Analysis of PDEs
All Serrin bands are unduloidal
We show that any Serrin domain in $\mathbb{R}^2$ with two boundary components is a member of the canonical unduloidal family
Papers
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High Energy Astrophysical Phenomena
GRB 181201A: Spectropolarimetric Constraints on Prompt Emission and Magnetic Field Structure
Gamma-ray bursts (GRBs) have served as testbeds for high-energy astrophysical phenomena since their discovery over 50 years ago. GRB detections reveal diverse properties across events, complicating efforts to constrain their emission mechanisms, magnetic fields, jet structures, and compositions. Spectropolarimetry is a powerful tool utilized to disentangle these properties. INTEGRAL/IBIS has previously detected three polarized GRBs 041219A ($65\pm 26$%), 061122 ($>$33%) and 140206A ($>$28%). We present the time-integrated and time-resolved analyses of the fourth-polarized GRB 181201A. This GRB exhibits high polarization ($81.5^{+17.2}_{-15.7}$%) over three time bins with the highest signal-to-noise ratio, and the polarization angle (PA) shows a modest temporal evolution. The photon index does not cross the synchrotron line-of-death and shows a hard-to-soft evolution. A high degree of polarization (PD) tends to disfavor a photospheric emission model, as previous studies indicate that this model yields PD $<$ 20%. A modest evolution in the PA points towards a non-axisymmetric jet with a multi-patch emission. Our results indicate that under standard synchrotron conditions, the magnetic field is coherent but lacks global structure. Moreover, the field has multiple patches, but only one or a few dominate due to high degrees of polarization, which overlap with the intrinsic maximum of synchrotron emission within 3$\sigma$ errors. The high PD is also indicative of the Compton Drag scenario, but only under certain conditions, such as viewing the relativistic jet near its edge. However, given our error bars and the scope for improvement in our pipeline, we cannot strongly favor either scenario; both may remain viable.
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Robotics
PingpongDuo: Agile Humanoid Table Tennis Doubles with Safe Team Coordination
Unlike singles, humanoid table tennis doubles requires teammates to strike in strict alternation while sharing a confined workspace. Rapid repositioning can compromise striking accuracy, while uncoordinated teammate movements introduce collision risks. We present PingpongDuo, a hierarchical framework for agile humanoid doubles with safe team coordination. At the team level, a planner jointly selects positioning targets and uses learned risk estimates to filter risky proposals, preferentially preserving the current striker's target. At the individual level, separate footwork and striking skills combine agile movement with precise racket control. The skills are guided by human motion references, including footwork collected from human doubles play, and trained from states produced by one another to support rapid transitions. A racket-arm residual further refines strikes after movement using return feedback from a simulator calibrated with real ball-flight and contact measurements. In simulation, PingpongDuo improves the ball-return success rate by 13.2% over the state-of-the-art baseline, while achieving approximately 2 cm positioning error during clearance. In real-world experiments, a robot completes a 2.15 m clearance-and-recovery cycle in 2.4 s with a peak speed of 2.23 m/s, while two robots sustain more than 10 consecutive strikes in strict alternation.
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Information Retrieval
Creating SquashFS Images to Support HPC and AI Datasets
HPC users often download datasets on HPC systems for analysis and processing. When these datasets are comprised of hundreds of thousands (or more) of small files, accessing them in parallel can put a tremendous burden on the metadata servers of central parallel file systems. If the dataset is read-only, an effective solution is to compress the dataset into a SquashFS image. There are, however, a number of workflows that can be used to create such a dataset image, and we observed that some were more efficient than others. To provide more effective guidance for our userbase, we benchmarked eleven different workflows for creating SquashFS dataset image files of datasets with thousands to millions of very small files. We took into account whether the data arrived as tar.gz, zip, or files-and-directories downloads, whether the image creation was on the central file system or local compute node storage, and the number of SquashFS file compression threads used. This paper shares the results of these benchmarks and provides recommendations to HPC system users toward the best workflows to use for SquashFS image creation.
