In this work, we investigate the use of a quantum circuit as a binary classification model in the context of quantum machine learning. We call this model, binary quantum classifier. First, we describe fundamental concepts of quantum computing and introduce the computational tool used: Qibo, an open-source framework for efficient quantum simulations and quantum hardware control. Then, we describe how to design a binary quantum classifier for the classification of images and small arrays of variables by showing how to input data in the circuit, defining a quantum circuit model Ansatz with trainable parameters and a loss function, and implementing multiple minimizers. We test our quantum classifier with two data sets. The first one is the MNIST data set which is composed of handwritten digits (reduced to only handwritten zeros and handwritten ones for binary classification). We study the behavior of different minimizers by increasing the number of layers of the Ansatz. The second data set represents two different high energy collisions that can occur at colliders such as LHC (CERN). Due to in-time proton-proton interactions known as pile-up, we distinguish two different data sets: "without pile-up" and "with pile-up". These collisions can be represented by images of size 32x32 or by six high-level variables that we call features. By increasing the size of the training data set and the number of layers of the Ansatz, we search for the best minimizer. Splitting the data set in training set and test set, we compute: ROC curve, AUC score, confusion matrices and test set accuracy. For "with pile-up" images, we compare the results obtained with the quantum classifier with a small convolutional neural network. We conclude that is possible to build a binary quantum classifier with a quantum circuit and we highlight its performances and limitations in comparison with classical technologies.

Observations of (giant) planets accreting material within their natal environment are crucial to constrain models for their formation. WRAY 15-1880 (aka RX J1842.9-3532) in the Corona Australis (CrA) complex has a prominent pre-transitional disk, and an age of ~2.8+-0.7 Myr, computed by comparison with isochrones using the accurate dynamical mass derived from disk kinematics. Hence, this star is in the late phases of disk evolution and might host accreting planets. We acquire new polarimetric imaging data with VLT-SPHERE and analyze archive observations taken with VLT-SPHERE, VLT-MUSE, and ALMA, finding a candidate Jupiter-like companion within the disk gap from high-contrast imaging. The mass estimates of the candidate companion, derived from various methods, are consistent with an object in the range of 0.3-7.6 MJup. The spectrum of the candidate companion is consistent with a T3 spectral type, in agreement with expectations of an object of a few Jupiter masses. We find an emission blob North-West of the star in the ALMA data rotating solidly with the candidate companion, that can be interpreted as a vortex/dust trap at the m=1 Lindblad resonance of the planet. Accretion on the candidate planet is not detected from the VLT-MUSE archival data. This may be due to insufficient contrast, an observational geometry that is unfavorable for viewing the planet's surface, or it could indicate that we are merely observing irregularities within the disk. Finally, we identify a microjet extending from the star perpendicular to the disk in these data.

We present a broadband spectral analysis of the neutron star LMXB GRS 1747-312 using $\sim$ 40 ks AstroSat data. The source was observed during the decay phase of the 2017 outburst, with an absorbed 1.0-5.5 keV flux of 1.67$^{+0.04}_{-0.07}\times$10$^{-11}$ erg s$^{-1}$ cm$^{-2}$, corresponding to a luminosity of $\sim$(0.9-1.80)$\times$10$^{35}$ erg s$^{-1}$. The continuum is modeled with thermal Comptonization of blackbody emission and interstellar absorption. A mildly broad iron line at $\sim$6.4 keV is fitted with a disc reflection component. Narrow lines below 2 keV are described by a hot plasma using the XSPEC model APEC. Additionally, there is a potential detection of an emission line at 4.19$^{+0.12}_{-0.10}$ keV with width $σ$ = 0.2 $\pm$ 0.2 keV and line flux of 13$^{+10}_{-9}\times$10$^{-5}$ erg s$^{-1}$ cm$^{-2}$. Examination of several short-duration ($\sim$ few kiloseconds) Swift observations at a few times the AstroSat source flux provided upper limits to the line flux of $<$30$\times$10$^{-5}$ erg s$^{-1}$ cm$^{-2}$. The 4.2 keV line likely originates from reflection off the neutron star surface. Shifting the neutral Fe K$_α$ line from its rest energy of 6.4 keV to 4.2 keV requires a redshift of z $\sim$ 0.6, consistent with that expected from the surface of a non-spinning 1.4 M$_\odot$, 10 km radius neutron star. If confirmed, this feature provides a potential direct measurement of gravitational redshift, allowing us to place strong constraints on the neutron star's mass-to-radius ratio and gain valuable insights into the equation of state (EOS) of dense matter.

