Papers

Answering a question of Chepoi and Hagen, we give two constructions of bounded degree CAT(0) square complexes that cannot be isometrically embedded into any finite product of trees. The first is based on Burling graphs and has degree at most five, which is optimal. These square complexes topologically embed into $\R^3$ since we further prove that every CAT(0) square complex whose vertices have degree at most five can be topologically embedded into the product of a line and a star. It turns out that in this setting, Burling graphs are the only obstruction: we prove that CAT(0) square complexes that topologically embed into $\R^3$ and whose crossing graph forbids some induced Burling graph can be isometrically embedded into a finite product of trees. Our second CAT(0) square complex has degree at most six and its crossing graph forbids an induced Burling graph. Of independent graph-theoretic interest, along the way we construct intersections of chordal and interval graphs with arbitrarily large girth and chromatic number. We also discuss connections to nice labellings of event structures.

Statistical heterogeneity limits federated learning when a single global classifier cannot represent client-specific label distributions. In this work, we propose Personalized Federated Knowledge Distillation with Head Adaptation (pFedKDH), which aggregates only the shared backbone, keeps persistent client-specific heads, and uses a recalibrated global head as a teacher during local training. Across MNIST, Fashion-MNIST, CIFAR10, and CIFAR100 under class-wise Dirichlet partitions, pFedKDH obtains the best accuracy in most settings, with accuracy gaps up to 37.67% over the weakest baseline and consistently low standard deviation across repetitions. Component-wise diagnostics and convergence results support the role of persistent heads and distillation-guided local optimization under label-skewed data.

We construct two complemented subspaces of $L_1[0,1]$. The first has the Schur property but fails the Radon–Nikodým property. The second contains a copy of $\ell_2$ but no copy of $L_1[0,1]$. Neither space is isomorphic to a Banach lattice. This gives a negative answer to the complemented-subspace question of Lindenstrauss and Rosenthal. A Lean 4 formalisation of the main results accompanies the paper.

In this work, we develop a fibrational approach to freely adjoining adjoints in an $(\infty,2)$-category. We construct the universal bifibration obtained from a cocartesian fibration of $(\infty,2)$-categories by adjoining cartesian lifts over a chosen class of $1$-morphisms in the base. We then use this construction to provide an explicit model for freely adjoining adjoints, together with a zig-zag formula for the resulting mapping $(\infty,1)$-categories. As applications, we give a model-independent proof of the universal property of the walking adjunction, providing an alternative proof of a theorem of Riehl–Verity, and establish the universal characterization of the simplex $2$-category conjectured by Dyckerhoff–Kapranov–Schechtman–Soibelman.

Standards bodies report cryptographic security as a single number of bits, but this value depends on the adversary cost model used to price time, memory, and quantum resources. Different conventions can therefore produce different rankings of cryptographic schemes. GAUGE represents security as a function over admissible cost models, called a security profile. Comparisons then become comparisons between profiles, and ranking reversals become an explicit structural property rather than a measurement error. We formalize price functionals over a cone of adversary cost models, show that security profiles are piecewise-linear and concave, and prove a rating trilemma: when two profiles cross, no rating can simultaneously be faithful to underlying costs, total over comparable pairs, and independent of the chosen cost model. We provide a polynomial-time linear-programming procedure that certifies whether the ranking of two schemes is robust, reverses under admissible models, or is genuinely incomparable. We extend GAUGE with a two-layer risk measure combining stochastic cryptanalytic decay with uncertainty over the appropriate cost model. We evaluate the framework on NIST post-quantum standards, classical anchors, and a 25-year chronology of cryptanalytic breaks. The analysis certifies a ranking reversal for ML-KEM-512 versus AES-128 from a 4-5% shift in memory pricing, and measures a lattice-sieving cost drift of 9.79 bits per year over eight years. A hybrid X25519 + ML-KEM-768 handshake reduces combined-break probability twenty-fold at a 2.3 kilobyte cost. The artifact reproduces all tables and figures in under seven seconds. GAUGE provides an explicit and auditable framework for reporting cryptographic security under competing cost models.

