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arXiv2026

The Proof-Theoretic Foundations of the Principle of Reiteration in Natural Deduction

This paper investigates the proof-theoretic foundations of the principle of reiteration (R) in natural deduction, arguing that its legitimacy originates in the structural preservation of formulae within sequent calculus rather than in an independent logical rule. By examining singlesuccedent and multisuccedent sequent calculus, we demonstrate how logical operations transform principal formulae while preserving unaffected antecedent and succedent contexts. We subsequently analyse the schematic formulation of reiteration and compare natural deduction derivations with corresponding sequent calculus derivations. This comparison identifies two fundamental functions of reiteration, namely the reuse of previously employed formulae and the restoration of previously derived conclusions. We conclude that reiteration introduces no independent inferential content but explicitly represents the structural continuity of inferential dependencies already included into sequent calculus.

cs.LO↗

arXiv2026

Multi-Fidelity Particle Flow Filters based on Log Homotopy

This work proposes a new Multi-Fidelity Particle Flow Filter (MFPFF) based on a linear control variate framework and multilevel Monte Carlo methods. Conventional particle filters often suffer from weight collapse and particle degeneracy in high-dimensional spaces. Particle flow filters address this by smoothly transporting prior particles toward the posterior distribution, thereby avoiding the need for resampling. This work constructs multi-fidelity particle flow filters by augmenting a small number of expensive high-fidelity particles (full-order model runs) with a large number of inexpensive low-resolution particles (reduced-order surrogates constructed via intrusive Galerkin projection). These surrogates act as control variates to enhance the statistical estimate of the full-order posterior, yielding enhanced analysis accuracy at comparable computational cost. The work focuses on two particle flows based on log homotopy, the stochastic Gromov flow and deterministic Exact flow. Numerical experiments with the Korteweg-De Vries (KdV) and Quasi-Geostrophic (QG) test problems demonstrate that the proposed MFPFF achieves accuracy comparable to high-fidelity simulations while significantly reducing computational expense.

cs.CE↗

arXiv2026

Mapping the Milky Way with SDSS-V: Galactic Genesis Selection Function and Mock Catalog

Robust chemodynamic mapping of the Milky Way requires accounting for the selection function of the survey used, the probability that a given star is included in the final catalog as a function of its observable properties. We derive the empirical selection function of the SDSS-V Galactic Genesis survey, the largest Milky Way Mapper program targeting red giant stars for Galactic structure studies. Treating the Galactic Genesis sample as a subsample of its 2MASS parent catalog, we model the selection function as a function of sky position, apparent H magnitude, and G-H color using a Bayesian binomial estimator, computing both a mean and maximum a posteriori (MAP) version. The resulting selection function reflects the survey's targeting strategy and observing history, including the transition from the pencil-beam SDSS-IV footprint to the fuller sky coverage of SDSS-V and the prioritization of the Magellanic Clouds. Using this selection function with the FIRE-2 Milky Way-mass simulations, we construct mock Galactic Genesis catalogs built on existing mock Gaia DR3 catalogs, injecting realistic photometric noise and applying the selection function via a per-star Bernoulli accept-reject procedure. We demonstrate the mock catalogs' utility with an example application to azimuthal metallicity variations in the disk. Furthermore, we release a Python package allowing users to recompute the selection function for their own samples and science cases. The package, selection function and mock catalogs will be updated and made available as the survey continues, extending the tools needed to reach the full scientific potential of SDSS-V Galactic Genesis.

astro-ph.GA↗

arXiv2026

Quantifying and Predicting Pitch Sequence Effectiveness Using Visual Deception Metrics