JWST discoveries of the earliest ($z \gtrsim 9$) supermassive black holes (BHs, $M_\bullet \gtrsim 10^6\,\rm{M}_\odot$) challenge the BH seeding and accretion models of most cosmological simulations. In this work, we compare early BH growth arising from three different accretion prescriptions characterized by distinct scalings between the accretion rate ($\dot{M}_{\rm \bullet}$) and the BH mass ($M_{\rm \bullet}$): the commonly used Bondi-Hoyle model ($\dot{M}_{\rm \bullet}\propto M_{\rm \bullet}^2$), and two free-fall models with shallower scalings ($\dot{M}_{\rm \bullet}\propto M_{\rm \bullet}^{1/2}$ and $M_{\rm \bullet}$). Bondi accretion tends to produce stronger runaway growth than the free-fall models when using heavy ($\sim10^5\,\rm{M}_\odot$) seeds in extreme environments owing to the steeper $M_\bullet$ scaling, but its sensitivity to the local gas sound speed makes it more susceptible to suppression from temperature increases due to AGN and stellar feedback. The free-fall models tend to produce stronger growth for lower-mass seeds ($\sim10^{3-4}\,\rm{M}_\odot$) in moderate environments as they are less dependent on the BH's mass to accrete effectively, however in this regime BH growth remains negligible for all accretion models in the presence of fiducial stellar feedback. Enhancing early BH growth via many BH-BH mergers disproportionately enhances subsequent accretion-driven growth for Bondi due to the steeper $M_{\rm \bullet}$ dependence. Our simulations can thus assemble BHs with masses of $\sim10^6-10^7~M_{\odot}$ at $z\gtrsim9$, as inferred by JWST, under two circumstances: 1) abundant heavy-seed formation that drives BH-BH mergers, or 2) Bondi accretion with weak feedback.

Similarity search is a fundamental operation in time series analysis. Most existing techniques, however, require users to supply a precise sequence of values (typically an entire time series object) as the query input. This rigid requirement limits real-world applications, where users instead want to express patterns, trends, or value ranges. Flexible, pattern-based search has been explored in text retrieval and complex event processing, but remains underexplored for large-scale distributed time series. To close this gap, we propose TSseek, a regular-expression-powered search framework for distributed time series datasets. TSseek's query language enables users to compose patterns encompassing trends, value ranges, and wildcard segments. We show that conventional approximation techniques (e.g., PAA and SAX) and their index structures are ill-suited for such queries because they cannot operate on regular-expression query constructs. In TSseek, we map the time series objects and the query constructs into the same space by approximating time series objects as sequences of line segments that retain both trend (slope direction) and value range, and translating query constructs into bounding rectangles. To support efficient processing, we build TSseek-X, a distributed spatial index over the time series segments. TSseek supports two fundamental query types, namely whole-matching queries (over entire series) and subsequence-matching queries (over arbitrary windows within a series). Across benchmark and real-world datasets, full-scan, model-based, and SAX-based baselines all sacrifice either accuracy or speed, whereas TSseek returns exact answers efficiently. Also, for subsequence workloads, it achieves significant speedups over state-of-the-art subsequence matching engines.