Conner, Gesmundo, Landsberg and Ventura (2019) determined the largest stabilizer dimension of concise $n\times n \times n$ tensors that are binding, and they determined the corresponding maximizing tensors to be the null algebra tensors. They left as an open problem to extend this to all concise $n \times n \times n$ tensors (i.e. dropping binding). We solve this problem: We prove that the largest stabilizer dimension of concise $n\times n\times n$ tensors is $n^2 + 1$ and the maximizers are the null algebra tensors (as in the binding case) and the skew symmetric tensor $e_1 \wedge e_2 \wedge e_3$. As part of our approach we obtain upper bounds on the stabilizer dimension of matrix tuples under left-right action (generalized Kronecker quiver representations), which we think are of independent interest.

Recent measurements of two-particle transverse-momentum correlations, $C_{p_T}$, in Au+Au collisions have revealed a statistically significant non-monotonic beam-energy dependence over the range $\sqrt{s_{NN}}=3.0$–$7.7$~GeV that has been interpreted as potentially indicative of critical phenomena associated with a critical end point (CEP) in the QCD phase diagram. This interpretation is assessed in light of the absence of a controlled framework establishing $C_{p_T}$ as a quantitative proxy for the underlying critical response. The implications of this limitation are examined by considering the expected finite-size and finite-time modification of critical fluctuations, substantial non-critical dynamical contributions, the lack of demonstrated critical scaling, and the sizeable discrepancy between the CEP region inferred from the observed $C_{p_T}$ non-monotonicity and that constrained by susceptibility-based measurements and finite-size scaling analyses. Taken together, these considerations indicate that the observed $C_{p_T}$ non-monotonicity does not, by itself, establish a critical origin nor provide reliable quantitative constraints on the existence or location of a possible CEP.

The emerging concept of data storytelling (DS) suggests that enhancing visualisations with annotations and narratives can make complex data more insightful than conventional visualisations. Previous works found that DS-enhanced visualisations are more effective than conventional visualisations for simple tasks like identifying key data points or the main message. However, no previous work has explored the extent to which DS enhancements influence task completion across different levels of cognitive complexity. We address this gap by presenting the results of a study where 128 participants completed tasks based on four visualisations (two line charts and two choropleth maps, either with or without DS elements) spanning a range of complexity based on Bloom's taxonomy, which has been applied in data visualisation to categorise tasks hierarchically from lower to higher-order thinking. Results suggest that while DS-enhanced visualisations effectively support lower-order tasks (finding data points and understanding insights), they don't necessarily aid the correct completion of higher-order tasks (application, analysis, evaluation and creation). However, DS enhancements improve how efficiently participants complete complex tasks.

We compute the $\operatorname{RO}^{\sigma}(C_p)$-graded Mackey functors $\underline{\pi}_* L_{\operatorname{KU}_{C_p}/p}\mathbb{S}_{C_p}$.

Digital halftoning aims to represent continuous-tone images by binary patterns while preserving their visually relevant low-frequency content. Among the many available approaches, error-diffusion methods implement noise shaping through causal feedback filters and can be interpreted as two-dimensional versions of the signal quantization paradigm Sigma–Delta modulation. On closed domains, however, the terminal state of the underlying recurrence relation need not match the initial one, producing boundary artifacts. We study this problem for bandlimited functions on the two-dimensional torus. By arranging all pixels along a single closed rank-one lattice, we replace the multiple mismatches associated with separately processed rows and columns with a single terminal contribution, while retaining exact reconstruction. For a uniform lattice with \(N=M^2+1\) points, we obtain first- and second-order error bounds of order \(N^{-1/2}\) and \(N^{-1}\). A suitable constant update eliminates the terminal mismatch and reduces the spatial localization of the error without changing these asymptotic orders. For fixed-direction rank-one lattices, the corrected first- and second-order reconstructions instead achieve rates \(N^{-1}\) and \(N^{-2}\). Numerical experiments illustrate a reduction in boundary artifacts compared with classical schemes applied on the Cartesian grid.

