Papers

Variable-size inputs are common in deep learning, but dense batching allocates a shared envelope and spends computation on padding. The cost multiplies across varying axes: an explicit pair state allocates $BN_{\max}^2$ positions instead of $\sum_i N_i^2$. Packing removes that waste, but composing packed operations still requires the logical axes and sample boundaries a flat buffer no longer exposes. We present DanLing NestedTensor, a PyTorch tensor abstraction that makes multi-ragged structure a property of the tensor itself. Packed values carry tensor-backed partitions and logical dimension order, so broadcasting creates ragged axes, feature transformations retain them, and reductions consume them. The same representation carries through autograd and both eager and compiled execution. On an A100, the geometric-mean speedup over same-mode padding is 2.74$\times$ eager and 3.39$\times$ compiled across four BERT scales, and 1.97$\times$ eager across four FCN backbones. A four-block Pairformer-style workload runs 2.40-4.32$\times$ faster than a padded reference using native PyTorch kernels across square length regimes in eager execution, with peak allocation falling from 38.08 to 5.41 GiB on its high-variation batch. The tensor interface lets model code built from its supported operators compose efficient variable-size computation without managing offsets at any call site. Code will be released publicly upon publication.

Deciphering the formation channels of the observed binary black hole mergers remains a central open problem in gravitational-wave astronomy. With hundreds of detections, the inferred distribution of masses and spins reveals a rich diversity which is difficult to reconcile with traditional formation scenarios from isolated binary stars or dense stellar environments. Here, we consider the large fraction of massive progenitor stars found in hierarchical triples and investigate black hole mergers driven by gravitational perturbations from tertiary companions. Simulations of their dynamics and stellar evolution reproduce key features of the merger population, including: i) a sharp primary mass peak at $m_1\sim10\,\rm M_\odot$ dominating the population; ii) substantial fractions of systems with large spin-orbit angles within and beyond the peak, matching the skewed distributions of the spin parameters $\chi_{\rm eff}$ and $\chi_p$; iii) a mass-ratio distribution favouring equal masses with matching slopes. We further predict a sharp decline of mergers near $m_1\sim30\,\rm M_\odot$, coincident with the location of inferred features that may signal another channel dominating the high-mass tail. Our models of hierarchical triples demonstrate, for the first time, a formation scenario which simultaneously reproduces the principal properties inferred for the low-mass bulk of binary black hole mergers.

Decoherence-induced phase transitions (DIPTs) are associated with singular changes in a quantum system's entanglement structure as the decoherence strength varies. In many cases, their critical strengths depend monotonically on the Rényi index of the entanglement diagnostic, forming a Rényi hierarchy. We identify a general mechanism for this hierarchy based on correlation inequalities in replicated statistical models that describe these DIPTs. We demonstrate it in $\mathbb{Z}_2$ topological stabilizer codes subject to independent phase-flip decoherence on each qubit and in a decohered rotor model with strong $\text{U}(1)$ symmetry. When the relevant correlations diagnose the DIPTs, these inequalities imply that the critical decoherence strength is nondecreasing with integer Rényi index $R\geq2$. We show that this mechanism also applies to a class of models with correlated decoherence.

Cosmic rays (CRs) drive galactic winds and regulate galaxy growth while contributing to heating the central cooling plasma in dense galaxy clusters, making the nonlinear saturation of the instabilities that govern their transport a problem of central importance in astrophysics. Using fully kinetic particle-in-cell (PIC) simulations, we find that the streaming instability driven by CRs with a shell momentum distribution saturates through gyro-phase bunching around driven Alfvén waves. Fluid-PIC (FPIC) simulations with both ideal and Landau closures reproduce the PIC saturation amplitude, and the same gyro-phase bunching mechanism, indicating that nonlinear Landau damping (NLLD) does not determine the saturation level at our simulation parameters ($v_{\rm A} = 0.01c$, $n_{\rm CR}/n_i = 0.01$). Notably, the CR ions fully isotropize in the Alfvén-wave frame in all simulations, including the FPIC run with an ideal closure in which NLLD is entirely absent, showing that this isotropization does not require NLLD. We additionally confirm, using the FPIC ideal closure, that this saturation amplitude is unchanged across a tenfold increase in domain size, indicating that the mechanism is local rather than dependent on domain-scale processes. Together, these results indicate that, at least in this regime, NLLD is not the dominant saturation mechanism for the CR streaming instability, in tension with common assumptions built into CR transport models used in galaxy formation and interstellar medium simulations. Whether this conclusion extends to the lower CR densities and Alfvén speeds characteristic of the interstellar medium remains an open question that we address in an upcoming work.

