Papers

Reconfigurable intelligent surfaces (RISs) have emerged as a key enabler for next-generation wireless networks, offering control over the propagation environment through nearly passive reflecting elements. When combined with spatial modulation (SM), an RIS shapes a finite set of noise-free signal points at the receiver, and the error rate performance under maximum-likelihood (ML) detection is governed by the smallest pairwise Euclidean distance among these points. In this paper, we propose a low-complexity RIS phase shift design algorithm for RIS-assisted SM under practical discrete phase shift control. The proposed method targets the minimum Euclidean distance directly through a reduced greedy search over the discrete set of RIS phase shifts, in contrast to existing approaches that align RIS phase shifts to maximize the effective channel gain and therefore do not directly address the dominant error events. The search effort is controlled by a small set of integer parameters, providing a tunable trade-off between bit error rate (BER) performance and computational cost. We evaluate the proposed method against continuous and quantized phase-alignment baselines, including a complexity-matched comparison against the most directly comparable benchmark. Numerical results show that the proposed method achieves a significant SNR gain over quantized phase alignment under the same discrete hardware model, and this advantage persists under imperfect channel state information.

We study the last iterate of stochastic gradient descent (SGD) on streaming least squares with discretely distributed features (Slock's model), which decouples the dynamics across eigendirections. Under power-law source and capacity conditions, we derive the exact finite-time risk and asymptotic equivalents of constant and Warmup-Stable-Decay (WSD) schedules. With a tuned base learning-rate, the resulting scaling law decays as $\Theta(T^{-q})$, where $T$ is the horizon, and $q$ is independent of the cooldown length $c \in (0,1]$ but is strictly smaller for the constant schedule: any cooldown of fixed relative length $c > 0$, however short, improves the risk by a polynomial factor, while its length only affects the constant, which is minimized by linear decay ($c = 1$). Finally, we show that the optimal risk depends on the batch size $b$ and horizon $T$ only through $bT$, up to a critical batch size.

Vision-Language-Action (VLA) models are often pretrained via imitation learning, making reinforcement learning (RL) post-training important when deployment moves beyond demonstration coverage. Existing refinement paradigms expose a reliability–efficiency tension: model-free refinement avoids simulator bias but is interaction-intensive, whereas model-based refinement can exploit unreliable imagination even as its simulator adapts. We propose Model-Evolving Reinforcement Learning (MERL), a trust-calibrated framework that couples policy optimization with an online-updated simulator comprising a world model and a reward proxy head. Across stages, simulator reliability controls the imagined-data ratio and rollout horizon; within rollouts, chunk-level trust controls replay selection and optimization weight. For recursive imagination without exact grounded continuations, a residual predictor estimates trust without querying future ground truth. On perturbed LIBERO-PRO tasks, MERL reaches 79.7% average success, improves high-threshold learning speed by 10.9% over the matched model-free control, and outperforms same-protocol external baselines across three training seeds. Fixed-data adaptation from 50 demonstrations per task achieves 80.0% average success on two physical-robot tasks.

In parallel decoding, diffusion language models commit several tokens per forward pass, so co-committed tokens cannot see each other, breaking multi-token format units that parsers need. On ECHO, an open-weight one-step chest X-ray (CXR) report generator, 32.7-36.7% of evaluation reports lack a parseable Impression heading and score as empty. We propose intent-triggered anchoring, a training-free decoding rule that completes a format unit once the model commits its first token, inserting only units with a unique, content-free completion; fallbacks write the unit when the model stops or loops without starting it. On three CXR evaluation sets, the rule raises readable rates from 63.3-67.3% to 100.0% with no regressions and a 95th-percentile latency ratio of 0.68-1.28 against official decoding. Broken headings state findings absent from the reference; adding the heading at the end leaves them in 15.5-31.0% of reports, our rule in at most 0.6%. For math answer markers, the rule raises accuracy in the most parallel setting of five diffusion language models by 5.8-20.8 points on GSM8K and 5.1-17.1 on GSM-Symbolic, held out from tuning. With lenient answer extraction, gains are 3.3-12.5 and 2.7-6.3 points; the rule adds 1.4-8.6 points over a stop-only fallback for four of the five models.