Fast radio bursts (FRBs) are bright, millisecond-duration transient radio signals of extragalactic origin with unknown source and emission mechanisms. While several thousand FRBs have been discovered at frequencies above 400 MHz, detections at lower frequencies have been exceptionally rare. Contributing to their rarity are the magnified dispersive delay, in the tens of seconds, and signal scattering that make low-frequency searches with established techniques computationally prohibitive. In particular, the only confirmed detection below 300 MHz came from a Low-Frequency Array observing campaign targeted at FRB 20180916B, a source already known to emit at higher frequencies. Here we present the first non-targeted detection of an FRB below 300 MHz, achieved in a wide-field, imaging-based survey with the Murchison Widefield Array. The implied FRB rate is consistent with that observed at higher frequencies, demonstrating that non-targeted wide-field surveys can uncover an unbiased, large low-frequency FRB population. This result challenges models invoking severe scattering or absorption to explain previous non-detections, and strengthens the case of low-frequency observations as promising avenue to study the local environment of FRBs.

AI agents increasingly act through agent skills, i.e., natural-language instructions, that direct a host agent toward shell, network, credential, file, and process actions, and public registries distribute them at scale. In the first half of 2026, the OpenClaw AI agent went viral, and its public skill registry boomed: the observable stock nearly doubled in 91 days, and a majority of the listings visible in June were created in just two months. By the end of our study window, the wave had crested, and monthly listing creation and core-repository activity were falling from their spring peaks. This paper measures what the boom left behind, drawing on the OpenClaw Git history, its GitHub issues and pull requests, and three ClawHub registry snapshots. Attention is concentrated: the top 10% of skills received 46.93% of all downloads. No simple skill features (like size or download counts) remained a stable predictor of continued listing once creation cohort and skill age were controlled. Human scrutiny did not stay: 77.86% have zero stars and zero comments, while 85.06% of the readable skills carry privilege evidence. And automated cleanup is not ready: the three security scanners disagreed on 23,702 of the 61,990 skills they all cover. After human adjudication, weighted scanner sensitivity against the reference standard ranged from 21.67% to 61.06%. Governing fast-growing agent-skill registries cannot rely on simple metadata or single scanner scores; it requires robust, transparent measurement and independent validation.

PyExoCross is a Python-based spectroscopic post-processing framework for converting large atomic and molecular line lists into scientifically useful quantities, including partition function, specific heats, cooling functions, lifetimes, oscillator strengths, line intensities, stick spectra, and absorption and emission cross sections. It is intended for applications in astrophysics, planetary atmospheres, laboratory spectroscopy, and other high-temperature environments where large modern databases require efficient and reproducible computational treatment. The new release provides both a configuration-file-driven command-line interface (CLI) and a Python application programming interface (API) within a unified computational framework. The original input file workflow is retained, while the Python API enables direct use in scripts, notebooks, and automated pipelines. The version PyExoCross 2.0 also adds explicit support for non-local thermodynamic equilibrium (non-LTE) calculations, including two-temperature models and user-defined density and population treatments for both absorption and emission spectra. In addition, database compatibility has been expanded beyond ExoMol, HITRAN, and HITEMP line lists to include high-resolution molecular database ExoMolHR and atomic database ExoAtom. GPU acceleration is also introduced for computationally intensive intensity and cross-section calculations and is available for all currently supported database formats. These developments improve workflow flexibility, reproducibility, and integration with modern data-analysis environments, while extending the physical modelling capabilities of the code. PyExoCross therefore provides a more general and extensible platform for large-scale spectroscopic simulations based on modern atomic and molecular databases.