We introduce the TRICEPS (Tracing Resolved Ionized Carbon Emission in Primeval Systems) survey. TRICEPS focuses on a sample of 16 massive galaxies at z = 4 - 5 with top-quality data: (i) ALMA band-7 observations of the [CII]-158 micron line, tracing the cold gas distribution and kinematics at spatial resolutions of about 0.1" (~0.8 kpc), (ii) ALMA maps of the rest-frame 160 micron continuum emission, tracing the dust distribution at similar spatial resolutions, (iii) multi-band JWST images from NIRCam and MIRI, tracing the stellar mass distribution and star formation activity at spatial resolutions of 0.1"-0.2", and (iv) multi-line CO observations from ALMA and the VLA, including the CO(1-0) line, tracing the molecular gas content. In this first paper, we describe the TRICEPS scientific goals, the basic properties of the galaxy sample, and the ALMA band-7 observations. TRICEPS galaxies were selected based only on bright [CII] fluxes (>2 Jy km/s). They lie on the top-end of the star-forming main sequence at z = 4-5, having stellar masses between about 10^10.5-10^12 Msun and star-formation rates between about 100 - 3000 Msun/yr. To date, TRICEPS is the largest sample of galaxies at z = 4-5 for which the gas distribution and kinematics are exceptionally well resolved: on average, 46 resolution elements per galaxy with signal-to-noise ratio higher than 3. By survey design, half of the TRICEPS targets are in galaxy pairs; clear signs of tidal interactions are present in three of the four pairs. In all galaxies, the [CII] velocity fields display regular rotation, albeit the interacting galaxies tend to be somewhat more disturbed. The TRICEPS observations suggest that regular rotation is ubiquitous among massive star-forming galaxies when the Universe was less than ~1.5 Gyr old.

Quantum resources can dramatically reduce the data required to learn physical systems, with exponential improvements in sample complexity demonstrated in several quantum learning tasks. However, these advantages have typically relied on quantum resources that scale with problem complexity, most notably increasing system dimension or entanglement. This raises a fundamental question: can exponential quantum learning advantages arise within a fixed, unentangled quantum system? In this paper, we address this question by considering the learning of an unknown random-displacement distribution whose complexity is determined not by the dimensionality of the physical system, but by the Fourier resolution of its features. We show that the quantum-limited noise of vacuum probes progressively obscures high-frequency features, leading to an exponential growth in sample complexity. We establish an information-theoretic lower bound for arbitrary classical-state probes and show that squeezing overcomes this classical limit by extending the accessible Fourier bandwidth. Experimentally, we demonstrate an exponential reduction in sample complexity using squeezed vacuum probes for both binary hypothesis testing and characteristic-function reconstruction. Our results show that a single bosonic mode can exhibit exponential quantum learning advantages without entanglement or an increase in system size, identifying accessible Fourier bandwidth as a fundamentally distinct resource for quantum-enhanced learning.