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Combinatorics
Decay-Ramsey Sequences
Given a sequence $\mathbf{a}=(a_i)_{i\geq 1}$ of positive real numbers, we say that a colouring $c:E(K_n)\to \mathbb{N}$ is $\mathbf{a}$-bounded if the proportion of edges coloured $i$ is at most $a_i$, for all $i$. We write \[ \mathbf{a}\, \to\, K_k \] if, for all sufficiently large $n$, all $\mathbf{a}$-bounded colourings $c:E(K_n)\to \mathbb{N}$ contain a monochromatic $K_k$. We say that the sequence $\mathbf{a}$ is Decay-Ramsey if $\mathbf{a}\to K_k$ for all $k\ge 2$. In this short paper we introduce the question of determining which sequences are Decay-Ramsey and present some initial results.
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Machine Learning
One Task, Many Interfaces: Simple Cross-Interface Consistency Training Improves LLM Agent Robustness
Post-training binds the competence of an LLM agent to the interface it was trained on. Semantics-preserving perturbations of that interface, such as renaming an action or changing the notation, leave the underlying task unchanged yet make the agent worse at it. Scoring each sample independently means interface randomization only broadens this dependence from a single interface to the training interface distribution, so out-of-distribution perturbations still degrade the agent. We propose Cross-Interface Policy Regularization (CIPR), a self-supervised objective that replaces action names with uninformative identifiers and presents each training sample under two interfaces in which equivalent actions are identified by construction. CIPR penalizes the KL divergence between the action distributions induced under the two interfaces, so the policy behaves consistently across them. We evaluate CIPR in both supervised and reinforcement-learning post-training, where it improves robustness. On agentic function calling, held-out interface perturbations reduce the accuracy of a post-trained agent by nearly 25%, and CIPR recovers 10.5% while leaving accuracy on the unchanged interface intact.
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Number Theory
Arithmetic Siegel–Weil formula on the product of modular curves
We prove the full generating series arithmetic Siegel–Weil formula on the product of two modular curves, with arbitrarily singular coefficients. This is the case $\operatorname{GSpin}(2,2)$ in Kudla's program.
Complex Variables
Every Gromov elliptic domain is meromorphically pseudoconvex
We prove that every Gromov elliptic domain $\Omega$ in a complex manifold has the following property, which we call meromorphic pseudoconvexity: each boundary point has a neighborhood $V$ such that $\Omega\cap V$ becomes Stein after removing a set which is, locally in $\Omega\cap V$, the union of the polar sets of finitely many meromorphic functions on $\Omega\cap V$. Since meromorphic functions on Hartogs figures extend to their hulls, it follows that, for a domain $\Omega=\operatorname{int}\overline\Omega$ in a Stein manifold, Gromov ellipticity is equivalent to being Oka and Stein, and also to being Oka and admitting a complete Kähler metric. This complements a theorem of Matsumura and the author that every weakly pseudoconvex Oka manifold admitting a positive line bundle is elliptic. As applications, we show that the Oka manifolds $\mathbb C^n\setminus\overline{\mathbb B^n}$ and $\mathbb C^n\setminus\mathbb R^n$, $n\geq2$, are not elliptic, and that no proper domain with Lipschitz boundary in $\mathbb P^n$, $n\geq2$, is elliptic.
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Logic in Computer Science
Beyond LLM Judge: Mechanical Verification for Agentic Autoformalization
We introduce a novel method for verifying Lean formalizations that goes beyond LLM-judged faithfulness. Unlike most verification methods, which rely on LLMs or trained models, our method combines LLM-based semantic review with mechanical numerical and vacuity checks, providing checkable feedback and detecting errors missed by LLM judges. We apply this method, along with our Extract-Verify-Proof autoformalization pipeline, to construct the Formalized Library of Mathematical Functions (FLMF), a partial formalization of the NIST Digital Library of Mathematical Functions (DLMF). On three labeled datasets, our method achieves the lowest accepted-error rate among the evaluated methods, measured as the fraction of incorrect statements accepted by the verification method. Expert review of the results also identifies translation and source defects in existing datasets. Code available at https://github.com/annamei1/FLMF-Ch7ErrFunc-Release.git.