The Spin Physics Detector (SPD) experiment at the NICA collider of the Joint Institute for Nuclear Research (JINR) aims to study the spin structure of the nucleon and spin-related phenomena. The experimental conditions, including the high interaction rate and the large number of readout channels, require a triggerless data acquisition system with high throughput and a scalable architecture. This work presents a hardware implementation of the readout chain that extends the previously proposed SPD DAQ architecture. The chain is based on two levels of concentrators. The L1 concentrator provides the interface between the front-end electronics and the next system level and distributes synchronous signals. The L2 concentrator aggregates data streams from several L1 concentrators before transmitting them to the computing system. A key feature of the L2 implementation is the offloading of data reception, buffering, and aggregation from the host CPU to the FPGA, motivated by the large number of small packets generated by the readout electronics. The developed hardware platforms and their operating logic are presented, together with experimental results for the main interfaces and data-path components. The obtained results demonstrate the feasibility of the proposed hardware architecture and its application in a scalable SPD data acquisition system.

Grid diagrams encode knots and links combinatorially through an (n,n) winding matrix W(G). A fundamental invariant of the grid diagram is its genus g(G), which records essential topological information about the underlying knot. We give an algebraic algorithm that computes g(G) directly from W(G). The method repurposes the Hungarian algorithm ,after a column normalization that makes the matrix non-negative, it applies row-column reductions and minimum-vertex-cover corrections until the zero entries admit a perfect matching, equivalently until the minimum marking number equals n. By Konig's theorem the resulting permutation defines a distinguished grid state, and g(G) is then read from this matrix via the classical grid homology formula (Ozsvath-Stipsicz-Szabo). The novelty of this paper is the algorithm and its strongly polynomial analysis; the underlying invariant is known grid-homology theory. We illustrate the method on the trefoil and additional examples, and discuss extensions to (m,n) matrices and grid-move navigation toward the knot genus g(K).

The ability to dynamically control topological order remains a central challenge in the exploration of quantum materials. Here, we investigate the lattice and electronic response of the topological crystalline insulator (TCI) Pb$_{1-x}$Sn$_x$Se to ultrafast optical excitation using time- and angle-resolved photoemission spectroscopy (tr-ARPES) in combination with X-ray diffraction (XRD) and first-principles calculations. Static XRD measurements establish the lattice constant as the key control parameter for the topological transition, with a critical value $a_\mathrm{c}=6.073$ Åseparating the normal-insulator and topological phases. Despite generating electronic temperatures far above the topological-to-normal transition temperature $T_\mathrm{c}$, optical excitation in the TCI phase does not induce a phase transition. Instead, it drives an ultrafast lattice contraction of $\Delta a \approx -0.45$ pm within less than 1 ps that counteracts thermal expansion and prevents the system from reaching $a_\mathrm{c}$. The optical excitation therefore pushes the system deeper into the topological phase, providing a direct explanation for the absence of an optically driven transition. Total-energy calculations reveal that this behavior originates from the band inversion in the topological regime, which reverses the character of the photoinduced charge transfer and transiently strengthens atomic bonding. These findings identify band inversion as a mechanism that fundamentally alters the nonequilibrium lattice response, with general implications for ultrafast optical control of topological materials.

Since ancient Greek times, geometry has been a method by which humans can make inferences, by the use of similar triangles, about the world far beyond their immediate senses. Similarity plays an equally important role in quantum measurement, except that instead of triangles, the similarity is between the infinitesimal generators of rotation, canonical transformation, or some other virtual symmetry. For many quantum optical measurements of a single mode, these generators produce Kraus operators that are contained within a twelve-dimensional Lie group: the Instrumental Weyl-Heisenberg group manifold ($\mathrm{IWH}^{\textbf{12}}$). In particular, $\mathrm{IWH}^{\textbf{12}}$ is general enough to include all diffusively generated 'dyne measurements. In this paper, $\mathrm{IWH}^{\textbf{12}}$ will be used to develop two more general classes of 'dyne measurement: one that interpolates between diffusive homodyne and diffusive heterodyne (“slomodyne”) and one that adds to 'dyne measurements adaptive squeezing and displacement. Our analysis uses an approach known as the Instrument Manifold Program (IMP). In particular, a Harish-Chandra-like decomposition of $\mathrm{IWH}^{\textbf{12}}$ is used to calculate the vielbein transformation from a right-invariant basis to the corresponding coordinate basis, allowing us to universally and autonomously navigate $\mathrm{IWH}^{\textbf{12}}$ and locate the Kraus-operator of whatever selective process is being considered as it evolves in time according to the measurement record.

