We discuss a new point of view of representation theory of Lie groupoids and algebroids: fat Lie theory. The category of fat extensions is introduced, as well as the category of abstract $2$-term representations up to homotopy (ruths) -- the intrinsic objects behind usual (split) $2$-term ruths. We obtain a one-to-one correspondence between them, and relate to the well-known equivalence between $2$-term ruths and VB-groupoids/algebroids. On the other hand, we show that fat extensions of groupoids correspond to general linear PB-groupoids. The differentiation procedure of fat extensions is discussed, as well as the functorial aspects of all mentioned correspondences. In particular, we upgrade the one-to-one correspondence between general linear PB-groupoids and VB-groupoids of Cattafi and Garmendia to an equivalence of categories. Fat extensions are intimately related to another notion we introduce: core extensions. We show that they correspond to vertically/horizontally core-transitive double groupoids, generalising work by Brown, Jotz-Lean and Mackenzie. This way, we also realise regular fat extensions as general linear double groupoids.

We introduce Extreme Quantum Cognition Machines, a class of quantum learning architectures for deliberative decision making that is tolerant to noisy and contradictory training data. Inspired by the quantum cognition paradigm, Extreme Quantum Cognition Machines are closely related to quantum extreme learning and quantum reservoir computing, where fixed quantum dynamics generates a nonlinear feature map and learning is confined to a linear readout. A dynamical attention mechanism, implemented through an input-dependent interaction term in the Hamiltonian, modulates the quantum evolution and biases the resulting feature embedding toward task-relevant correlations. The approach is validated on linguistic classification tasks, which serve as paradigmatic examples of deliberative inference. Hardware-compatible quantum implementations of the proposed framework are discussed, together with potential applications in symbolic inference, sequence analysis, anomaly detection, and automatic diagnosis, with direct relevance to domains such as biology, forensics, and cybersecurity.

Solar flare simulations are commonly initialised using non-linear force free field (NLFF) extrapolations derived from photospheric vector magnetograms. However, the force free assumption neglects plasma forces and may limit the available free magnetic energy. In this work, we perform a controlled comparison of two three-dimensional resistive magnetohydrodynamic simulations of the X2.1-class flare that occurred on 2011 September 06 in NOAA Active Region 11283. The simulations differ only in their initial magnetic configuration: one is based on a conventional NLFF extrapolation, while the other employs a non-force free extrapolation. Both models are evolved in an identical stratified atmosphere using the same numerical framework, enabling direct assessment of how the initial magnetic assumptions influence flare dynamics and energetics. We find that the non-force free model undergoes more extensive magnetic restructuring and releases approximately twice as much magnetic energy ($\approx4.4 \times 10^{31}$ erg) as the NLFF case ($\approx2.3 \times 10^{31}$ erg), bringing the energy budget into closer agreement with expectations for X-class flares. Synthetic extreme ultraviolet emission in the 94A channel is computed for both simulations and compared with observations from the Solar Dynamics Observatory. The non-force free model produces a brighter and more spatially extended emission structure that more closely resembles the observed flare morphology and light curve. These results demonstrate that assumptions made in constructing the pre-flare coronal magnetic field can significantly affect flare energetics and observable signatures, and suggest that non-force free extrapolations provide a promising pathway toward more realistic data-constrained flare modelling.

We calibrate a physically motivated, super-Eddington eruptive mass-loss prescription for red supergiants (RSGs) using Local Group stellar populations. Building on MESA models that add eruptive mass loss with a free scaling parameter $ξ$, we generate stellar evolution tracks and isochrones, and synthesize mock populations at metallicities of $Z/Z_\odot=0.2,\ 0.4$, and $1.0$. We compare model luminosity functions to observations of RSGs in the SMC, LMC, and M31, restricting to $3.5<\log T_{\rm eff}/K<3.75$ and $\log(L/L_\odot)>4.5$. By-eye fits to the observations yield values of $ξ_\mathrm{SMC}=0.0-0.05$, $ξ_\mathrm{LMC}=0.1$, and $ξ_\mathrm{M31}=0.35$, implying a positive, linear trend between the strength of eruptive mass-loss and metallicity. This calibrated eruptive mass loss prevents stars with initial masses $\gtrsim 20~M_\odot$ from evolving to become red supergiants, with implications for the mass spectrum of core-collapse progenitors, compact remnants, early supernova interaction signatures, and the spectral energy distributions of unresolved galaxies.

