Papers

Fix a strip width \(\rho>0\), a Diophantine frequency \(\alpha\), an integer \(N\ge2\), and \(\lambda>1\). For the family \[ V_{\varepsilon,\delta}(x) =2\lambda\cos(2\pi N x)+\varepsilon\delta(x), \] we prove that there is an open prevalent set \(\mathcal P_{\rm strat}\) of real-analytic strip-\(\rho\) perturbations such that every \(\delta\in\mathcal P_{\rm strat}\) admits \(\varepsilon_0(\delta)>0\) for which \[ \begin{gathered} \operatorname{Leb}\left\{ E\in\Sigma(V_{\varepsilon,\delta},\alpha): \omega(\alpha,E;V_{\varepsilon,\delta})=s \right\}>0, 0<\varepsilon<\varepsilon_0(\delta), \qquad s=1,\ldots,N. \end{gathered} \] The proof relates acceleration to the total multiplicity of real zeros of analytic overlap coefficients for first-return cocycles. Under quantitative control of the return products, Poisson integration and Kac normalization identify acceleration with half this multiplicity. A positive analytic dual state gives the finite-volume spectral gaps and Schur curvature needed at the upper spectral edge. Schur variations separate the perturbed maxima, and parameter exclusion preserves \(s\) pairs of simple zeros on a positive-measure spectral set.

Identifying kinetic parameters and conserved quantities that support multistationarity and multistability remains challenging in chemical reaction network analysis. Structural theory provides existence and exclusion results, but does not always yield explicit, interpretable descriptions of the corresponding parameter regimes. We present a computational and machine-learning framework for discovering and characterizing parameter regimes with numerical evidence of multistationarity and multistability in mass-action systems. We refer to these numerically detected behaviors as approximate multistationarity and approximate multistability. The framework combines Latin hypercube sampling, adaptive sampling, and interpretable surrogate modeling. Logistic-regression and neural-network surrogates are trained separately on accumulated detection labels and independently guide later sampling toward regions with high scores for approximate multistationarity or multistability. Boundary refinement targets transitions between detected and undetected numerical classes. Buckingham–Pi groups are then used with CN2 rule induction to obtain interpretable empirical descriptions of detected regimes. Illustrative networks yield rules consistent with known multistationarity conditions, while the Schlögl model demonstrates adaptive enrichment of multistationarity detections. In the hybrid histidine kinase model and the sequential dual phosphorylation cycle, adaptive sampling substantially increased the number of parameter - total pairs with detected multistability relative to global sampling under equal sampling budgets. The framework complements analytical chemical reaction network theory by providing efficient, parameter-resolved discovery and characterization of multistationary and multistable regimes.

LLM agents combine reasoning, tool use, and persistent memory to support work across tasks by reusing stored operational records as premises for later actions. However, environmental or requirement changes can invalidate these records, while existing action review, provenance tracking, and clarification mechanisms may leave the underlying persistent state uncorrected. Our audit of coding-agent trajectories identifies candidate failure chains in which invalid records are reused, leading to task failures and unsafe modifications. We propose StateWise, a framework for diagnosing and repairing persistent operational state before action execution. StateWise uses record-level counterfactual replanning to identify decision-critical records, then establishes their current validity through reliability checks, read-only verification of machine-observable facts, and targeted clarification of developer-owned intent. Typed evidence grounding binds evidence to specific records and scopes, enabling persistent corrections with repair lineage. The agent then replans from the repaired state, followed by an independent state-action check before execution. We evaluate StateWise on 150 executable coding-agent cases across diverse runtime environments, workspace configurations, and repository settings, complemented by cross-model evaluations. Under corrupted persistent state, StateWise achieves 93.3% overall correctness, compared with 38.7% for the baseline agent, with no unsafe actions. Component ablations, multi-task experiments, and transfer evaluations further demonstrate effective recovery, persistent corrections, and transferability across repositories and tool interfaces.

