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arXiv2026

An Arboricity-Sensitive Algorithm for the $K_r-e$-Free Graph Sandwich Problem

For a fixed integer $r\geq4$, the $K_r-e$-free graph sandwich problem asks whether, given graphs $G_1\subseteq G_2$ on the same vertex set, there is an induced-$K_r-e$-free graph $H$ between them. We give a deterministic algorithm taking $O(n+α(G_2)^{r-3}m_2)$ time and space, where $m_2=|E(G_2)|$ and $α(G_2)$ is the arboricity of $G_2$. In particular, the diamond-free case takes $O(n+α(G_2)m_2)$ time. This improves the direct $O(n^r m_2)$ implementation of the previously known forced-edge closure. Our implementation maintains components of common neighborhoods indexed by $(r-3)$-cliques. A filtered frontier supports their merges within the clique-listing bound, while completion events avoid repeatedly searching for affected cliques. On feasible instances the output is contained in every feasible sandwich, independently of processing order. Applying the closure to $(G,K_n)$ gives an $O(n^{r-1})$-time bound for partitioned and nonpartitioned probe $K_r-e$-free recognition, improving the $O(n^{r+2})$ bound obtained from the direct sandwich closure. We also describe a direct static recognizer based on the same local characterization.

cs.DS↗
arXiv2026

Homological critical points for hypergraphs and simplicial complexes

In this paper, we study the homological critical points for persistence hypergraphs and persistence simplicial complexes. With the help of the relative homology groups, we define the homological critical points for persistence morphisms between persistence hypergraphs and persistence simplicial maps between persistence simplicial complexes. We prove some commutative diagrams of subset relations for the homological critical points of persistence hypergraphs as well as persistence morphisms between them. We also prove some commutative diagrams of subset relations for the homological critical points of persistence simplicial complexes as well as persistence simplicial maps between them. As examples, we use the parametric configuration spaces to construct the parametric independence complexes as the space of parametric packings and construct the parametric dominating hypergraphs as the space of parametric coverings.

math.AT↗
arXiv2026

TaskAnchor: Grounding Task State in Reactive VLAs for Long-Horizon Manipulation

Reactive vision-language-action (VLA) policies suffer from task-state aliasing in long-horizon manipulation, where identical multimodal inputs call for distinct, context-dependent actions. Given that pretrained VLAs already possess rich control primitives to express diverse behaviors, we hypothesize that the execution bottleneck lies not in policy capacity, but in input ambiguity. In this paper, we propose TaskAnchor, a lightweight adapter that grounds task state by injecting execution context into the VLA's native input space. During post-training, TaskAnchor learns to represent the semantic execution stage as a milestone-supervised coordinate prepended to the language instruction, while incorporating fine-grained historical evidence via a residual update to the current visual tokens. This formulation avoids generating complex subtask instructions and leaves the backbone architecture unchanged. Across long-horizon benchmarks, TaskAnchor delivers substantial gains, achieving approximately 6 times the average success rate of the pi0.5 and X-VLA baselines on RMBench and more than doubling the task success rate of pi0.5 on RoboMemArena. Real-robot experiments further validate reliable multi-stage execution, with the same policy adapting its subsequent behaviors using earlier human interactions as in-context cues. Our project website is available at https://taskanchor.netlify.app/.

cs.RO↗
arXiv2026

Casimir force in a water nanolayer confined by graphene sheets

Casimir forces, arising from quantum and thermal fluctuations, depend strongly on the electromagnetic susceptibilities of the interacting materials. Here, we theoretically investigate the Casimir force between two graphene sheets separated by a nanometer-thin layer of liquid water. We find that deviations from the bulk case can be as large as 24 \%, mostly due to the static susceptibility components. This effect does not decrease monotonically as a function of the layer thickness: it increases up to a maximum at 70 nm and it slowly declines to the bulk limit only at 1 micron. This is due to two competing effects: on one hand, the anisotropy decreases with the layer thickness; on the other hand, the relative contribution of the most anisotropic, static susceptibility components increases.