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Machine Learning
Recovering Reliable Supervision via Critique-Guided On-Policy Distillation
On-policy distillation (OPD) trains a student model on its own rollouts with token-level supervision from a teacher, assuming that the teacher can reach a correct answer from any prefix the student writes. We call this property the recoverability of the teacher and show it fails on incorrect rollouts: the teacher follows student errors, although it recognizes them. We propose CriticOPD, using error recognition to restore recoverability. The teacher critiques an incorrect rollout, allowing the student to rewrite its solution following the error. The resulting output, including the critique as privileged information, is scored by the teacher while the student uses the revision without the critique for training. On two Qwen3 students and six mathematical reasoning benchmarks, CriticOPD improves OPD, with the largest gains on competition problems.
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Computer Vision
Any Time, Any Space: A World-State-Centric Framework for Agentic Video Generation
Long-form agentic video generation must turn a screenplay into shots that remain spatially and temporally consistent across nonconsecutive requests. Passing prompts or recent frames between shots does not provide a shared spatial frame for revisiting a scene or a time-indexed record for replaying an earlier event. We present Any Time, Any Space (ATAS), which compiles a screenplay into shot requests with explicit location, camera, and event-time references. Before generation, it retrieves relevant evidence from a scene memory of registered static geometry and an event memory of dynamic observations indexed by scene, event, and time. After generation, ATAS reconstructs and registers the clip. It updates memory only when review and state checks accept the observation, while film delivery remains independent of memory admission. Across four video generators, ATAS improves all reported cross-shot consistency measures and achieves the highest aggregate benchmark score for each backbone. It also outperforms the compared agents and 3D-guided methods on target-image spatial revisit, leads three event-recapture criteria, and receives the highest human ratings on all six criteria. The video results and code are available on our project page: https://lhmd.top/atas/.
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Computation and Language
Manacá-1B-Instruct-2: Reproducible Safety Alignment for a Native Brazilian-Portuguese LLM. Negative DPO Results, a Controlled Composition Scan, and a Silent Failure Mode of the LLM Judge
Brazilian Portuguese remains underserved by open-source language models, and the few that are safety-aligned rarely document what did not work or validate comparisons with statistical significance. We present Manacá-1B-Instruct-2, the second-generation post-training alignment of Manacá-1B (1.72B parameters, trained from scratch for PT-BR), with an SFT corpus of 291,223 examples. We document three DPO attempts, all negative, including a case where the training reward margin reaches 1.0 while free generation does not change at all, and show that safety came from a dedicated safety-SFT (LLM-jp AnswerCarefully style), refined over three iterations until closing the safety-helpfulness frontier. A controlled scan of the fraction of general data in the safety-SFT mix (10% to 60%) reveals a non-monotonic over-refusal curve with a knee point at 40-50%. The final model is compared against four external PT-BR models on the same items, with Wilson confidence intervals and paired McNemar tests with Holm-Bonferroni correction: the lower bound of its safety interval (94.1%) lies above the upper bound of all four baselines. We also report a methodological finding for LLM-judge evaluation: on two of six safety items in MT-Bench-PT, the judge categorically refuses to assign a score regardless of the evaluated response, silently reducing the effective N of that category in every prior report of the project. We complement this with an n-gram decontamination check and a Chinchilla-anchored compute-budget table that attributes the gap in general capability to pre-training scale rather than alignment methodology. All code, raw data, logs, and scripts that produce every reported number are publicly released.