Diffuse star clusters (DSCs) occupy a poorly explored region of the size-luminosity plane between classical globular clusters (GCs) and dwarf galaxies. Here we report the discovery of four faint DSCs in the halo of the nearby starburst galaxy M82 using archival JWST/NIRCam imaging. We resolve individual stars in all four systems, whose color-magnitude diagrams are consistent with predominantly old ($\sim10$ Gyr) stellar populations, based on comparison with isochrones. DSC 1 hosts a metal-poor population ($[\mathrm{M/H}]\sim-2$), while DSCs 2, 3 and 4 are better represented by $[\mathrm{M/H}]\sim-0.8$ isochrones. To establish their nature, we measure their sizes and integrated magnitudes using curve-of-growth and radial profile fits, which yield consistent results between these methods. The sizes of DSCs range from $\sim$ 5.4 to 10.5 pc, making them more extended than typical GCs (2-3 pc). Their luminosities span M$_{\rm V}\simeq-4.1$ to $-6.4$, reaching $\sim$ 1 mag fainter than the previously known M82 star cluster (SC) population. At these low luminosities, the systems occupy a sparsely sampled region of the size-luminosity plane where the distinction between SCs and dwarf galaxies becomes increasingly ambiguous. Most notably, DSC 3 is the faintest SC candidate identified in M82 to date and approaches the regime occupied by Milky Way ultra-faint compact satellites. These faint DSCs were identified through visual inspection alone, suggesting they are likely underrepresented in existing star cluster catalogs, and that a JWST-based archival search of nearby galaxies would be fruitful.

There is disagreement in the literature concerning whether the nodal point of a three-dimensional Weyl semimetal survives weak short-range disorder: instanton calculations including fluctuations claim that the zero-energy density of states $\rho(0)$ vanishes, while exact numerics find a systematically finite number. We settle this disagreement with a full saddle-point calculation, including both instanton and fluctuations. Within the supersymmetric formulation for disorder, the instanton obeys a nonlinear Weyl equation whose solution is an exact $j=1/2$ hedgehog whose full functional form we numerically compute. We then compute the fluctuations about this saddle point, carefully identifying all zero modes, and computing the reduced superdeterminant as a convergent Fredholm determinant. No fermionic zero mode beyond a Kramers doublet exists, and at finite disorder $w$, the fluctuations become a finite one-loop prefactor, $\rho(0)=\mathcal{A} w^{-4} \exp(-s^*/w^2)(1+O(w^2))$, in normalized units with $s^* = 6.4163(2)$ and $\mathcal{A} = 27.47(8)$ for Gaussian-correlated disorder. This expression matches exact numerics on a single Weyl cone over four orders of magnitude with no fitted parameters (the amplitude is $\times 0.76$ the one-loop value), establishing that the density of states is finite for any disorder strength.

We study boundary conditions of the compact free boson theory by coupling the bulk scalar to one-dimensional topological edge modes. We show that a single compact edge mode realizes the Dirichlet family, while a two field system realizes the Neumann family; more general compact edge theories can describe superpositions of boundary conditions and reproduce the expected boundary operator spectra. We then study this system in the framework of boundary SymTFT. We show that the edge mode theories of Dirichlet and Neumann boundaries are encoded in the degrees of freedom localized on the corners and the choice of polarization on the topological face of the boundary SymTFT. We further show that the T-duality defect exchanges the data associated with the Dirichlet and Neumann configurations. Finally, we explore extensions involving non-compact edge modes and multiple bulk fields, obtaining continuous boundary spectra in the first case and mixed boundary conditions in the second.

Cosmological correlators are calculated through the in-in formalism in (quasi-)de Sitter background. Its effective description is best represented by a reduced density matrix. In this work, we study how integrating out a massive field in de Sitter space determines the reduced density matrix of a light field at a finite observation time. Starting from a quasi-single-field model with non-linear couplings, we first evaluate the massive field wavefunctional at fixed final value and then trace over this value. The trace generates branch-mixing terms which are generally present in the Schwinger–Keldysh description. For a conformally coupled massive field, we show explicitly that the light field bispectrum from the effective description agrees with a full theory calculation. This example also shows that decay of a field at the future boundary does not by itself justify discarding its contribution to the trace. We discuss the differences between an exact nonlocal effective description and the local effective field theory obtained through a large mass expansion. We then identify which local cubic terms affect the late-time probability and which contribute only a wavefunctional phase. Finally, we organize the resulting kernels by response, noise, and Schwinger–Keldysh consistency conditions, and discuss the symmetry constraints on the reduced density matrix.