quant-ph↗
arXiv2026

Tail-Weight Control and Localized Generalization in Nearly Low-Rank Adversarial Classification

Empirical ramp fitting can assign weight to pure-noise features even when the population optimum ignores them. We quantify this gap for norm-constrained adversarial classification with Gaussian signal and noise. The variance cost relative to normalized signed mean separates into two factors: selecting observations inside the active margin window and the curvature induced by the norm constraint. Changing the tail variance leaves the activewindow probability unchanged but changes the second factor. With positive attack budget and a signal-only predictor of risk below one half, we prove a uniform quadratic tail-deletion bound, including at zero tail variance. Sufficiently accurate approximate global empirical minimizers admit exact fixeddimensional asymptotic covariances in the low-risk regime with isotropic principal covariance. For positive tail variance at most principal variance, the product exceeds one; an additional moment condition transfers it to expected excess ramp and robust classification risks. A wide window analysis characterizes when this ordering reverses. Controlled experiments test the decomposition, and a separate contamination study examines its scope outside the Gaussian training model.

cs.LG↗
arXiv2026

Matching Rules for a Three-Dimensional Strongly Aperiodic Monotile

A recent pre-print [arXiv:2609.19214] proposed a three-dimensional (3D) strongly aperiodic monotile: a shape that tiles Euclidean space only non-periodically and which admits no symmetry of infinite order. The proof takes the 3D Chair tile identified previously by Lee and Moody, and adds geometric decorations to the faces so as to force non-periodicity (without these decorations The Chair also admits periodic tilings). Here we establish general requirements on face decorations to achieve the same end, in order to facilitate the search for physical realisations. We find that the requirements are minimal. We provide matching rules using three colours of arrow that are equivalent to the original rules, in that they force the same local and global configurations. These rules force Chairs to compose into `Superchairs' with doubled linear dimensions. In this process the matching rules themselves compose uniquely. We find that the same global structure can be forced using simpler rules based on the colours of squares, regardless of orientation. Any physical system encoding these rules (geometrically or otherwise) will force the same strongly aperiodic monotilings. We provide simple examples.

cond-mat.other↗
arXiv2026

A Physics-Conditioned Neural Operator for Generalization of Atrioventricular Valve Mechanics across Pressure and Tissue Properties

Mitral and tricuspid regurgitation are the most common regurgitant valvular lesions, yet only a minority of severe cases undergo corrective surgery. Rapid assessment of valve mechanics could enable earlier, more precise intervention, but finite element (FE) analysis is slow to repeat across the many loading and tissue-property values of interest, which for a given valve are not known in advance. We introduce the Physics-Conditioned Neural Operator (PCNO), a transformer-based neural operator predicting leaflet displacement, strain, and stress fields conditioned on systolic blood pressure and tissue properties. PCNO is trained on, and evaluated against, FEBio simulations of functional and regurgitant mitral and tricuspid valves and of three mitral pathologies. With pressure and all material parameters simultaneously outside the training support, displacement error against FE reaches 4.48% and the mean errors of unsupervised geometric measures of valve function stay within 3.5%, indicating a conditioned solution operator over parameter space rather than an interpolator of the training set. Under this shift, PCNO is also more accurate than graph neural network and graph neural operator baselines trained on the same simulations, with the largest margins in stress.

cs.LG↗
arXiv2026

Bulk-edge sticking beyond the Perron mode in Gaussian softmax attention

We study row-softmax self-attention with independent Gaussian query and key weights in the proportional regime, at fixed inverse temperature. Hayase, Collins, and Karakida proved Gaussian equivalence for the empirical squared singular-value distribution after removal of the Perron direction. A global law alone does not exclude finitely many nonleading outliers. We prove that no such outliers persist: the rescaled squared singular value $\ell s_k(A)^2$ converges in probability to the upper edge of their bulk law for every fixed $k\ge 2$. In fact, this convergence is uniform over any deterministic sublinear number of leading non-Perron indices. The proof uses an exact decomposition of the softmax normalization, conditions on the key matrix, identifies the conditional covariance exactly with a diagonally conjugated inner-product kernel, linearizes that kernel in operator norm, and applies the outside-support local law of Fan, Ma, Paquette, and Wang. A separate stability argument identifies the finite conditional deformed Marchenko-Pastur edge with the limiting bulk edge. We also derive a scalar formula for that edge throughout the proportional regime and recover the explicit square-model formula of Hayase, Collins, and Karakida, including its physical branch.

