Papers

We study a family of quantum subsystem codes defined on rectangular coordinate grids of any dimension, with even side lengths of at least four. The directly measured operators act along coordinate lines. For every member of the family, we derive the number of protected logical qubits and prove its dressed distance without a numerical search. To illustrate the resulting design choices, we impose a budget of at most 10,000 data qubits and determine the complete tradeoff between encoding rate and measurement weight within this family at distances 16, 32, and 64. At distance 16, one code protects 4,096 logical qubits among 10,000 data qubits using weight-ten measurements. At distances 32 and 64, codes with 7,776 and 9,216 data qubits protect 1,024 and 256 logical qubits, respectively, using weight-six measurements. We include and explain Lean code snippets throughout the paper to guide readers through the formal verification of our subsystem-code construction and its dressed and bare distances.

We measured the 198-310 GHz flux densities of 18 Class II protoplanetary disks in the Ophiuchus star-forming complex using the Submillimeter Array (SMA). The $\sim$200-300 GHz spectral indices ($\alpha_{200-300}$) of these disks are $2.3^{+0.2}_{-0.5}$. In this observed frequency range, emission properties of the Ophiuchus disks are very similar to the 48 spatially compact Class II disks in the Taurus-Auriga region observed in a previous SMA survey. Combining the Ophiuchus and Taurus-Auriga samples, the Pearson correlation coefficient between $\alpha_{200-300}$ and the flux density at 250 GHz ($F_{250\,\mathrm{GHz}}$) is 0.27 ($p=0.02$). We do not find a convincing correlation between $\alpha_{200-300}$ and the $R_{95\%}$ radius of the disks. Our interpretation for the $\alpha_{200-300}$ values being close to 2 in the spatially compact disks is that at $\gtrsim 200$ GHz frequencies, the continuum emission in these disks is dominated by optically thick dust thermal emission, independent of $F_{250\,\mathrm{GHz}}$ and $R_{95\%}$. As a result, the (sub)millimeter luminosity and the apparent disk size are positively correlated, which has been found in numerous resolved emission surveys of Class II disks. In young clusters with ages of $\sim$1-2 Myr, Class II disks with smaller radii or lower (sub)millimeter luminosities are not necessarily those in which the dust mass budget has been consumed or dispersed.

Astronomical foundation models are increasingly used as reusable representations across surveys, but it is unclear when the same object remains consistently represented across instruments or whether a model can warn us before transfer fails. We present a conformal framework for auditing cross-survey representations using cross-matched Legacy Survey–HSC, HSC–JWST, and SDSS–HSC objects. Astronomy-specific AstroPT embeddings show lower translation errors and tighter conformal regions than general-purpose visual backbones at comparable coverage, while different model families fail on different objects. We then use adaptive conformal prediction to test whether the source embedding contains information about its own future error. Using a ridge difficulty model fitted to source embeddings, we find that this warning signal is consistent across the tested backbones for Legacy$\rightarrow$HSC, backbone-dependent for HSC$\rightarrow$JWST, and largely absent for SDSS$\rightarrow$HSC. When informative, adaptation improves coverage for the hardest objects. Matched-control analysis further reveals silent failures not explained by magnitude, apparent size, or nearest-neighbor distance. Hence, we show that conformal uncertainty provides a realistic way to identify when astronomical representations transfer reliably and when they fail without warning.

Near-field radiative heat transfer (NFRHT) is of great interest for energy conversion and thermal management. Recent work on NFRHT has shown that metasurfaces can enhance NFRHT and reshape its spectral characteristics. Here, we show that the vortex lattice of a type-II superconductor represents a self-assembled metasurface whose lattice dimensions, in contrast to most other metasurfaces, can be tuned by magnetic fields, allowing NFRHT to be varied by orders of magnitude. Specifically, we show that for two Nb surfaces at 4.2 K and separated by a 100 nm gap, NFRHT can be magnetically tuned by a factor >200. Further, we show that the tuning range grows upon cooling, exceeding 10^5 at 2 K, which is far beyond the order-unity modulation of many proposed schemes for tuning NFRHT. Our results establish vortex matter as a magnetically programmable thermal metasurface and open new opportunities for tuning the flow of heat at the nanoscale.