Time-series foundation models offer a unified approach to forecasting across heterogeneous domains. Textual context and auxiliary observations provide complementary information about temporal dynamics, yet reusable multimodal predictive representations remain underexplored. We introduce Pythia, a foundation world model that learns context-conditioned latent dynamics across datasets through a joint-embedding predictive architecture. A stop-gradient numerical reference guides contextual corrections to predicted future states. A separate probabilistic decoder then adapts to the frozen predictive representation and observed history, decoupling world-model pretraining from observation-space forecasting. On MUSE, Pythia-Tiny's normalized mean absolute scaled error (MASE) and weighted sum quantile loss (WSQL) are 0.6879 and 0.4269, reducing errors by 6.26% and 5.00% relative to the strongest model evaluated in the published MUSE leaderboard. Through a series of controlled experiments, we investigate how to design a time-series world model through shared pretraining and how joint-embedding predictive learning can incorporate multimodal information. The results support separating predictive representation learning from probabilistic readout and show complementary contributions from entity descriptions, events, and covariates.

Movable antennas (MAs) have emerged as a promising technology for enhancing wireless communication performance. However, in delay-sensitive systems, MA movement incurs non-negligible delay, which may degrade the service process for bursty traffic. This paper investigates a delay-outage problem in an MA-enhanced multiuser multiple-input multiple-output (MU-MIMO) downlink system. Unlike existing studies that mainly focus on physical-layer performance optimization, a cross-layer framework is developed that accounts for the overall delay due to antenna movement, along with service interruptions and queue accumulation at the medium access control (MAC) layer. Considering the different timescales of antenna movement and packet-level queue evolution, we establish a two-timescale transmission protocol and a cross-layer queueing model with Markov-modulated bursty arrivals. A long-term transmit-power minimization problem is then formulated to jointly optimize the destination antenna positions and transmit beamforming under delay-outage and practical MA movement constraints. To tackle the probabilistic delay-outage constraints, a backlog martingale is constructed to derive a deterministic sufficient condition in terms of service rate, thereby transforming the probabilistic constraints into deterministic service rate requirements. An alternating optimization (AO) algorithm based on a short-horizon approximation is further developed to obtain a high-quality suboptimal solution. Numerical results demonstrate that the proposed algorithm outperforms baseline schemes by effectively balancing the MAs' spatial reconfiguration capability and the temporal service loss.

Amid the intensifying competition in artificial intelligence between the United States and China, the emergence of the DeepSeek-R1 model has sent significant ripples through the technology sector, capital markets, and policy circles. This Article offers a comprehensive analysis of legal and policy landscape surrounding DeepSeek, drawing upon its key technical features-including reinforcement learning, mixture-experts architecture, multi-head latent attention mechanism, knowledge distillation, and open-source approach. Firstly, DeepSeek's success raises crtitical questions about the efficacy of the United States' increasingly robust export control measures on chips and semiconductors, components essential for training large language models. Secondly, akin to Chinese technology giants such as TikTok and Huawei, DeepSeek is confronted with information security scrutiny in the United States and other jurisdictions. Thirdly, despite its domain-specific capabilities and competitive API pricing, DeepSeek has faced criticism for producing outputs laden with political and ideological biases, igniting debates over free speech and censorship. Further more, this Article delves into intellectual property and contractual concerns stemming from the knowledge distillation technique employed by DeepSeek. Ultimately, it concludes that geopolitical consideration will continue to exert a profound influence on the legal challenges and prospective solutions related to the DeepSeek models.