math.PR↗
arXiv2026

Binding-Motivated Contextuality: A Cross-Domain Cyclic Test in Perception and Judgment

Psychophysics and decision research study perceptual binding and judgment contextuality apart. We argue both are scored against the same cyclic noncontextuality inequalities and share one convex global-consistency geometry -- not one cohomology class -- though only contextuality is tested, since binding's own residual vanishes here. Building on sheaf formulations of predictive coding (Seely 2025) and contextuality (Abramsky & Brandenburger 2011), a cyclic set of pairwise judgments admits a noncontextual explanation exactly when the cyclic (Suppes-Zanotti or n-cycle) inequalities hold, and its severity is measured by the complete contextual fraction CF (Abramsky, Barbosa & Mansfield 2017) rather than by the Cech invariant, which can miss it (Caru 2017). We build the perceptual arena from two binary judgments per cyclic-dominance pairing, scored against the same inequalities as the survey; an appendix rejects the one-bit alternative on construct-validity grounds. The central test is cross-domain: one cohort performs both arenas, and a shared latent tolerance predicts a positive correlation between their signed cyclic margins V*, the pre-clamp quantities behind CF. Both are inconsistency scores, so general response consistency confounds a bare correlation, and the prediction is therefore confound-residualized against a variance- and reliability-matched control. A positive result would support a shared residual association, not a common causal mechanism, which we prove this design cannot identify at any sample size. All three tests are designed but unrun, and the perceptual arena is a proposed instantiation with pilot gates -- a methodological proposal, not a confirmatory report.

q-bio.NC↗
arXiv2026

Object-Centric Conditioning for Visuomotor Flow Matching

Robot visuomotor policies are commonly formulated as autoregressive, diffusion-based, or more recently, flow matching models. Among them, Action-to-Action (A2A) flow matching improves inference efficiency by initializing generation from historical action priors rather than stochastic noise. However, stale historical motion patterns and entangled global visual representations can jointly reduce robustness under spatial out-of-distribution (OOD) shifts and visual distractors. In this work, we propose SlotFlow, an object-centric flow matching policy for robust visuomotor manipulation. SlotFlow decouples scene observations into semantic ("what") features and lightweight image-plane spatial ("where") cues to provide object-aware policy conditioning and current-state grounding. The semantic representation suppresses irrelevant background correlations, while the spatial cue improves adaptation to shifted object configurations. Extensive simulation and real-world experiments demonstrate improved robustness under visual distractors and severe spatial perturbations while preserving the low-step inference efficiency of A2A. Controlled initialization and perception ablations further identify object-centric grounding as a major source of the gains and show that it complements, rather than replaces, useful historical motion priors.

cs.RO↗
arXiv2026

ME-Brain-1.0: Memory, Cognition and Action for Evolving Embodied Intelligence

Current embodied systems largely rely on pretrained capabilities that remain fixed after deployment, limiting their ability to learn from physical interaction. We introduce MachEmbodied-Brain (ME-Brain), a self-evolving embodied system organized around a closed loop of action execution, experience acquisition, experience evolution, and improved execution. Evolvable Memory consolidates multimodal trajectories into hierarchical, reusable experience; Cognitive Core transforms physical experience into transferable skills; and the Action Model combines event-driven keyframes, EventCell local-world prediction, and action-conditioned memory modulation to focus computation on decision-critical moments, regions, and historical evidence. Together, these modules shift embodied intelligence from train-and-freeze to deploy-and-evolve without model retraining. Cognitive Core outperforms the strongest comparison models by 8.2 and 9.6 points on embodied and agent benchmarks. The Action Model achieves 47.88% mean success on RoboMME, a 3.26-point improvement over the strongest baseline. On RoboDojo, it reaches a 21.51 mean Score and 16.03% success rate, exceeding $π_{0.5}$ by 10.10 and 9.12 points. On the six-task ME-RealBench, ME-Brain achieves a 69.5 mean Score and 66.7% success rate, outperforming DM0.5 by 12.8 and 11.7 points, respectively.