We study entanglement transitions for pairs of disjoint intervals in two-dimensional holographic interface conformal field theories. We consider several holographic models with equal central charges on the two sides of the interface: thin-wall geometries with one and two branes, the Janus solution, and the super-Janus solution. We first discuss the finite interface contribution to the entanglement entropy of a single interval, distinguishing intervals that cross the interface from those that lie entirely on one side. We then use the mutual information to locate the transition between connected and disconnected Ryu–Takayanagi geodesic configurations for two intervals. When the interface lies between the two intervals, increasing the boundary entropy $\log g$, which provides a measure of interface strength in the models considered here, generally decreases the critical separation at which the connected configuration ceases to dominate. When both intervals lie on the same side of the interface, the behavior is model dependent: the connected phase persists to larger separations in the Janus and super-Janus models, while the critical separation is unchanged in the thin-wall models. Thus, as diagnosed by the two-interval transition, the interface weakens correlations across the interface while preserving or enhancing correlations between regions on the same side. We also identify a universal “Silver Blaze” configuration, in which the interface lies inside one of the intervals and the transition occurs at the same location as in a CFT without an interface, independently of the interface parameters and of the holographic model. This universality follows from a cancellation between crossing and non-crossing interface contributions to the mutual information.

The observation of superconducting behaviour near a fractional Chern insulator in twisted MoTe$_2$ has sparked excitement about a possible direct "anyon superconducting" transition between a topologically ordered and a symmetry-broken phase. We carefully examine the experimentally measured transport data in the relevant region of the low-temperature tMoTe$_2$ phase diagram and propose a scenario where the nearby reentrant integer quantum Hall effect (RIQHE) acts as an intervening phase between the two. While the RIQHE is most prominent at large displacement fields, we propose that it extends to smaller fields at very low temperatures. Based on this picture, we model the sample as a patchwork of the three phases and show that such a model can explain the main qualitative features of the transport phase diagram, including its dependence on temperature and displacement field. The model predicts that at lower electronic temperatures the apparent FCI-SC transition at zero displacement field should split into two transitions separated by a narrow RIQHE region.

Large-scale magnetic reversals in planets, stars, and accretion disks require a non-linear theory coupling the magnetic field to its sustaining flow. We derive exact non-linear solutions to incompressible magnetohydrodynamics in background rotational shear, with large-scale velocity and magnetic fields linear in position (affine form). They reveal a cyclic feedback between meridional circulation, shear, magnetic tension, induction, and the Coriolis force. The steady-circulation reversal orbit, or dynamo wave, periodically reverses all magnetic components and supports slower modulations. In the solar near-surface shear layer (NSSL), moderate shear permits stable 11-year reversals with poleward speeds of 8-12 m/s and poloidal and toroidal amplitudes of 4-11 G and 2.2-3.8 kG near 1 Mm depth, in reasonable agreement with regional observations. At stronger shear, an 88-year reversal exhibits a 203-207-year modulation, reproducing the Gleissberg and Suess-de Vries activity timescales but requiring weaker poloidal fields. Such reversals, however, remain observationally unestablished. At tachocline density, an 11-year reversal and the inferred return flow require toroidal fields of hundreds of kilogauss over a broad shear range, exceeding large-scale-field reconstructions but partly permitted by seismic upper limits. This favors a shallow NSSL origin for a local cycle, while leaving open the issue of a global dynamo. Toroidal dominance prolongs the cycle because shear acting on a weak poloidal field changes only a small fraction of the stronger toroidal field per rotation. Balancing the weak magnetic torque against advection and the Coriolis force also requires slow circulation, which gradually turns the poloidal field and reverses toroidal induction. Efficient poloidal regeneration would shorten this delay. A long solar cycle therefore favors a primarily shear-driven dynamo.

