Papers

It is well known that the set of Mahler measures of single variable polynomial has limit points of which a list established by D. Boyd and M. Mossinghoff has been extended through approaches based on genetic algorithms. In this paper, we wish to further extend the list of known limit points by adapting a method of missing data restoration.

The categorization of cognitive and resting states derived from electroencephalography (EEG) signals is crucial for comprehending fluctuations in brain activity linked to various mental states. EEG provides a non-intrusive approach for documenting brain function in both resting and task-oriented cognitive conditions, whilst deep learning techniques enable the automatic extraction of significant patterns from intricate EEG data. This study presents a deep learning framework to distinguish between resting and cognitive states through EEG records. The proposed framework integrates a Convolutional Neural Network (CNN) stacked with a Gated Recurrent Unit (GRU) for the extraction of features from EEG signals. Time-frequency analysis is conducted to explore the salient aspects of signals, and the derived features are then assessed utilizing conventional deep learning and machine learning classifiers, including the suggested 2D-Net architecture. The proposed approach and feature extraction strategy outperform the evaluated comparative methods, achieving accuracies of 83.177% for resting-versus-mathematical task classification, 76.107% for resting-versus-memory task classification, and 83.432% for resting-versus-music task classification. The findings illustrate the efficacy of integrating signal processing with deep learning methodologies to discriminate resting from cognitive states utilizing EEG signals.

We study best modular approximation in Musielak-Orlicz spaces. A geometric classification near the origin of Orlicz functions is introduced to isolate weighted $L^1$-like behavior. We establish existence results under minimal hypotheses and provide a variational characterization of minimizers via lateral derivatives. Finally, we establish uniqueness criteria, including a one-dimensional Haar-type theorem and characterizations in $0$- and $1$-spaces in higher dimensions.

We train neural networks on synthesized frames to approach the optimum Bayes estimator for dense emitter localization. The result justifies the future work on training neural networks to achieve high-throughput large-FOV super spatiotemporal resolution SMLM.

Neutral atom arrays have emerged as versatile platforms for performing both digital and analogue quantum computing and simulation, with demonstrations ranging from large-scale programmable Hamiltonians realising topological phases or weighted graph optimisation to error-corrected logical qubits with transverse gate operations. This paper provides a broad overview to the neutral atom platform, and the potential applications relevant to materials science and quantum chemistry.

Streaming target speaker extraction must maintain a representation of whom to extract while the target may fall silent, be masked by interference, or drift acoustically away from enrollment. Existing systems typically hold this state as a stored embedding updated by hand-designed rules. Across 22 configurations, including confidence-gated and oracle-activity-gated updates, we show that this family lies on a stability-plasticity frontier: even perfect target-activity information cannot combine robustness to target absence with adaptation to enrollment-mixture mismatch. We therefore meta-train speaker-state dynamics through the closed streaming loop, exposing the updater to its own contaminated evidence. Our proposed 41k-parameter anchored fast-weights (AFW) memory moves beyond the measured heuristic frontier, gaining 3.0 dB over the best heuristic under severe mismatch while staying within 0.9 dB of static enrollment after 30 s of absence, at under 5% runtime overhead. A gated recurrent unit (GRU) control confirms that the gain is not AFW-specific, while AFW is smaller and more interpretable: under severe mismatch, its write residual grows and aligns with the target rather than the interferer. Code is publicly available at https://github.com/ym2976/anchor-fast-weight.

Organizations often invest substantial effort in improving internal mechanisms such as processes, governance, and technology, yet realize only modest performance gains. This paper proposes a structural explanation for this pattern. We introduce the concept of internal externalities: unpriced cross-effects generated by internal organizational mechanisms that act simultaneously on multiple objectives. When these effects oppose one another, effort cancels internally, limiting attainable performance even without incentive misalignment or informational constraints. We formalize this mechanism by modeling internal mechanisms as primitives that exert signed effects across performance objectives. This structure gives rise to internal conflict, a measurable property that captures the fraction of organizational activity lost to cancellation. We show that conflict constitutes a form of structural inefficiency that constrains the returns to effort and renders allocative optimization ineffective unless addressed first. The framework implies a natural sequencing of interventions, in which structural cleanup precedes effort reallocation and optimization. The analysis yields testable predictions and governance implications for how organizations should scale, constrain, redesign, or deprioritize internal mechanisms.