cs.RO↗
arXiv2026

Statistical mechanics of multipartite entanglement in hypergraph states

We investigate multipartite entanglement in a particular family of pure $n$-qubit hypergraph states through a statistical-mechanics framework, where the average bipartite purity maps onto an effective Hamiltonian of $2^n$ classical binary spins. In this correspondence, each hypergraph state uniquely corresponds to a classical spin configuration, while temperature serves as a control parameter that continuously interpolates between a uniform ensemble of random hypergraph states at high temperature and maximally multipartite entangled states (MMES) at zero temperature. Remarkably, the exponential of the zero-temperature entropy directly gives the number of MMES within the set of hypergraph states. For small system sizes ($n \leq 5$), we perform an exact enumeration, fully characterizing the energy landscape and associated thermodynamic observables, and validating known MMES counts. For larger systems ($n = 6$ and $7$), where exact methods become computationally infeasible, we employ simulated annealing and parallel tempering algorithms to efficiently sample the exponentially large state space. Our analysis yields quantitative predictions of the number of MMES and reveals how entanglement is statistically distributed across the sets of hypergraph states. These results establish hypergraph states as an ideal platform for investigating multipartite entanglement through thermodynamic methods, offering both computational advances and physical insights into the structure of quantum entanglement in restricted families of quantum states.

quant-ph↗
arXiv2026

From Semantic Decisions to Feasible Trajectories: Self-Evolving LLM-Guided Optimal Control for Narrow-Space Parking

Autonomous parking in nonconvex and narrow environments remains challenging. Although optimal-control methods can explicitly enforce vehicle dynamics and collision constraints, nonconvexity compromises solver robustness and can cause failures. Large language models (LLMs) exhibit strong semantic reasoning capabilities, but directly generating dense trajectories makes it difficult to guarantee physical feasibility. We introduce SE-LLM-OCP, a unified framework in which LLMs make high-level discrete maneuver decisions, while an optimal-control module enforces low-level vehicle dynamics and collision constraints. Online, the LLM proposes sparse maneuver plans, decomposing the parking task into a sequence of short-horizon trajectory-optimization problems. A low-level solver then sequentially solves optimal-control problems. If the solver fails, the LLM aggregates failure evidence from the solver and validation stages to guide replanning. Offline, SE-LLM-OCP automatically evolves a structured decision-making knowledge base from scratch, driven by accumulated online failures. We validate our proposed framework in simulation on a car-like vehicle model and on a differential-drive robot. Our experimental results show that SE-LLM-OCP enables safer autonomous parking in narrow scenarios and demonstrates transfer of the same maneuver representation to a different kinematic platform.

cs.RO↗
arXiv2026

Superconducting qubit based on altermagnets

Altermagnets, characterized by vanishing net magnetization and momentum-dependent spin splitting, provide a promising platform for next-generation Josephson devices. Here, we exploit the Josephson effect in superconductor-altermagnet-superconductor junctions and show how to engineer prescribed current-phase relations by device design. Based on these programmable Josephson potentials utilizing altermagnetism, we propose a new class of superconducting qubits that combine large anharmonicity with enhanced robustness against decoherence via coherent two-Cooper-pair tunneling. We show that in the $2ϕ$-junction regime, this kind of qubit is intrinsically protected against both charge and flux noise due to parity protection. Magnetic flux can be used to precisely control the qubit and, under appropriate bias, this architecture further suppresses charge and flux noise. Our results establish altermagnets as a versatile platform for Josephson-potential engineering and open a new route toward high-performance superconducting qubits combining high coherence, large anharmonicity, and broad tunability.

quant-ph↗
arXiv2026

Anomalously enhanced lifetimes of low angular momentum Rydberg states in singly charged alkaline-earth metal ions