We study the problem of computing an allocation of indivisible items that maximizes egalitarian welfare, i.e., the utility of the worst-off agent, when agents' item values or marginal values belong to a small set. For additive valuations with values in $\{p,q\}$, where $q>p>0$ and $\gcd(p,q)=1$, we give a polynomial-time algorithm when $p=2$ and prove constant-gap hardness when $p\geq3$, already with exactly three high-valued goods per agent. We also give an $\sqrt{3/2}$-approximation for common positive bi-valued additive valuations. For mixed additive valuations in $\{-p,0,c\}$, where $p\in\{1,2\}$ and $c$ is a positive integer, a reduction to maximum-weight perfect matching resolves the conjectured tractability of $\{-2,0,c\}$-valuations. For submodular valuations with marginals in $\{-2,0,c\}$, where $c$ is odd, we establish an exact unit-gap hardness result and exponential value-query lower bounds, even when all but one agent are additive. Finally, for $\{-1,0,1\}$-submodular valuations, we prove that no finite multiplicative approximation exists unless $\p=\np$. Together, our results resolve open questions and provide a complete picture of the computational complexity of max-min allocation with ternary valuations.

The nature of ultra-luminous X-ray sources (ULXs) is shrouded in mystery as they're believed to be point sources with luminosities above the classical Eddington limit for a 10$M_{\odot}$ black hole (BH), but generally fit into the classification tree of super-Eddington X-ray binaries. Studies of reverberation lags and lag-energy spectra provide some insight into the nature of viscous turbulence in optically thick, super-Eddington discs, and are useful in conjunction with modelling multi-wavelength spectra and covariance spectra. In this study, we focus on the timing properties of two classically distinct ULXs: NGC 5204 X-1 and NGC 55 ULX-1, both of which are known to emit relativistic winds, as observed by modelling emission line spectra with photo-ionisation models such as SPEX, but are thought to be viewed at slightly different inclinations due to differences in the hardness-ratio of their X-ray continuum. Here, we perform an extensive timing study of the two ULXs to reveal new constraints on the accretion disc size scale and structure. We also perform an accelerated search for pulsations (including the correction for an orbital modulation of the signal) to discover significant spin-periodicities in both NGC 5204 X-1 and NGC 55 ULX-1 (at $> 3\sigma$ significance).

Surface electromyography (sEMG) is a low-power, cost-effective biosignal for hand-pose estimation and gesture classification. In this work, we examine whether self-supervised pretraining on sEMG can yield transferable representations for continuous hand-pose estimation. We introduce EMG-GPT, a causal transformer-based model that operates on discrete sEMG representations from a frozen residual vector quantization (RVQ) tokenizer and learns temporal dynamics through depth-autoregressive future-code prediction. The model combines within-frame integration with causal temporal modeling while preserving the geometry of the pretrained codebook. EMG-GPT shows competitive results in both Regression and Tracking tasks, supporting EMG-only pretraining as a viable approach for learning transferable sEMG representations.

We study single-copy exact deterministic transformations of bipartite quantum states under local operations and classical communication (LOCC), and give a complete classification of the states in two three-level systems that can be transformed into each other. This classification applies to finite protocols and to the countable protocols specified in this paper. If two entangled states can be transformed into each other but do not satisfy local unitary equivalence, then both can be decomposed into an entangled block and a separable part, and the two parts can be distinguished by local measurements. The two entangled blocks have the same probability weight and satisfy local unitary equivalence, while the separable parts may differ. We further prove that every entangled state has a unique least retained block; after retaining its probability weight, the local unitary equivalence class of this block completely determines the reversible equivalence class of the original state. For negative partial transpose states, one only needs to compute the negative spectral subspace of the partial transpose and perform at most three matrix zero tests to determine this retained block.