Immersed boundary methods (IBMs) are widely used to simulate flows around complex geometries and moving bodies, but they often involve a trade-off between precision and computational efficiency. Eulerian formulations require special treatments for moving walls and may generate spurious force oscillations, whereas Lagrangian formulations can suffer from slip errors at the immersed surfaces. We propose a novel sharp-interface IBM for incompressible flows involving moving, deformable, and arbitrary-thickness bodies. The method combines a fast tagging algorithm, a two-sided Eulerian forcing strategy, and a consistent mass correction that reduces the splitting error of fractional-step schemes, while preserving the structure of the discrete Laplacian operator. This formulation retains the efficiency of direct Poisson solvers, thus avoiding the overhead of cut-cell, multigrid, and projection-based approaches. The method naturally handles moving boundaries, and yields small transpiration errors with second-order accuracy in the enforcement of the no-slip condition. Numerical tests using rigid, deformable, turbulent, and biologically inspired flows demonstrate the accuracy, robustness, and efficiency of the method, without compromising computational cost.

We present an $\textit{ab initio}$ framework for predicting resonant inelastic X-ray scattering (RIXS) in optically pumped materials. Our methodology is based on the Kramers-Heisenberg formula for the double-differential cross section formulated using the results of the Bethe-Salpeter equation (BSE) from many-body perturbation theory. To extend this approach to the time domain, we incorporate non-equilibrium charge-carrier distributions obtained from real-time, time-dependent density-functional theory (RT-TDDFT). Generalizing the RIXS implementation with respect to arbitrary polarizations, allows us to consider different orientations of incoming and outgoing light. We demonstrate our method's capabilities by studying RIXS at the K-edge of graphite for various non-equilibrium charge-carrier distributions, representing different delay times after optical pumping. Our results reveal angular dependencies in $π$- and $σ$-orbital-derived spectral regions, in good agreement with experiment.

Inspired by the $P$-wave molecular interpretation of the recently observed vector state $G(3900)$, we analyze the production of its possible pseudoscalar partner, denoted here as $G_0(3900)$, via the radiative decay $Y(4230) \to γG_0(3900)$. The $G_0(3900)$ is interpreted as a $P$-wave molecular state with quantum numbers $J^{PC}=0^{-+}$, dominated by the $D\bar{D}^{\ast}/\bar{D}D^{\ast}$ components. Although not yet experimentally established, such a structure is expected to appear near the $D\bar{D}^*$ threshold and to exhibit characteristic production patterns. The decay is assumed to proceed through a triangle mechanism. Depending on the model parameters and the binding energy of $G_0(3900)$, the resulting branching fraction lies in the range $\mathcal{B}(Y(4230) \to γG_0(3900)) = 3.8 \times 10^{-5} - 3.3 \times 10^{-4}$. Our results offer a pathway to search for signatures of $G_0(3900)$ in radiative channels and also provide a test of the consistency of loop-mediated radiative decays with a molecular description of the $Y(4230)$.

Resonant $Z$-boson production is a cornerstone of precision electroweak physics, with its vacuum line shape set by the $Z$ mass, width, and collision kinematics. We show that a strong laser field can significantly alter this picture. By treating the field nonperturbatively, we find that laser dressing of the incoming fermions alters the effective collision kinematics and opens laser-photon exchange channels, including multiphoton processes, in $e^{+}e^{-}$ collisions. As a result, the $Z$-resonance profile develops distinct intensity-dependent regimes, evolving from the vacuum limit to saturation at intermediate field strengths and to an approximately quadratic enhancement at higher intensities. Additionally, the polarization composition of the produced $Z$ bosons is redistributed. In particular, at high intensities the laser-induced contribution can compensate the intrinsic chiral asymmetry of the electroweak interaction, leading to nearly parity-balanced $Z$-boson production. Our results identify that strong classical fields can dynamically control electroweak resonance phenomena, opening a bridge between strong-field QED and high-energy collider physics.