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Statistical Mechanics
Droplets obstruct Onsager-type solutions of the Ising model in a magnetic field
Onsager solved the two-dimensional Ising model in zero field, but no solution is known in a magnetic field. We prove that in any dimension $d\ge2$, at every fixed dimensionless field outside a countable set, the free energy obeys no algebraic differential equation in the coupling, even locally. The obstruction arises from droplet geometry: the maximal droplet volume grows as the $d/(d-1)$ power of its boundary size, while an integer band in the pressure coefficients protects the extremal contributions against cancellation. Our result excludes Onsager-type solutions and closed forms in elliptic, hypergeometric, or Painlevé functions of the coupling at these fields.
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Differential Geometry
Complex generalized spin-c Killing spinors in low dimensions
We classify all complex generalized spin-c Killing spinors with complex Killing function $i\mu-\alpha$ on complete Riemannian surfaces, presenting an explicit list of all possible cases. We show that, contrary to previous statements in the literature, there exist complex generalized spin-c Killing spinors on Riemannian surfaces for which $\alpha\mu\not\equiv0$. We illustrate the classification by providing several explicit local, compact, and complete examples, including a complete example for which $\alpha\mu>0$ everywhere. We then move to three dimensions, proving that a spin-c Riemannian three-manifold admits a complex generalized spin-c Killing spinor with complex Killing function $i\mu-\alpha$ if and only if it is a $\mu$-exact trans-Sasakian manifold of type $(\alpha,\mu)$. In addition, we construct a geodesically incomplete Riemannian three-manifold equipped with a complex generalized spin-c Killing spinor for which neither $\mu$ nor $\alpha$ vanishes identically, and then prove that this is not possible if the characteristic vector field of the associated trans-Sasakian structure is complete. These results settle a conjecture by Große and Nakad (Results in Mathematics, 2015) stating that on two- and three-dimensional Riemannian manifolds the complex Killing function of any complex generalized spin-c Killing spinor must be either globally real or globally imaginary.
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Networking
Prioritizing Microservice Requests via Retries
Cloud services rapidly shift towards independently-managed microservices architectures. This independence may lead to temporary microservices miscoordination, resulting in overloads and rejections of valuable transactions. This weakness may further be exploited by attackers to launch overload attacks inflicting performance and cost damages. Retry operations are a key machinery aiming at overcoming seldom rejections. However, during overload periods they: a) Fail protecting valuable transactions from rejections, and b) Trigger large-scale performance-degrading retry storms. We propose simple modifications in retry operations, overcoming these deficiencies by transforming retries into a rejection prioritization mechanism, DiffTry (Differential Retries). It is based on a simple, lightweight, distributed and stateless design and requires neither overload sensing nor microservices coordination. We develop an analytical model capturing DiffTry's effectiveness for two services in tandem, then generalize it to networks of services. Our theoretical framework lets practitioners quantify, for a given network, the resulting prioritization and rejection rates, and yields formal guarantees that DiffTry substantially reduces the impact of both incidental and adversarial orchestrated overloads. We validate these predictions in simulation and on a live Kubernetes deployment, where DiffTry is a simple drop-in service-mesh plugin requiring no application changes; the measured rejection closely matches the analysis.
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Dynamical Systems
Completely parabolic surfaces are Veech
We prove that completely parabolic translation surfaces are Veech, answering a question of Smillie-Weiss.
Commutative Algebra
Minimal Resolutions of $k$-divisible and $(k-1)$-dominant Ideals
We introduce invariants we call $k$-divisibility and $d$-dominance, which are combinatorial constraints on the minimal generators of monomial ideals. We then prove that $k$ (respectively, $d$) is an upper bound (respectively, lower bound) for the projective dimension of a $k$-divisible (respectively, $d$-dominant) monomial ideal. This leads us to an explicit minimal resolution of $k$-divisible, $d$-dominant ideals when $d=k-1$ via a Lyubeznik resolution. This framework allows us to prove a conjecture made by Alesandroni. Using these invariants, we also provide a characterization of monomial ideals whose minimal free resolution is attainable from the Taylor resolution by performing exactly one consecutive cancellation. We also prove that for all $q,k,d$ in the range $1\leq d<k \leq q-1$, there exist monomial ideals that are $k$-divisible and $d$-dominant with $q$ minimal generators.