Studying the dynamical behavior of a system often depends on characterizing how it transitions between long-lived states. Because such transitions are rare, observing them usually requires specialized enhanced sampling techniques. Transition Path Sampling (TPS) is a well-established method for generating reactive trajectories, which is simple to implement and does not require the definition of a preconceived reaction coordinate. However, its efficiency is limited by its sequential nature and the resulting correlations between sampled paths. Previous work addressed this limitation by combining TPS with a sampling scheme based on conditioned Boltzmann Generators, a generative machine learning model capable of sampling a given target probability distribution. This approach produces uncorrelated transition paths but relies on an accurate reaction coordinate, which is rarely known in advance. Building on recent advances in committor learning, specifically on the Artificial Intelligence for Molecular Mechanism Discovery (AIMMD) method, in this work we introduce GenAIMMD, an iterative algorithm that actively and self-consistently learns the ideal reaction coordinate (the committor) and trains a conditioned Boltzmann Generator to sample from arbitrary bias windows along it. GenAIMMD thereby provides a correlation-free and fully parallelizable path sampling scheme that does not require prior knowledge of the system's transition mechanism. We apply GenAIMMD to a two-dimensional toy model and a higher-dimensional polymer system. In both cases, GenAIMMD succeeds in training the Boltzmann Generator and learning the committor. Benchmark results show a substantial increase in performance compared to standard TPS.

We determine the order of the low moments of partial sums of random multiplicative functions associated with Euler products of bounded degree whose unitary local parameters satisfy a prime-square cancellation condition, thereby generalizing Harper's seminal work. The result applies to irreducible compact-group representations of unitary or symplectic type, including the higher-rank Sato–Tate model $SU(d)$ and the odd symmetric-power Sato–Tate model $\operatorname{Sym}^{m}SU(2)$.

We prove an $\varepsilon$-regularity theorem for $m$-varifolds with mean curvature in $L^p$, $p>m$, with respect to an anisotropic integrand satisfying a Michael-Simon inequality and the quadratic exposed condition: near sufficiently flat density-one points, such varifolds are representable as $C^{1,\alpha}$ graphs. Combined with the recent proof of the anisotropic Michael-Simon inequality, this establishes an anisotropic Allard regularity theorem in arbitrary codimension for a large class of anisotropic integrands, including those close to the area functional. We also exhibit the first examples of anisotropies satisfying both the uniform scalar atomic condition and the Michael-Simon inequality, that are not close to any ellipsoidal norm. These include the $\ell^q$ norms in every dimension and codimension, for explicit ranges of $q$, and a new class of axisymmetric anisotropies.

Let $F$ be a field of characteristic zero and consider $M_2(F),$ the algebra of $2\times 2$ matrices over $F,$ with canonical $\mathbb{Z}_2$-grading and endowed with transpose superinvolution. In this paper, we present the generators of the $T_2^*$-ideal of $*$-identities and of the $T_2^*$-subspace of central $*$-polynomials of $M_2(F).$ As a consequence, we determine the sequences of $*$-codimensions and $\langle n\rangle$-cocharacters of $M_2(F)$. In particular, we prove that the $n$-th $*$-codimension grows like $4^nn^{-1/2}$.

While multimodal large language models (MLLMs) enable a wide range of image-text reasoning tasks, recent incidents indicate that they are vulnerable to illicit deployment and unauthorized distillation. Existing solutions for model provenance are typically confounded by shared language backbones in MLLMs and struggle to detect violations of distillation. To bridge this gap and safeguard model ownership, we present the first study on multimodal model fingerprinting. Inspired by recent findings that self-attention acts as a low-pass filter and that its low-frequency components are informative, we develop AttnPrint for white-box provenance. Specifically, we extract cross-modal attention distributions and isolate their low-frequency components to serve as model fingerprints. To facilitate black-box auditing, we further introduce DistillTrace, which employs hypothesis testing of MLLM outputs to identify potential model infringement. We conduct extensive experiments on 154 model instances across 19 multimodal architectures. Notably, AttnPrint achieves strong derivative-model detection performance while remaining robust to five downstream modification techniques. DistillTrace also provides evidence of distillation relationships under three parameter-independent techniques.