Unmanned Aerial Vehicle (UAV) mounted Base Stations (UAV-BSs) provide flexible coverage for temporary hotspot scenarios; however, efficiently optimizing 3D deployment to satisfy heterogeneous user distributions remains a significant challenge. While Deep Reinforcement Learning (DRL) approaches have shown promise, they often suffer from prohibitive training overhead and poor generalization in cold-start scenarios where the user topology is unknown a priori. To address these limitations, this paper proposes Satisfaction-driven Coverage Optimization via Perimeter Extraction (SCOPE), which is a deterministic and training-free 3D deployment framework. Unlike existing heuristics that rely on fixed-altitude assumptions, SCOPE integrates a perimeter-based peeling strategy with the Welzl Smallest Enclosing Circle (SEC) algorithm to dynamically optimize 3D positions. Theoretically, we provide a rigorous convergence proof and derive a polynomial time complexity of $O(N^2 \log N)$, ensuring predictable execution for real-time applications. Experimentally, we evaluate SCOPE in unpredictable hotspot environments against both traditional heuristics and state-of-the-art DRL baselines under a matched hardware budget. Simulation results demonstrate that SCOPE maintains a high user satisfaction rate between 82% and 88% while generating solutions within millisecond-level latency on commodity hardware. Furthermore, SCOPE demonstrates exceptional resilience by maintaining an approximate 40% functional coverage rate at a minimum altitude constraint of 60 m; in this challenging regime, baseline methods suffer a significant performance degradation, dropping to approximately 20% due to altitude-induced path loss. These findings validate SCOPE as a robust and agile solution for establishing instantaneous digital lifelines in zero-day disaster response missions.

Ultrafast spin dynamics in a magnetically compensated rare earth iron garnet film driven by femtosecond optical pulses through the inverse Faraday effect is theoretically investigated. Numerical simulations based on the equations of motion for the Néel vector reveal the temporal evolution of the system and its trajectories in the effective potential landscape tuned by external field and temperature. The results demonstrate a clear threshold behavior: weak pulses induce only oscillations around the initial equilibrium state, while a stronger excitation results in a deterministic magnetization switching. The switching threshold is determined by the magnetic state of the sample on its phase diagramme as well as on the laser pulse helicity. This mechanism demonstrates a non-thermal and even non-absorptive pathway towards optomagnonic logic and memory devices.

A size-extensive, converging, black-box, ab initio coupled-cluster ($Δ$CC) ansatz is introduced that computes the energies and wave functions of stationary states from any degenerate or nondegenerate Slater-determinant references with any numbers of $α$- and $β$-spin electrons, any patterns of orbital occupancy, any spin multiplicities, and any spatial symmetries. For a nondegenerate reference, it reduces to the single-reference coupled-cluster ansatz. For a degenerate multireference, it is a natural coupled-cluster extension of degenerate Rayleigh-Schrödinger perturbation ($Δ$MP) theory. For ionized and electron-attached references, it can be viewed as a coupled-cluster Green's function, although the present theory is convergent toward the full-configuration-interaction (FCI) limits, while Feynman-Dyson many-body Green's function (MBGF) theory generally is not. Additionally, a new state-universal multireference coupled-cluster theory for general model spaces is developed by slightly modifying the $Δ$CC ansatz. This quasidegenerate coupled-cluster (QCC) theory is size-extensive, converging, but not black-box, which is expected to be well suited for strong correlation. Determinant-based, general-order algorithms of $Δ$CC and QCC theories are implemented, which are compared with configuration-interaction (CI) and equation-of-motion coupled-cluster (EOM-CC) theories through octuple excitations and with $Δ$MP and MBGF theories up to the nineteenth order. For transition energies, the order of performance is: QCC $\approx$ $Δ$CC $>$ EOM-CC $>$ CI at the same excitation order or QCC $\approx$ $Δ$CC $>$ $Δ$MP $>$ MBGF at the same cost scaling.