A highly coarse-grained model for the lipid monolayer is formulated by considering a two-dimensional system of spherical particles with distinct types of S, U, and C, corresponding to the saturated, unsaturated, and cholesterol molecules. Their interactions are defined as modified Lennard-Jones type with distinct interaction strengths. The phase behavior of the system is studied for various cholesterol compositions, $x$ ranging from 0.1 to 0.6. From the simulation results, we observe that the S- and C-type particles segregate together to form ordered microdomains, with U-type particles at their outer leaflet; consistent with observations in literature. An order parameter $\Phi$ is defined to quantify the extent of phase separation among the constituents. The time averaged value of $\Phi$ is found increasing with the $x$ value. Radial distribution function calculations indicate the structural ordering within the phase separated domains.

We develop a parity-resolved spectral-connection construction for a one-dimensional Dirac particle in an attractive soft-core Coulomb potential. The square-root dependence of the potential produces algebraic branch points in the coordinate plane. We uniformize these branch points by introducing \(t=\sqrt{x^2+\beta^2}\), while retaining the full-line \(Z_2\) symmetry generated by \(\Pi=\sigma_z P_x\). In each parity sector the resulting problem is formulated as a global connection problem between a solution selected at the physical origin and the decaying solution at infinity. This defines parity-resolved spectral connection functions whose zeros determine bound-state energies. We further construct a quasi-exact Bethe-ansatz sector directly from the same Dirac equations and use its polynomial solutions as independent benchmarks of the spectral condition. The comparison clarifies the distinction between local quasi-exact solvability and the global spectral determinant. The construction is inspired by the role of discrete symmetry and global analyticity in the quantum Rabi model, without identifying the present spectral function with Braak's \(G\)-function.

AI foundation models pretrained on weather and climate data are increasingly fine-tuned to Earth science tasks well beyond weather forecasting. Their development and adoption are outpacing the scientific community's ability to evaluate them. These models are judged almost entirely by benchmark skill metrics, which measure how closely a forecast reproduces a reference product but not whether a model represents the physical processes governing the system it predicts. Forecast skill and physical reliability are therefore distinct properties. The distinction is most consequential under the nonstationary conditions of a changing climate for which these models were never trained. We identify five priorities for the physical evaluation of AI models in Earth science from task-specific emulators to foundation models, spanning training data, fine-tuning, behavioral testing, mechanistic interpretability, and output validation. We recommend three activities for the coming decade: 1) open AI-ready evaluation datasets, 2) a shared reporting standard for physics-based evaluation, and 3) a dedicated research program on the safety of these models.

We investigate whether the geometry of a curved conductor–dielectric interface can modify the effective mass and propagation of scalar surface plasmons (SSPs). In the hydrodynamic limit, we describe SSPs as density perturbations in a semiclassical jellium electron gas. Using a thin–layer dimensional reduction procedure, we derive a massive Klein–Gordon equation for SSPs on the curved interface with a geometric potential. We find that under specific conditions, the geometric potential allows SSP propagation with a vanishing effective mass. We then apply the formalism to a well known analogue black hole configuration, determining the corresponding quasinormal mode frequencies. Our results show that interface curvature provides a geometric handle on plasmon propagation and localization, suggesting new possibilities for plasmon transport and analogue gravity experiments with surface plasmons.

The new approach is develop to determine the hyperfine structure of the rotationally excited $1 s_{\mu} n \ell_{e}$-states in the three-body helium muonic ${}^{3}$He $\mu \; e$ and ${}^{4}$He $\mu \; e$ atoms. The formulas derived in this study allow one to evaluate the hyperfine structure splittings for an arbitrary rotationally excited (bound) $1 s_{\mu} n \ell_{e}$-state in the three-body helium muonic atoms. Similar formulas have never been produced in earlier studies and this explains why these hyperfine structure splittings are still unknown for these bound states.

