Papers

Molecular quantum dynamics simulations that treat both electrons and nuclei quantum mechanically are crucial for predicting chemical reactions. With classical computation, a full wave-function representation of both types of particles requires resources that grow exponentially with their number. Oscillator-qubit processors, including trapped-ion and circuit QED devices, represent electronic states with qubits and nuclear vibrations with oscillators. Their native operations produce linear vibronic interactions, from which programmable anharmonic interactions can be built. Product-formula approaches build the corresponding phase gates by repeating small noncommuting phase steps, and quantum signal processing (QSP) approaches approximate each gate directly with a Fourier series. Simulations apply many such gates in sequence, so accumulated cost and error limit how long the dynamics can be followed. We propose near-optimal quantum primitives for molecular quantum dynamics simulation, covering the representations of both types of particles and their interactions. We synthesize nonlinear and multimode bosonic phase gates using generalized Jacobi-Anger (GJA) expansions within QSP, with a cost that grows near-optimally in both interaction strength and precision. Our interaction model and gate synthesis each have their own accuracy setting. Chosen together, these settings make our multimode benchmark circuits about one-third shorter than those of the previous direct QSP approach. We then simulate energy exchange between the stretching and bending vibrations of a simplified carbon dioxide model. With circuit-QED noise, a short simulation narrowly misses our accuracy criteria at qubit and oscillator lifetimes near 2 ms and 5 ms. These lifetimes mark a concrete checkpoint on the way to simulating anharmonic multimode molecular quantum dynamics on near-term oscillator-qubit processors.

We study irrevocable maximum-cardinality matching in trees revealed by successive leaf attachments, with a known horizon and an exogenous growth law that is misspecified or unknown. For deterministic affine attachment forecasts with nonnegative degree reinforcement, the optimal threshold policy loses at most twice the cumulative expected conditional total-variation error relative to an online oracle knowing the actual growth law. This follows from a unit-span property of the Bellman continuation score and has no additional horizon factor. A four-vertex example attains the coefficient two for the specified deterministic policy, and a two-model argument gives a lower bound linear in the model-error budget for arbitrary policies under general misspecification. For uniform-preferential attachment, the local error has an exact expression through the leaf count. When its constant mixture parameter is unknown, we estimate it from the same growing tree and update the threshold policy at geometric times. A parameter-sensitivity bound for individual Bellman prices and uniform degree-moment estimates yield expected regret $O(\sqrt{n}\log^2 n)$, using $O(n^2\log n)$ arithmetic operations and $O(n)$ stored entries. The exact minimax rate remains open.

In the adjacent transposition shuffle on a cycle, $n$ distinct cards are placed at the vertices of a cycle, and adjacent cards swap positions according to independent Poisson clocks of rate 1. We prove that this Markov chain exhibits total variation cutoff at time $n^2\log n/(8\pi^2)$, with a window of order at most $n^2\log\log n$.

Partial Optimal Transport (POT) extends the classical optimal transport problem by relaxing the strict mass conservation constraint, enabling its use in a wide range of real-world applications. In many of these settings, sparse transport plans are preferred for their interpretability and computational benefits. While smooth and strongly convex regularizers - such as quadratic or elastic net - have been vastly used in various machine learning applications to induce sparsity and accelerate computation, they have received less algorithmic attention compared to entropic approaches for computational POT. In this paper, we propose a new optimization framework that leverages these regularizers through a penalty-based reformulation, enabling efficient gradient-based updates while preserving the structure of the original problem. Our method accommodates a broad class of regularizers that promote structured and sparse transport plans. Building on this formulation, we design an accelerated first-order algorithm that alternates between smooth updates and simple projection steps. Through empirical benchmarks on color transfer, domain adaptation, and point cloud registration, our approach consistently outperforms established baselines - achieving lower transport cost, higher sparsity, and faster convergence - making it a practical and scalable solution for modern transport problems.