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Materials Science
Exchange Interactions and Magnon Spectra in bcc Fe(001) Thin Films: A Computational Study
We combined density functional theory with atomistic spin dynamics to understand how surfaces influence magnon dispersion. For this purpose, we investigate thin layers of body-centered cubic iron and compare them with the bulk material. We present how the broken symmetry affects exchange interactions and magnon behavior. Our results reveal enhanced magnetic moments and exchange interactions for surface atoms compared to bulk Fe. The increase in exchange interaction integrals is mostly visible for first- and second-nearest neighbors. We also find a significant spread in exchange values within each coordination shell. Magnon dispersion analysis shows, for the layered system, pronounced band blurring, a significant reduction of maximum frequencies relative to the previously reported bulk values, and the emergence of a low-frequency band outside the \g{}-point. Our study shows that relying on bulk exchange parameters introduces errors in the magnon spectra of ultrathin systems, underscoring the need for a detailed, system-specific approach.
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Artificial Intelligence
Scaling Discovery Requires Forgetting
Automated research with LLM agents has shown promising results in various domains. Through iterative refinement and scored verifiers, LLM agents are capable of discovering new ideas. There are different ways to scale automated research: let one agent iterate for longer, run several agents in parallel, or further let the parallel agents communicate and build on one another's candidates. However, we find that all three strategies eventually plateau as the agents accumulate history. Each agent becomes anchored to its own past attempts, making fewer and smaller edits. Beyond this point, additional budget brings little further improvement. In this paper, we show that the key to scaling discovery further is to forget. Periodically discarding the search state, including every agent's session and the candidate history, and restarting from the best candidate found so far, unblocks the search and pushes the same budget further. We implement forgetting in a team of agents with communication and evaluate it on four tasks spanning heuristic programming, kernel optimization and model training. The results show up to 15% improvement compared to parallel agents, and up to 39% compared to a single agent. Our results suggest that, for open-ended discovery, what an agent is allowed to remember matters as much as how much compute it is given.
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Combinatorics
Hypergraphs with the smallest Hall ratio are still hard to colour
For $H$ a hypergraph, the Hall ratio $\rho(H)=\text{max}_{X\subseteq V(H)}\frac{\lvert{X}\rvert}{\alpha(H[X])}$ is a natural lower bound for its chromatic number, and among non-empty $k$-uniform hypergraphs the smallest possible Hall ratio is $k/(k-1)$. For graphs ($k = 2$), having minimum Hall ratio $2$ forces chromatic number $2$. Nešetřil, Rödl, and Sales asked whether a similar phenomenon holds at higher uniformities. We answer this question negatively in a strong form, showing that for every $k \geqslant 3$ there are $k$-uniform hypergraphs with Hall ratio exactly $k/(k-1)$ and arbitrarily large fractional chromatic number.
