical pointwise estimates for the scalar field and its derivatives. Second, we obtain refined estimates in an exterior self-similar domain within the triangular causal past region. Third, we establish a family of higher-order Morawetz-type identities and identify the ranges of $\mu$, with which there are coercive spacetime estimates. The unweighted identity yields the threshold $\mu\leq\frac14$, while employing extra self-similar weight raises the threshold to $\mu<\frac38$ and provides a weighted control, which implies that the solution's BV norm along an outgoing null cone is small, so that Christodoulou's theory of bounded variation solutions gives the extension.

Line intensity mapping (LIM) provides a unique window into the high-redshift universe, but the separation of signals from overlapping emission lines and bright continuum foregrounds remains a central analysis challenge. At millimeter wavelengths in particular, [CII], [CI] and numerous CO transitions overlap with comparable brightness, leading to significant spectral confusion. This work presents a joint likelihood framework that incorporates multi-tracer cross-correlations both between distinct LIM tracers and with external galaxy surveys. By jointly fitting all auto- and cross-spectra between the LIM and galaxy data, this approach combines the spatial and spectral information in each dataset to break degeneracies between overlapping lines and recover individual bias-weighted line intensities at fixed cosmology, even at redshifts where no direct cross-correlation is available. We validate this framework on realistic mocks of an extended SPT-SLIM-like survey spanning 125-175 GHz over 100 deg$^2$, combined with an LSST Y1-like photometric galaxy catalog, and recover CO(2-1) through CO(6-5) and [CI](1-0) over $0.3\lesssim z\lesssim4$ in the presence of bright continuum foregrounds. We demonstrate that adding the photometric galaxy data tightens line constraints by a factor of $\sim$3-4 where the galaxies overlap the lines in redshift, and by $\sim$20-50% at higher redshifts beyond the galaxy coverage, where the gain comes indirectly from constraining the low-redshift interlopers. These results highlight external tracer overlap as a primary consideration when optimizing the frequency coverage and footprint of near-future LIM experiments.

We study the category of constructible $p$-Kummer-étale sheaves on the log adic generic fiber $(\mathrm{X},\mathcal{M}_{\mathrm{D}})_\eta$ for the stratification induced by a horizontal normal crossings divisor $\mathrm{D}$, showing that it is antiequivalent to a category of finitely generated unit Laurent crystals on the log prismatic site. We give a local description of finitely generated unit crystals on a framed log affine in terms of $(\varphi,\Gamma)$-modules, and show pushforward compatibility for strict log smooth proper morphisms.

Generating datasets with audio plugins requires preserving how each audio observation was produced. vst-bench-ml is a Python package that samples plugin parameters, coordinates rendering through a separately installed host, and records software identities, rendering settings, and output hashes for later verification. A sealed manifest binds this evidence and supports offline integrity checks without loading the plugin. A companion repository provides a sample-free VST3 test plugin, a deterministic offline host, and additional checks linking rendering attempts to recorded outputs. On a pinned macOS arm64 and Python 3.12 stack, functional validation of the pre-release versions reproduced package and host tests. Two runs in fresh processes reproduced the same render-plan hash and all eight expected output hashes, covering four sampled parameter configurations and two fixed MIDI signals; 12 negative cases also passed. Later licensed 0.1.0 release candidates passed producer-run continuous integration and local validation. Version 0.1.1 adds public Git source repositories, package-index installation, and user documentation; a separate release check reproduced the expected plan and output hashes. These checks establish integrity and repeatability within the tested setup; they do not establish portability, scientific suitability, or perceptual quality.

We establish topological recursion for the spin enumeration of hypermaps, or, in the dual language, spin dessins d'enfants. This problem has remarkable features distinguishing it from other applications of topological recursion to enumerative combinatorics. First, the spectral curve is elliptic rather than rational, as in most cases studied before. Second, it contains degenerate ramification points, and one has to apply a version of degenerate topological recursion. Finally, the meromorphic correlator differentials have "moving" poles on the antidiagonals between pairs of distinct arguments, and one has to adjust the loop equations to this kind of degeneracy as well. The computations involve concepts of different kinds, such as BKP integrability, Gaussian integrals, the x-y swap, and symplectic duality.

Value-based Q-learning for continuous control can discretise the action space, but the resolution of the discretisation trades early exploration against final precision. Growing Q-Networks (GQN) grow the resolution uniformly from coarse to fine. We introduce Selective Growing Q-Networks (SGQN), which keeps decoupled Q-learning and replaces uniform growth with an adaptive action grid: bins are added next to bins with high estimated Q-value, bins with low Q-value are pruned, and actions are chosen epsilon-greedily. On eight DeepMind Control Suite (DMControl) tasks with 2 to 12 action dimensions, SGQN has the highest mean final return among the compared methods on four, is within 1.1% of the best method on three more, and is 3.4% below Bang-Bang MPO on Walker Run, using on average 7.5 of 9 available bins per dimension. We then test whether the adaptive grid explains these results, and find that it does not. Growth activates every candidate bin and behaves like uniform growth, and removing pruning changes the return by at most 1.1%. Two other choices matter: starting from a coarse grid, since starting with all 9 bins produces collapsed seeds, and epsilon-greedy selection, since an annealed softmax lowers the return by 23% to 100%. SGQN is insensitive to its growth and pruning hyperparameters. It also differs from the GQN and DecQN baselines in other respects, notably one gradient update per environment step instead of one per eight, which we did not control for, so we do not attribute its advantage to a single component. We present SGQN as a competitive value-based method and as an analysis of which ingredients of a growing action grid matter.

Foundation models have shown strong generalization across scientific domains, but their use in power systems remains largely task-specific. We investigate whether a pretrained tabular foundation model (TFM), TabPFN, can serve as a general-purpose neural solver for power grid steady-state analysis. We evaluate the TFM on three tasks: power flow (PF) prediction, N-k contingency screening (NCS), and voltage stability margin (VSM) prediction. We performed experiments on 118- and 2000-bus systems, comparing the TFM against task-specific neural baselines. Without retraining or fine-tuning, the TFM matches or outperforms the best task-specific model in several settings across the three tasks. For 118-bus PF prediction, a variant of the TFM achieves errors of $1\times 10^{-3}$ pu for voltage magnitudes and $0.30^\circ$ for voltage angles, outperforming all baselines. On unseen N-1 contingency and close-to-infeasible PF cases, the TFM is competitive with the DCPF approximation. For millions of unseen N-2 contingencies, the TFM achieves AUCs of 0.92 and 0.95 for branch and voltage violation screening, respectively. The TFM also attains accurate VSM prediction performance for the 2000-bus system with limited labelled data. The TFM attains strong results across the tested tasks despite pretraining without any power-system-specific dataset and requiring no fine-tuning step. These results offer a glimpse into the potential of pretrained TFMs as a neural solver for a range of power grid analysis tasks.