We compute the Morse index of several complete nonorientable minimal surfaces immersed in Euclidean three-space. In particular, we prove that the Meeks minimal Möbius band has Morse index two, which is the least possible Morse index for such nonorientable minimal surfaces, by previous works of Ros and Chodosh-Maximo. This is the first known minimal surface with index two. We show that the López minimal Klein bottle has Morse index three. As a consequence of this computation, we extend results in the literature and observe that any complete minimal surface immersed in Euclidean three-space with total curvature $8 \pi$ has Morse index three. We also compute the Morse index of the Oliveira family of minimal Möbius bands in terms of their total curvature and show that every non-negative integer is the Morse index of a complete minimal surface immersed in Euclidean three-space. We show that five is a sharp lower bound for the Morse index of any minimal oriented double cover in Euclidean three-space, and equality is attained by the double cover of the Meeks minimal Möbius band. Finally, we prove results towards the classification of complete minimal surfaces with Morse index two immersed in Euclidean three-space, obtaining topological and geometric restrictions on such surfaces.

Linear combination of unitaries (LCU) is a fundamental primitive in quantum algorithms, whose cost is typically governed by the most expensive unitary appearing in the combination. We develop a transducer-based LCU framework that reduces this worst-case dependence to a weighted average query complexity, when the constituent unitaries share access to a common set of primitive oracles. Consider $A=\sum_j c_j U_j$, where $c_j>0$ and each unitary $U_j$ can be implemented using $C_j$ primitive queries. Given an upper bound $a\geq \|A\|$, our algorithm implements a block-encoding of $A/\alpha$ with rescaling factor $\alpha=\mathcal{O}(a)$, using $\widetilde{\mathcal{O}} (C_{\max}+\overline{C} {\lambda}/{a} )$ primitive queries, where $\lambda=\sum_j c_j$, $C_{\max}=\max_j C_j$, and $\overline{C}= {\sum_j c_j C_j}/{\lambda}$. By comparison, the standard LCU construction requires $\widetilde{\mathcal{O}} (C_{\max} {\lambda}/{a} )$ primitive queries. The improvement can therefore be substantial when costly unitaries have small weights and $\lambda/a$ is large. As applications, we obtain improved block-encodings of sparse matrices, leading to quantum algorithms for sparse Hamiltonian simulation and quantum linear systems with near-optimal query complexity up to polylogarithmic factors in all relevant parameters. Our main technique is the transducer framework developed by Belovs, Jeffery, and Yolcu [Quantum, 8:1444 (2024)]. Here we develop a complementary operator-level theory tailored to block-encodings. We identify the resolvent norm $K$ as a key complexity measure for transducer implementation besides the existing catalyst complexity. We show that the transducer action can be converted into an $\epsilon$-approximate block-encoding using only $\mathcal{O}\left(K \log(1/\epsilon)\right)$ queries to the transducer, improving the precision dependence from polynomial to logarithmic.

Tauonic flavour-changing neutral-current transitions ($b\to s\tau^+\tau^-$) are sensitive probes of New Physics connected to third-generation quarks and leptons. Motivated by the persistent anomalies in $R(D^{(*)})$ and the indications of enhanced $B^+\to K^{+}\nu\bar\nu$ rates, we revisit and update the predictions for $b\to s\tau^+\tau^-$ processes. Building upon a previous work on a data-driven approach to include the dominant $\psi(2S)$ resonances, we provide predictions for $B\to K^{(*)}\tau^+\tau^-$ ($B_s\to\phi\tau^+\tau^-$) over the full kinematic range. To include possible New Physics contributions within the Weak Effective Theory, we provide semi-analytic expressions for the corresponding branching ratios. We then perform a comprehensive dimension-6 SMEFT analysis of New Physics realised at the TeV scale. We identify regions of parameter space preferred by current data where the branching ratios of $b\to s\tau^+\tau^-$ processes can be enhanced by several orders of magnitude. While current experimental sensitivities remain far above the SM rates, the enhancements suggested by present flavour data imply that forthcoming limits from LHCb, CMS, and Belle~II will probe significant regions of the relevant SMEFT parameter space. Furthermore, we highlight that while different scenarios can lead to the same predictions for $B\to K^{(*)}\nu\bar\nu$ branching ratios, they can be disentangled by measuring $B\to K^{(*)}\tau^+\tau^-$, $B_s\to\tau^+\tau^-$ and $B_s\to\phi\tau^+\tau^-$.