We show that for a generic real or complex-valued compactly supported potential, the corresponding Schroedinger operator achieves maximal resonance density, in the sense that its integrated resonance counting function achieves the optimal asymptotic upper bound. For odd dimensions this follows from results of Dinh-Vu once we adapt an argument of Christiansen Hislop. The proof for even dimensions constitutes the bulk of the paper, and we prove several new results on resonances which have analogues in the odd dimensional case. This includes a sharp upper bound on the integrated resonance counting function for any compactly support potential, a proof that the characteristic function of a ball has resonance counting function which achieves the optimal upper bound, and an even-dimensional analogue of the result of Dinh-Vu on asymptotics of the resonance counting functions for complements of pluripolar subsets of analytic families of potentials. We use the characterization of resonances as zeros of certain Fredholm determinant functions related to the scattering matrix, allowing us to apply techniques and results from the theories of one and several complex variables. Our proof that the characteristic function of a ball has counting function achieving the optimal upper bound uses the uniform asymptotics of Bessel functions and follows ideas of Zworski, Christiansen-Hislop, and Dinh-Vu.

Ballantine, Beck, Merca, and Sagan conjectured four identities, collectively Conjecture 19, relating the image of the map pre_k on integer partitions to four OEIS sequences. We prove parts (i) and (iii) unconditionally, prove part (iv) unconditionally using the injectivity of pre_2 on partitions of n (Conjecture 1 of the same paper, proved by Li in arXiv:2508.00971), and show that this injectivity is in fact equivalent to part (iv). For part (ii) we prove the partition-theoretic half unconditionally and reduce the remaining content to a 2006 conjecture of Dean Hickerson on the OEIS concerning Huffman coding. We also correct a sign error in the published statement of part (iii): the correct identity is chi(ImP_3(n)) = A213213(n) - 1, not 1 + A213213(n) as stated.

Large language models can translate a researcher's intent into runnable matplotlib code, yet the resulting chart rarely lands in a paper without multiple rounds of manual revision. We argue that the open problem is not chart code generation but chart publication: making the output look like a top-venue figure, survive the target layout, and respond to precise author edits. We present chart-plot, an agentic harness that closes this last mile through three components: (1) a style-aware code generator conditioned on a textual style skill distilled from accepted figures at the target venue, (2) a deployment-aware render loop that compiles the chart inside the target LaTeX context and revises until layout constraints are met, and (3) a structured edit layer that exposes every chart element as a directly manipulable handle. We report early results on three chart-type case studies (grouped bar, scaling line, paired distributions) and a small user study.

We analyze five-neighbor particle cellular automata whose conventional two-dimensional fundamental diagrams are multivalued, but whose mean flow is uniquely determined by introducing a second density. We first consider binary rules for which the second density is conserved, and then examine rules for which the second density is not conserved but converges asymptotically. These examples give three-dimensional fundamental diagrams in which the mean flow is determined by the particle density and the second density. We then investigate whether this single-valued structure is preserved under real-valued max-plus extensions. There are some rules where two different max-plus extensions are introduced, and numerical simulations show that both extensions preserve the same single-valued three-dimensional fundamental diagram. These observations imply that, in constructing real-valued max-plus extensions, it is important to choose the flux function and the second density consistently.

An entire slice regular function $f:\mathbb H\to\mathbb H$ can omit four prescribed quaternionic values only in the affine-dependent case. More precisely, four affinely independent omitted values force $f$ to be constant, while the converse follows from the plane-omission theorem of Bisi--Winkelmann. The proof passes to the real-symmetric stem function. For each omitted value a quadratic zero-divisor criterion gives a zero-free entire function $Q_j$, and the component normal to the affine span is governed by a square-discriminant identity. Finite-order data are excluded by Hadamard factorization and a rigidity argument on the real axis. In the general case, logarithmic Bloch--Ochiai places the $Q$-curve in a translated algebraic torus. The Laurent-square case reduces to the finite-order contradiction, and the nonsquare case is excluded by an even-ramification argument together with the level-one truncated Second Main Theorem of Noguchi--Winkelmann--Yamanoi.