Streaming head-avatar reenactment aims to animate a reference image according to a live driving video, requiring robust motion transfer, long-term identity stability, and low latency. Existing methods often rely on specialized identity or motion representations, which can discard useful visual information and inherit failure modes from external extractors. In addition, many recent diffusion-based reenactment methods use offline, clip-based generation, jointly processing and denoising an entire video clip before producing its output, making continuous low-latency streaming difficult. We introduce PixReenact, a pixel-conditioned streaming reenactment framework built on causal video diffusion. PixReenact conditions directly on VAE-encoded reference and driving frames, without specialized identity or motion representations. To separate reference identity from driver motion, we train with cross-identity pseudo supervision together with corrective objectives anchored to the original reference and driving inputs. Long self-rollouts reduce autoregressive drift, while state-aware dual-teacher distillation separately addresses cold-start and steady-state generation. Across three cross-identity benchmarks and a long-horizon streaming benchmark, PixReenact demonstrates robust cross-identity reenactment, particularly under challenging conditions such as extreme viewpoints, occlusions, and pronounced facial expressions, while maintaining the reference identity over long streams. A 4-NFE rolling student continuously emits four frames per update with a mean emission latency of 239 ms.

In this paper, we study the rigidity of Thurston's hyperbolic sphere packings on 3-dimensional manifolds. We prove that Thurston's hyperbolic sphere packing is locally determined by combinatorial scalar curvature. We further prove the infinitesimal rigidity that Thurston's hyperbolic sphere packing can not be deformed while keeping the combinatorial Ricci curvature fixed. The main tools include a characterization of the admissible space of Thurston's hyperbolic sphere packings, a variational formula for the dihedral angles of a tetrahedron and an identity for the variations of dihedral angles in a tetrahedron generated by Thurston's hyperbolic sphere packings.

A geometrically-exact planar beam finite-element framework is developed for the analysis of beams with hyperelastic constitutive models. A conventional three-field beam model is first formulated with full geometrical nonlinearity and a linear elastic material law. The kinematics are then enriched by an additional global field that permits deformation through the in-plane thickness. The out-of-plane direction is incorporated separately through plane-strain and plane-stress constitutive reductions, allowing the cross-sectional deformation assumptions and constitutive behaviour to be formulated independently. Numerical results for the present benchmarks show that the plane-stress condition gives essentially coincident centreline deformations for the Poisson's ratio values considered. In contrast, the plane-strain condition, which is widely employed in the literature, makes the formulation sensitive to Poisson's ratio coupling, with the beam becoming significantly stiffer at higher Poisson's ratios. Comparisons between Saint Venant-Kirchhoff and Neo-Hookean hyperelastic models further demonstrate close agreement in the global deformation and in-plane thickness response, with small constitutive differences becoming more apparent in the local out-of-plane stretch. The proposed approach offers a simple and consistent framework to integrate hyperelastic material models into planar geometrically-exact beam models.

Most vision-language-action models represent future motion as fixed-rate action chunks, tying temporal resolution and prediction horizon to a fixed output budget. This pointwise representation wastes capacity on highly correlated neighboring actions, leaves temporal continuity and smoothness to be learned implicitly, and forces a tradeoff between long-horizon coverage and the local precision required for contact-rich manipulation. To address these limitations, we introduce Vela, a vision-language-action foundation model that represents future robot behavior as continuous trajectories. Vela combines a compact spline-based action representation with motion-dependent temporal support and a shared action interface for heterogeneous embodiments, allowing a fixed output budget to adapt its temporal resolution across motions. We pretrain Vela on large-scale multi-embodiment robot data and evaluate it on LIBERO-X, EBench, and two real-world long-horizon tasks, egg-cake cooking and potato shredding, obtaining promising results across simulation and physical manipulation. These results highlight the potential of continuous action representations as a foundation for future embodied foundation models. Project page and more results: https://clementine24.github.io/Vela/ .

The integrated universal linear optical processor realized via multi-plane light conversion (MPLC) features low hardware complexity and high fabrication robustness, suitable for diverse photonic processing tasks. However, the lack of validated calibration protocols limits its universality and potential. Here, we propose a machine-learning-based calibration method and verify it using an eight-mode silicon photonic processor composed of interleaved multiport directional couplers and phase-shifter arrays. We characterize coupler transfer matrices and current-phase responses of individual phase shifters. To validate the robustness, we demonstrate its universality with Haar-random unitary matrices at wavelengths of 1500, 1550, and 1580 nm, and under partial phase-shifter deactivation. With this white-boxed device, we also demonstrate high-dimensional quantum gates and quantum reservoir computing for handwritten digit classification. Our work advances integrated MPLC-based universal linear optics and paves the way for large-scale, fabrication-robust, broadband hardware for classical and quantum photonic information processing.