Digital twins increasingly support downstream analytical tasks that depend on time-series data, motivating interest in time-series foundation models (TSFMs) as scalable backbones. However, TSFMs are primarily pretrained for temporal continuation and often underperform on unseen tasks such as regression, and systematic empirical comparisons against state-of-the-art dedicated models in digital twin contexts remain limited. This paper makes three contributions. First, we benchmark five well-known TSFMs with frozen backbones on remaining useful life (RUL) prediction using the C-MAPSS dataset, finding that multivariate architectures substantially outperform univariate ones, particularly under varying operating conditions. This raises a deeper question: when cross-channel dependencies can be modeled through pretrained weights, target-task adaptation, and digital twin-derived representations, how much does each contribute, and are they complementary? Second, we propose a topology-informed fusion approach in which topological constraints, derived from the asset structure the digital twin stores among its information models, explicitly shape cross-attention, so that fused representations respect the physical system's local connectivity rather than relying on unconstrained all-to-all interactions. Third, we conduct an ablation study across C-MAPSS subsets of varying operational complexity that isolates the three sources and their interactions. The sources prove complementary rather than redundant, and topology-constrained attention outperforms unconstrained fusion, though by a small margin, enabling a frozen TSFM informed by digital twin representations to remain competitive or in some cases exceed state-of-the-art performance on this regression task.

When inference demand exceeds available compute capacity, model providers must decide which requests should be served first. Users have different tolerances for delay from an LLM API, but current priority pricing schemes compress these differences into coarse fixed-price service tiers. We design an inference auction that allows users to bid for faster service. Our auction allocates priority in an economically efficient way without sacrificing latency, and we develop fast algorithms for implementing prices that incentivize truthful bidding. We also design an autobidding agent for our inference auction, where users specify an inference budget and the autobidder dynamically adjusts its bids over time to maximize user utility subject to the budget constraint. Experiments validate the practicality of our auction: it increases system welfare while maintaining the cache utilization and latency advantages of SGLang, a state-of-the-art inference serving framework.

Generative Engine Optimization (GEO) shapes content to increase its likelihood of being cited by answer engines built on retrieval-augmented large language models. GEO is typically evaluated as a single-turn property: for a fixed query, an evaluator measures a source's visibility in one answer. We argue that the single answer is an inadequate unit of analysis. Human-agent information seeking forms a closed loop: the agent's answer changes the user's beliefs and therefore the next question, which in turn determines what the agent retrieves. We introduce conversational capture, a phenomenon in which a source cited early becomes substantially more likely to be cited again. Capture operates through a machine-side channel, history-conditioned retrieval, and a human-side channel, follow-up questions directed toward the captured source. We formalize the interaction as a two-layer closed-loop system and derive trajectory-level constructs: cumulative conversational visibility; a direct/feedback decomposition of trajectory gain; a nested split of the feedback term into machine-side and human-side channels; a capture coefficient; a compounding ratio; and a misranking diagnostic. Using reinforcement-process (Pólya-urn) theory, we prove that the feedback term is zero under single-turn evaluation and that GEO's cumulative payoff grows superlinearly with conversation length while capture develops. A model-derived illustration shows that the feedback term can exceed the direct term, the compounding ratio exceeds two within ten turns, and single-turn and trajectory rankings agree only weakly (Kendall's $\tau = 0.4$). We connect the human channel to information foraging, trust calibration, and Bayesian persuasion, and discuss design implications for answer engines.