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Computer Vision
A$^3$PreCore: Robust Rigid Registration for Native FLAIR-Space Brain-Mask Transfer
Reliable brain-mask transfer into native fluid-attenuated inversion recovery (FLAIR) space can fail when T1-to-FLAIR rigid registration is unstable. We developed A$^3$PreCore, a six-degree-of-freedom rigid-registration strategy that aligns the full bias-corrected T1-weighted image to native FLAIR using normalized mutual information while preserving the established T1-space anatomical mask. We also introduced extended quantitative quality control (E-QC), which characterizes mask extent, field-of-view-relative position, FLAIR intensity support, boundary support, inferior morphology, and pairwise geometric disagreement. In 78 participants with paired T1-weighted and FLAIR imaging, A$^3$PreCore was compared with fsl_anat and the Brain Extraction Tool (BET). Gross rigid-body misregistration occurred in 21/78 fsl_anat outputs (26.9%) and 0/78 A$^3$PreCore outputs (exact two-sided McNemar p=9.54 x 10^-7). Among 57 participants without gross fsl_anat misregistration, A$^3$PreCore preserved close agreement (median Dice=0.993; median paired Delta NMI=-0.00007, p=0.429). A$^3$PreCore remained broadly concordant with BET (median Dice=0.955), with less inferior and extracranial extension in representative comparisons. Method-blinded neuroscientists ranked A$^3$PreCore first in 35/40 participants (87.5%). E-QC additionally exposed severe orientation-related disagreement not evident from global descriptors or centroid displacement alone. These findings support A$^3$PreCore as a robust native-FLAIR brain-mask transfer strategy and E-QC as a complementary framework for multidimensional mask characterization and participant-specific geometric quality control.
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Artificial Intelligence
PhySGA: A Physics-Space Grounded Agentic Framework for Generalizable and Interactive 3D Composition
3D object composition is pivotal to digital content creation and robot simulation, while also serving as a critical testbed for physical intelligence in foundation models. Previous methods either leverage large language models to directly predict object coordinates, or utilize generative diffusion priors to synthesize composite images for visual alignment, both of which rely on static priors in digital spaces. However, these methods consistently struggle with complex compositions such as precise hanging, gravity-driven settling and hidden containment, as these tasks require interactive construction processes involving global planning, fine-grained alignment, and physical simulation. To address these challenges, we propose PhySGA, a Physics-Space Grounded Agentic Framework for 3D composition via agent exploration and physical simulation, enabling the universal interactive assembly of rigid, articulated, and deformable objects. Directly applying vanilla LLMs or VLMs to this task proves insufficient, as current models inherently lack grounded physical understanding and interactive construction experience. To overcome this limitation, we design a collaborative feedforward-feedback architecture: an Assembly Agent focuses on geometric and kinematic reasoning for global step planning and coarse adjustment, while a Critic Agent reasons over contact dynamics for simulator state diagnosis and fine-grained closed-loop correction. Furthermore, Action Routers map semantic planning and analysis onto executable physical primitives within the simulator, while a task-specific Self-Evolving Skill Library distills historical trial-and-error feedback into reusable experiences, boosting success rates and minimizing exploration attempts. Extensive experiments within Isaac Sim demonstrate that PhySGA significantly surpasses existing methods in relation fidelity, physical plausibility, and visual quality.
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Differential Geometry
Proof of the Penrose Conjecture for Maximally Parameterized Initial Data Sets
We prove the spacetime Penrose inequality for asymptotically flat initial data sets $(M^n,g,k)$ in all dimensions $n\geq 3$, under the dominant energy condition, for data admitting the 'maximally parameterized form' defined in equation (4.7). In this case, the second fundamental form $k$ is locally parameterized by $n(n+1)/2$ functions, giving the same formal local functional degrees of freedom as an arbitrary symmetric $2$-tensor. The proof is based on a new 1-parameter family of generalized Schoen-Yau identities and their gauge-invariant specialization, inspired by the generalized Jang framework of Bray-Khuri [8, 9]. For maximally parameterized data, these identities produce a Riemannian comparison metric \[ \bar g=g+\beta\otimes\beta \] with nonnegative scalar curvature $R_{\bar{g}} \geq 0$. Under a natural nondegeneracy condition (5.7) at the apparent horizon, the comparison metric admits a smooth minimal completion up to $\partial M^n$. Together with suitable asymptotic control, this reduces the Penrose inequality to its Riemannian counterpart. The all-dimensional conclusion uses the Riemannian Penrose theorem of Bi-Zhu [6], together with a minimizing enclosure argument that allows singular boundaries. More generally, in the spirit of [8, 9], we note that the Penrose conjecture follows whenever a certain system of PDEs (3.18) involving $k$ can be solved, in which case our new identity (3.15) immediately implies $R_{\bar{g}} \geq 0$. A natural problem is thus to regularize our degenerate system to prove a general existence theory, thereby proving the Penrose conjecture. Essentially, we believe this is what the OpenAI paper [27] posted last week on October 6, 2026 claims to have done.