Sodium chloride is a major component of extraterrestrial oceans, but it is generally assumed to be excluded from the high-pressure ice mantles of water-rich planets. Here we show that a concentrated NaCl solution, when quenched in an amorphous state before compression, crystallises in a metastable NaCl-bearing ice VII phase. Synchrotron x-ray diffraction and neutron diffraction reveals an expanded and strongly disordered ice VII lattice with no detectable crystalline NaCl. Ab initio calculations reproduce lattice expansion by substituting water molecules for Na$^+$ and Cl$^-$ ions and show that the structural response increases strongly with salt concentration. Upon decompression at 300 K, the phase expels crystalline NaCl at $5.1 \pm 0.3$ GPa and does not reform upon recompression, demonstrating that its formation is controlled by the thermodynamic pathway. Despite an 8.5% larger unit-cell volume, NaCl-bearing ice VII has a density close to that of pure ice VII and is substantially less dense than an equivalent mechanical mixture of ice and halite. These properties suggest that salty ice may be transported through deep convecting mantles but release salt near the 5 GPa boundary, where the denser products could inhibit further upward transport. Pathway-dependent salt trapping may therefore provide a previously unrecognised control on chemical exchange between rocky interiors and subsurface oceans.

We study leading parity-even four-derivative corrections to the linear Christodoulou regularity criterion for a neutral, massless, minimally coupled spectator scalar in four-dimensional charged de Sitter black holes. We derive the corrected static solution, cold extremality relation, near-horizon geometry, Cauchy-horizon surface gravity, and neutral scalar quasinormal spectrum within Einstein-Maxwell effective theory. Near cold extremality, the scalar equation reduces analytically to the finite-temperature anti-de Sitter two-dimensional throat problem. We find that the dominant nonstationary spherically symmetric mode retains its cold-limit regularity ratio through first order, while higher angular sectors respond to the deformation of the relative throat radii. The finite-distance neutral-scalar Christodoulou boundary nevertheless shifts because the relevant exterior scalar spectrum and the unequal horizon surface gravities enter the regularity ratio. At smaller and intermediate cosmological scales, positive effective coefficients move the Christodoulou threshold to larger normalized separation of the Cauchy and event horizons. Toward the larger cosmological-scale part of the cold branch, the same coefficient directions move that threshold back toward the cold endpoint. The reversal accompanies a transition in the quasinormal family that supplies the spectral gap. We further show that the coefficient combination governing the fixed-charge extremal mass parameter differs generically from those governing the cold throat and the finite-distance neutral-scalar boundary. Extremality therefore does not determine a universal direction for the neutral-scalar Christodoulou-threshold correction. Our results identify cosmological scale and spectral-family competition as essential elements in relating effective gravity, black-hole extremality, and Cauchy-horizon regularity in this spectator sector.

We reconsider the Bardeen black hole surrounded by a Kiselev fluid, obtained by adding a Kiselev term to the Ayon-Beato-Garcia-Bardeen metric. Contrary to claims in the literature, the solution is regular at the origin only for $c=0$: for $c\neq0$ curvature invariants diverge as $r\to0$, and the spacetime is asymptotically de Sitter-like rather than flat, with a cosmological horizon $r_c$ for $0<c<c_N(q)$. We map the full $(q,c)$ domain of horizon structures in closed form, locating the extremal and Nariai-type boundaries and their cusp. Using the Ma-Zhao prescription for the mass-dependent nonlinear-electrodynamics source, we derive the corrected entropy and verify the extended first law and Smarr relation to machine precision by computer-algebra differentiation, not through the entropy's own definition. The heat capacity shows a single Davies-type divergence, located as a closed-form quartic and expanded analytically in $c$. In thermodynamic geometry, the Quevedo-metric curvature has a spurious second singularity generated by the entropy's integration constant and the non-uniqueness of its conformal factor; we isolate this artefact and show only the Davies-point divergence is physical. The Ruppeiner curvature, identically zero for pure Bardeen, becomes non-zero once $c\neq0$. For the shadow, we compute the critical impact parameter $b_c(q,c,w)$ and show the nominal bound $c\lesssim10^{-2}/M$ from the EHT image of Sagittarius A* is not self-consistent: the same $c$ places the cosmological horizon nine orders of magnitude closer than Earth's distance to Sgr A*, and the bound is fourteen orders of magnitude larger than $H_0/c$, the true cosmological dark-energy scale. We reinterpret the EHT constraint as bounding $c$ only near the horizon, not as an astrophysical or cosmological bound on the quintessence parameter.