Trapped ions excited to high-lying electronic states, so-called Rydberg states, open new opportunities for quantum simulation and quantum computing. Generally, the fidelity of quantum coherent operations critically depends on the longevity of Rydberg states. However, scaling laws predict that the lifetimes of Rydberg states in singly charged alkaline-earth metal ions are 16 times shorter, compared to their neutral atom counterparts. Here, we show that this is not generally the case. We report an anomalous lifetime enhancement of certain low angular momentum ionic Rydberg series by factors larger than eight. The anomaly is present at both zero and finite temperature, although it is caused by different mechanisms. At zero temperature, the anomalously enhanced lifetimes are caused by accidental cancellations of the relevant dipole transition matrix elements, while at room temperature the anomaly originates from the enlarged energetic separation of ionic Rydberg levels with respect to neutral-atom levels.

physics.atom-ph↗
arXiv2026

The Copy Ceiling: An Input-Exposure Control for Ontology-Grounded Generation over Curated Corpora

We built a node that grounds a replaceable language model in a maintained ontology corpus, then asked what its successful-looking evaluation could support. Across ten models, grounding raised target-name recall from 0.265 unaided to about 0.92. A copy baseline, the recall a verbatim copy of the shown context already achieves, scores 0.964, and every model sits 0.022 to 0.067 below it. Copying therefore scores higher on this limited recall measure, which does not assess whether answers are better. The comparison tests what a recall score establishes; it does not test whether reasoning occurred, because a reasoned answer and a copy score alike when the answer name is already in context. We report exposure accounting (four counts classifying each gold item by whether the context exposed it and the answer recovered it) and a model-judged audit of 423 sampled item observations. A separate paired production study found a model-judged quality gain of +0.27 [+0.11, +0.45] on a 0-5 scale. Operational studies found failures that recall alone would not show: rephrasing questions out of the graph's vocabulary cut exposure from 0.964 to 0.328, yet the absence-keyed fallback would have fired on only 2 of 506; and inserting extracted facts degraded judged pages in every arm, so that step was disabled. Five-arm controls show that any well-formed on-corpus block beats no context but do not establish that the specific content matters, and no matched comparison against flat-text retrieval was run. The corpus is public and largely LLM-generated, which establishes neither training exposure nor novelty. Each study has its own outcome measure. Where gold derives from the injected corpus, we recommend reporting the accounting beside quality judgements, not in place of them.

cs.CL↗
arXiv2026

Improving the Loss Tolerance of Heralded Photonic GHZ States for Long-Distance Device-Independent Conference Key Agreement

Heralded multipartite entanglement distribution is a key requirement for device-independent conference key agreement (DI-CKA) over lossy quantum networks. Although locally equivalent in the absence of loss, different single-rail photon-number encodings of Greenberger--Horne--Zeilinger (GHZ) states respond differently to photon loss. Here, we investigate the critical detection efficiencies for detection-loophole-free parity--CHSH violations of computational-basis GHZ states---a coherent superposition of the vacuum and an $n$-photon component---and of fixed-photon-number GHZ states, deriving exact analytical conditions for both. We show that for states that are not permutation symmetric, such as the latter, the assignment of measurement roles to physical modes affects loss tolerance. We introduce a star-network protocol employing heterogeneous sources to directly herald the loss-tolerant vacuum-$n$-photon GHZ states while retaining the favourable long-distance scaling $O(η_{\text{c}}^{n/2})$, where $η_{\text{c}}$ is the channel transmittance. For four users, we characterize the heralded state under photon loss and show that tunable source parameters allow genuine multipartite entanglement to persist at any finite channel distance. With ideal Pauli and displacement-based measurements, our protocol achieves positive DI-CKA key rates at lower detection efficiencies than previous schemes, while retaining comparable or greater rates and communication distances at high efficiency. Overall, our work improves the loss tolerance of heralded photonic GHZ states for DI-CKA both by directly heralding a more loss-tolerant encoding and by optimizing existing schemes. These results identify photon-number encoding, source architecture, and measurement-role assignment as key design parameters for loss-resilient multipartite quantum networks, offering a practical route toward near-term DI-CKA.

quant-ph↗