Pitcher performance is influenced not only by individual pitch characteristics, but also by the relationship and sequencing between consecutive pitches. In this study, we construct a sequence-level framework using MLB Statcast data from 2021-2025 to quantify the value of pitch deception with two geometric features: Decision Angular Separation (DAS) and Average Angular Separation (AAS). These metrics measure visual similarity of back-to-back pitches from the batter's perspective at a hitter's swing "decision point" during the flight of the ball from the pitcher's hand to the plate. We introduce Swinging Strike Lift (SwStr Lift), a residualized outcome isolating sequencing value beyond player identity, pitch type, location, and count. Across more than 740,936 two-pitch sequences, we find that tighter tunnels (low DAS/AAS) produce significant behavioral changes, for well-tunneled FB-to-BR (fastball-to-breaking-ball) sequences in the Shadow/Chase regions. This elevated swing propensity is consistent with swing induction as a primary behavioral pathway underlying the observed gains in swinging strikes. Our predictive modeling confirms the importance of tunneling, as adding DAS/AAS to gradient-boosted models yields substantial relative improvements in out-of-sample R-squared (e.g., +38% for FB-to-BR and +163% for FB-to-OS [fastball-to-off-speed]). These results demonstrate that tunneling generates a measurable and behaviorally coherent sequencing advantage, offering a tractable, perceptually grounded tool for evaluating pitcher deception which informs pitch design and game strategy. Quintile analyses confirm the effect is not confined to extreme tunnels; ICE plots show model-predicted lift declining sharply as DAS increases. Keywords: pitch tunneling; pitch sequencing; baseball analytics; predictive modeling; XGBoost; perceptual geometry; decision point; Statcast

stat.AP↗

arXiv2026

Quantitative Generalization Bounds for Multi-Layer Transformers: A Few Long Strings can Beat Many Short Ones

Transformer-based language models exhibit an astonishing capacity to generalize to longer and more difficult problem instances than those seen in training. However, theoretical understanding of this phenomenon still lags behind. Unlike most machine learning models, the generalisation abilities of transformers inherently require considering two axes. On one hand, one must examine in-distribution statistical generalisation, which concerns the ability of a model to broaden a function from training samples to novel samples of the same distribution. On the other hand, given the sequential nature of language data, one must also consider length generalisation, which reflects whether a model trained on inputs of a given length can extrapolate to longer ones.These two notions have mostly been studied separately, leaving open how they interact. In this work, we give a joint treatment of both axes for fixed-precision transformers. We give generalisation guarantees in terms of the parameter sizes of the involved models, as well as the quantization space and the alphabet size that supply the sequences. Finally, we illustrate how the requirements in the sample count and training length trade off. In particular, we find that increasing training length can be exponentially more efficient than increasing the sample size. Experiments support predictions of the theory.

cs.LG↗

arXiv2026

Audit Where Hacks Pay: Budgeted Strong-Verifier Audits Against Reward Hacking in GRPO

Reinforcement learning with verifiable rewards trains on cheap checks, such as unit tests, that a policy can learn to game, while a stronger check is too expensive to run on every rollout. We study how to spend a limited strong-verifier budget in GRPO, separating which weakly passing rollouts to audit from what reward a caught hack receives. At a fixed policy state with centered advantages, the expected update depends on a design only through each rollout's marginal audit probability and correction; reflecting a caught hack's reward about the failure reward negates the advantages of an all-hack group; and auditing whole groups with the fewest weak passes first (low-pass budgeted audits, LB) minimizes the advantage mass left on hacks among pass-count designs with a fixed correction when a label's value falls with the pass count. We tested this analysis in actual LLM training: from each run's starting state, the sign of this mass on a frozen panel predicted whether hacking would be suppressed in 33 of 39 runs, including 13 of 16 preregistered ones. In LeetCode (Wong et al., 2026) and Countdown-Code (Khalifa et al., 2026), LB drives hacking to near zero, while random audits with the same penalty and budget do not and use more labels. We also find that the randomness of the update affects training: in Countdown-Code, two unbiased corrections, per-item reward-level IPW and a group-level advantage correction, bring hacking down too but end 6.1-11.8 and 8.0-11.5 points lower in held-out accuracy than LB at the same budget. A full audit, which the group-level correction reproduces in expectation, stays within about two points of LB in three seeds, while LB uses 28% of its labels, and allocating the same correction by pass count recovers most of the loss (one seed). Training outcomes thus depend not only on the expected update but also on the randomness of its estimate.

cs.LG↗

arXiv2026

Lepton polarization and sensitivity to the form factors in $Λ\to p\,\ell^-\barν_\ell$ with lattice QCD