Coherent alias sampling implement an important subroutine for block encoding and qubitization based quantum simulation using quantum lookup table. Related constructions exploit data lookup and matrix structure to implement block encodings for use in quantum singular value transformation. For a state on $n$ qubits, constructing and storing the alias table requires both classical and quantum resources exponential in $n$. We show that when the amplitudes are samples of a polynomial of degree at most $d$, the table can be represented and evaluated coherently with cost polynomial in $n$, $d$, exponentially reduced from $\Theta(2^n)$ classical and quantum cost. We construct a quantum circuit for coherently computing the alias table for polynomial states using reversible integer arithmetic. By employing fast arithmetic, we construct a deterministic circuit for preparing polynomial states over Clifford+$T$ with a complete gate count of $\tilde{O}(ndB+B^2)$, where arithmetic width $B=\tilde{O}(dn+d\log(d+1))$. In the high precision limit for state fidelity $\epsilon$ with fixed $n$ and $d$, it is sufficient have $B=\Theta(\log(1/\epsilon))$ and the complete gate count becomes $O(\log^3(1/\epsilon)\log\log(1/\epsilon))$. Additionally, the effective representation of the alias table can also be used for classical sampling algorithms. Furthermore, we develop a novel technique for uncomputing the auxilary register generated by coherent alias sampling. This technique opens a research direction in sampling based initial state preparation.

We study how a radially oscillating thin shell outside a black hole (BH) affects gravitational wave ringdown and derive matching conditions for polar and axial perturbations from the linearized Israel junction conditions on the moving worldtube. Periodic shell motion produces Floquet sidebands in the scattered wave. For a distant shell, the motion has little effect on the prompt ringdown and only weakly modifies the late time echoes. When the shell is closer to the BH, a replica of a long lived shell mode enters the incident frequency band, increasing the late time echo amplitude by roughly two orders of magnitude. We also identify an exceptional point where two polar modes coalesce and find the contribution of its second order pole in the late time waveform.

Formal verification of quantum circuits becomes difficult as circuit size grows because exhaustive reasoning over the Hilbert space is computationally expensive. In previous work [1], we introduced a bit-vector abstraction that separates superposition tracking from basis-state behavior, enabling SMT-based verification of fixed-size error-detection and entanglement circuits built from H, X, and C-NOT gates. This paper extends the framework in five directions. First, we generalise correctness properties to parametrised repetition and concatenated phase-flip codes with up to 101 logical elements. Second, we verify syndrome extraction for CSS codes specified by arbitrary parity-check matrices, including the Steane, [[15,7,3]] Hamming, [[15,1,3]] Reed-Muller, and rotated surface codes with distances up to 101. We consider arbitrary error patterns, detection up to a specified weight, and recovery using a classical decoder, with counterexamples beyond each code's correction or detection capability. Third, we characterize the {H,X,C-NOT} fragment for which the abstraction faithfully represents Hilbert-space semantics. We prove soundness, demonstrate necessity with counterexamples, validate the characterisation against state-vector simulation, and prove the six lemmas from the original work. Fourth, a mutation study using 13 operators identifies equivalent mutants and detects all 622 non-equivalent mutants within the evaluated fault model. Fifth, a direct Z3 implementation verifies GHZ circuits with up to 262,144 qubits across three topologies on a 16GB laptop. Random H+C-NOT networks show verification cost rises sharply with depth when outputs depend on many inputs. The approach does not target general stabilizer circuits, Y-type stabilizers, fault-tolerant protocols, or physical noise; we identify extensions needed to address these cases.