We explore the space of non-gravitational, maximally supersymmetric, planar 4d effective field theories (EFTs) that have $\mathcal{N}=4$ super Yang-Mills (SYM) at leading order. We show that in the weakly-coupled regime, highly non-trivial nonlinear constraints on the 4-point Wilson coefficients follow from enforcing $\mathcal{N}=4$ supersymmetry and $SU(4)$ R-symmetry together with the requirement of standard tree-level factorization on the massless poles of the 4-, 5-, and 6-point EFT scattering amplitudes. Additionally, when these novel constraints are combined with positivity, the resulting bounds on the 4-point Wilson coefficients converge to the values of the open string Veneziano amplitude. Our results strongly suggest that supersymmetry, R-symmetry, and positivity are sufficient to single out this unique UV completion at tree level. Our findings, moreover, highlight the power of higher-point amplitudes in constraining EFT data and imply that the space of consistent quantum field theories is even more restricted than previously suggested by causality or swampland-based approaches.

Given $n$ random variables, when does the matrix of pairwise $f$-mutual informations define a PSD kernel over variables? For convex finite generators $f:(0,\infty)\to\mathbb{R}$ with $f(1)=0$ and finite boundary value $f(0)$, we give a closed characterization up to linear transformation $f\sim f+c(t-1)$, which leaves every $f$-divergence and every $f$-mutual-information matrix unchanged. The matrix $M^{(f)}_{ij}:=I_f(X_i;X_j)$ is PSD for every finite-alphabet family if and only if the normalized representative has a globally convergent expansion $\bar f(t)=\sum_{m\ge2}a_m(t-1)^m$, with $a_m\ge0$, on all of $(0,\infty)$. Sufficiency follows from a replica embedding for monomial generators plus closure under nonnegative mixtures. Necessity first extracts the local Taylor cone at $1$ using biased three-point kernels $H_a$, the Belton--Guillot--Khare--Putinar (BGKP) low-rank Hankel positivity-preserver theorem, and then bootstraps analyticity to the divergence. This is a kernel characterization problem, not a metric one: PSD of the variable-indexed matrix is distinct from Hilbertian properties of divergences between distributions. The result explains why Shannon MI and Jensen--Shannon fail, why $χ^2$ succeeds, and why non-analytic divergences such as total variation and ReLU are excluded.

Motivated by variational inference methods, we propose a zeroth-order algorithm for solving optimization problems in the space of Gaussian probability measures. The algorithm is based on an interacting system of Gaussian particles that stochastically explore the search space and self-organize around global minima via a consensus-based optimization (CBO) mechanism. Its construction relies on the Linearized Bures-Wasserstein (LBW) space, a novel parametrization of Gaussian measures we introduce for efficient computations. LBW is inspired by linearized optimal transport and preserves key geometric features while enabling computational tractability. We establish well-posedness and study the convergence properties of the particle dynamics via a mean-field approximation. Numerical experiments on variational inference tasks demonstrate the algorithm's robustness and superior performance with respect to deterministic gradient-based method in presence of low-dimensional non log-concave targets.

Long Short-Term Memory (LSTM) models are trained to predict forecast errors for the High-Resolution Rapid Refresh (HRRR) model using the New York State Mesonet and Oklahoma State Mesonet near-surface weather observations as ground truth. When evaluated using mean-absolute-error and percent improvement relative to the HRRR, LSTMs predict precipitation error most accurately, providing, on average, a 48% improvement relative to the HRRR forecast, followed by wind error, providing, on average, a 15% improvement, and then temperature error, providing, on average, a 25% improvement. Precipitation errors exhibit an asymmetry, with overforecast precipitation detected more accurately than underforecast, while wind error predictions are consistent across over- and underforecast predictions. Temperature error predictions are relatively accurate but smoother, with respect to variance, than true observations. This paper describes an overview of LSTM performance with the expressed intent of providing forecasters with real-time predictions of forecast error at the point of use within the New York State and Oklahoma State Mesonets. In practice, the predicted errors can be used to adjust deterministic HRRR forecasts at the point of use, identify locations and variables with elevated uncertainty, and provide supplemental guidance for high-impact decision-making. This research demonstrates the potential of LSTM-based machine learning models to provide actionable, location-specific predictions of forecast error for high-resolution operational numerical weather prediction (NWP) systems. However, model performance is variable-dependent, and the approach relies on the availability of dense mesonet observations, which may limit applicability in data-sparse regions.