We use an analogue of the Springer resolution to describe the $G$-module structure on the ring of regular functions on the universal cover $\widetilde{\mathcal{O}}$ of any nilpotent orbit for $G = SL_n$. Building on previous work on the extended Springer resolution, we construct a variety $\widetilde{\mathcal{M}}$ that is finite over the cotangent bundle of a partial flag variety $G/P$, and proper and birational over the affinization $\mathcal{M}$ of $\widetilde{\mathcal{O}}$. We use techniques in birational geometry to show that $\widetilde{\mathcal{M}}$ has rational singularities, which provides the cohomology vanishing needed to describe the ring of functions on $\widetilde{\mathcal{O}}$ as an induced representation from a Levi subgroup of $G$. Our results also yield a description of the structure of $R(\widetilde{\mathcal{O}})$ as a graded $G$-module. We describe the minimal embedding of $\mathcal{M}$, study the lifting of characters of the component group of $\widetilde{\mathcal{O}}$ to parabolics and Levi subgroups, and make a more general vanishing conjecture.

We develop the convergence analysis of the Interface Control Domain Decomposition (ICDD) method, an overlapping domain decomposition method based on an optimal control framework with Dirichlet interface control functions and interface observation. We consider elliptic problems with possible discontinuous coefficients approximated by $hp-$FEM in each subdomain. When the discretizations are conforming on the overlap between 2D domains, we provide theoretical estimates of the number of GMRES iterations needed to solve the non-symmetric interface Schur complement system associated with ICDD. Our results are obtained by combining novel spectral estimates for the Schur complement matrix of ICDD and classical GMRES convergence theory. We prove that the convergence rate behaves as $\mathcal{O}(\delta^{-1} p^{3/2}\log p)$, where $\delta$ denotes the overlap width and $p$ the local polynomial degree, while remaining independent of the mesh size $h$. Numerical experiments verify the theoretical predictions and show the effectiveness of ICDD in the presence of large coefficient jumps in the computational domain. Since in the conforming case, the considered ICDD formulation coincides with the Substructured Restricted Additive Schwarz (SRAS) method, the analysis also provides convergence estimates for SRAS in two dimensions and, through its known equivalence, for the Restricted Additive Schwarz (RAS) method.

We present a comprehensive ab initio study of the effect of higher-order anharmonicity and polymorphism on the lattice thermal conductivity, ${\bm \kappa}$, of single-layer transition metal dichalcogenides. We show that four-phonon processes are responsible for an additional suppression of ${\bm \kappa}$ ranging from 15% to 35% in the ground-state 2H phase. Conversely, their effect is almost negligible on the thermodynamically competitive \1Tp\ phase. The ${\bm \kappa}$ difference between the 2H higher-conductivity phase and the \1Tp\ lower-conductivity phase can be exploited for the design of thermal switches that may find applications in thermal management and in the development of phonon-based logic elements, particularly in the case of tellurides, where field-controlled ultrafast and reversible phase transitions have already been demonstrated experimentally.

Multimodal large language models generate natural-language responses from visual inputs, yet may mention objects absent from an image. In medication assistance, accessible perception, and environmental decision-making, such hallucinations can create real-world safety risks. We propose Semantic-Spatial Agreement Verification (SSAV), a training-free method for verifying object claims. A visually grounded claim should remain stable across semantically equivalent queries and repeatedly localize to the same image region. SSAV aggregates multiple prompts to estimate semantic support and reduce sensitivity to query wording. Query-Induced Regional Verification (QIRV) combines cross-query region persistence, spatial overlap, and relative candidate dominance to identify isolated high responses and dispersed localizations. A geometric mean fuses semantic and spatial evidence, lowering the verification score when either branch lacks support. Experiments on three base models and multiple evaluation protocols show that SSAV effectively mitigates object hallucination. On LLaVA-1.5-7B, accuracy averaged across COCO, A-OKVQA, and GQA improves by 1.81 and 3.17 percentage points under POPE Popular and Adversarial, respectively, while CHAIRs decreases from 49.40% to 32.80%. These results show that cross-query semantic stability and regional consistency provide interpretable external visual evidence for object claims.