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Geometric Topology
Minimal $\mathfrak{sl}_N$ Complexes of Rational Tangles via the Fukaya Category
We compute minimal $\mathfrak{sl}_N$ complexes for oriented rational tangles, denoted $[\![\tau_{u/v}^{O}]\!]_N$, in terms of the topological Fukaya category of the $3$-punctured disk. This demonstrates that the complexes stabilize, allowing us to define a HOMFLY-PT homology for rational tangles.
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Astrophysics of Galaxies
Binary-lens amplification of starlight: from magnification flares to quasi-periodic tracking of orbital evolution
Supermassive black hole binaries (SMBHB) are expected at the center of galaxies as a result of galaxy mergers. The dynamics and evolution of SMBHBs shed light on the evolution and formation of galaxies, the gravitational wave background and the nature of gravity. Many methods have been proposed to identify sub-parsec SMBHBs via the detection of gravitational waves or the modulation of the emission from the surrounding gaseous environment. In a previous study, we proposed a new method of identifying SMBHBs in non-active galactic nuclei via gravitational lensing. The caustics, i.e. the source positions with a divergent magnification, exhibit a complex extended geometry which rotates with the binary period. Each caustic-crossing produces an extreme magnification by up to a factor of $10^{6}$. In this work, we generalize the previous study and describe the rich phenomenology of binary-lens amplification of starlight (BLAST). We explore the electromagnetic transients produced when accounting for the relative proper motion of the source, either a single or a binary star, the eccentricity and precession of the SMBHB, and the relative inclination. Systems where a star rapidly drifts across the caustic produce a single- or double-peaked flare. In the opposite limit, a star with no relative proper motion produces quasi-periodic lensed starlight (QPLS), i.e., repeated peaks that track the system's orbital evolution. We determine the expected magnification and peak duration in different circumstances, and calculate the magnification curves and their Fourier transforms. This study may help construct search pipelines to identify SMBHBs in electromagnetic time-domain surveys.
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Computer Vision
Speculative Sampling in Interactive Video Generation
Interactive video generation commonly relies on small bidirectional chunks to reduce response latency. Yet our preliminary experiments show that larger chunks improve video quality and better utilize GPU parallelism, allowing more latents to be sampled with only a modest increase in sampling time. Motivated by these observations, we propose Speculative Sampling, a strategy that combines the modeling power of large bidirectional windows with the low-latency interaction of small ones. It expands the modeling window by appending noise latents as padding and caches the resulting predictions for reuse when the condition remains unchanged. Predictions are delivered incrementally, while the uncommitted future remains replaceable. Our latency analysis shows that this removes the waiting-time lower bound imposed by chunk boundaries, shifting the optimization focus from reducing chunk size to accelerating per-chunk sampling. Bidirectional window size thus becomes a decision variable for jointly optimizing visual quality and sampling time, rather than a necessary constraint on low-latency interaction. This opens a path to serving large bidirectional models in interactive streaming systems without complex streaming post-training.