The Page curve and the island formula describe a reorganization of quantum information in Hawking radiation across the Page time. We study how this reorganization appears in correlations among emissions collected at several retarded times. The late radiation is treated as a covariant multi-time process, or process tensor, and $\chi_{\mathrm{island}}=\mathcal{N}_{\varnothing}-\mathcal{N}_{R}$ measures the temporal memory removed when the early radiation register $R$ is supplied. Operationally, this quantity is the corresponding change in the optimal distinguishability of the radiation process from a Markovian reference. We exhibit evaporation processes whose single-bin states and all process marginals below a finite order $k_\ast\geq 3$ remain fixed and coincide with a CP-divisible reference, while $\chi_{\mathrm{island}}$ changes by order one at order $k_\ast$. The Page transition can therefore appear as a transition in the Markov order of the radiation process. When the interior mediates the late-time memory, entanglement-wedge reconstruction of the predictive interior from $R$ Markovianizes the late process; conversely, when the late process has a minimal predictive memory and its future-affecting information is mediated by that memory, Markovianization by $R$ supplies a simulator of its influence. A Hayden–Preskill evaporation comb and an evaporating-JT calculation realize this mechanism. The late radiation retains temporal memory across the transition, while the early radiation becomes sufficient for predicting its future multi-time statistics.

External skills provide domain knowledge and procedures without updating model parameters, but flat text makes their applicability, dependencies, and composition difficult to express. Existing skill graphs organize rules into nodes and relations mainly for retrieval and composition. They give less attention to what should change after a failure, which examples should be retested, and which edits should be reverted. We introduce GraphSkillAA, short for Graph-Skill Abductive Attribution, which connects rule use, error localization, and update validation through the same skill graph. Nodes record applicability, procedures, and exclusion conditions, while edges describe prerequisite and enhancement relations. The student records the nodes and edges used during execution. The teacher contrasts related successful and failed trajectories to identify the fields or relations that need repair, keeping changes as small as possible. Execution lapses or insufficient evidence leave the graph unchanged. A Local Gate retests affected examples, while a Big Gate checks the merged graph on the complete update pool. Rejected edits are rolled back, and model parameters remain frozen throughout. With GPT-5.6-sol, GraphSkillAA reaches 81.5%, 66.7%, and 91.2% on SearchQA, LiveMath, and DocVQA, respectively, and achieves the highest mean performance in every main setting. These results show that graph structure supports skill selection and composition while also providing explicit targets for repair, retesting, and rollback.

Accurate optimization of a supervised spectral objective need not produce an accurate population subspace or a better predictive representation. We investigate these distinctions for Online Kernel Supervised Principal Component Analysis (OKSPCA), which combines a centered cross-moment in finite random-feature coordinates with an Adam-style orthonormal basis update for an established objective. Fixed-map consistency, concentration and perturbation results describe the estimator and its exact subspace; same-target comparisons then assess the practical iterate separately. Across six predictive benchmarks, performance depends on the declared pipeline: replacing the tracker with the exact empirical target leaves the two regression deficits largely unchanged. Direct classification-rank models capture nearly all terminal objective energy on average, but a saved intermediate state exhibits substantial geometric deviation; a controlled sample-size study further separates empirical accuracy from population recovery. In distinct numerical-service workloads, exact on-request computation is faster in the tested classification settings, whereas Adam saves time relative to the tested full thin-SVD service for some dense wider-regression requests, alongside persistent geometric error. These diagnostics limit explanations based solely on terminal optimization accuracy and distinguish numerical cost from quality, rank coverage and freshness; they establish neither practical-tracker convergence nor predictive or deployment benefits from basis availability.

The dimension of a Galois hull is an important parameter in the construction of entanglement-assisted quantum error-correcting codes. In this paper, we study generalized Roth-Lempel (GRL) codes with prescribed Galois hull dimensions over finite fields of arbitrary characteristic. We develop a common construction method based on normalized Lagrange coefficients and suitable choices of column multipliers, and obtain six explicit constructions from multiplicative cosets, trace fibers, additive-subspace cosets, and mixed additive–multiplicative fibers. For extension sizes $s=2$ and $s=3$, we construct MDS and AMDS GRL codes with Galois hulls of specific dimensions. The resulting codes provide EAQECCs with explicit dimension, entanglement consumption, and relatively large minimum distance. Taking zero-dimensional hulls also gives Hermitian LCD GRL codes and the corresponding maximally entangled EAQECCs.