Pattern mining is a valuable tool for exploratory data analysis, but identifying relevant patterns for a specific user is challenging. Various interestingness mea- sures have been developed to evaluate patterns, but they may not efficiently estimate user-specific functions. Learning user-specific functions by ranking patterns has been proposed, but this requires significant time and training samples. In this paper, we present a solution that formulates the problem of learning pattern ranking functions as a multicriteria decision making problem. Our approach uses Analytic Hierarchy Process (AHP) to elicit weights for different interestingness measures based on user preference. We also propose an active learning mode with a sensitivity-based heuristic to minimize user ranking queries while still providing high-quality results. Experiments show that our approach significantly reduces running time and returns precise pattern ranking while being robust to user error, compared to state-of-the-art approaches.

This is preliminary, AI-generated note on the Dudley-type bound for stationary Bernoulli processes postulated by M. Talagrand based on the unpublished notes of the authors and the recent note \cite{invariant} which in turn is an alternative proof of the result by Hu, Wang, Wu.

Excitation of carbon and oxygen ions is the primary mechanism by which collapsing gas clouds dissipate heat to form new stars. At early cosmic times, in galaxies with chemically pristine gas, many stars are expected to have masses far larger than the mass of our sun due to the deficit in these elements. We searched for ultra-metal-poor galaxies using their spectroscopic absorption signatures in front of bright background quasars, employing the new GHOST high-resolution spectrograph. Here we report the discovery of the first galaxy containing a reservoir of neutral hydrogen gas with metallicity below the ultra-metal-poor threshold: with a measured carbon-to-hydrogen ratio 11,000 times lower than the Sun, it is the most pristine ever found by a factor of four. UMP-DLA-1 is the only known galaxy with measured carbon and oxygen abundances too low to enable efficient formation of stars with solar mass or below. The low metallicity alone therefore guarantees a top-heavy stellar population, providing a direct view of the chemical composition imprinted by massive low-metallicity stars that perished long before the present day: an elevated oxygen-to-carbon ratio. The abundance pattern of UMP-DLA-1 is likely a close representation of the atomic yields of first- or early second-generation stars.

We study the entanglement generated by Newtonian self-gravity in a two-particle system of mixed neutrinos and quantify it by means of the concurrence. Starting from the gravitational coupling between the mass operators, we show that the two-particle Hamiltonian splits into local single-particle terms and an effective Ising interaction in the mass basis, the latter being solely responsible for the generation of correlations. For initially separable flavor states the concurrence is obtained in closed analytic form: it oscillates between zero and a maximum fixed by the mixing angle alone, while the gravitational coupling sets the recurrence time. We further establish a one-to-one correspondence between the concurrence and the reduced-state purity previously derived for this model, thus providing an independent quantum-information description of the same gravitationally induced correlations. Finally, we show that the concurrence does not depend on the Majorana phase, so that Dirac and Majorana parametrizations yield identical entanglement dynamics. These results isolate the genuinely entangling sector of the gravitational evolution and provide a compact analytic characterization of gravity-induced quantum correlations in mixed neutrino systems.

Unconventional superconductivity in correlated systems often appears in the vicinity of a magnetically ordered state. This situation is also relevant for altermagnets, characterized by a nonrelativistic spin-split electronic structure in the presence of Néel order. Many proposed altermagnetic candidates, however, never cross the magnetic instability. We study superconductivity arising from altermagnetic fluctuations in such systems and show that the sublattice polarization (SLP) of the normal-state bands plays a pivotal role in determining the superconducting state. SLP, an inherent property of altermagnetic band structures that persists even without magnetic order, prevents Cooper pairs from forming between different sublattices. This suppresses pairing mediated by the nearest-neighbor antiferromagnetic exchange, which favors spin-singlet superconductivity, and leaves longer-range same-sublattice bonds dominant. When the next-nearest-neighbor exchange is ferromagnetic, as expected for frustration-free Néel order, this results in spin-triplet superconductivity. This mechanism is fundamentally different from that in altermagnets with long-range Néel order, where the spin-split Fermi surfaces favor equal-spin pairing. Finally, when longer-range interactions in the disordered phase instead favor singlet pairing, SLP leads to singlet states with characteristic properties distinct from nearest-neighbor pairing states.