In the present paper, we extend the results in the sequence of works \cite{KS-GCM1} \cite{KS-GCM2} \cite{KS:Kerr} by Sergiu Klainerman and the author, \cite{GKS22} by Elena Giorgi, Sergiu Klainerman and the author, and \cite{Shen} by Dawei Shen from the slowly rotating regime $|a|\ll m$ to the full subextremal range $|a|<m$, thereby completing the proof of the Kerr stability conjecture. The restriction $|a|\ll m$ enters in fact only through the estimates for wave equations and for the Bianchi system established in \cite{GKS22}. To remove this restriction, we crucially rely on the two companion papers \cite{MaSz24} \cite{MaSz26} by Siyuan Ma and the author, in which we prove energy-Morawetz estimates respectively for the inhomogeneous scalar wave equation and for inhomogeneous Teukolsky equations on perturbations of Kerr with $|a|<m$. Additionally, some of the results of the present paper are proved in our companion paper \cite{Sze}.

Community Notes is a crowd-sourced approach for adding context to posts on X. Contributors propose and rate notes, forming the inputs to an open-source, open-data algorithm that determines which notes show broadly to users. Since September 2025, Community Notes' AI Note Writer API has provided an open, public interface for using AI to propose notes, while adhering to the founding principle that users, not the platform or an AI, control which notes show on X. Explicit note requests and user posts on X determine the AI API post feeds, ensuring that AI note writing responds to demand from X users. We present the design, operation and impact of the AI API, including analysis of the interaction between AI and human generated notes across topics. Unless otherwise stated, measurements and system description reflect June 2-29, 2026. The Community Writer is the largest AI API client and contributes the bulk of AI API output, generating 52% of notes selected as Helpful and shown broadly on X. The writer is guided by community input during both training and operation to prioritize, draft, evaluate and delete proposed notes. Beyond scale, the writer also offers speed, submitting the first proposed, non-deleted note on 60% of posts when compared to other writers. AI note writing is additive on top of human note writers, extending coverage of Community Notes on X. Among posts that have Helpful notes, 42% have only AI notes, indicating human raters did not feel motivated to propose an alternative. In contrast, 30% have only human notes, reflecting contribution beyond the scope of AI writing. The Community Writer is open-source software released under the Apache 2.0 license.

Dark matter N-body simulations that resolve halo substructure (subhalos) with high accuracy can be used for generating reliable catalogs of central and satellite galaxies via galaxy-halo connection models. However, such simulations are computationally expensive, especially when large numbers of realizations are required for statistical analyses such as robust estimations of covariance matrices for (statistical) cosmological quantities. In this work, we present a fast method for populating dark matter halos in a given simulation box with subhalos extracted from a high-resolution simulation box with the same cosmology but arbitrary initial conditions. For each halo in a given test set, the method first predicts whether it hosts at least one subhalo above a given mass threshold using a classifier built on a decision tree regressor. Then, for each predicted host, the method finds another host halo in a given high-resolution box, using a nearest neighbor search in the space of selected halo properties, and appropriately maps subhalos from that halo to the test one. By applying the method to different test sets, we make predictions for abundances, distributions and three-dimensional and projected (two-dimensional) two-point correlation functions of various subhalo populations and sub-populations. In most cases, the percent errors of our predictions are well below 5%. In general, the method can be used to populate halos in low-resolution simulation boxes with subhalos from a high-resolution simulation and also to investigate which halo properties are (more strongly) correlated with subhalo abundance and clustering in a given dark matter simulation.

Quantized Hall transport is traditionally anchored to a bulk spectral gap, which isolates the occupied subspace and exponentially suppresses thermal deviations. Recently discovered critical topological flat bands (CTFBs) challenge this paradigm: an exactly flat band touches a dispersive continuum while retaining a well-defined integer Chern number. However, their finite-temperature transverse transport properties remain entirely unexplored. Here, we develop a low-temperature theory of the intrinsic electrical, thermoelectric, and thermal Hall responses in CTFBs. At fixed particle number, the macroscopic flat-band degeneracy forces a singular Lambert-$W$ drift of the chemical potential, generating an algebraic-logarithmic hierarchy of low-temperature corrections: $T\ln(1/T)$ for electrical Hall, $T[\ln(1/T)]^2$ for thermoelectric Hall, and $T[\ln(1/T)]^3$ for thermal Hall conductivity, replacing the activated thermal protection of a gapped Chern insulator. By contrast, externally pinning the chemical potential to the flat-band energy locks the flat band to half occupation at any nonzero temperature, obstructing the recovery of the fully filled topological ground state as $T\to0^+$. Our results establish that a bulk spectral gap is unnecessary for zero-temperature Hall quantization, but indispensable for its exponential thermal protection.