We develop Hybrid Partial Dressing (HPD), a simple diagrammatic resummation scheme for finite-temperature effective potentials in scalar field theory which is valid at all temperatures. HPD improves on earlier resummation schemes such as Daisy Resummation and Partial Dressing by being two-loop exact at all temperatures and free of the overlapping momentum problem. Renormalization group improvement is straightforward to implement. We illustrate the scheme in multi-scalar theories with a spontaneously broken $\mathbb{Z}_2$ symmetry, and compare it against existing approaches, showing in particular that it reproduces the two-loop Dimensional Reduction (DR) potential exactly in the high-temperature regime where DR applies, while remaining valid at all temperatures. This makes HPD suitable for the general study of strong first order phase transitions beyond the Standard Model, as we demonstrate through gravitational wave predictions from HPD and its RG-improved version, RGHPD.

We demonstrate repulsion-driven topological superconductivity of a single species of Dirac fermions, motivated by valley-polarized phases observed in two-dimensional materials such as rhombohedral graphene. Using density-matrix renormalization group calculations on the Qi-Wu-Zhang lattice model on cylinders of width up to eight, we find a robust phase of spinless chiral $p$-wave superconductivity. Pairing already starts at low doping and thus occurs on a small, nearly isotropic Fermi pocket, and is therefore not tied to the particular details or anisotropy of the dispersion but instead seems tied to the non-trivial quantum geometry of the bands. In fact, the winding of the superconductor order parameter is opposite ("$p-ip$") to that of the anomalous Hall metal which forms the parent state, in agreement with expectations recently derived from weak coupling calculations. At larger doping, we find that a pair-density-wave component develops alongside zero-momentum pairing. Our work shows that the combination of strong repulsion, absence of time-reversal in the parent state, and non-trivial quantum geometry form a promising platform to realize topological superconductivity.

Jeans-based measurements of the Milky Way (MW) rotation curve (RC) have revealed a declining outer RC. The interpretation, however, depends sensitively on the tracer selection, the tracer density profile, gradient terms in the Jeans equation, and non-axisymmetric perturbations in the outer disk. We present a more self-consistent Jeans analysis of the MW RC and reassess whether the outer decline remains after a revised treatment of the main Jeans terms and their associated systematic uncertainties, including those related to non-axisymmetric perturbations. We select a kinematically homogeneous disk tracer sample designed to retain stars on nearly circular disk orbits, removing only 12% of the original sample. We estimate the tracer density profile from the same stars used for the kinematic moments, rather than adopting an external scale length. We find that the tracer density profile is better described by a double exponential over the validated range 12.5 < R < 21 kpc. We also assess the main systematic uncertainties associated with the fiducial Jeans equation terms, including the often neglected cross term, and account for different rotational velocities in the outer disk substructures. The derived RC remains nearly flat in the inner disk and declines at large radii. Over the adopted outer interval, $R\gtrsim16\,\mathrm{kpc}$, the RC slope is consistent with a Keplerian decline even after accounting for the systematic uncertainties. The corresponding mass modeling gives an extrapolated dynamical mass of $2.01^{+0.10}_{-0.08}\times10^{11}\,M_\odot$.

Commuting-projector Hamiltonians with integer spectrum such as the 1+1d Ising ferromagnet and the 2+1d toric code may be regarded as the generators of non-on-site $U(1)$ symmetries. In this paper we study whether these symmetries can be made on-site in the presence of finite and infinite-dimensional ancillae. In the finite-dimensional case, we prove that the fractionalized excitations, such as domain walls and anyons, make it impossible to on-site these Hamiltonians. On the other hand, we show that when infinite dimensional ancillae (e.g., rotors) are allowed, both the 1+1d Ising ferromagnet and the 2+1d toric code can be disentangled, yielding on-site symmetries. This is not in contradiction with the non-trivial ground state order of these Hamiltonians, since the ancilla Hamiltonians are no longer bounded from below. Our results indicate agreement between lattice and quantum field theory anomalies in the presence of infinite-dimensional ancillae, while with finite-dimensional ancillae the obstruction to on-siteability may even be non-invertible.