Exact reversible locally adaptive step sizes are introduced by Bou-Rabee et al. (2026) in the context of the No-U-Turn Hamiltonian Monte Carlo (HMC) sampler for the purpose of high performance HMC sampling in challenging target distributions. This paper carefully explains and illustrates the locally adaptive step size procedure under more general assumptions. Alternative error measures are introduced with the aim of further enhancing MCMC performance by reducing the prevalence of reversibility failure rejections. In addition, the paper shows how to introduce the locally adaptive step sizes also within standard HMC and Metropolis-corrected kinetic Langevin/generalized HMC (GHMC). Finally, a numerical study of the relative merits of the proposed error measures in the context of different Hamiltonian flow-based MCMC methods is provided.

We consider Hecke modules of orthogonal modular forms attached to definite even ternary lattices of half-discriminant $N^2$, where $N > 1$ is odd and square-free. We prove explicit Jacquet-Langlands style correspondences with spaces of classical modular forms (in the spirit of Birch and Hein-Tornaria-Voight). This is done by applying sequences of Watson-style transformations that reduce the discriminant while preserving the adelic orthogonal group.

Developing reliable predictive models for multi-physics systems often forces a compromise between computationally demanding physical simulators and data-hungry, opaque machine learning (ML) algorithms. While incorporating dimensional analysis into directed computation graphs offers a structurally sound alternative to explicitly solving partial differential equations (PDEs), such formulations typically yield underdetermined systems that act as imperfect simulators. We introduce pi-Net, a physics-informed latent variable model that resolves these imperfect simulators. The hybrid pi-Net architecture consists of an encoder that maps inputs into physically normalized latent space, which are then decoded into final predictions by a differentiable physics head. Evaluated on a real-world, data-scarce Gas Metal Arc Welding (GMAW) case study, the framework achieves an R2 of 0.864 with only 60 experimental samples. The results demonstrate that pi-Net significantly outperforms purely data-driven baselines in data-scarce regimes while providing causal, process-level explainability.

We propose a heteroskedasticity-robust and dimention-adaptive test for multiple linear restric- tions in sparse high-dimensional linear regression models. It combines desparsified LASSO estimation with a ridge-regularized quadratic form statistic and critical values that adapt to the restriction dimension. Under stated regularity conditions, our approach is asymptotically valid under a fixed or diverging number of restrictions without specifying the asymptotic regime in advance. Our random-design theory allows independent non-identically distributed covari- ate rows with marginal sub-Weibull tails and heteroskedastic errors satisfying finite polynomial moments. Monte Carlo simulations demonstrate improved finite-sample size control relative to conventional Wald tests, particularly as the number of restrictions increases.

Discovering and disambiguating entities from multimodal and heterogeneous data is a key challenge in discovery science, where relevant knowledge is often implicit and distributed across modalities. We present KARAMEL, a framework for multimodal entity linking (MEL) - the task of aligning visual and textual mentions to entities in a knowledge base - in the cultural heritage domain. Unlike prior vision-language models that primarily rely on surface-level multimodal alignment, our approach incorporates sociohistorical and contextual knowledge through a knowledge-aware architecture that fuses a vision-language encoder with a heterogeneous graph neural network. This design enables contextual reasoning over complex relational structures and supports robust entity disambiguation under ambiguous or underspecified evidence. To benchmark multimodal discovery in this setting, we introduce WikiMuSA (Wikidata-based Multimodal Semantic data for Art), a new dataset that links artworks to Wikidata entities via images, textual descriptions, and structured contextual knowledge. Experimental results show that KARAMEL surpasses strong baselines, particularly on implicit or abstract mentions, while ablation studies highlight the critical role of domain-specific, structured context in learning expressive representations. While instantiated in the cultural heritage domain, KARAMEL addresses a general knowledge discovery problem and applies to other scientific settings involving multimodal observations and heterogeneous background knowledge. Both the dataset and source code are made publicly available.