Purpose: This study examines whether domain-specific public mood is associated with stock-market dynamics and whether these relationships vary across communication domains and market conditions. It distinguishes public mood from investor sentiment and investigates whether heterogeneous sources of public communication exhibit different relationships with market behaviour. Design: The study analyses 610,422 posts published by 176 curated X accounts between January 2022 and December 2023, covering Politics and Government, Economy and Finance, and Media and Society. Posts are classified using fine-tuned Turkish transformer models under three domain-specific and one pooled regime. Public mood measures are constructed at daily, weekly, and monthly frequencies and examined alongside BIST100 and BIST30 market measures using correlation, Granger causality, vector autoregression, and impulse response analyses across the full period and selected market conditions. Findings: Public mood is not associated with the direction of stock-market returns but is associated with the magnitude of price movements, particularly for Media and Society and pooled communication. These relationships become stronger at longer aggregation frequencies. Predictive relationships are concentrated in Economy and Finance communication, while their magnitude and direction vary across market conditions, particularly during the 2023 election period. The pooled measure largely reflects the most active communication domain. Originality: The study contributes to behavioral-finance research by incorporating communication - domain heterogeneity into the analysis of public mood and market dynamics. It also demonstrates how aggregating heterogeneous sources can obscure domain-specific relationships between public communication and financial markets.

Low-Rank Adaptive Residual Connections (LARC) give a frozen model a compact numerical state that can learn from feedback. The map $h+BAh$ adds a low-rank correction to a hidden representation. A slow state $\rho$ learns starting factors across tasks; a private fast state $\Phi$ copies them, changes with feedback, and resets to the trained initialization. This report specifies an input-side realization of the numerical policy carrier in Memory-Mediated Learning Architecture and examines its factor-space dynamics and learning lifetime. We study a rank-4 input residual with 12,288 trainable parameters on a frozen MiniCPM5-1B-SFT substrate. In a four-candidate program-selection task, two feedback-gradient steps reduce expected query execution error by 24.65 and 36.65 percentage points relative to resetting to the respective trained static and post-adaptation initializations. These development results cover 16 parameter groups and three paired training seeds. A direct support-loss selection rule is much more accurate, reaching 0.78125% error. In a repository-balanced chronological replay of public continuous-integration jobs, retaining online updates raises half-Brier loss from 0.1274 to 0.1808. A fixed follow-up intervention records same-batch non-descent and inconsistent future benefit from shrinking updates. Together, the algebra and measurements distinguish residual capacity, adaptation relative to a starting point, and usefulness on later decisions.

We establish a no-go theorem for a broad class of quantum algorithms for the dihedral coset problem (DCP). We consider the Fourier-sampling and subset-sum-measurement template proposed by Regev (SIAM Journal on Computing, 2004), which is one of the main approaches to solving DCP. Suppose that, after measuring the lower $n-1$ bits of the subset sum, the algorithm discards any $\omega(\log n)$ bits from each of the Fourier labels. Then we prove that the algorithm cannot succeed in solving DCP. This shows that any algorithm following this template must make extensive use of the Fourier labels, and thus serves as a useful guide for developing algorithms for DCP. As a main application, we show that the recent algorithm by Simon (IACR ePrint:2026/1591, August 11 2026) does not solve DCP. We show that after the subset-sum measurement, this algorithm can be implemented (up to exponentially-small error) using only the most-significant third of the Fourier labels, and is therefore subject to our general no-go theorem. To help with verifiability, we release Lean 4 code for our results.

The bosonic quantum entropy power inequality bounds the entropy of a beam-splitter output in terms of the input entropies. We determine its complete equality class among independent inputs of finite mean photon number: for any number of modes and any transmissivity strictly between zero and one, equality in either the linear or the exponential form holds if and only if the inputs are Gaussian with the same covariance matrix, allowing arbitrary displacements. The main step shows that equality for one output forces the two outputs to be independent: a thermal auxiliary converts equality into preservation of mutual information by a fixed noisy channel, and a two-outcome instrument shows that preservation of mutual information requires a product state with the reference. The quantum Darmois–Skitovich theorem then gives Gaussianity, while a central-limit argument reduces exponential equality to linear equality.