Digital geographic maps remain largely inaccessible to blind and low-vision individuals (BLVIs), despite global legislation adopting the Web Content Accessibility Guidelines (WCAG). A critical gap exists in defining "equivalent purpose" for maps under WCAG Success Criterion 1.1.1, which requires that non-text content provide a text alternative that serves the "equivalent purpose". This paper proposes a systematic framework for evaluating map accessibility, called the Map Equivalent-Purpose Framework (MEP Framework), defining purpose through three items (Generalized, Spatial Information, and Spatial Relationships), and establishing 15 measurable criteria for equivalent information communication. Eight text map representations were evaluated against visual map baselines using the proposed MEP Framework. Results show that legacy methods such as tables and turn-by-turn directions fail to meet the MEP Framework criteria, while Audiom Maps, Multi User Domain (MUD) Maps, and Audio Descriptions meet the criteria. The evaluation highlights the necessity of holistic, systematic approaches to ensure non-visual maps convey all generalized spatial information and relationships present in visual maps. The MEP Framework provides a replicable methodology for comprehensively assessing digital map accessibility, clarifying WCAG's "equivalent purpose", and guiding compliant and usable map creation. Compliant maps will support BLVIs' participation in map-dependent professions and civic engagement.

We derive predictions for the hadronic matrix elements of radiative semileptonic decays of beautiful hadrons within Heavy Quark Effective Theory (HQET), relevant for future measurements at Belle II and LHCb. Our study considers Lambda(b) -> Lambda(c), Lambda(*)(c1) and B -> D(*), D** transitions. The symmetries of HQET highly constrain the number of structure-dependent form factors in all cases. In the soft and sub-leading soft regions, all the form factors are fully determined in terms of non-radiative Isgur-Wise functions and the magnetic dipole moments of the heavy hadrons. The structure of higher order corrections is also briefly discussed.

We discuss how to model the surface of celestial bodies (such as stars) in quantum gravity to ensure the regularity of quantum corrections to classical solutions of general relativity at the surface of such bodies. Specifically, we use the Vilkovisky--DeWitt unique effective action to calculate universal quantum corrections to the exterior metric for a class of stellar models. Previous descriptions, obtained via a Heaviside density profile, are ``pathological'' at the surface of the star due to the divergence of the metric functions and associated curvature invariants. Introducing a modified version of the Tolman VII density profile, we determine the minimal degree of differentiability required for this function to generate regular quantum corrections at the star's surface.

In the maritime sector, tramp shipping companies manage fleets to maximize profit while navigating market uncertainties. The International Maritime Organization (IMO) recently introduced the Carbon Intensity Indicator (CII) to reduce greenhouse gas emissions, further complicating deployment decisions. This paper introduces a novel two-stage stochastic programming model for long-term fleet deployment under market uncertainty and CII regulation. It is the first to integrate key operational uncertainties such as fuel prices, freight rates, and cargo demand into a unified tactical planning framework under CII regulation, simultaneously optimizing routing, cargo allocation, and speed. Furthermore, we develop an novel efficient heuristic algorithm that reliably converges to solutions within a 5\% optimality gap, enabling practical decision-support under uncertainty. Numerical analysis highlights two key findings based on our model: (1) It uncovers the ``CII paradox,'' a critical counterintuitive phenomenon where the present Supply-based CII regulation may increase total emissions significantly and drastically reduce profits. This challenges the conventional wisdom that stricter carbon-intensity rules invariably reduce emissions. (2) It demonstrates the advantage of stochastic modeling, showing that accounting for future uncertainties significantly narrows the revenue gap with perfect-foresight solutions, thereby offering superior economic performance over deterministic approaches. Collectively, these results deepen the understanding of environmental regulation's operational impacts and pave the way for more effective and sustainable fleet management strategies.

Many philosophers of physics maintain that a physical theory that exhibits (certain kinds of) symmetries is flawed, on the grounds that such theories posit "excess structure". In an influential paper, Dewar [2019, "Sophistication about Symmetries", \emph{Brit. J. Phil. Sci.} \textbf{70}: 485-521] introduces a distinction between "reduction" and "sophistication" as alternative ways of removing excess structure. In this paper we re-examine the distinction as Dewar draws it, and we argue that there is no physically or philosophically important distinction between what Dewar calls "reduction" and what he calls "internal sophistication". We then argue that there are multiple notions of "reduction" in the literature that ought to be distinguished, both in motivation and in outcome.