Renormalization group (RG) is a core concept from statistical mechanics to quantum field theory, yet its schemes differ widely across literature. We formulate Wilsonian RG for generic, including finite-dimensional, quantum systems as a quantum channel combining coarse graining with isometric rescaling, whose Kraus representation yields pure conditional trajectories for pure inputs and recovers mixed-state flows upon averaging. We then develop an algebraic extension without assuming tensor-product factorization: the retained low-energy algebra is constructed from the one-particle spectrum, and coarse graining is a conditional expectation onto it. Identifying the channel's Cesàro mean with a resource-destroying map onto fixed states establishes a resource theory of RG and yields a relative-entropy monotone without variational optimization. For thermal states in the zero-temperature limit, the resulting Bogoliubov–Kubo–Mori metric per unit spacetime volume is proportional to the Zamolodchikov metric, directly relating the resource density to $c-c_{\rm IR}$ near a two-dimensional IR fixed point. We also introduce the relative entropy of coarse graining to measure discarded UV information, prove its monotonicity along successive coarse grainings, and evaluate it holographically in global $\mathrm{AdS}_3$.

We identify effectively single-visit imaging hidden within the deep co-added images of the NSF-DOE Vera C. Rubin Observatory Early Data Preview 2 (EDP2). These shallow regions contain only one or two contributing visits, providing access to single-visit-depth imaging ahead of the full Data Preview 2 (DP2) release in late 2026. We develop a workflow to locate known small Solar System bodies in these data, using our Ponder orchestrator with the Sorcha survey simulator to predict their positions and the Rubin Science Platform (RSP) to identify shallow coadds and extract image cutouts. Because cometary activity and near-Earth-object (NEO) trails produce extended morphologies, both remain identifiable in these shallow coadds. From approximately 700 comet and active-object cutouts, we identify 59 activity detections spanning 32 objects. We discover activity in 2025 NC6, previously unknown to be active; identify the first reported pre-perihelion activity of 2008 QZ44; and independently rediscover known comets 243P/NEAT and 510P/Boattini through their activity. We also recover 336 NEO cutouts, including 29 with predicted trails longer than 25 pixels. We provide accompanying galleries and tabular data, and highlight 99P/Kowal 1, 510P, and 303P/NEAT as targets for immediate follow-up. Shallow coadds are a relatively unexplored facet of Rubin data with applications beyond the Solar System examples presented here: regions with varying numbers of contributing visits will persist throughout the Legacy Survey of Space and Time (LSST).

Inspired by the problem of identifying the best model from a collection of large language models (LLMs) with heterogeneous querying costs, we formulate and analyse a variant of the multi-armed bandit (MAB) with (i) dueling feedback, where pairwise comparisons between model responses provide robust preference signals, and (ii) heterogeneous sampling costs, reflecting the differing costs of querying different LLMs. Assuming the existence of a Condorcet winner, a condition we empirically validate across multiple real-world datasets, we propose a Track-and-Stop style algorithm for best-arm identification with prescribed confidence. We prove that the algorithm almost surely achieves the asymptotically optimal cost as the error tends to zero. Finally, we extensively evaluate our approach on both synthetic and real-world instances, demonstrating consistent improvements over classical cost-unaware algorithms and their cost-aware extensions.

I show that the initial conditions imposed by Balan [Phys. Fluids 35, 113108 (2023)] are incompatible with a nonzero retardation time, so that the problem solved is not impulsive start-up, but, as I prove exactly, the start-up of a plate ramped as $1 - \mathrm{e}^{-t/\lambda_2}$ on the retardation timescale $\lambda_2$ (a material parameter, not a setting in a rheometer). Values digitized from that paper's viscoelastic figures fall on the ramped-plate solution, not on Tanner's start-up solution. The large negative wall normal stress reported for the corotational model is a grid-dependent artifact due to the same error in the initial data. An open-source code repository provides annotated notebooks reproducing every figure and number in this Comment.