We investigate the polarization of the charged lepton in the semileptonic hyperon decay $Λ\to p\,\ell^-\barν_\ell$ ($\ell=e,μ$) within the Standard Model, using the form factors obtained from lattice QCD. We compute the longitudinal, transverse and normal polarization of the lepton, the forward-backward asymmetry of each lepton spin state, and the lepton flavor universality ratio $R_{μe}$. We show that the longitudinal polarization determines the ratio $g_1/f_1$ of the axial-vector to vector couplings, and that the forward-backward asymmetries of the electron and of negative-helicity muons determine the weak magnetism. The asymmetry of positive-helicity muons is fixed by kinematics up to a small dependence on the second-class form factors, whereas $R_{μe}$ is nearly independent of $g_1/f_1$ and the weak magnetism. For comparison, we also use the QCD sum-rule form factors, whose $g_1/f_1$ and weak magnetism are opposite in sign to experiment and lattice QCD, and find very different values for the observables that depend on them. Moreover, the $q^2$ dependence of $R_{μe}$ fixes the longitudinal polarization of the muon, which can thus be measured from the decay rates, without measuring the muon spin. The normal polarization is generated by the electromagnetic final-state interaction and provides the Standard Model reference for searches for time-reversal violation. The electron forward-backward asymmetry and $R_{μe}$ can be measured at BESIII and the proposed Super Tau-Charm Facility, and $R_{μe}$ also at LHCb. These measurements can test the Standard Model and the lattice-QCD form factors.

hep-ph↗

arXiv2026

The topological vertex is finitely generated

The topological vertex computes all genus amplitudes for the open topological A-model in $\mathbb{C}^3$ with branes on three toric Lagrangians and, via gluing, both open and closed string amplitudes on any toric Calabi-Yau threefold. In this note we show that the topological vertex is generated by boundary interactions of three disks and three annuli. A generalization of this result is shown to hold for the refined topological vertex.

hep-th↗

arXiv2026

Quantifying the failure of symmetry learning in linear diffusion models due to initialization and finite-sample effects

Data distributions often possess one or more symmetries: for example, all orientations of any specific dog are included in the distribution of all possible dog pictures. Despite the omnipresence of such symmetries, modern generative modeling approaches may fail to incorporate or learn them, which can lead to lower sample efficiency and poorer generalization. To what extent do diffusion models fail to learn data distribution symmetries, and what sources of symmetry breaking are most responsible? Here, we answer this question in the theoretically tractable setting of linear diffusion models. We show that of three potential sources of symmetry breaking---a non-symmetric initial weight matrix, a noisy learning target, and finite-sample noise---target noise produces the most robust symmetry breaking, since it persists even in the sample-rich regime. Using local laws from random matrix theory, we derive formulas for average symmetry error in fairly general cases involving symmetry within a subspace and show that smaller symmetries are harder to learn.

cs.LG↗

arXiv2026

Can JEV Support Clinical Trial Criteria Assessment?

Clinical trial prescreening requires distinguishing unmet conditions from insufficient evidence in patient records. Given patient records, criterion questions, and predefined answer options, we retrospectively compared JEV, a non-generative decision model returning native option probabilities, with schema-constrained Qwen Flash across 2,048 test patient-condition pairs from TrialGPT and question-answer datasets derived from MIMIC-III and MIMIC-IV, all evaluated under strict Zero Data Retention (ZDR) policies to ensure clinical data privacy. Both models assessed conditions individually or in batches sharing the same patient context, with performance measured against reference labels. In batch mode, JEV and Qwen achieved similar macro-F1 scores on TrialGPT (0.652 vs. 0.660) and MIMIC-IV (0.807 vs. 0.814), whereas JEV substantially outperformed Qwen on MIMIC-III (0.768 vs. 0.534; $Δ$ = +0.234, 95% CI: 0.187-0.281). This advantage largely reflected higher recall for conditions labeled as having insufficient information (56.3% vs. 9.9%). Across all three datasets, JEV also had lower observed median job latency (1.18-1.40 vs. 2.80-8.90 s) and 53%-74% lower estimated cost per condition. These findings position JEV as an initial assessment component that provides criterion-level judgments and flags potential information gaps for review. JEV's observed errors in interpreting clinical evidence underscore the need to verify its outputs against patient records before they inform eligibility decisions.