Changing-look active galactic nuclei (CL-AGNs) exhibit dramatic spectral variability on unexpectedly short timescales, challenging standard accretion flow models. Despite growing samples, the physical drivers of this extreme variability, and the potential link to host-galaxy properties, remain unknown. Regardless of the underlying mechanism, the transition between AGN-dominated and host-dominated spectra offers a unique opportunity to study relations between AGNs and their hosts within the same objects. We present intermediate-resolution spectroscopy of 23 CL-AGNs identified by the Sloan Digital Sky Survey V (SDSS-V), obtained with the Very Large Telescope/X-shooter and Gemini-N/GMOS. An analysis of the Mgii emission line observed in the spectra demonstrates that the majority of these sources cannot be driven by variable obscuration. Our CL-AGNs roughly follow the M_BH-sigma_* and M_BH-M_* relations of inactive galaxies, with a median black hole-to-stellar mass ratio of 0.38%. We find no evidence that the stellar population properties of our CL-AGNs, including stellar mass, age, young stellar fraction, and star-formation rate, differ from those of type 2 AGNs in SDSS. These results suggest that CL-AGNs reside in typical AGN host galaxies and that their extreme variability is likely unrelated to host-galaxy environment, supporting the idea that CL-AGNs are not a distinct population, but rather represent a phase of normal AGN activity. This result, in turn, implies that CL-AGNs can serve as useful probes of the AGN-host connection, providing access to both AGN-dominated and host-dominated spectra of the same systems.

Applications of algebraic geometry have sparked much recent work on algebraic matroids. An algebraic matroid encodes algebraic dependencies among coordinate functions on a variety. We study the behavior of algebraic matroids under joins and secants of varieties. Motivated by Terracini's lemma, we introduce the notion of a Terracini union of matroids, which captures when the algebraic matroid of a join coincides with the matroid union of the algebraic matroids of its summands. We illustrate applications of our results with a discussion of the implications for toric surfaces and threefolds.

Ardila and Brugallé conjectured that double tropical Welschinger invariants of Hirzebruch surfaces are piecewise quasipolynomial. In this work, we prove the conjecture holds in full generality, i.e. for toric surfaces corresponding to h-transverse polygons. Furthermore, we define new combinatorial Welschinger-type numbers for h-transverse polygons and show that they are likewise piecewise quasipolynomial.

Controlling the dispersion of a subset of decision variables in an optimization problem is crucial for enforcing fairness or load-balancing across a wide range of applications. Building on the well-known equivalence of finite-dimensional norms, the article develops a family of parameterized convex models that regulate the dispersion of a vector of decision-variable values through its coefficient of variation. Each model has a single parameter taking values in the interval $[0,1]$. When the parameter is set to zero, the model imposes only a trivial constraint on the optimization problem; when set to one, it enforces equality of all the decision variables. As the parameter varies, the coefficient of variation is provably bounded above by a monotonic function of that parameter. The article also presents theoretical results relating the space of feasible solutions across all models. Finally, it compares the models' solution quality on a variant of the assignment problem that regulates the dispersion in the assignment costs.

In [I. Arzhantsev and M. Zaidenberg, Borel subgroups of the automorphism groups of affine toric surfaces, arXiv:2507.09679 (2025)] we described the Borel subgroups and maximal solvable subgroups of the automorphism groups of affine toric surfaces. In the present paper, we introduce the notion of an integrable Borel subalgebra in the Lie algebra of the automorphism group of an affine variety. We show that they are precisely the tangent algebras of the Borel subgroups. We classify the integrable Borel subalgebras in the Lie algebras of the automorphism groups of toric affine surfaces, notably of the affine plane and its cyclic quotients.