We present the largest study to date of star cluster mass and age distributions in nearby galaxies. The analysis is based on a uniformly selected catalog of over 15,000 (36,000) human (machine) classified compact clusters across 38 spiral galaxies in the PHANGS-HST survey, with improved photometric SED age dating that mitigates key degeneracies with reddening and metallicity. The galaxies span a factor of ~100 in star formation rate (SFR) and in their surface density of star formation and molecular gas (Sigma_SFR, Sigma_H2), and cover a broad range of morphologies. We find that cluster mass functions are well described by a power law, dN/dM ~ M^beta, with beta=-1.9 +/- 0.2, and that this shape is remarkably similar across all galaxies in our sample and eight composite groups of galaxies with similar SFRs, with no significant dependence on SFR, Sigma_SFR}, or Sigma_H2. Cluster age distributions decline steeply and can be described by dN/dt ~ t^gamma with gamma=-0.83 +/- 0.24, again with little dependence on host-galaxy properties or cluster mass. The independence of the mass and age distributions implies a separable joint distribution, g(M,t) ~ M^beta t^gamma, and suggests that cluster populations in spiral disks are dominated by strong, mass-independent dissolution over their first ~Gyr. These results establish a benchmark for interpreting cluster demographics across diverse galactic environments and provide context for studies of young cluster populations at high redshift.

Conventional catalytic descriptors evaluate symmetric, dissipative responses ($\mathcal{D}$), remaining blind to the antisymmetric, non-dissipative circulation ($\mathcal{L}$) associated with cyclic catalyst turnover. We address this by applying an augmented Onsager operator, $\mathcal{A} = \mathcal{D} + \mathcal{L}$, to catalytic interfaces. Through Onsager–Casimir parity rules, we show that electron spin governs this non-dissipative circulation within the reduced state space, as antisymmetric coupling necessitates a time-reversal-odd coordinate. We map these multi-physical couplings (Thermo-Hydro-Mechanical-Chemical-Electrical-Spin) using a Hasse diagram and introduce a basis-invariant Gateway number to quantify circulation relative to dissipation, thereby expanding standard one-dimensional volcano plots into a two-dimensional activity surface. Using metal–nitrogen single-atom sites on doped carbon as a model, published electronic-structure calculations supply the static response quantities from which both operator components can be constructed. Finally, we propose an explicitly falsifiable experimental test utilising magnetic field modulation near a spin-crossover to probe the effect of quantum spin on this non-dissipative regime.

Cosmic-string loops generate a broadband gravitational-wave background (GWB) that is typically modeled via two distinct formalisms: a discrete harmonic expansion, commonly used in pulsar-timing-array (PTA) studies, and a continuous burst superposition, employed in ground-based GWB searches. In this work, we formally unify the two formalisms, showing that they provide discrete and continuous representations of the same underlying radiation process and converge on the scale-invariant spectrum plateau. On the rising low-frequency branch, where the first few harmonics dominate, the discrete nature becomes important, causing the two formalisms to diverge. Within this unified framework, the spectral calculation is more consistent across frequency bands, enabling multi-band inference. Leveraging this physical insight, we perform joint Bayesian inference across four representative loop-distribution models using the NANOGrav, EPTA, and LIGO–Virgo–KAGRA (LVK) datasets. By jointly sampling the string tension $G\mu$ alongside the average cusp and kink numbers $\{N_c, N_k\}$, the loop-radiation uncertainties are accounted for. We find that employing the harmonic expansion strengthens the LVK bounds by $21\%-31\%$ for three of these models. Additionally, the stringent LVK bounds preclude three of these models from explaining the observed PTA common signal. For the sole surviving model, our multi-band analysis improves the inferred limit on $G\mu$.

Elusive dwarf galaxy groups provide a rare opportunity to study hierarchical galaxy assembly at the lowest-mass scales, but whether such associations are gravitationally bound systems or transient configurations remains uncertain. We present the largest catalog of isolated dwarf galaxy groups, identified using the DESI Survey, comprising 74 systems with three to six members per group. The groups have a median line-of-sight velocity dispersion of $\sim53$ km s$^{-1}$ and a median crossing time of $\sim0.37$ Gyr. We find that stellar mass alone is generally insufficient to bind the observed configurations. On the other hand, when dark matter is included using independently inferred stellar-to-halo mass relations and NFW potentials, 69 of 74 systems ($93\%$) favor a bound interpretation after propagating observational and halo-model uncertainties. For the 69 bound-favored systems, dynamical-friction estimates indicate that substantial orbital decay within a Hubble time is plausible if their members retain significant dark-matter subhalos. Our results suggest that many of these groups are systems caught during the assembly of more massive descendants, representing some of the lowest-mass sites of ongoing hierarchical galaxy growth in the nearby Universe and accessible laboratories for a mode of assembly expected to have been prevalent at early cosmic epochs.