Nanodrones require accurate, real-time state estimation under severe sensing and computational constraints. We present TinyCVIO, a visual-inertial odometry system that co-designs miniature sensing, visual processing, and estimation for a commodity dual-core microcontroller with 520 kB SRAM. Lightweight LED constellations provide known geometry without surveyed positions or yaw angles, assuming placement on a common level plane. A streaming visual frontend tracks LED observations from a millimeter-scale camera at 29.2 FPS, while a rigid-board measurement model retains inter-LED constraints and streaming QR bounds estimation workspace for a fixed filter-state size. Across 19 hand-held hardware-in-the-loop datasets, the rigid-board model reduces mean absolute trajectory error by 27% relative to planar points. The complete system runs onboard a Crazyflie across nine flights at three speeds, achieving 3.5-3.7 cm mean absolute trajectory error and 0.50-0.60% relative pose error over 10 m segments, with mean estimate latency of 15.7-16.3 ms.

As the accuracy of experimental results in high energy physics (HEP) increases, so does the demand for precision Monte Carlo (MC) simulation. Higher-accuracy event generation at next-to-leading order (NLO) and beyond brings with it negatively weighted events. These negatively weighted events reduce the statistical power of samples, increasing the number of events that need to be produced and straining already limited computational resources. We present a post-hoc reweighting scheme that employs cell-based resampling using an IRC-safe metric to define the cell radii. An optimal metric embeds kinematically similar events within the same cells, minimizing bias when reweighted. This motivates our exploration of a Optimal Transport (OT) based distance metrics. We compare the performance of the reweighting algorithm with different choices of metric, and explicitly demonstrate the performance on simulated Z+jets events produced at NLO accuracy.

Cities differ in built form, land cover and development history, complicating comparison across places and time. Satellite foundation models map Earth's surface onto common numerical representations. Yet the tasks and targets used to shape them typically do not focus on cities: globally consistent labels for urban function do not exist, and many datasets - especially land cover and land use classifications - collapse the built environment into few classes. Here we audit the representation, focusing on AlphaEarth but with broader applicability to other Earth embeddings, by probing the geometry and geography of embeddings for 1,000 urban areas in 162 countries. We find that cities occupy a shifted but overlapping region on the hypersphere, 62.7{\deg} from the global mean direction, and continent and climate predict 24.3% of variation among the mean directions of urban centres in excluded countries. Inside cities, degrees of urbanisation carry 8.9% of the variation, and what they leave holds shared directions whose local orientation varies, not one universal axis of urbanisation. Retained variation is itself unequal: dispersion within urban centres is 14.1% greater per standard deviation of national development, even after adjusting for population, land area and continent. Further controls suggest cities in developing countries present less contrast in vegetation and texture, and dispersion follows that contrast: full adjustment for it leaves at most 6.4% of the gradient. Annually, a city's representation moves nearly eight times more than redrawing its own pixels explains, and contracts where the 2022 loss of Sentinel-1B removed a pass direction. AlphaEarth's representations therefore support comparison across regions, while the differences between its annual layers are not yet validated for comparison over time.

This note addresses Theorem 12 in the seminal paper “$F$-degrees in graphs” by G. Chartrand et al. (1987), which asserts the existence of $K_n$-irregular graphs for each $n \ge 3$. Although this result is widely cited in the literature as an established fact, the original text lacks a complete proof. We show that for $n = 5$ and all $n \ge 7$, the constructions as presented are not $K_n$-irregular, presumably due to typographical errors. Consequently, referencing this foundational work as containing a rigorous proof for the general case is not entirely accurate.