cs.LG↗

arXiv2026

Distillable entanglement is continuous

We prove continuity of distillable entanglement, the optimal asymptotic rate at which copies of a bipartite state can be converted into maximally entangled pairs by local operations and classical communication (LOCC) with vanishing error. We establish an explicit asymptotic continuity bound that holds for arbitrary bipartite states and depends logarithmically on the system dimension. This bound has the same structure as known continuity bounds for conditional entropy, entanglement cost, and relative entropy of entanglement. Our proof constructs an explicit LOCC protocol that converts either of two arbitrary bipartite states into the other at an ebit cost that vanishes as their trace distance tends to zero.

quant-ph↗

arXiv2026

Learning Behavioral Parameters of Network Equilibrium Models from Aggregate Mobility Data

Estimating travel behavior parameters is essential for understanding current travel patterns and for forecasting how travelers may respond to future changes in transportation systems. However, reliable estimation remains difficult when behavior must be inferred from sparse and aggregate observations, especially when jointly recovering several behavioral components. In this paper, we develop a bi-level estimation program for a combined destination, mode and route choice model with congestion. The inner level is a convex program at given scale parameters, and returns the taste coefficients as its dual variables together with the equilibrium travel pattern. The outer level selects the scale parameters by out-of-sample prediction, measured by how well the modeled travel pattern predicts observations withheld from estimation. To solve the bi-level problem at scale, we propose a matrix-free Hierarchical Lagrangian Dual algorithm as the inner solver and an outer search by implicit differentiation, which uses the sensitivities of the inner solution to enable efficient search over the scale parameters and reaches the calibrated scales in a handful of iterations. We validate the approach on Los Angeles County using public origin-destination, mode-share and traffic-count data. Our approach scales to a county-level problem with 2.7 million variables and substantially improves computational efficiency over a general-purpose conic solver. Compared with the fixed-scale benchmark, the calibrated model improves predictive performance at the destination and mode levels, with consistent gains across complementary goodness-of-fit measures.

math.OC↗

arXiv2026

MatAnyone-E: Sparse Memory Propagation for Efficient High-Resolution Video Matting

High-resolution video matting requires preserving fine details, such as hair strands and soft transparency, while maintaining consistency across frames. Memory-based methods achieve strong matting quality by matching current-frame features with information stored from earlier frames, but this process becomes increasingly costly as resolution grows. We present MatAnyone-E, an efficient extension of MatAnyone 2 that focuses computation where it is most needed. Our approach first performs low-resolution propagation to identify uncertain regions that require closer inspection and the memory candidates most relevant to them. It then performs high-resolution matching only for these regions using the selected memory, while reusing low-resolution matching results elsewhere. This strategy reduces both the number of locations requiring detailed matching and the amount of memory searched, while preserving the information needed to produce a complete matte. We further reduce the cost of generating high-resolution mattes with a lightweight decoder designed around measured runtime bottlenecks and trained to reproduce the original decoder's representations. Experiments show that MatAnyone-E maintains matting quality comparable to MatAnyone 2 while achieving an estimated 7.4x inference speedup and reducing peak GPU memory usage to 7.6% of the usage of MatAnyone 2 at 4K. With compilation-enabled inference on a single NVIDIA H200 GPU, it reaches 73.07 FPS at 1080p and 28.62 FPS at 4K.

cs.CV↗

arXiv2026

The Watchtower Imperative: Lifespan-Calibrated Evaluation for Frontier AI

The gap between AI capability deployment and safety assurance is structural and cannot be closed through internal evaluations alone. Analyzing documented harms (2017-2026) across the human lifespan reveals that disparate incidents --- from voice assistants endangering children to AI companions implicated in adolescent suicide and automated care denials for the elderly --- reflect a single failure: evaluating systems against an implicit adult user model. We introduce five developmental moderators structured into a Lifespan Vulnerability Matrix across six life stages. The matrix reveals a nonmonotonic risk distribution: vulnerability peaks at both ends of the lifespan, governance coverage is asymmetrical, and authority to convert model errors into real-world impact is scrutinized least. We then propose a set of lifespan design principles generalizing existing child-protective instruments, and an institution-agnostic, three-tier external evaluation framework --- comprising automated simulation, expert red teaming, and post-deployment monitoring --- indexed directly to matrix risk cells.

cs.CY↗

arXiv2026

Characterizations of the unit vector basis of $c_0$ or $\ell_p$ among minimal systems