For a quantum affine superalgebra with a fixed Drinfeld current presentation, we study shifted quantum affine superalgebras through a two-sided shifted Drinfeld current presentation, in which the leading degrees of the Cartan–Drinfeld currents are modified while the remaining current and Serre relations are retained. We then focus on the standard-parity type A algebras $\mathcal U_q^{\mu_+,\mu_-}(\widehat{\mathfrak{sl}}_{m|n})$. For arbitrary shifts and $m,n\ge1$, $m\ne n$, we prove a triangular decomposition. When $m,n>1$, we obtain PBW–Drinfeld bases for arbitrary shifts and a Levendorskii-type finite presentation of the one-sided algebra $\mathcal U_q^{0,\mu}$ for every antidominant $\mu$. For antidominant two-sided shifts, we construct shifted RTT realizations and prove the corresponding Ding–Frenkel isomorphisms. We construct a shifted formal Drinfeld coproduct for arbitrary two-sided shifts, coassociative in a completed tensor product. Shifted RTT realizations yield non-completed one-sided coproducts in the antidominant region, made explicit on finitely many generators by the finite presentation; injective shift homomorphisms extend them to arbitrary one-sided shifts. Their ternary coassociativity holds whenever the middle shift is antidominant, including boundary cases. Finally, for two-sided antidominant shifts $\mu_+,\mu_-\in\Lambda^-$, a shifted full general-linear Ding–Frenkel isomorphism identifies the special-linear simple-current algebra as the fixed algebra under common scalar rescalings and yields coassociative two-sided non-completed coproducts.

We consider the one-level density of zeros of the Riemann zeta function weighted by its special values on the line ${\rm Re}(s)=\sigma$, where $\sigma$ is a fixed real number such that $1/2\le \sigma\le1$. We show that the density function for the Riemann zeta function changes if and only if $\sigma=1/2$.

The projected offset of a Gamma-Ray Burst (GRB) from its host galaxy is an important diagnostic of its physical origin, where the host associations are usually evaluated through chance-coincidence probabilities. However, as shown by observations, the host associations given by this approach may be ambiguous in some cases. In this work, we revisit the modelling of the offsets of double-neutron-star (DNS) mergers with controlled numerical experiments using Monte Carlo simulations. To isolate the dynamical effects of the second supernova (SN) from uncertainties in the upstream binary evolution, we parametrise the direct progenitor of DNSs and integrate the post-SN trajectories in galactic potentials using galpy. Complementary to previous population synthesis calculations, our Monte-Carlo tool, GRB-offset, provides a lightweight framework to identify sensitivities and expose degeneracies in offset modelling. With GRB-offset, we have investigated the following physical ingredients, supernova physics (ejected mass and kick velocity), galactic potential (potential shape, galaxy virial mass), DNS birth location, star formation history, and redshift. The offset distributions given by our reference Monte-Carlo simulation peak at around 30 kpc and 1000 kpc for the DNSs bound to and unbound from the host galaxy, which sensitively depends on the considered physical ingredients. A given offset can arise from various combinations of these ingredients, introducing substantial degeneracies when interpreting observed offsets. Therefore, an observed offset alone can hardly constrain the properties of the DNS progenitor and of the host galaxies.