Terrestrial network (TN) failures during disasters can overload surviving base stations (BSs) and disrupt emergency services. A non-terrestrial network (NTN) provides fallback, but its feeder link can become a bottleneck as users migrate. This paper studies post-disaster network resilience through service-priority-aware orchestration of constrained NTN feeder capacity in a post-failure snapshot. A lightweight Cross-Entropy Method (CEM) tunes feeder, offload, and user-ranking parameters offline, not as an online artificial intelligence (AI) controller. A Python system-level simulator sweeps operating regions under abstract TN-NTN link and queueing models. Gains depend on failure severity. At a 180-Mbps feeder under total TN outage, the proposed policy increases the absolute emergency-weighted continuity metric Cemg from 0.399 to 0.666 relative to the matched rule baseline with uniform feeder scaling (paired gain: 0.267; 95% bootstrap CI: [0.264, 0.271]); mild damage can reduce aggregate continuity. Offline CEM feeder-weight tuning further improves severe-failure continuity over fixed service priorities, whereas tuned offload and user ranking provide no detectable incremental gain.

Image-space reward requires decoding and a separate judge; unified visual generators can instead reuse their understanding pathway for decode-free, self-supplied reward. Optimizing against this verifier closes the self-reward loop; shared trainable weights let one update move generation and scoring even with the reward gradient stopped. We call the resulting failure self-verifier capture: self-reward rises while independently measured quality falls. Matched semantic/denoising by shared/frozen cells on Scale-RAE isolate two routes: the policy exploits on-manifold blind spots of a frozen semantic judge, while shared updates additionally rewrite the judge. A frozen judge also becomes stale, and repeated self-refresh yields progressively weaker recoveries. The diagnosis yields a two-part repair: locking the warmed reward read blocks rewriting, while sparse, parameter-disjoint external anchors counter residual exploitation. Unanchored rollouts retain semantic reward across multiple latent noise levels, providing dense latent reward that terminal image-space judging cannot supply, while a drift-triggered controller allocates anchors to high-drift rollouts and propagates their calibration within each group. At matched budgets, the controller improves on fixed-dose anchoring, increasingly so as coverage tightens. Both the unanchored failure and the repair transfer to the higher-performing, architecturally distinct Show-o2. Across both bases, the complete method significantly outperforms a construct-matched every-rollout judge on GenEval and DPG-Bench while externally scoring only 1/16 of rollouts. At 1/32 coverage, it scores higher in all four comparisons and remains jointly non-inferior.

One main aim of our paper is to formulate noncommutative versions of the Lebesgue dominated convergence theorem in the setting of quantum integration theory on von Neumann algebras. Our starting point is a reformulation of classical dominated convergence in terms of weak* convergence. Using our recent sequential-continuity theorem, we obtain dominated convergence formulations for sequentially normal states and, under domination by a fixed bounded integrable majorant, for sequentially normal weights. Integrable, possibly unbounded, majorants are treated first in the tracial setting, then for arbitrary von Neumann algebras using Haagerup's L1 space, and finally using normal semifinite weights and their GNS representations. For any faithful normal semifinite weight $\phi$, weak* convergence of norm-bounded sequences is characterized by `integrating against' bounded positive integrable majorants. We also study noncommutative almost uniform and local almost uniform convergence. In particular, for norm-bounded sequences, local $\phi$-bilaterally almost uniform convergence implies weak* convergence and L1 convergence to 0 of $h^{1/2}(x_n-x)h^{1/2}$ for every positive Haagerup L1 density h, without assuming sigma-finiteness. We also prove a dominated convergence theorem in the predual: fixed positive order domination and Petz's almost uniform convergence imply convergence in the predual norm. We establish implications and equivalences among these convergence notions, connecting dominated convergence with tracial and nontracial integration.

Generative Social Simulation (GSS) leverages Large Language Models (LLMs) to create sophisticated personas that define agents with demographics, emotions, and political opinions. While prior work shows that personas compress outputs into stereotypical caricatures, there is no comprehensive study of how these caricatures evolve into collective artifacts when they interact. Using a Twitter-like GSS platform with personas derived from the American National Elections Study (ANES), we ablate three layers of partisan identity: affective polarization markers, party identification, and vote choice, while retaining demographics, ideological positioning and important issues. We find that collective outcomes depend heavily on how survey responses are translated into personas. Removing a few explicitly partisan statements moves the network from near-complete segregation to cross-party ties approaching those of real Twitter networks. We argue that matching one outcome is not evidence for behavioral validity and point to salience as a possible explanation. Surveys ask for a position on every question regardless of its importance to the respondent, and persona construction turns each answer into a direct behavioral instruction. We conclude with a checklist for more comprehensive evaluation of personas in future works.