In the early stage of a pandemic, rapidly identifying a small number of infected individuals through large-scale screening is critical for pandemic control. Group testing has been widely used to improve testing efficiency and numerous studies have investigated the problem under noisy measurements, typically modeled as bit-flipping of test outcomes. However, these methods do not consider the constraints imposed by dilution, pool size, and the limit of detection (LOD), which can lead to false negatives when the viral load in a pool falls below the LOD. In addition, liquid dispensing errors, common in laboratory settings, affects diluted viral loads in a nonlinear manner. In this work, we introduce a novel measurement model that characterizes the process of sample pooling and dilution, incorporating LOD-induced binary quantization as well as liquid dispensing errors. For the case with known sparsity level, we propose a low-complexity decoding algorithm and provide theoretical guarantees for exact support recovery under both noiseless and noisy settings. For the case with unknown sparsity level, we develop a blind support recovery algorithm, along with a heuristic variant to enhance robustness, which can achieve exact support recovery with only O(klogn) measurements. Extensive simulations show that the proposed algorithms outperform existing combinatorial group testing algorithms, validating the effectiveness, efficiency and robustness in large-scale screening.

Numerical site-response predictions often deviate from observations, yet correcting these discrepancies is difficult because records are limited in both sensor coverage and number of events. This study proposes the Transfer-Enabled Forced Latent Autoencoder for Response Equations (FLARE-T) to improve these predictions by learning and calibrating low-dimensional latent dynamics that connect the base acceleration input to acceleration outputs at multiple depths. FLARE-T learns a low-dimensional response manifold and input-driven dynamics from dense finite-element simulations. It then trains a sparse encoder to map simulated sensor responses into the learned coordinates and uses limited records to calibrate the dynamics within them. A short response window initializes each prediction, while the complete base motion drives the response. The framework was evaluated using a layered-soil centrifuge test and the Lotung field vertical array. Test-set results show that FLARE-T improved multi-depth acceleration histories and 5%-damped pseudoacceleration response spectra relative to the original finite-element models, reducing errors at every evaluated sensor for motions of different intensities and, at Lotung, for both horizontal components. Two Lotung source models with different constitutive parameters achieved comparable test-set accuracy, indicating reduced dependence on precise prior calibration. FLARE-T therefore provides a data-efficient means of combining dense numerical response information with limited field records to improve future site-response predictions.

This paper studies resource-limited external influence in time-varying opinion networks when a controller must choose both a small set of agents and a scalar intervention at each update. We use the affine free response, which includes DeGroot and Friedkin–Johnsen dynamics, followed by a direct sparse action. Eliminating the scalar action reduces the one-step problem to a cardinality-constrained support objective whose global optimum is obtained from the largest or smallest residual components. Hence exact sparse one-step-ahead optimal control requires one sort and \(O(|\mathcal T|\log|\mathcal T|)\) operations, where \(\mathcal T\) is the support set. For periodic affine dynamics, the resulting state-dependent low-rank feedback admits cycle-based ultimate bounds and exact tracking of model-invariant targets. The DeGroot and Friedkin–Johnsen specializations expose the role of target invariance and the affine mismatch term. With several competing external players, each sparse best response retains the same sorting structure and the complete binary–continuous stage game is an exact potential game, so a pure-strategy equilibrium exists at every frozen state. Same-state welfare benchmarks separate loss due to scalar competition from the additional loss due to strategic support selection. Numerical examples validate exact support selection and illustrate switching-order effects, DeGroot/Friedkin–Johnsen tracking, resource tradeoffs, and competitive implementations.

The economic value of inference depends on how capacity and task information are distributed across stages of AI production. We study these organizational margins using controlled workflow experiments on externally verified software-engineering tasks. In two matched resource panels, direct execution records the same success rate of 59.6 percent at logical-token ceilings of 12,000 and 24,000, while success under information-constrained planning rises from 36.2 to 51.2 percent. The planning disadvantage narrows by 15.0 percentage points (95 percent task-cluster bootstrap interval: 4.2 to 25.8). A strict read-only planning campaign varies whether the planner sees the task issue. At 12,000 tokens, issue access raises success by about 16 percentage points over issue-hidden planning. Compared with direct execution, task-informed planning is about 10 points lower at 12,000 tokens; at 24,000 tokens, it shows a 29.6-point advantage. In the resource panels, direct execution uses substantially less than either ceiling, while the planning workflow's binding rate falls from 46.2 to 0.8 percent and downstream execution accounts for 89.9 percent of the increase in total use. Scale determines the capacity available to a system; workflow and information structure shape the productive value