Comparative analyses of mortality dynamics across countries have long shaped our understanding of mortality inequalities and patterns of divergence and convergence over time. However, most existing studies focus on either mortality differences across countries at a single point in time or on country trajectories, without considering both factors simultaneously. In this paper, we address this gap by introducing a multi-stage clustering framework, applied to 94 countries by sex over the period 1960-2019 using data from the World Population Prospects. Specifically, we model life-table probabilities of death using a time-dependent beta latent variable model and identify a small set of “mortality states” that characterise the mortality pattern of each country at any given point in time. We then cluster countries based on their sequences of mortality states. Our results reveal substantial heterogeneity in the timing and pace of transitions between mortality states, including a persistent East-West divide in Europe and distinctive Latin American patterns associated with elevated young-adult male mortality. Cross-country inequality increased for both sexes until the 1990s, before plateauing and subsequently declining. Our proposed multi-stage clustering framework provides an interpretable, time-explicit description of mortality dynamics that jointly captures within-country change and between-country differences, and can be applied to other settings where trajectories of categorical or discretised profiles are of interest.

We present a complete calculation of the non-singlet splitting functions in four-loop quantum chromodynamics.

We give a deterministic polynomial-time algorithm that, given rational Hermitian matrices $H_1,\dots,H_N$ of rank at most one, finds signs $s\in\{\pm1\}^N$ with $\|\sum_i s_i H_i\|\le 13\|\sum_i H_i^2\|^{1/2}$. As a corollary, for vectors $v_i$ with $\sum_i v_iv_i^*=I$ and $\|v_i\|^2\le\delta$, the signs yield a partition $[N] = S_1 \cup S_2$ such that each part satisfies $\|\sum_{i \in S_j} v_i v_i^* - \frac{I}{2}\| \leq \frac{13}{2}\sqrt\delta$ for $j = 1,2$. This gives a deterministic polynomial-time algorithm for the Kadison–Singer problem, in Weaver's equivalent discrepancy-theoretic $\mathsf{KS}_2$ formulation, with a universal constant.

Training multi-agent drone-swarm policies directly in high-fidelity (HF) rigid-body physics is accurate but computationally expensive. This cost scales poorly with team size, as each additional agent multiplies contact-resolution complexity and sharply raises the in-simulation crash rate. To address this, we propose a mixed-fidelity training scheme that eliminates HF reinforcement learning entirely. A single shared, decentralized policy is optimized inside a fully-differentiable, JAX-native low-fidelity (LF) point-mass simulator. The simulator is corrected by a small, per-agent bagged residual ensemble fit once, offline, using short calibration flights in the HF simulator. Because calibration requires only one isolated drone, the data collection budget does not compound with team size. Reference trajectories are generated by rolling out an existing LF-only policy and tracked in the HF simulator by a zero-training PD controller. Evaluated across four cooperative drone tasks and team sizes from 3 to 18, the residual-corrected policy outperforms an uncorrected LF baseline in all combinations, and a from-scratch HF policy in 22 of 24 combinations tested. It trails an HF-finetuned policy by a margin that narrows steadily with team size. Ultimately, the proposed method achieves near-equivalent performance at the largest team sizes at a fraction of the computational cost, completely avoiding the high crash rates typical of HF training.

We study cover times on discrete tori and ranges on $\mathbb{Z}^d$ for elephant random walks with memory parameter $p\in[0,1)$. In dimension one there is a phase transition at $p=3/4$. Away from criticality we determine the exact first-order asymptotics of the mean cover time, while at $p=3/4$ the mean is of order $L^2/\sqrt{\log L}$, a factor $\sqrt{\log L}$ larger than the natural fluctuation scale $L^2/\log L$. We identify the limiting distribution under each of the three natural fluctuation normalizations. In dimensions $d\geq2$, for every fixed $p<1$, the cover time has the same order as for simple random walk, in expectation and with high probability. The leading constants also agree when $p<(2d+1)/(4d)$, and at equality when $d\geq3$. For the range on $\mathbb{Z}^d$, we prove $L^1$ convergence to the simple random walk asymptotics when $d=2$ and $p<5/8$, and for every $p<1$ when $d\geq3$. Finally, we give a cover-time upper bound for generalized step-reinforced random walks on finite groups in terms of a conditional $L^\infty$ mixing profile.