Foundation machine-learning interatomic potentials cover broad configurational and chemical spaces, but their reliability can vary across the atomic environments encountered during a simulation. Here we introduce the calibrated Mahalanobis (CALM) extrapolation grade $\gamma$, a piecewise differentiable per-atom quantity integrated into GRACE foundation models and evaluated alongside energies and forces in a single model pass. We define $\gamma$ from nearest-cluster Mahalanobis distances in latent feature space, setting $\gamma=1$ from the training-distance distribution separately for each element and cluster. Controlled tests show that a normalized random projection of the invariant many-body basis detects structural and chemical extrapolation. On different foundation datasets, OMat24 and SMAX, $\gamma$ correlates with atomic force errors and separates structures with different error distributions. The CALM grade adds percent-level computational cost, and its spatial gradient guides uncertainty-biased data collection toward configurations with larger absolute force errors.

Superconductor and two-dimensional hole gas heterostructures are promising platforms for quantum devices, but their intrinsic properties, e.g., unconventional pairings, are hard to access experimentally. Here, we show that the in-plane-field dependence of the superfluid stiffness and spin susceptibility exhibits nonanalyticities encoding the induced gap structure in the hole gas. Additionally, Fourier harmonics of the stiffness tensor's field-angle dependence, accessible via kinetic-inductance measurements, provide fingerprints of unconventional pairing and cubic Rashba coupling.

Titan, a unique body in the solar system, resembles a life-size Miller-Urey experiment where pockets of liquid water might interact with abundant organic matter. Its young surface (less than a billion years) shows signs of material exchange with the interior, and an isotopic signature is detected in the atmosphere. Cryovolcanism and meteor impacts represent potential high energy mechanism for these exchanges. Although cryolava or impact melt properties are largely unknown, Titan's internal structure makes a significant water content in these fluids highly probable. The temperature of these fluid mixtures at the onset of the flows is above 0~$^\circ$C. The primary objective of this work is to investigate the dynamical and thermal properties of potential Titanian flows, while ensuring their spatial extents remain broadly consistent with the few available observations. We also aim to assess whether their evolution could enable the hydrolysis of encountered organic material. On Earth, in the context of lava flow risk assessment, numerical techniques based on cellular automata have been developed for many years. This approach allows simulating the flow of Bingham fluids over distance scales of several tens of kilometers. In the context of Titan's surface, and within the explored parameter space, flows with a spatial extent of several tens of kilometers can be produced with our model. The resulting flow thickness is about a meter. The flow extent is primarily controlled by the total erupted volume and the terrain topology. As expected, the rheology and thermo-physical properties of the erupted fluid have significant influence on the flow's extent and the cooling rate of the cryolava. We predict hydrolysis reactions between an aqueous cryolava and the organic matter likely ubiquitous on Titan's surface. Our model code is publicly available.

The nature of dark matter sets the shape of galactic halos: collisionless cold dark matter (CDM) predicts triaxial halos, while scattering in self-interacting dark matter (SIDM) rounds them toward sphericity. We show that a large catalog of projected stellar stream tracks can statistically constrain halo shapes, and therefore the particle nature of dark matter, without detailed modeling of any individual stream or gravitational potential. We develop a new geometric diagnostic for stellar streams: if the curvature of any segment along a stream points away from the host galaxy's projected center of mass, then that stream falsifies broad classes of potentials, including spherical ones. We call such a segment convex. The diagnostic needs only a projected stream track and a host-center estimate, requiring no kinematics, distances, progenitor model, or fit to individual host potentials. Halo triaxiality sets the rate at which streams show convex segments, making this rate an observable of the halo-shape distribution and the underlying dark-matter model. We forecast that upcoming survey-scale stream morphology catalogs can discriminate between CDM and SIDM at up to $5\sigma$.