Let $f(n,k)$ be the minimum size of a collection of bicliques such that (i) every edge of the complete graph $K_n$ is covered by at least one and at most $k$ bicliques in the collection, and (ii) for each edge $\{u,v\}$, the number of bicliques in which $u$ appears in the first class and $v$ in the second class differs by at most one from the number of bicliques in which $u$ appears in the second class and $v$ in the first class. For $k=1$, $f(n,k)$ reduces to the biclique partition number of $K_n$, and the Graham-Pollak theorem gives $f(n,1)=n-1$. For $k=2$, $f(n,k)$ is the ordered biclique partition number of $K_n$, for which it is known that $c_1 n^{1/2} \le f(n,2) \le c_2 n^{1/2+o(1)}$ for some positive constants $c_1$ and $c_2$. In this note, we give almost tight bounds for $f(n,k)$ for fixed $k \ge 2$: \[ (1+o(1))c_1(k)\cdot n^{\frac{1}{\lceil k/2\rceil+1}} \le f(n,k) \le (1+o(1))c_2(k)\cdot n^{\frac{1}{\lfloor k/2\rfloor+1}+o(1)}, \] where $c_1(k)$ and $c_2(k)$ are positive constants.

Mobile phone overuse and attention fragmentation have become pressing societal and public health concerns. Cyberpsychology research highlights addictive engagement loops driven by intermittent rewards, persuasive design, and habit formation. In this article, we use current evidence on mobile-phone addiction and propose "Digital White Spaces" (DWS), a socio-technical framework that combines privacy-preserving monitoring, AI-driven detection of addictive loops, device-mode interventions, and physical signal-limited zones to minimize digital stimulation and internet addiction.

Reduced-precision arithmetic offers significant opportunities to improve performance, memory usage, and energy efficiency in numerical applications, provided that numerical accuracy is preserved. This work investigates automated precision tuning through customized floating-point formats with user-defined exponent and significand sizes, enabling the emulation of emerging low-precision formats and the exploration of non-standard precision configurations within a unified mixed-precision framework. The proposed methodology, implemented in the PROMISE precision autotuning tool, combines numerical validation with a systematic search to generate program variants that satisfy user-defined accuracy requirements. To address the computational cost of this exploration, a containerized benchmarking framework supports parallel execution across multiple algorithms and parameter configurations. The approach is evaluated on a suite of numerical programs, including linear solvers and applications from the Rodinia benchmark. Results show that a substantial proportion of variables can be safely reduced to lower precision while preserving accuracy, indicating that standard double precision is often over-provisioned. These findings highlight the potential of automated precision tuning to derive efficient mixed-precision configurations tailored to application-specific accuracy requirements.

The 1970 spectral extension of Mantel's theorem, proved by Nosal, states that every graph with $m$ edges and spectral radius $ρ_1>\sqrt{m}$ contains at least one triangle. Its quantitative refinement by Ning and Zhai later established that any graph $G$ with $m$ edges and spectral radius $ρ_1\geq\sqrt{m}$ contains at least $\lfloor\frac{\sqrt{m}-1}{2}\rfloor$ triangles, unless $G$ is a complete bipartite graph. In this paper, we further investigate the minimum number of triangles guaranteed under the strengthened spectral condition $ρ_1\geq\sqrt{m}+c$, where $c$ is a positive constant. We prove that for any constant $c\in (0,\frac{1}{2}]$ and all sufficiently large $m$, if $s=s(m)$ is a real-valued function satisfying $\lim_{m\to\infty} \frac{s}{m}=c$, then every $m$-edge graph $G$ with spectral radius $ρ_1$ satisfying $ρ_1^2\geq m-1+\frac{2s}{ρ_1-1}$ contains at least $s$ triangles. Moreover, we characterize the extremal graph achieving the minimal number of triangles. In particular, when $s=\frac{m-1}2$, our result settles a conjecture proposed by Li, Feng, and Peng.