Assembly Sequence Planning (ASP) remains a challenging problem due to its combinatorial nature, making exhaustive planning approaches impractical for complex industrial assemblies. Furthermore, many CAD models lack reliable semantic contact information or require extensive manual preprocessing, limiting the applicability of existing methods. This paper presents a hybrid ASP framework combining learning-based relation extraction with geometric-symbolic reasoning to generate feasible robotic disassembly sequences from imperfect CAD data. A neural network predicts semantic geometric relations from point clouds, while human-in-the-loop verification enables correction of uncertain predictions and planning failures. Extracted relations are transformed into a symbolic assembly graph, enabling a geometric-symbolic planner to efficiently compute locally valid sets of robotic manipulation primitives. A visibility-based ray-casting strategy guides the search for feasible disassembly directions without requiring an exhaustive combinatorial search, while the local solution space enables efficient sequence optimization. The framework is evaluated on an introduced assembly dataset and on the ASAP test dataset. On the ASAP test dataset, the proposed planner achieves an 85.83% planning success rate while reducing the median planning time by more than one order of magnitude across all assembly sizes and by more than a factor of 50 for assemblies with more than 30 components compared to the baseline. The results demonstrate that the proposed hybrid framework enables efficient robotic assembly sequence planning from imperfect CAD data while substantially reducing planning time. By combining learning-based feature segmentation, human-in-the-loop verification, and geometric-symbolic reasoning, the framework provides a practical foundation for scalable and adaptable robotic assembly and disassembly planning.

We consider scaling limits of integer-valued random walks whose transition probabilities are translation-invariant everywhere except on a set that we will call a membrane or an interface. If the jumps outside the membrane are i.i.d. mean-zero random variables with finite variance, then possible examples of the corresponding limit processes include reflected Brownian motion, skew Brownian motion, and Brownian motion with a jump-type exit from zero. We also discuss the question of what the possible limits are if the jumps outside the membrane belong to the domain of attraction of a stable law.

We prove rigidity near the Euclidean metric for the anisotropic Calderón problem on smooth bounded connected domains in dimensions three and higher. Any smooth Riemannian metric sufficiently close to the Euclidean metric in a suitable Hölder norm and having the same Dirichlet-to-Neumann map agrees with it up to a diffeomorphism fixing the boundary pointwise. The result applies to general smooth anisotropic perturbations, without analytic or quasianalytic regularity assumptions, a prescribed conformal class, or a transversal product structure, and requires no convexity of the boundary. The proof combines harmonic coordinates with a Carleman estimate for compactly supported correctors to obtain a quadratic Fourier estimate on a frequency range determined by the perturbation. A frequency decomposition then yields rigidity.

Cyber-Physical Systems (CPS) operate through a continuous sense-compute-act loop within an open context environment, making it impossible to anticipate all the situations the system will face. To cope with this openness, stakeholders rely on assumptions, formalized into design models. However, these assumptions may no longer hold once the system is confronted with runtime reality, resulting in a discrepancy between expected and observed behaviour known in literature as the reality gap. Existing approaches mainly focus on reducing or overcoming it by making simulations more faithful to reality, with no unified methodology to structure and exploit invalidated assumptions that give rise to this gap as reusable design knowledge. We refer to the persistent reliance on invalidated assumptions -and the resulting false confidence in the design model's operational validity -as design illusions, and argue that they need to be made explicit, structured, and exploited as knowledge to support better design decisions. We propose a conceptual pipeline for illusions-awareness that identifies, classifies, characterizes, and leverages illusions to transform them into actionable design knowledge.