Control design for high-order converters with nonlinear dynamics is generally difficult. Nonlinear controls introduce formidable model complexity whereas linear controls suffer from poor disturbance rejection. Our objective in this paper is to develop a simple neural-network-based controller that learns the control law from supervised trajectories generated by a model-based bounded inversion framework. First, we establish strong invertibility for the converter models. Next, we prescribe the desired closed-loop behavior through a trajectory model that defines the target dynamics. We then invert the converter dynamics numerically to obtain the corresponding duty-cycle and state trajectories. We use these model-based trajectories as supervision and train a neural network to approximate the resulting state-to-duty control law. The results show that the learned controllers accurately recover the inversion-based control action and achieve effective regulation under load and input-voltage disturbances. We validate the method on fourth order Cuk, SEPIC, and zeta converters.

On-policy distillation (OPD) provides dense supervision directly on student-generated trajectories, making it an effective post-training strategy for vision-language models in temporal video grounding (TVG). However, existing pipelines typically construct the training curriculum from a fixed teacher and the initial student state, implicitly assuming that selected examples retain positive supervision value throughout optimization. We show that supervision trustworthiness and supervision necessity are distinct yet coupled: the former concerns target credibility, while the latter varies with the student's current task competence; together, they shape supervision value. Building on this coupled view, we introduce Student-Curriculum Coupling (SCC), a closed-loop framework in which a compact Anchor-Frontier curriculum defines the candidate supervision space and the evolving student dynamically determines its active subset. Supervision can therefore be activated, suspended, or reactivated as competence changes, concentrating teacher computation and optimization on current task-level deficits. Across three TVG benchmarks, SCC achieves a 5.1% relative improvement in mean recall over Video-OPD on its original curriculum, while using 60.0% fewer training examples and reducing training time by 50.4%. Ablations support the complementary roles of capability-structured curriculum design and student-dependent supervision in achieving these gains. Together, these results establish SCC as a data- and compute-efficient framework for TVG post-training, delivering stronger temporal grounding by aligning trustworthy supervision with the student's evolving learning needs.

We develop a theory of exact transmission of finite-dimensional $C^*$-algebras through quantum channels. These algebras describe hybrid classical-quantum information, allowing the dimension of the quantum system to depend on the classical message. Allowing arbitrary encodings and decodings yields a transmission set of algebra types, ordered by embedding, that unifies zero-error information theory with operator-algebraic error correction. We ask if this set admits a dominating algebra into which every transmittable algebra embeds. Our central finding is that domination can fail even in small dimensions. In its absence, several incomparable maximal algebras can describe different optimal uses of the same channel, forcing the user to select one depending on the operational task and the type of information to be preserved. We introduce hybrid capacities that reconstruct the only possible dominating algebra type and present a complete finite characterization of domination using minimal forbidden algebra types. We identify dominating algebras for channels whose operator systems are graph-isomorphic to $*$-algebras, including highly divisible channels, and for channels with zero one-shot zero-error quantum capacity. Under tensor products, we prove that joint coding can produce new algebra types, giving an algebraic analogue of superadditivity from Shannon theory. Domination can fail for the joint use of two channels, even when both channels separately admit dominating algebras. Finally, we construct a channel whose $n$-fold tensor powers have doubly exponentially many maximal algebra types, attaining the largest possible growth scaling for finite-dimensional channels. Consequently, new transmittable algebra types appear at arbitrarily large block-lengths for this channel, so its full transmission structure cannot be generated from any finite collection of bounded-block-length codes.

We present an analytical study of impurity-induced density correlations in interacting one-dimensional Luttinger liquids using the Unified Field Bosonization Technique (UFBT). Unlike conventional approaches that treat impurities perturbatively, UFBT incorporates localized impurities exactly at the free-fermion level while treating interactions non-perturbatively. Closed analytical expressions for fermionic Green functions and density-density correlation functions are obtained for strongly inhomogeneous systems, enabling a unified description of the impurity-induced $2k_F$ Friedel oscillations and the $4k_F$ Wigner-crystal like correlations. The corresponding scaling behaviour is derived analytically, revealing a crossover in the dominant long-distance correlations at $g=1/3$: Friedel correlations dominate for $g>1/3$, whereas Wigner-crystal like correlations become dominant for $g<1/3$, corresponding to the regime of sufficiently strong repulsive interactions. A reflection-coupled harmonic analysis is developed to account for the left-right mixing induced by impurity backscattering and to consistently reproduce the resulting density correlations. The spinless limit is also obtained as a direct reduction of the spinful formulation. These results provide an analytically controlled framework for describing impurity-induced and interaction-driven density correlations in strongly inhomogeneous one-dimensional quantum systems.