We address two mass-dependent properties among early-type galaxies (ETGs): (1) abundance ratios [N/Fe] and [Na/Fe], and (2) the centrally concentrated "UV upturn" at far-UV (FUV) wavelengths, which is likely produced by extreme horizontal branch stars with supersolar helium abundances. Using new HST/WFC3 observations of one FUV-weak and one FUV-bright ETG, we probe the "MP scenario" by Goudfrooij who posited that the UV upturn and the mass-dependent abundance variations of N and Na within and among ETGs are physically connected and produced by dissolution of metal-rich globular clusters, which represent the only galactic environment where mass-dependent enrichment of He, N, and Na is known to occur (i.e., second-generation stars of the "multiple stellar populations" (MPs) phenomenon). We show that passbands F275W and F390W are uniquely sensitive to correlated changes in $Y$ and [N/Fe] in integrated-light photometry when combined with archival data in F475W and F850LP. While F475W-F850LP is found to decrease with increasing radius in both galaxies, consistent with known metallicity gradients, F275W-F390W increases with increasing radius, as expected if the UV upturn is caused by second-generation stars with supersolar $Y$ and [N/Fe]. Furthermore, the radial gradient in F275W-F390W and the implied fractions of He- and N-enhanced stars are found to be significantly larger in the FUV-bright ETG than in the FUV-weak one, consistent with the predictions of the MP scenario.

Generative retrieval offers a new paradigm for e-commerce search by mapping user queries directly to product Semantic Identifiers (SIDs). However, e-commerce queries are often short, noisy, attribute-heavy, and associated with multiple category-consistent products, creating a substantial representation gap between natural-language shopping intent and artificially constructed item SIDs. Explicit Chain-of-Thought (CoT) reasoning can help bridge this gap, but its extra generation cost is difficult to reconcile with the low-latency requirements of online e-commerce systems. To address this challenge, we propose CaLIR (Category-guided Latent Intent Reasoning), a category-guided latent intent reasoning framework for e-commerce generative retrieval. Rather than generating explicit textual rationales, CaLIR learns continuous latent intent states before SID decoding and uses product category hierarchies as a natural scaffold for coarse-to-fine intent reasoning. Specifically, we introduce hierarchical semantic reasoning to align latent states with category-level shopping intent, and query-wise reasoning enhancement to model diverse intent paths under multi-positive queries. CaLIR further combines a query-specific dynamic prefix trie, assembled from pre-indexed category-level tries, with reasoning-aware constrained decoding. Experiments on multilingual e-commerce search datasets show that CaLIR achieves a better balance between retrieval effectiveness and inference efficiency than existing methods, while also demonstrating transferability and robustness across induced hierarchies and different generative backbones.

We study inner products and partial amplitudes of graph states--a commonly employed class of quantum states, which are specified by graphs. We find that the magnitudes of these quantities are simply related to the rank of the adjacency matrix of the graph over F_2 while the phase is determined by the Arf invariant of its quadratic refinement. These facts motivate a nonlocal tensor factorization of the Hilbert space, with respect to which all graph states are products of Bell pairs with unentangled ancillae. These results may illuminate the quantum advantage in the framework of Measurement-Based Quantum Computation and suggest that graph states can be usefully visualized in the language of algebraic topology. In addition, we develop a specialized technique for computing expectation values of qubit-wise permutations in graph states, which is useful for calculating multi-invariants.

Machine-learned interatomic potentials (MLIPs) have had a profound impact on molecular modelling in recent years, promising to resolve the long-standing tension between the scale and accuracy of simulations. There has been a proliferation of new models and designs, and recently the paradigm of ``foundational'' MLIPs has become prevalent. Broadly speaking, foundation models are trained on large diverse datasets and promise to work well for new systems with minimal updates required. However, in such a new and fast moving field, there are many unanswered questions. In this article, we set out to articulate and explore what we see as the most important among these questions. We start by developing a working definition for foundational MLIPs and use this definition to frame the subsequent open questions. Despite the rapid progress in the field of MLIP models, we believe that these are fundamental questions which will continue to define cutting edge research in MLIPs in the years to come.

We study a one-dimensional long-range Su-Schrieffer-Heeger model with third-nearest-neighbor hopping and subject to quasiperiodic disorder. In the clean limit, the model hosts phases characterized by winding numbers $W=-1,0,1$ and $2$. The introduction of quasiperiodic disorder profoundly modifies the phase diagram and induces a series of topological phase transitions. Owing to the competition between topological dimerization and localization, topological Anderson insulating (TAI) phases with different winding numbers emerge and can persist even when the spectral gap becomes nearly closed in the strong-disorder regime. In addition, we uncover multiple reentrant topological phase transitions induced by varying either the quasiperiodic disorder strength or the hopping amplitudes. Remarkably, the system exhibits staircase-like topological Anderson transitions, where the real-space winding number evolves through successive quantized steps with increasing disorder strength. Our results demonstrate that the interplay between long-range hopping and quasiperiodic disorder generates a rich landscape of disorder-induced topological phases and reentrant topological transition phenomena.