Quantum Key Distribution (QKD) leverages the principles of quantum mechanics to exchange a secret key between two parties. Unlike classical cryptographic systems, the security of QKD is not reliant on computational assumptions but is instead rooted in the fundamental laws of physics. In a QKD protocol, any attempt by an eavesdropper to intercept the key is detectable: this provides an unprecedented level of security, making QKD an attractive solution for secure communication in an era increasingly threatened by the advent of quantum computers and their potential to break classical cryptographic systems. However, QKD also faces several practical challenges such as transmission loss and noise in quantum channels, finite key size effects, and implementation flaws in QKD devices. Addressing these issues is crucial for the large-scale deployment of QKD and the realization of a global quantum internet. A whole body of research is dedicated to the hacking of the quantum states source, for example using Trojan-Horse attacks (THAs), where the eavesdropper injects light into the system and analyzes the back-reflected signal. In this paper, we study the vulnerabilities against THAs of the iPOGNAC encoder, first introduced in Avesani, Agnesi et al., to propose adapted countermeasures that can mitigate such attacks.

We report an advanced formulation of the Fourier modal method developed for two-dimensionally periodic multilayered structures containing materials with non-zero macroscopic magneto-electric coefficients (also known as coefficients of chirality and bi-anisotropy) represented as arbitrary 3 by 3 tensors. We consider two numerical schemes for this formulation: with and without generalized Fourier factorization rules. For both schemes, we provide explicit expressions for the Fourier tensors of macroscopic material parameters and demonstrate that, in the absence of magneto-electric coupling, they reduce to the conventional factorization rules. We show that the scheme employing factorization rules facilitates improved convergence, even when the macroscopic chirality coefficient is large. The described formulation represents a fast and rigorous technique for theoretical studies of periodic structures with chiral, bi-anisotropic, or non-reciprocal materials in the widely used framework of the Fourier modal method.

The Alternating Current Optimal Power Flow (ACOPF) problem is a core task in power system operations, aimed at determining cost-effective generation dispatch while satisfying physical and operational constraints. However, conventional ACOPF formulations rely on steady-state models and neglect generator dynamics, which can result in operating points that are economically optimal but dynamically unstable. This paper proposes a novel, data-driven approach to incorporate generator dynamics into the ACOPF using Gaussian Process (GP) models. Specifically, it introduces an exponential surrogate function to characterize the stability of solutions to the differential equations governing synchronous generator dynamics. The exponent, which indicates whether system trajectories decay (stable) or grow (unstable), is learned as a function of the bus voltage using GP regression. Crucially, the framework enables probabilistic stability assessment to be integrated directly into the optimization process. The resulting dynamics-aware ACOPF formulation identifies operating points that satisfy both operational safety and dynamic stability criteria. Numerical experiments on the IEEE 39-bus, 57-bus, and 118-bus systems demonstrate that, compared with existing data-driven approaches, the proposed method efficiently captures generator dynamics with limited training data, yielding more reliable and robust decisions across a wide range of operating conditions.

We propose a novel, data-driven method for determining total charm cross sections in proton-proton collisions by extrapolating measured fiducial cross sections without assuming any particular fragmentation model. The recently observed charm fragmentation non-universality at the LHC experimentally establishes strongly increased baryon production fractions and correspondingly decreased meson production fractions compared to electron-positron collisions, with a very significant $p_T$ dependence. The novel method accounts for this non-universality and its $p_T$-dependence through a data-driven extrapolation function called ddFONLL. Applied to $D^0$ production at 5 and 13 TeV, this approach yields total charm cross sections that fully incorporate the fragmentation non-universality and increase significantly compared to the previous measurements still based on fragmentation universality. The results are consistent with NNLO QCD predictions and enable direct comparisons free from fragmentation assumptions. We use this to evaluate the sensitivity of total cross-section measurements to parton distribution functions and the charm-quark mass. An outlook is given on the potential of further expanding the use of the ddFONLL method.

We consider several definitions of the quantum Wasserstein distance based on an optimization over general bipartite quantum states with given marginals. Then, we examine the quantities obtained after the optimization is carried out over bipartite separable states instead. We prove that several of these quantities are equal to each other. Thus, we connect several approaches in the literature. We prove the triangle inequality for some of these quantities for the case of one of the three states being pure. As a byproduct, we show that the square root of the Uhlmann-Jozsa quantum fidelity can also be written as an optimization over separable states with given marginals. We use this to prove that some of these quantities equal the Uhlmann-Jozsa quantum fidelity for qubits. We also find relations with the superfidelity.