Production model uncertainties in long-lived particle searches can affect both the inclusive yield and the kinematic distributions sampled by the experimental acceptance. We isolate the latter effect by comparing the modified Weizsäcker–Williams description with the effective quasireal approximation for dark photon production via proton bremsstrahlung after normalizing both spectra on a common physical domain. At fixed production yield within this domain, the resulting acceptance difference directly measures the departure from rate factorization. In the NA62 beam dump geometry, the central calculation gives a fractional acceptance shift $\delta_{\rm NF}>0.3$ at every numerically converged grid point within the displayed NA62 sensitivity overlap. This conclusion persists for effective QRA off-shell scales of 1.0, 1.5, and 2.0~GeV and under the aperture variations considered. Separately, the public NA62 full selection acceptances give a nonconstant dimuon acceptance ratio between the Mixing and Bremsstrahlung production categories, ranging from approximately 0.58 to 4.23, with a median absolute departure from unity of approximately 0.79 over the analyzed HEPData grid. This provides complementary evidence that the published full selection acceptance depends on the production category. More generally, the projection criterion provides a quantitative test of rate factorization. The normalized production shape variation must have negligible projection onto the acceptance response at the required accuracy. When this condition is not satisfied, production model dependence must be propagated through the acceptance calculation or treated as an acceptance uncertainty.

Estimating causal effects from observational data is central to science and policy, but the effects are not identified when confounders are unmeasured. Proximal causal inference addresses this problem with proxies of the unmeasured confounders. However, existing proxy-based approaches either designate proxy roles and solve an inverse problem, which is ill-posed and hard to estimate with high-dimensional proxies, or use a latent-variable model, which assumes that the learned latent variable matches the hidden confounder and leaves bias when it does not. To address these challenges, we introduce proximal balancing. It carries the classical idea of covariate balancing to confounders that are observed only through proxies: it learns a low-dimensional summary of the covariates and proxies that makes the treatment groups comparable, and then adjusts for this summary. It needs no designated proxy roles, inverse problem, or latent model. We give identification theory, finite-sample guarantees, and a practical algorithm, PROBE. We demonstrate the method on low-dimensional, high-dimensional, and image proxies and on real-world data.

We consider quantum devices restricted to local operations in 2D and subject to local stochastic noise below a constant threshold. We show that such circuits are computationally more powerful than AC0-circuits, i.e., noise-free, geometrically-unconstrained constant-depth classical circuits with unbounded fan-in AND, OR and NOT gates. To this end, we exhibit a computational problem with the following properties: (i) Any instance of the problem is correctly solved with high probability by a certain geometrically 2D-local quantum circuit even if the latter is imperfectly implemented, but (ii) any polynomial-size AC0-circuit fails to solve certain instances of the problem with constant probability. To our knowledge, this isthe first complexity-theoretic separation which applies to planar quantum devices, incorporates noise-resilience and is unconditional, i.e., does not rely on complexity-theoretic assumptions. This brings the experimental demonstration of an unconditional quantum advantage closer to experimental realities.

We review the discrete theory of differential-geometric Poisson brackets as introduced by B. A. Dubrovin, and we present a complete proof of their characterisation in the non-degenerate case. We use this characterisation to show several novel examples of such structures, providing a complete classification for non-degenerate four-dimensional differential-geometric Poisson brackets under the additional assumption of the Lie algebra to be of quasi-Frobenius type. We also present a complete classification of quasi-Frobenius filiform N-graded Lie algebras, including two families in arbitrary dimensions.