We discuss the phenomenological use of the next-to-leading order (NLO) eigenfunctions of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) kernel. We first recall the BFKL representation of high-energy scattering amplitudes and the role played by the eigenfunctions in the spectral representation of the Green's function. We then compare two equivalent representations of the next-to-leading logarithmic approximation (NLLA) amplitude, respectively based on the leading-order (LO) and NLO eigenfunctions. The two formulations are equivalent within NLLA, while differing by terms beyond this accuracy which could influence the phenomenological stability of high-energy observables. The aim is to test the possible role of NLO eigenfunctions-induced terms in improving this stability, discussing the amplitude dependence on the renormalization and energy scales. As an application, we consider first the forward electroproduction of two light vector mesons and then we comment on preliminary applications to Mueller-Navelet jet production.

Digital Twins (DTs) are widely adopted across a variety of application domains. In industrial sectors, particularly in mechanical engineering, they accelerate product development, reduce risks, enable early issue prediction, and lower sustainment costs . In practice, DTs increasingly integrate physics-based (deductive) and data-driven (inductive) models into hybrid models combining the complementary strengths of both modeling paradigms. In this paper, we refer to this integration paradigm as hybridization. Despite this trend, the engineering of hybrid DTs that is, remains insufficiently documented. Hybridization is often introduced in an ad hoc manner, and its implementation is only partially made explicit, which limits reproducibility and transferability. This paper reports on the development of an existing fluidic loop digital twin at Centre Technique des Industries Mécanique (CETIM). The DT is described using the characterization framework of Gil et al., providing a structured view across its lifecycle dimensions. To make hybridization explicit, the case is further analyzed through a complementary characterization structured along two dimensions: motivation and realization. The resulting description provides a traceable account of hybridization decisions and supports the documentation and transfer of hybrid DT engineering practices.

Semantic occupancy prediction gives an embodied agent a voxel-level account of where space is free, occupied, and semantically meaningful. In RGB-D pipelines such as EmbodiedScan, the image encoder is often left as a default module, even though its features are the visual evidence later sampled into the 3D grid. We study this design choice directly. A central finding is that changing the 2D backbone improves occupancy accuracy more than several carefully designed occupancy architectures or modules. We keep the main RGB-D projection, depth branch, and occupancy head fixed, and replace only the image backbone. The compared encoders are CLIP-ResNet, CLIP-ViT, BLIP2, and DINOv2. Under the controlled setting, the measured mIoU changes substantially: DINOv2 obtains 30.55%, BLIP2 obtains 29.49%, CLIP-ViT obtains 24.33%, and CLIP-ResNet obtains 17.41%. The stronger encoders also exceed the original EmbodiedScan ResNet-50 baseline without modifying the downstream 3D fusion pipeline. Class-level results give a more detailed picture: DINOv2 is stronger on many layout and structural categories, whereas BLIP2 remains close on several object-centered classes. CLIP-ViT improves clearly over CLIP-ResNet, showing that the way CLIP features are exposed as dense tokens matters for voxel lifting. These results indicate that the image backbone is not a secondary engineering detail in embodied semantic occupancy, but a major source of variation in the final 3D prediction.

Entanglement in indistinguishable particle systems can be characterized by the impossibility of unambiguously attributing a complete set of physical properties to the individual constituent particles. In this work, we introduce a geometric quantifier of the incompatibility of such simultaneous property attribution for pure states of $N$ indistinguishable bosons. Using the Majorana stellar representation, any symmetric multi-qubit state can be expressed as the symmetrization of constituent single-particle states, allowing the associated single-particle properties to be directly linked with the corresponding Majorana stars. This establishes a direct connection between the geometry of the Majorana representation on the Bloch sphere and the entanglement criterion based on the attribution of single-particle properties in systems of identical two-level bosons. We then generalize this geometric approach to higher-dimensional bosons, extending the quantifier from qubits to qudits, while retaining a geometric interpretation of property-attribution incompatibility in terms of Fubini-Study angles.