In the context of graph reconstruction studies, this paper addresses the problem defined as follows: given a sample of vertex-coloured graphs, each associated with a number, does there exist a connected graph containing exactly the given number of induced subgraphs isomorphic to each graph in the sample, such that every edge of the solution graph is included in at least one of these subgraphs. This paper first shows that this problem is $\Sigma$______-complete. The associated optimisation problem is to determine the minimum number of vertices in a solution graph, if one exists. For instances consisting of two paths, we prove NP-completeness in general and give a polynomial-time dynamic programming algorithm when one path is monochromatic.

Recent measurements from DESI baryon acoustic oscillations (BAO) have reported a moderate preference for dynamical dark energy, challenging the standard $\Lambda$CDM paradigm. Nonetheless, such a trend could reflect a tension between the shape and the offset of the Hubble diagrams predicted by current BAO and Type Ia supernovae (SN) data, which may underpin a possible breakdown of the cosmic distance duality relation (CDDR) linking luminosity distances $D_{\rm L}$ and angular-diameter distances $D_{\rm A}$. We explore this possibility by parametrizing deviations from this relation as $\eta(z) \equiv D_{\rm L} / [{(1+z)}^2 D_{\rm A}] = \alpha{(1+z)}^\varepsilon$, and investigate how the preference for a Chevallier-Polarski-Linder (CPL) dynamical dark energy is modified once $\varepsilon \!\neq\! 0$ is allowed. Using DESI DR2 and uncalibrated SN data (Pantheon$+$, DES-Dovekie, Union3, and Union3.1), we find that allowing $\varepsilon$ to vary freely in both $\Lambda$CDM and CPL reduces the CPL preference with respect to $\Lambda$CDM by a larger amount than the addition of spatial curvature $\Omega_k$; only Union3.1 exhibits comparable reductions. We also find that the preference reduction is robust to alternative $\eta(z)$ parametrizations, and that the $\eta(z)$ constraints remain stable under the removal of BAO tracers or low-redshift cutoffs for Pantheon$+$, whereas the DES-Dovekie preference largely disappears once $z < 0.1$ SN are removed. In a separate calibrated analysis, illustrative Planck sound-horizon and SH0ES absolute-magnitude priors give $\alpha \simeq 0.942 \pm 0.014$, quantifying the normalization mismatch under those assumptions. We also map the CDDR violation onto photon-loss and varying-$G$ scenarios, concluding that the cosmological constraints are much weaker than existing constraints on these physical mechanisms.

This paper investigates the geometric detection of latent dynamic transitions (where the latent space is defined as a finite-dimensional state space reconstructed via a delay-embedding Hankel matrix) in mutually coupled phase-locked loops (PLLs) exhibiting on-off intermittent chaos. We propose a data-driven approach to identify the transition of the effective dimension in latent dynamics as a precursor to physical bursting events. By applying Singular Value Decomposition (SVD) to a Hankel matrix constructed from high-resolution oversampled data, we extract the effective dimension that reflects the dynamical shift of intrinsic variables - from a synchronized two-dimensional manifold to a higher-dimensional chaotic state - prior to the actual burst. This geometric indicator enables a proactive, event-driven intervention using Pyragas-type delayed feedback control, which is activated only when the detected dimension exceeds a critical threshold. Simulation results demonstrate that this geometric precursor effectively compensates for control latencies and substantially reduces accumulated control energy compared to conventional continuous feedback. The findings establish a methodological strategy for stabilizing infinite-dimensional delayed systems by exploiting early warning signals embedded in dimensional transitions of latent dynamics.

The Shannon-Rényi (SR) entropy characterizes the probability distribution of many-body wave functions in a chosen basis and is directly accessible from single-shot measurement snapshots in cold-atom experiments, yet its theoretical evaluation in interacting systems carries exponential cost. Here we construct a field-theoretic spacetime manifold for the SR entropy in which $q$ replicas are glued at the imaginary-time boundaries, recasting it as a ratio of generalized partition functions amenable to large-scale quantum Monte Carlo simulation. On this basis we develop a reweight-annealing framework with two complementary strategies: a virtual-parameter scheme interpolating between unglued and fully glued limits via binomial-weighted partial gluing, and a real-parameter scheme using a physical coupling constant as the annealing variable within stochastic series expansion. Both reduce the computational cost from exponential to polynomial. Most importantly, we establish for the first time a finite-size scaling theory for the SR entropy near a quantum critical point, $S_q=a(g)L^2+S_q^0\left((g-g_c)L^{1/\nu}\right)$; data collapse of its first derivative yields the correlation-length exponent $\nu$ for both the O(3) and Ising universality classes, realized in the spin-$\frac{1}{2}$ columnar dimerized Heisenberg model and the bilayer Heisenberg-Ising model. The same simulations extract the Goldstone-mode count $N_G=2$ and the $Z_2$ ground-state degeneracy $\ln 2$ from subleading terms. These results elevate the SR entropy to a standalone, order-parameter-free diagnostic of quantum criticality with the same scaling status as the entanglement entropy, and close the loop between theory and quantum simulation by enabling quantitative benchmarking of experimental snapshots from state-of-the-art quantum simulators.