Explainable artificial intelligence (XAI) encompasses methods that draw on different sources of information and address different explanatory needs. A common framework is needed to describe how this information becomes evidence and is communicated as an explanation for a particular recipient. We propose the General Framework for Generating Explanations (GFGE), grounded in interpretative frameworks and the complementary activities of sense-reading and sense-giving. Its conceptual foundation is the Interpret/Explain Schema (IES), which connects an analyst's interpretation of system evidence, the communication of a selected account, and the recipient's interpretation of that account. GFGE operationalises this schema through five roles: data interpretation, model interpretation, output interpretation, optional post-hoc analysis, and aggregation. A role-typed operation graph records method-specific dependencies, while evidence records retain the sources, assumptions, and limitations of explanatory claims. The explanatory question, audience, and context guide the procedure. We instantiate GFGE for attribution, surrogate, counterfactual, concept and prototype, intrinsic rule, argumentation, and language-model methods. These instantiations show how intrinsic, post-hoc, and hybrid workflows can be represented through the same roles while preserving their distinct evidential requirements. GFGE provides a common basis for analysing explanation workflows, tracing communicated claims to their evidence, and identifying unresolved explanatory dependencies.

We obtain presentations of Borel subgroups of certain Chevalley groups and Kac-Moody groups of simply laced type. More precisely, we show that Borel subgroups of simply laced Chevalley groups over a commutative, unital ring (satisfying a minor technical condition), are the amalgamated product of their rank 2 subgroups, generalising a result of Tits over fields (different from $\mathbb{F}_2$). We moreover show that Borel subgroups of Kac-Moody groups over local Bézout domains also have a presentation as an amalgamated product of their rank 2 subgroups as soon as this holds for their rank 3 subgroups. In particular we deduce that Borel subgroups of simply laced Kac-Moody groups over a local Bézout domain (with residue field different from $\mathbb{F}_2$) have such a presentation if and only if they are of 3-spherical type.

The architecture of modern LLMs consists of a profound cognitive polarization. LLMs possess implicit intuition encoded in their parameters, yet rely on a disconnected, explicit mechanism to access the outside world. Agentic frameworks have not bridged this gap; instead, models are often compelled into pathological "induced amnesia." Under the prevailing "Retrieve-Always" paradigm, agents must distrust their internal knowledge, making every user interaction a "tabula rasa" event that must be checked externally. This creates reflexive dependence that can be thermodynamically wasteful, cognitively fragile, and susceptible to irrelevant context. We propose a return to first principles, operationalizing the biological maxim "Look Before You Leap." We introduce MARTA (Metacognitive Adaptive Retrieval and Thought Architecture), a neuro-symbolic framework that bridges parametric and non-parametric knowledge. Rather than treating retrieval as mandatory, MARTA models it as a cost, taking the leap only when perceived internal inadequacy warrants external information. By allowing the agent to gauge the entropy of its own thoughts before acting, MARTA enables deliberative retrieval and uncertainty-aware decision making. Our approach suggests that giving agents the capacity for introspection can restore a more efficient balance between internal knowledge and external information.

Fidelity estimation is a fundamental tool for assessing quantum resource states across quantum information science. For small infidelity $\epsilon$, tomography and direct fidelity estimation (DFE) have worst-case sample complexity $O(1/\epsilon^2)$ at fixed relative accuracy and confidence. Direct target projections achieve $O(1/\epsilon)$ but generally require non-Clifford operations whose reliability depends on the resource states that are typically the target of benchmarking. Here, we introduce the Bell–coherence fidelity estimation (BCFE) with optimal sample complexity $\Theta(1/\epsilon)$ using only Clifford gates and Pauli measurements. We prove that BCFE is applicable to arbitrary pure targets, possibly multi-qubit, with the statistical error of the single-copy coherence part explicitly controlled. To evaluate BCFE in a practical setting, we apply BCFE to analog rotation resource states in the candidate early-FTQC architecture called the Space-Time Efficient Analog Rotations (STAR) architecture. In the simulations using surface codes, BCFE is estimated to require up to approximately $27$ times fewer resource states than DFE for the same standard error in the infidelity estimate, while its estimates remain close to reference values despite circuit-level noise in the additional Bell measurement operations. These results support efficient resource benchmarking within fault-tolerant quantum computing.