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Instrumentation and Methods for Astrophysics
Refurbishment and Cryocooler Upgrade of the CPAPIR Wide-Field Near-Infrared Camera: Design, Integration, and Lessons Learned
The CAmera PAnoramique Proche Infrarouge (CPAPIR) is a wide-field near-infrared imager that has been operating at the Observatoire du Mont-Mégantic (OMM) since 2004. After more than two decades of service, the instrument required a major refurbishment due to detector degradation, including the loss of one quadrant, as well as operational constraints associated with its liquid-nitrogen cooling system. To extend the instrument's lifetime and reduce maintenance requirements, the detector was replaced and the cooling system upgraded through the integration of a Sunpower CryoTel DS30 cryocooler. This paper presents the thermal and mechanical redesign of the instrument, including finite element analysis (FEA), three-dimensional CAD modeling, hardware selection, and laboratory validation. Particular attention is given to the challenges encountered during integration and testing, notably vibration mitigation and cryogenic system implementation. The resulting performance improvements and lessons learned from the upgrade are discussed. The upgraded instrument is scheduled for on-sky commissioning at the Observatoire du Mont-Mégantic in summer 2026.
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Number Theory
The large sieve inequality and additive decompositions of sums of squares
Building on the large sieve, we prove a new sieve estimate for sets which are missing various residue classes modulo prime squares. For certain interesting residue class configurations, our bound is a significant improvement over the corresponding Johnsen-Selberg sieve inequality. Our application of this sieve estimate is motivated by Ostmann's problem. We study additive decompositions of sums of squares and show that any non-trivial sumset decomposition must consist of two sets of roughly equal size: If $A_1, A_2 \subseteq \mathbb{Z}$ with $A_1 + A_2 = \{x^2 + y^2 : x, y \in \mathbb{Z}\}$ and $|A_1|, |A_2| \geq 2$, then $\sqrt{x}/(\log x)^{9/2} \ll |A_i \cap [1, x]| \ll \sqrt{x}(\log x)^4$ for $i \in \{1, 2\}$.
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Strongly Correlated Electrons
Metallic electron crystals in rhombohedral graphene as a bridge to twisted WSe$_2$
Superconducting phases have recently been discovered both in twisted bilayers of transition metal dichalcogenide WSe$_2$ (tWSe$_2$) and in rhombohedral multilayer graphene (RMG). While both have generated extensive interest, they appear to be driven by qualitatively different physics. Here, we propose a unified picture in which the superconductivity in RMG arises from a strongly correlated metallic state with a spatial length scale that is compatible with the moiré length scale of tWSe$_2$. Central to this mechanism is a Wigner crystal phase in RMG that is metallic, driven by a "W"-shaped dispersion in the flat part of the underlying graphene band structure. We demonstrate this effect through calculations of Wigner crystal states in pentalayer RMG, focusing on dilute electrons in the quarter-metal regime relevant to experiment. In a region of the phase diagram we find the Wigner crystal breaks three-fold rotation symmetry, which guides our construction of a $t$-$V$ model on a triangular lattice as an effective description of the low-energy electronic physics. This construction suggests a surprisingly similar low-energy description of RMG and tWSe$_2$. Broader implications for superconductivity in dilute carrier systems are also discussed.
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Robotics
KinoGen: Customizable Humanoid Loco-Manipulation References via Kinematically Grounded Video Generation
We present KinoGen, a framework that synthesizes customizable humanoid loco-manipulation references through kinematically grounded video generation. KinoGen conditions a pretrained video generator on calibrated renders of the target robot and object in a simulated task instance and recovers the reference by fitting the same models to the generated two-view video, so that the reference lies in the robot configuration space by construction without a human body proxy or retargeting. Body, hand, and object priors initialize the reconstruction, and direct optimization against cross-view evidence refines it. Since an edited keyframe is simply another rendered state, a user can prescribe a goal object pose, regenerate the video around the edited keyframe, and obtain a reference that satisfies the pose exactly. Across eight loco-manipulation tasks, KinoGen yields lower penetration and foot skating than video-based baselines and preserves over 90% of annotated contacts, and its customized references satisfy every prescribed target with substantially less penetration than direct interpolation. Tracking policies trained on the synthesized references are deployed on a Unitree G1 humanoid with dexterous hands. Project webpage: https://kinogen-humanoid.github.io/.