The present high precision determination of $|V_{ud}|$ from superallowed beta decays of $J^P=0^+$, $T=1$ nuclei is largely built on top of the “standard” calculation of the isospin breaking correction $\delta_C$ to the Fermi matrix element, which assumes the splitting $\delta_C=\delta_{C1}+\delta_{C2}$, where $\delta_{C1}$ and $\delta_{C2}$ represent the “isospin mixing” correction and the “radial mismatch” correction, respectively. In this paper I show that this formalism violates the rule of nucleon basis independence, similar to the gauge invariance requirement in quantum field theory, therefore its outcome is inevitably subject to uncontrolled systematic errors. I further argue that the perturbative formalism is the only approach that allows the computation of $\delta_C$ at the precision level required for the test of the Cabibbo unitarity. Advancing from existing literature, I develop the full “generating function approach” to compute $\delta_C$ perturbatively, with connections to nuclear mass splittings and the isospin breaking in nuclear charge radii as theory benchmarks.

We show that there exists a set $S \subset \mathbb{Z}^2$ containing no four points on a circle or a line such that $|S \cap [n]^2| = \Omega(n)$ as $n \rightarrow \infty$. Since any no-four-on-a-circle set in $[n]^2$ has size $O(n)$, this resolves (up to a constant) a question raised by the current authors and Keevash concerning the density of extensible no-four-on-a-circle constructions. Our construction is based on weighted random sampling from the integer lattice followed by careful deletion.

Coding agents and evolutionary code-search systems can improve implementations once a target and evaluation criterion have been specified. Applying these methods to an existing software repository raises an earlier question: which implementation choices are worth investigating for a high-level engineering objective? We introduce optimization-opportunity discovery, the repository-level task of identifying candidate source regions, explaining how they relate to the objective, and proposing possible changes. The task takes as input a repository, an engineering objective, and optional runtime evidence such as offline telemetry observations or profiles. It does not require the user to specify a defect, bottleneck, or code location. We present Spotlights, a system that performs this task through logical repository mapping, successive agent reviews, and optional research linking candidates to relevant techniques. We evaluate Spotlights across model serving, document retrieval, blockchain ordering, and document processing. Across three cases, it recovers seven of nine expert-selected targets. In the reliability study, 70% of the top ten candidates meet the stated correctness and severity thresholds. Across five repeated retrieval runs, 73.6% of candidate occurrences have a matching source region in all five runs. Spotlights also rediscovers the target of a withheld retrieval optimization and connects it to a relevant tiling technique. In an implementation study, a discovered change reduces end-to-end page-processing runtime by 10.6% while preserving measured output quality. These results establish optimization-opportunity discovery as a distinct and empirically evaluable step between a broad engineering objective and subsequent implementation and validation.

We prove that for each $3\le k\le n-1$ a convex $C^2$ entire solution of $\sigma_k$ equation in $\mathbb{R}^n$ with positive constant right hand side is a quadratic polynomial, without a growth assumption on the solution itself.

We design and analyse a hybrid high-order (HHO) method for the linear elasticity problem with a linear slip interface, i.e.\ with interface conditions of spring type, in which the jump of the displacement across the interface is proportional to the traction through a compliancy tensor $\bK=\alpha\bI+(\beta-\alpha)\udl{n}\otimes\udl{n}$. The mesh is fitted to the interface, the discrete unknowns are polynomials of degree $k\ge 1$ on the mesh faces and of degree $k+1$ in the mesh cells, and general polytopal cells are allowed. The two novelties of the method lie in the local symmetric strain reconstruction, which incorporates the interface condition, and in the interface stabilisation, which is built from a regularised interface stiffness $\bS_h$ in the spirit of Hansbo and Hansbo \cite{HH04}. As a consequence, a single formulation covers the whole range of compliancies, from the perfectly bonded interface $\alpha=\beta=0$, where the interface stabilisation acts as a Nitsche-type penalty, to the traction-free interface obtained as $\alpha,\beta\to+\infty$, and no unknown is attached to the jump. We prove that the discrete bilinear form is coercive and that the errors converge as $h^{k+1}$ in the energy norm and as $h^{k+2}$ in the $L^2$ norm, with constants that are independent of the compliancy parameters and of the Lamé coefficient $\lambda$, so that the method is also locking free. Various numerical examples and comparisons are provided to confirm the theoretical results.