Harnesses are increasingly unlocking the potential of large language model (LLM) agents by making their actions more controllable. In automatic heuristic design (AHD) for combinatorial optimization (CO), LLMs iteratively revise solvers using execution and verification feedback. However, these revisions often break previously validated solver behavior, making refinement unstable and costly. We characterize this pattern as feasibility oscillation and document it across CO benchmarks, AHD methods, and backbone LLMs. Tracing this oscillation, our analysis reveals that feasibility degradation often follows large solver revisions, while substantial feedback redundancy makes it harder to identify which failures deserve attention. Motivated by these findings, we introduce DiSH, a harness that jointly controls revision direction and scope. It selects representative failure evidence to guide each update and progressively narrows the revision scope as feasible behavior accumulates. Across nine CO benchmarks, DiSH consistently improves QYI scores and reduces feasibility oscillation, while roughly halving feedback token consumption relative to prior methods that use full feedback. These results establish DiSH as a strong baseline for solver refinement under harness control.

Carousel interfaces allow a recommender system to directly observe how far a user has browsed. This signal distinguishes displayed but unclicked items from items that were never displayed, whereas conventional ranking-bandit models, including cascade and position-based models, generally treat examination as latent. We formulate a ranking-bandit problem in which a learner presents a list of $L$ items, observes the user's maximum browsing depth, and receives click feedback only for positions up to that depth. The objective is to maximize the expected number of clicks under an unknown item-attractiveness vector and a browsing-depth distribution. We propose three algorithms based on UCB, Thompson Sampling, and DMED, all of which update item statistics only from observed exposures. We derive an instance-dependent logarithmic upper bound for our UCB-based algorithm and an asymptotic upper bound for our DMED-based algorithm that coincides with the lower bound as its parameter $\alpha\downarrow 0$, establishing asymptotic optimality in this limit. Simulations in synthetic shallow- and deep-browsing environments, together with experiments parameterized from RecGaze interaction logs, show that OD-TS attains final mean regret similar to PBM-TS, while the proposed methods achieve lower final mean regret than PBM-UCB.

Most Large Language Models exhibit a fundamental tension between two sequential tasks, such as logical reasoning and safety alignment. The high-variance internal states required for sophisticated Chain-of-Thought (CoT) deduction can geometrically interfere with latent representations encoding safety constraints. We identify this phenomenon as Sequential Subspace Interference, showing that standard fine-tuning on logical tasks such as multi-step mathematics and code generation can result in a 23.3% interference penalty on alignment benchmarks, substantially weakening the model's safety priors. This Reasoning Drift is not adequately captured by current adaptation methods because gradients for logical tasks are rarely orthogonal to safety objectives. To address this issue, we propose AURA (Adaptive Unique Residual Allocation), a spectral regularization framework that enforces Spectral Independence between reasoning and safety. By explicitly estimating the null space of the alignment manifold and constraining reasoning updates to its orthogonal complement, AURA enables models to improve logical reasoning without compromising safety. Empirically, AURA recovers 23.0% of the lost performance while preserving greater than 0.98 cosine fidelity to the safe state, demonstrating that reasoning and alignment can be effectively decoupled through geometric regularization.