Fractionally charged elementary excitations, the quasi-electron and quasi-hole, are one of the hallmarks of the fractional Chern insulator (FCI). In this work, we observe that spontaneous spin polarization in twisted MoTe$_2$ leads to multiple species of low-energy quasi-particles distinguished by their spin quantum numbers. We perform large-scale exact diagonalization (ED) calculations to investigate the nature of these excitations and develop a method to extract their fundamental energetic properties. Focusing on $θ= 3.7^{\circ}$ and filling factor $ν= -2/3$ relevant to recent experiments, we show that spin-preserving (spinless) charge excitations have smaller gap than spin-flipping (spinful) excitations both with and without band mixing. This result is in qualitative agreement with the measured magnetic field dependence of the transport gaps. Beyond the spinless and spinful quasi-particle gaps, we extract the full quasi-electron and quasi-hole ``band structure'' and find significant dispersion with emergent magnetic translation symmetry -- a fundamental departure from the immobile excitations of the quantum Hall fluid. Our results establish a framework for computing the properties of novel elementary excitations in FCIs.

We propose a framework for the fair democratic governance of federated digital communities that form and evolve dynamically, where small groups self-govern and larger groups are represented by assemblies selected via sortition. Prior work addressed static fairness conditions; here, we formalize a dynamic setting where federations evolve over time through communities forming, joining, and splitting, in all directions -- bottom-up, top-down, and middle-out -- and adapt the fairness guarantees. The main technical challenge is reconciling integral seat allocations with dynamic, overlapping federations, so that child communities always meet their persistent floors while long-run averages converge to proportional fairness. Overcoming these challenges, we introduce a protocol that ensures fair participation and representation both persistently (at all times) and eventually (in the limit after stabilization), extending the static fairness properties to handle structural changes. Prior work shows how grassroots federations can be specified via atomic transactions among assembly members, Constitutional Consensus can realize these transactions and the democratic processes leading to them, and Constitutional Governance in Metric Spaces lets a community govern itself and amend its own constitution. Together, these works form a comprehensive design for an egalitarian, fairly governed, large-scale decentralized sovereign digital community platform.

We consider voting rules in settings where voters' identities are difficult to verify. Voters can manipulate the process by casting multiple votes under different identities or abstaining from voting. Immunities to such manipulations are called \emph{false-name-proofness} and \emph{participation}, respectively. For the universal domain of (strict) preferences, these properties together imply \emph{anonymity} and are incompatible with \emph{neutrality}. For the domain of preferences defined over all subsets of a given set of objects, both \emph{false-name-proofness} and \emph{participation} cannot be met by rules that are also \emph{onto}, \emph{object neutral}, and \emph{tops-only}. However, when preferences over subsets of objects are restricted to be separable, all these properties can be satisfied. Furthermore, the domain of separable preferences is maximal for these properties.

High-dimensional planted problems, such as finding a hidden dense subgraph within a random graph, often exhibit a gap between statistical and computational feasibility. While recovering the hidden structure may be statistically possible, it is conjectured to be computationally intractable in certain parameter regimes. A powerful approach to understanding this hardness involves proving lower bounds on the efficacy of low-degree polynomial algorithms. We introduce new techniques for establishing such lower bounds, leading to novel results across diverse settings: planted submatrix, planted dense subgraph, the spiked Wigner model, and the stochastic block model. Notably, our results address the estimation task -- whereas most prior work is limited to hypothesis testing -- and capture sharp phase transitions such as the "BBP" transition in the spiked Wigner model (named for Baik, Ben Arous, and Péché) and the Kesten-Stigum threshold in the stochastic block model. Existing work on estimation either falls short of achieving these sharp thresholds or is limited to polynomials of very low (constant or logarithmic) degree. In contrast, our results rule out estimation with polynomials of degree $n^δ$ where $n$ is the dimension and $δ> 0$ is a constant, and in some cases we pin down the optimal constant $δ$. Our work resolves open problems posed by Hopkins & Steurer (2017) and Schramm & Wein (2022), and provides rigorous support within the low-degree framework for conjectures by Abbe & Sandon (2018) and Lelarge & Miolane (2019).