Dwarf-dwarf interactions are a major driver of galaxy evolution in the early Universe, but observational constraints on their impact across mass, separation, and environment remain scarce. Using the Dark Energy Spectroscopic Instrument Early Data Release, this study constructs the largest sample of dwarf galaxy pairs, spanning stellar masses $6.5 \leq \log(M_\star/M_\odot) \leq 9.5$ and redshifts $0.015 \leq z \leq 1.5$. We analyze the evolution of star formation rates and multiwavelength colors ($NUV-r$, $U$-$V$, $V$-$J$, $r$-$K$, and $g$-$r$) as a function of projected separation, stellar mass, and external tidal environment. Low-mass/low-redshift pairs exhibit interaction-triggered star formation at intermediate separations. At the smallest separations ($\lesssim$10 kpc), these systems display divergent behavior: isolated pairs show the onset of dust-obscured star formation, those embedded in weak external tidal fields undergo extended, dust-unobscured star formation, while those embedded in strong external tidal fields experience rapid quenching of star formation. High-mass/low-redshift pairs follow a more uniform evolutionary track, with generally weaker dependence on environment. Interaction-triggered star formation occurs at intermediate separations, followed by increased dust obscuration and rapid quenching at the smallest separations. At higher redshifts, high-mass dwarf systems display an initial suppression of star formation, followed by renewed activity at smaller separations, consistent with early-stage gas removal and later interaction-driven inflows. These results demonstrate that dwarf-dwarf interactions do not follow a single evolutionary pathway. Instead, we reveal a complex picture of dwarf galaxy evolution, with significant implications for dust-obscured star formation, abrupt quenching, and the formation of compact, dusty, intensely star-forming systems.

Realistic models of polarized Galactic dust emission at high angular resolution are essential for component separation in next-generation cosmic microwave background (CMB) $B$-mode experiments. However, existing dust polarization templates are constrained only to ~1 degrees, and it remains challenging to develop models that can generate realistic small-scale complexity that is also coherently connected to the well-measured large-scale structures. In this work, we develop a data-driven super-resolution framework that predicts small-scale dust polarization structure directly from multiple tracers observed at high resolution. We combine the Planck dust optical depth $\tau_{353}$, \ion{H}{1}-based Stokes templates, and coarse Planck GNILC $Q$ and $U$ maps in a transformer-based model trained to recover native-resolution GNILC polarization from a $4\times$ beam-smoothed version of itself, so that the network solves a deconvolution problem informed by the structure of multiple tracers rather than generating structure to match a target statistic. Applying the model to the uniform-resolution GNILC maps, we produce $Q$ and $U$ predictions at 20' over the high-latitude (|b|>30 degrees) sky. Using scalar and tensorial Minkowski functionals and scattering transform statistics, we find that our maps exhibit more coherent, anisotropic, and filamentary small-scale structure than the latest PySM dust model. Our results establish data-driven learned deconvolution as a promising route to foreground models whose small scales are inferred from data rather than prescribed.

High-fidelity solubility prediction is fundamental to pharmaceutical development and environmental partitioning, where accurate modeling must couple molecular structure with thermodynamic behavior across diverse chemical environments. However, recent advancements have been dominated by deep learning architectures that often sacrifice physical interpretability for predictive power. We challenge this trend by showing that state-of-the-art performance does not require such non-transparent architectures. To address this, we introduce DISSOLVR, a transparent framework for molecular solubility prediction. In addition, we perform a comprehensive literature review and a benchmarking study against various methods. We show that DISSOLVR approaches the aleatoric limit of experimental uncertainty and achieves OOD generalization through structural invariance, derived by mapping molecules to physically-grounded descriptors. Then, we present an LLM-assisted post-hoc explanation pipeline that bridges the gap between symbolic model artifacts and chemically grounded narratives. Finally, a comparative benchmark of a survey involving 22 expert chemists reveals that expert evaluators provide deep insights.