Given a minimal system E for a Banach space X, Casazza, Dilworth, Kutzarova and Motakis introduced a multiplication $\otimes$ on span(E) and studied the Schauder bases for which $\|x \otimes y\|\approx \|x\|\|y\|$ asking whether every such basis is equivalent to the canonical unit vector basis of $c_0$ or $\ell_p$. We continue this study in the more general setting of minimal systems that are not assumed to be Schauder bases, and we obtain positive answers under hypotheses that are formally weaker than the ones considered so far: partial democracy instead of democracy or bidemocracy, and truncation quasi-greediness instead of quasi-greediness. Along the way we show that the above multiplicative estimate forces invariance under translations, we characterize when such a minimal system is a Schauder basis, and we give examples showing that the one-sided variants of the estimate behave very differently.

math.FA↗

arXiv2026

TRACE: Memory-Efficient Time Series Class-Incremental Learning via Temporal-Spectral Reconstruction

Web-connected sensing applications continuously generate multivariate time series with evolving behavioral categories, making Time Series Class-Incremental Learning (TSCIL) essential for adapting to new classes without forgetting previously acquired knowledge. However, preserving diverse and evolving class distributions under strict privacy and memory constraints remains a fundamental challenge. Existing approaches often face a trade-off between retaining sufficient historical knowledge for accurate recognition and minimizing the memory required for continual adaptation. To address these limitations, we propose TRACE, a memory-efficient, replay-free framework that preserves class-specific knowledge through generative modeling rather than sample rehearsal. TRACE employs a compact, frozen temporal-spectral representation and lightweight class-specific autoencoders to capture complex intra-class variations. By independently preserving each class model, TRACE avoids recursive generation and catastrophic forgetting, while enabling direct classification through reconstruction-based scoring without retaining historical samples or large statistical matrices. Extensive experiments across five TSCIL benchmarks demonstrate that TRACE achieves competitive classification accuracy while reducing mean retained memory by approximately 98.26% compared with TS-ACL, the strongest evaluated analytical baseline, and achieving an approximately 33.43% relative improvement in accuracy on GrabMyo.

cs.LG↗

arXiv2026

Critical velocity and dissipation mechanism in finite superfluid $^4$He nanodroplets

A hallmark of superfluidity is the frictionless motion of an object below the Landau critical velocity; Whether this concept applies to nanoscale droplets remains unclear. Using time-dependent density functional theory, we investigate the motion of a sodium atom on the surface and inside a superfluid helium nanodroplet. For surface motion, we identify a critical velocity above which energy dissipation through ripplon excitation and the formation of surface-bound quantized vortices leads to rapid deceleration. Inside the droplet, the atom is slowed down to a steady-state velocity that depends on the initial speed, contrasting experiments reporting a critical velocity for dopants ejected from droplets [Phys. Rev. Lett. 111, 153002 (2013)]. Remarkably, the velocity of the ejected atom is nearly independent of its initial velocity. We demonstrate that this behavior results from the bursting of the bubble surrounding the atom at the droplet surface, challenging the previous experimental interpretation.

physics.atm-clus↗

arXiv2026

A Category-Selective Encryption Framework for Privacy Protection of UAV Images

Imagery captured by unmanned aerial vehicle (UAV) systems increasingly raises privacy concerns, as UAV aerial surveillance routinely captures sensitive objects such as pedestrians and vehicles alongside ordinary scene content. Existing privacy-preserving approaches typically employ class-agnostic saliency detection to indiscriminately obfuscate all visually salient regions, leading to unnecessary information loss and hindering downstream scene analysis. This paper proposes a category-selective encryption framework for privacy-preserving UAV surveillance. The core advance over prior class-agnostic approaches is semantic-level selectivity: the system first recognizes what is present in the scene via an 80-class detector, then encrypts only user-specified sensitive categories while leaving non-sensitive objects and background intact for downstream analytics. The framework supports two complementary encryption schemes: Thumbnail-Preserving Encryption (TPE), which applies adaptive pixelation with a learnable blend parameter and recovers content through a jointly trained Enhanced U-Net, and XOR stream cipher encryption, which offers parameter-free, mathematically exact reversibility. The architectural design, composite loss formulation, and joint training methodology are presented in detail, establishing a foundation for practical privacy-preserving UAV surveillance that balances protection strength and scene utility.

cs.CR↗