We give a polynomial-time algorithm that constructs, in every connected $n$-vertex graph of minimum degree at least $7$, a spanning tree with at least $\frac{25200}{46189}n>0.5455\,n$ leaves. No bound specific to minimum degree $7$ was known: the best bound available for this class was $\frac{11}{21}n\approx0.5238\,n$, inherited from Simarova's theorem for minimum degree~$6$. The algorithm and its analysis are carried out for an arbitrary minimum degree $\delta$, and yield a recursion that gives an explicit lower bound on the number of leaves for every $\delta$. The resulting bounds improve all previously known ones for every $\delta\ge7$; for $\delta=8,9,10$ they are $0.5850\,n$, $0.6151\,n$ and $0.6413\,n$, and they are tabulated for $\delta\le25$ at the end of the paper.

This volume contains the proceedings of ICE'26, the 19th Interaction and Concurrency Experience, which was held in Urbino, Italy, as a satellite event of DisCoTec'26. The ICE workshop series features a distinguishing review and selection procedure: PC members are encouraged to interact, anonymously, with authors. The 2026 edition of ICE received 8 submissions, each reviewed by three PC members, and about 60 comments were exchanged during the review process, witnessing very lively discussions. Five papers were accepted for publication plus two oral communications, which were accepted for presentation at the workshop. We were proud to host one invited talk, by Emilio Tuosto. The abstract of his talk is included in this volume, together with the final versions of the research papers, which take into account the discussion at the workshop and during the review process.

Self-consistency has become a popular technique for enhancing the reasoning abilities of large language models by generating multiple reasoning paths and selecting the final answer through a majority vote. However, because model providers typically charge users in proportion to the number of reasoning paths generated, they have a financial incentive to artificially increase the path count. In this work, we show that an unfaithful provider can exploit this incentive using a simple, efficient algorithm while avoiding detection by an auditor: by generating and strategically reordering additional reasoning paths, the algorithm makes every path appear necessary to reach the majority. To validate our algorithm, we conduct experiments with multiple instruct models from the Llama and Qwen families, as well as reasoning models distilled from DeepSeek-R1, on benchmark datasets spanning mathematics, science, and question answering. Our results suggest that the distribution of additional reasoning paths generated by our algorithm is heavy-tailed and that substantial capacity to overcharge remains even under the best possible audit designed to keep the false-positive rate below $\alpha = 0.1$.

Context: Code recommender systems (CRSs) are specialized software systems operating on source artifacts to provide automatically generated recommendations to software developers in all phases of development. The goal is to improve software quality while enhancing developers' efficiency, effectiveness, and experience. Problem: Despite the growing importance, little is known about the state of evaluating these systems in a human-centric manner. Research Approach: We conducted a systematic literature review to identify and to synthesize primary studies evaluating CRSs (2017-2024). Ninety-two publications were included and subjected to a systematic content analysis. Results: Our study confirms that Offline Evaluations are the most common, system-centric evaluation type, whereas user-centric evaluations (Online Evaluations, User Studies) are rarely reported. Evaluations are concentrated on the Software Construction phase. Most studies explicitly report threats to validity, with External threats to study Materials being the most common. Conclusion: The state of evaluations on CRSs is narrowly focused on single or a few system qualities. There is an imbalance between a majority of system-centric evaluations and a minority of user-centric evaluations. Combined, multi-type evaluations are rarely reported.

The Delannoy numbers $d(n,k)$ count lattice paths from $(0,0)$ to $(n-k,k)$ using steps $(1,0),(0,1)$ and $(1,1)$. This paper introduces a graded poset $\mathcal{D}_n$ on the Delannoy paths ending on the line $x+y=n$, whose rank-generating function is the Delannoy polynomial $d_n(x)=\sum_{k=0}^n d(n,k)x^k$. We prove that $\\mathcal{D}_n$ is a self-dual lattice, which is call the Delannoy lattice. By establishing an explicit symmetric Boolean decomposition, we show that $\mathcal{D}_n$ is a symmetric Boolean order, thereby recovering the $\gamma$-positivity of $d_n(x)$. Such a decomposition is refined to a symmetric chain decomposition with the chain cover property, and is applied to determine all maximum antichains. We also investigate other combinatorial aspects of $\mathcal{D}_n$, including supersolvability, the Möbius number, characteristic polynomials, and zeta polynomials.