Many physical and biological systems -foams, membranes, elastic shells, or tissue sheets- can be mathematically described as 2D surfaces. These surfaces can host complex dynamics, like reaction-diffusion systems, and undergo drastic deformations. Here, we present triangulax, an open-source Python library for simulations and geometry processing that discretizes surfaces using triangular meshes available at https://github.com/nikolas-claussen/triangulax. It combines two features. First, discrete differential geometry provides coordinate-free discretization, which allows simulating strongly deforming surfaces. Second, the library is built on the machine-learning framework JAX, so mesh-based energies and entire simulations can be differentiated automatically (including simulations with stochastic forces or topological modifications). This simplifies multi-physics simulations by computing forces automatically and allows fitting model parameters to experimental data or design objectives. We implement an algorithm to preserve mesh quality in strongly deforming surfaces and apply it to a model of membrane mechanics coupled to an on-membrane concentration field. We validate our approach against exact solutions and existing software, and demonstrate triangulax across a range of problems, including membrane mechanics, vertex models, and inverse design of a shape-morphing elastomer sheet.

Constraint satisfaction problems (CSPs) with operator assignments to the variables provide a well-structured setting to study the decision complexity of the entangled value of classes of nonlocal games. Due to the CSP dichotomy theorem, the complexity of constraint satisfaction problems with classical assignments can be fully understood by studying the symmetries of the CSP, in terms of the polymorphisms of the underlying relational structure. In this work, we show that the polymorphism-based reductions between CSPs can be generalised to gap-preserving reductions between entangled CSPs based on an entangled analogue of the polymorphisms. This reduction allows us to show undecidability of entangled graph colouring with more than three colours, a problem that has proved resistant to prior hardness reductions based on commutativity gadgets.

Precipitation intensity varies with both spatial and temporal resolution, with broad implications across climate science, yet the nature of this dependence is poorly characterized. We investigate how precipitation intensity distributions change with spatial and temporal resolutions and introduce a framework that approximates these changes between resolutions. Using merged satellite-gauge data regridded to various grid sizes, we construct precipitation amount distributions for spatial resolutions ranging from a base resolution of 0.1$^\circ$ for IMERG and 1$^\circ$ for the FROGS database to a coarse 10$^\circ$. Similarly, we use gauge observations coarsened to temporal resolutions ranging from 1-minute to 24-hours to construct precipitation amount distributions. This approach allows us to remove physical differences in order to isolate the effect of resolution on precipitation. Results show that the precipitation intensity distribution varies across spatial and temporal resolutions even without changes in physical processes. We demonstrate that these resolution-dependent changes in the precipitation amount distribution can be effectively characterized by shifting the distribution in logarithmic space without changing its shape, called the shift mode. Our findings emphasize the need to account for the effects of scale on precipitation when comparing and interpreting differences in gridded precipitation from models or observations.

Fusion energy technology is rapidly approaching demonstrator deployment, but relatively little consideration has been given to publics' perceptions of or engagement with the technology. This research explores the perspectives of diverse professionals involved with the US fusion energy industry as to their knowledge on, valuation of, and preparedness for community and public (C&P) engagement on fusion energy. Participants perceived multifaceted value in C&P engagement from both industry and personal perspectives including an expressed desire for self-involvement in engagement activities, though ideally with increased support from home organizations and from engagement experts. Participants also revealed framings of fusion C&P engagement that align with deficit and contextual models of science communication thinking. These findings suggest an opportunity for collaboration between fusion professionals and engagement experts beyond one-way science communication to more participatory engagements with implications for the future of fusion energy.