The mean travel time to work is one of the most cited statistics of the American Community Survey (ACS), yet its distribution, its dependence on mode and departure time and its relation to other measurement bases are rarely set out together. Using ACS 1-year tables, we report that US workers aged 16 and over who did not work from home averaged 27.2 minutes one way in 2024, against 25.0 minutes in 2006, a peak of 27.6 in 2019 and 25.6 in 2021. Dividing published aggregate minutes by workers, commuter rail, long-distance train and ferry riders averaged 71.0 minutes, 2.68 times the 26.5 minutes of solo drivers, and all public transportation 49.5 minutes. In 2024, 9.3% of commuters, about 13.3 million people, travelled 60 minutes or more each way and 3.0% 90 minutes or more; commuters leaving between 5:00 and 5:29 a.m. averaged 35.1 minutes. State means ranged from 33.2 minutes in New York to 17.5 in North Dakota, and big-metro means from 36.5 minutes in New York to 21.5 in Buffalo. Working from home rose from 5.7% of workers in 2019 to 17.9% in 2021 and stood at 13.3% in 2024. The 2022 National Household Travel Survey recorded an average commute trip of 13.43 miles at 25.51 mph. On different definitions, the 2019 EU labour force survey module gave an EU average of 25 minutes and 30 minutes for the United Kingdom, and England's travel diary a commuting trip of 31.5 minutes in 2025 against 26.5 in 2002. The three bases are reported side by side and never pooled. All inputs are public.

We prove that the Calabi flow extends past any finite time on compact Kähler surfaces if its Sobolev constants remain uniformly bounded. Moreover, we show the long-time existence of Calabi flow in certain Kähler classes on compact Kähler surfaces when the initial Calabi energy is strictly below an explicit threshold.

Rota-Baxter Lie groups are the group-level counterparts of Rota-Baxter Lie algebras of weight $1$. In this paper, we first establish a correspondence between representations of Rota-Baxter Lie groups and representations of Rota-Baxter Lie algebras of weight $1$ via differentiation and integration. We then develop a cohomology theory for Rota-Baxter Lie groups with coefficients in a representation by constructing an explicit cochain complex in arbitrary degrees. We justify this theory by proving a van Est type theorem, which relates the cohomology of a Rota-Baxter Lie group to that of its Rota-Baxter Lie algebra of weight $1$. As an application, we prove that equivalence classes of central extensions of a Rota-Baxter Lie group are classified by the second cohomology group.

Speech watermarking offers proactive traceability for synthetic speech, yet most existing models operate only after text-to-speech (TTS) synthesis by adding a watermark perturbation to the generated waveform. This post-hoc design leaves watermarking as an external step that can be omitted or bypassed and restricts the watermark to a shallow waveform representation. We propose NeuMark-Native, a TTS-native watermarking framework for neural codec-based synthesis. It embeds payload information into every generated codec-latent layer before waveform decoding, improving watermark persistence under downstream digital signal processing (DSP) and neural codec resynthesis. NeuMark-Native keeps the pretrained TTS model and the neural codec frozen, while optimizing only the watermark modules on generated codec tokens. Experiments on two corpora under 11 DSP attacks and 9 neural-codec attacks demonstrate robust watermark detection while preserving naturalness, intelligibility, and speech quality close to synthetic speech.

In Part I, we introduced a general framework for constructing logical gates in quantum CSS codes from cohomology invariants, focusing on cup products and their generalizations from topological to qLDPC codes. In particular, we produced a family of $C^{k-1}Z$ logical gates that we called copy-cup on $k$ copies of the same quantum code implemented by finite-depth circuits. Here, we vastly extend this framework by introducing twists incorporating code automorphisms, higher twisted cohomology operations, and folding operations in relative cohomology. The framework includes operations lifting coefficients from $\mathbb{Z}/2$ to $\mathbb{Z}/2^k$, enabling all diagonal logical gates such as single-qubit rotations $\operatorname{R}(2\pi/2^k)$. Composing these operations with maps that select cohomology classes yields addressable logical gates. Examples include addressable $T$ gates on three- and four-tori and gates in qLDPC codes beyond topological ones. We introduce cohomology operations, such as the higher twisted Pontryagin powers, that to our knowledge have not previously appeared in the mathematics literature. These operations arise from $E_\infty$-structures on cochains, with explicit constructions using cyclic resolutions and the surjection operad. We expect these results to be of independent interest in homotopy theory. Our formalism applies much more broadly to chain complexes carrying suitable operadic structures, and we expect this operadic perspective to uncover further connections between homotopy theory and fault-tolerant quantum gates.