We present a rigorous theoretical framework for symmetry breaking and quantum irreversibility arising from stochastic Ito field reversal within a cubic-quintic nonlinear Schrodinger equation (CQ-NLSE) formalism. Starting from three physically motivated considerations, forward and backward nonlinear stochastic differential equations are derived via the Ito calculus. Kinematic time-reversal is shown to be fundamentally incompatible with the Ito stochastic structure, yielding the universal asymmetry-coupling parameter of 2/3. An energy-driven collapse operator proportional to the product of noise strength, local probability density, and excitation energy squared is introduced, amplifying the collapse in high-density, high-excitation regions. Exactly bright soliton solutions are obtained for a quasi-one-dimensional BEC of attractive Li-7 atoms, with forward and backward amplitude ratio of 1.870. Heat map analysis of the parameter planes reveals that the forward collapse operator grows monotonically in time while the backward counterpart decays, achieving a ratio approximately 1030, sharply distinguishing this framework from conventional symmetric collapse models.

Galaxy rotation curves exhibit systematic discrepancies between the observed dynamics and the gravitational contribution expected from baryonic matter. Identifying empirical regularities in these discrepancies may provide insight into the organization of galaxy dynamics. We investigate whether the residual component of galaxy rotation curves contains a common structure across galaxies spanning a broad range of masses and morphologies. Using rotation-curve data from the SPARC and LITTLE THINGS surveys, we analyze residual velocity-squared profiles after accounting for the baryonic contribution and allowing for uncertainties in the baryonic normalization. We find that the residuals are not randomly distributed but instead follow a common linear pattern across a diverse galaxy population. Population-level analysis shows that the data preferentially select this linear residual structure over alternative radial dependences. The residual component separates into a mass-coupled contribution and a second contribution that remains nearly independent of galaxy mass. These empirical trends are observed across both spiral and dwarf galaxy samples. The existence of a common residual structure across galaxies spanning a broad range of masses and morphologies provides a new empirical constraint on theories of galaxy dynamics.

Chain-of-thought (CoT) answer-hijack templates can flip the final numeric answer of a 7B-8B language model on GSM8K or MATH-500 even when the visible reasoning trace looks fluent. Activation patching is the standard probe for locating where this hijack can be undone, and a successful clean-source patch is often read as evidence that the patched activation carries the recovered content. We show that this reading is unsound: clean-only localization profiles (peak, spread, thresholded band) underidentify the frozen-hook source contrast, and the clean-only profile is an intervention map, not a mediation certificate. We then construct an audit that turns each candidate patch into a source-control certificate with a pre-registered Type-I guarantee. The certificate runs in three stages: SELECT (clean-source band sweep with permutation calibration and held-out validation), FREEZE (lock the hook), and AUDIT (paired-bootstrap source contrasts at the frozen hook). It emits an incorrect mechanism label with probability at most alpha = alpha_sel + alpha_audit under sample-split disjointness. A matching-rate sample-complexity theorem (n_star = Theta(Delta^{-2} log(1/alpha))) bounds the audit cost. On Qwen2.5-7B and Llama3-8B, three few-shot/puzzle cells pass confirmatory K=1 localization with held-out gaps +32.6, +45.1, +17.7; fixed-hook reruns recover 47.0% (Qwen-puzzle) and 39.0% (Llama3-puzzle) at n=100; frozen MATH-500 transfer recovers 26.0%. After audit, Llama3-PZ and Qwen-PZ are identity-light with moderate magnitude (Qwen-PZ also layer-sensitive); Llama3-FS is a single-seed moderate-positive candidate (multi-seed replication queued); Qwen-FS is exploratory non-separation with a layer-sensitive flag. The method is a diagnostic auditing protocol, not an adaptive safety defense.