Bell's theorem is popularly stated as the inconsistency of quantum theory with local realism. Realism is here formalized by the ontological models framework, where elements of reality are points of a measurable space and probabilities obey the Kolmogorov axioms. In the Bell scenario, locally causal ontological models posit a common cause supporting a global valuation, a joint assignment of outcomes to all measurements at once, across incompatible contexts. Within this notion of realism, Bell's theorem makes any realist explanation of the quantum predictions conspiratorial: any mechanism, whether superluminal, superdeterministic, or retrocausal, must be finely tuned so as never to manifest operationally. We redefine realism through a new ontological framework that generalizes the standard one. The elements of reality, which we call records, are no longer points but relational parts of a point-free generalization of a topological space (sublocales of a locale). A record shared by two incompatible contexts establishes the sameness of a measurement across them, without such pairwise identities composing into a global valuation, and the common cause is then a web of such records. Within this framework, Bell's no-go theorem becomes a go theorem: local causality, restated for records, is no longer at odds with the quantum statistics. This is possible because modularity, the inclusion-exclusion law of classical probability, fails across incompatible contexts, so that the probability theory generalizes Kolmogorov's. We exhibit explicit models reproducing several quantum strategies, including the optimal CHSH violation. More broadly, locally causal models of this kind attain every Bell-CHSH value up to the algebraic maximum. A realist explanation of the quantum predictions need not be conspiratorial; every causal influence posited by these models is reflected in the operational predictions.

We prove that the restarted Arnoldi algorithm for real symmetric matrices with restart length $s=2$ has a cyclic limiting behavior. In the terminology established in (arXiv:2209.14579), this is a proof of the ACI($s$) conjecture for $A=A^T\in \mathbb{R}^{n\times n}$ and $s=2$. As explained in (arXiv:2209.14579), this also proves the Forsythe conjecture (Numerische Mathematik, 11 (1968), pp. 57-76) about the limiting behavior of the conjugate gradient method and positive definite $A=A^T\in\mathbb{R}^{n\times n}$ for $s=2$. The proof we give is an extensively rewritten and simplified version of a proof found using Codex with GPT-5.6 Sol. At the end of this paper, we discuss its origin and evolution, as well as related recent developments around the Forsythe conjecture. Our motivation is to present a proof that is instructive and transparent, so that it can enhance the knowledge of interested human readers.

Improving an agent through successive revisions requires balancing exploration and evaluation under a limited budget. A narrow search can miss useful sequences of edits, while fully evaluating every intermediate version can exhaust the budget before those sequences yield a verified improvement. We introduce Speculative Recursive Self-Improvement (SpecRSI), which drafts executable successor agents before their predecessors are fully evaluated, while requiring complete verification before adoption. Verification-Aware Tree Search (VATS) allocates the budget between further edits and outstanding checks using the predicted verified return of a continuation. Group Verification Optimization (GVO) learns the improver from completed searches while keeping the real evaluator fixed. In the main scientific comparison, terminal gains exceed Janus by 33.3%–40.0%. Additional evaluations show that SpecRSI outperforms Janus in all 50 scientific backbone–task pairs and exceeds MetaRSI-v1 by 1.85%–2.38% in macro-average system score across twenty backbones. Coding-validation success reaches 69.4% versus HGM's 64.3% at a 20.8% lower target-cost index.

The contention is that the current batch of Large Language Models don't *understand* language, but they *do* it. Rather than LLMs forming some kind of “distributed representation” of symbols, the claim is that LLMs are capturing “Cultural Intelligence” and grounding symbols in what the sociologists call practices.