We recently proposed a framework for the steady mass flux of particles through circular apertures [R.~S.~Sharma et al., Phys. Rev. Lett. 136, 068204 (2026)]. Here, we combine experiments and discrete-element simulations of spherical particles discharging through triangular and rectangular apertures to test this framework beyond circular openings. Despite changes in aperture shape, we observe a similar free-fall flux, with a modified relevant transport length. Deviations due to confinement reflect packing modifications, which are explained by geometry. A boundary layer dilation imposed by the aperture edge is shown to be a mechanism for the decrease of flux across various aperture shapes. By integrating the local packing deficit over the opening, we identify a hydraulic diameter $D_h=4A/P$, where $A$ and $P$ are the aperture area and perimeter, respectively, as the leading confinement length. This length also provides a reference scale, $\sqrt{gD_h}$, for the mean outlet velocity when the aperture is much larger than an individual particle. The same local packing model predicts the field in a lens-shaped aperture without further fitting, while the normalized discharge rates follow a common trend across the tested shapes.

External potentials break the translational invariance of nonlinear Schrödinger (NLS) equations and generally convert a continuous family of standing wave solutions into isolated pinned states. We study this mechanism for the prototypical case of a kink in the NLS equation with competing focusing cubic and defocusing quintic nonlinearities. The Lyapunov–Schmidt reduction method is used to prove that the location $s_0$ of the pinned kinks is selected near roots of an effective potential $V_{\rm eff}(s)$. We then determine how the translational zero eigenvalue of the Jacobian operator splits under the perturbation and prove that the sign of $V_{\rm eff}'(s_0)$ distinguishes eigendirections of positive and negative energy. We further show that if the Jacobian operator admits a negative eigenvalue, then the stability problem contains a real unstable eigenvalue. The derivation of the asymptotic expansion for the unstable eigenvalue is nonstandard because the zero eigenvalue is embedded in the continuous spectrum of the linearized operator. Finally, we show that the persistence of kinks lacks parity symmetry even if the external potential is odd. Numerical continuation, spectral computations with domains adapted to the slowly decaying eigenfunctions, and direct dynamical simulations of the time evolution corroborate the analytical predictions for different representative examples.

We present libterachem.py, a Python interface and method framework that facilitates development and prototyping of electronic structure methods while leveraging TeraChem's optimized graphical processing unit (GPU) operations. Direct access to these building blocks and their intermediate quantities allows users to assemble and modify methods within Python while reusing the underlying GPU implementations. A layered architecture, programmable at both the operation level and the method level, supports numerical experimentation, composition of complete electronic structure methods with interchangeable components, and integration with external scientific libraries. We illustrate operation-level use with grid pruning for least-squares tensor hypercontraction and with exchange–correlation functionals supplied through LibXC and by the machine-learned Skala functional. We illustrate method-level use with dispersion corrections, periodic calculations, and geometry optimization with an external optimizer. Python-driven self-consistent-field calculations using libterachem.py incur no significant computational overhead compared to native TeraChem and preserve its multi-GPU scaling. A photoactive yellow protein QM/MM molecular dynamics application further demonstrates throughput comparable to native TeraChem in a workflow composed with external simulation libraries. These results establish libterachem.py as a platform for method development and interoperable molecular simulation that retains the performance of TeraChem's GPU operations.

We study rumor-spreading models on the one-dimensional integer lattice, with particular emphasis on the effect of forgetting mechanisms on the long-term behavior of the rumor. We consider the spatial version of the classical Maki–Thompson model together with two variants that incorporate forgetting. Each model is formulated as an interacting particle system and describes the propagation of information through local interactions between neighboring individuals. Our results show that the introduction of forgetting fundamentally changes the behavior of the process. In the classical Maki–Thompson model, the rumor becomes extinct, whereas the two models with forgetting exhibit nontrivial phase transitions between extinction and survival. More precisely, we establish the existence of critical transmission rates that separate regimes in which the rumor dies out almost surely from regimes in which it survives with positive probability. We also investigate the dependence of these critical thresholds on the stifling rate. Combining rigorous arguments with numerical simulations, we prove the existence of the phase transitions, obtain estimates for the critical values, and explore the corresponding phase diagrams. These findings show that forgetting, despite acting as a mechanism that removes spreaders, can qualitatively alter the dynamics of rumor propagation by creating regimes of sustained information spread. Our work provides new insight into the critical behavior of spatial rumor models and raises several questions for future research.