We introduce the calibration energy for oriented immersions into Euclidean space, quantifying the deviation from calibrated geometry. A key property is that this energy may remain finite for infinite-volume immersions, while a null-Lagrangian structure ensures that it has the same first variation as the volume functional. We establish an exact dissipation identity for the calibration energy along oriented, proper mean curvature flows in arbitrary dimensions and codimensions, under a mild local-volume bound. This provides a new, finite variational framework for mean curvature flow beyond the finite-volume setting. Our result yields several applications, including rigidity for solitons and convergence for two-dimensional immortal solutions. In particular, every proper self-expander with finite constant-coefficient calibration energy must be a plane in all dimensions and codimensions.

In this work, we adapt and apply techniques from machine learning to the exploration of physics beyond the Standard Model in the leptonic sector. Namely, we employ initialization and optimization, as they are applied in machine learning, to minimize a loss function that describes textures or conditions which we want in the neutrino mass matrix. The model free parameters are explored during the optimization, and after training for a number of optimization steps, we obtain matrices that approximately follow the desired forms, as well as their corresponding optimized parameters. We also discuss extensions and additional applications of the ideas presented here in conjunction with other methods based on artificial intelligence.

We give a quantitative impossibility result for pass-only prompt hardening of code LLMs. For any deterministic prompt filter $h$ and a registered family of finite executable-equivalence task variables $\mathcal Y_{\mathrm{exec}}$, the shared filtered-prompt channel $\rmI(h(p);h(\tilde p))$ is lower-bounded by a worst-$Y$ Fano floor; on HumanEval and MBPP the universal pass-only floor evaluates to $\mathcal F^{\mathrm{op}}\ge 0.84$ and $1.20$ nats at $η=0.05$ task-collapse tolerance, and the identity row realizes $\mathcal F^{\mathrm{id}}\ge 1.67$ and $1.80$ nats. An estimator-invariance corollary lifts the floor to any deterministic embedding pipeline; a dataset-agnostic corollary states the floor in visible-spec entropy and is empirically witnessed by $164/164$ HumanEval+ and $224/224$ MBPP+ $V(p)$-invariance. We operationalize the floor as the \emph{Tri-Audit Protocol}, a two-axis reporting protocol that separates a prompt-side deductive registry attribute (Shannon nats on the visible-spec representation) from a model-side empirical proxy (KSG-1 primary, MINE secondary, on hidden states). A constrained best-of-family search over deterministic and guarded learned filters on CodeLlama-7B, Qwen2.5-Coder-7B/1.5B and DeepSeek-Coder-6.7B at $n=164$ yields the \emph{Cross-Model Tri-Audit Invariance}: of twenty-eight pass-preserving rows, twelve antecedent-preserving deterministic rows fail proxy-axis leakage reduction on every backbone with sign-invariant positive deviations, twelve antecedent-changed-of-record learned-canonicalizer rows fail proxy-axis leakage on every backbone, and four antecedent-violating rows are reported as registered-family collapse; no filter produces a shared Tri-pass on a nine-cell gate-sensitivity sweep. Pass@1 alone cannot certify code-LLM prompt hardening.

We study a class of Sturm--Liouville problems of the form $$ -(p\,y')' + q\,y = λ\, p\, y, $$ on a finite interval with complex-valued coefficients, where $p$ is piecewise smooth and $q$ is bounded. We prove that all eigenvalues in the open left half-plane are contained in a bounded set, which implies that only finitely many eigenvalues lie in this region. A canonical instance of this class arises in transverse-magnetic (TM) diffraction by metallic lamellar gratings, a benchmark problem in computational photonics that has been central to the development of Fourier modal methods. These methods exhibit long-standing convergence difficulties in this setting, associated with the loss of definiteness of the underlying operator and the emergence of spurious modes. Our result yields a rigorous criterion for identifying such non-physical modes in low-loss metallic gratings. Numerical examples illustrate the practical utility of the criterion.