Robots searching for a target from a natural-language description must determine not only where to search, but also which observed candidate is the desired target. These decisions reflect two distinct sources of uncertainty - spatial uncertainty over candidate locations and semantic uncertainty over target identity - that are often conflated in VLM-based search systems. We introduce a spatial-semantic uncertainty formulation that maintains separate beliefs over each component and integrates probabilistic VLM evidence into a global target-identity posterior, including probability mass for undiscovered targets. This decomposition allows an information-theoretic planner to independently value candidate discovery and target disambiguation through spatial and semantic expected information gain (EIG), providing an explicit mechanism for trading broader exploration against earlier identification. We evaluate six VLM uncertainty-elicitation interfaces on 500 synthetic targets and show that similar recognition accuracy can conceal substantial differences in calibration and false confidence. In degraded-observation search-and-identify experiments, EIG-based planners reach confident decisions in 75.0%-92.5% of trials, compared with 20.0% for Random search, while different spatial-semantic weightings achieve comparable identification accuracy once confidence is attained. Increasing semantic emphasis reduces unnecessary exploration and VLM queries, demonstrating that explicitly planning over semantic uncertainty can accelerate target resolution without sacrificing decision quality. These results highlight the distinct roles of uncertainty representation and uncertainty-driven planning in embodied VLM systems.

We employ constrained hydrodynamic simulations of the Coma galaxy cluster from the ELUCID project to study its substructures and assembly history. Our simulations accurately reproduce the global properties of Coma, including its position, virial mass, radius, and surrounding large-scale filaments. Using a combined HBT+SKID method, we obtain a total intracluster light (ICL) fraction of $12.2\%-23.5\%$, consistent with recent observations. The mass-weighted ICL profiles of velocity dispersion, stellar age, and iron abundance generally agree with MaNGA measurements, and its clumpy east-west elongation is closely linked to the merger history of the two brightest cluster galaxies (BCGs). The simulation also successfully reproduces the north and west intracluster filaments (ICFs) detected by weak lensing, and the surrounding galaxy groups are distributed in alignment with the directions toward the nearby A2199 and A1367 clusters. The simulation further predict a complex cluster assembly history, with two major mergers at $z=0.74$ and $0.45$, and a pericentric passage of the two BCGs occurring $\sim 0.64 \ {\rm Gyr}$ before its current state. Our results demonstrate that constrained simulations are a powerful tool for connecting observed structures to the unobservable assembly histories of individual galaxy clusters.

Geospatial foundation models can provide strong flood-segmentation performance, but their size limits deployment on memory-constrained edge hardware. We distill a 300-million-parameter Prithvi-EO-2.0 teacher, fine-tuned on the 252 manually labeled Sen1Floods11 training scenes, into a 0.7-million-parameter EfficientViT-B0 student. The teacher supervises additional unlabeled Sentinel-2 imagery, allowing the student training set to grow without new manual annotations. At the matched budget of 252 scenes, teacher-supervised training is competitive with direct training and improves STURM-Flood performance across tested configurations; a geometry-matched control shows that label source alone does not explain the difference. Scaling the teacher-supervised pool to 2,500 scenes narrows the remaining student–teacher gap: the float student reaches 0.787 water intersection over union on the Sen1Floods11 test split against 0.822 for the teacher, matches the teacher on STURM-Flood under our evaluation protocol, and remains below it on WorldFloods-v2. After activation replacement and quantization-aware training, the student runs as a 1.5-megabyte 8-bit integer (INT8) TensorRT engine on a Jetson Xavier NX at 5.57 milliseconds of graphics processing unit (GPU) compute per 512-by-512 image, with approximately 14 megabytes of runtime device memory. A fixed modified normalized difference water index (MNDWI) threshold is competitive with both models on the two clean external benchmarks, so we interpret those benchmarks as generalization tests rather than as evidence of learned-model superiority over a spectral rule. The results support the conclusion: foundation-model supervision can amplify a fixed manual annotation budget into a substantially larger training set and yield a compact, deployable edge model.

In recent years, the inventory of interstellar molecules has rapidly grown, yet detections of complex species are confined to a few chemically rich sources, raising the question of whether such complexity is genuinely rare or shaped by observational biases. We present the Galactic Centre G+0.633-0.0604 molecular cloud, located in the southern part of the Sgr B2 complex, as a new and very promising laboratory for the discovery of new interstellar molecules. We analysed data from a high-sensitivity molecular line survey of G+0.633, covering nearly 100 GHz of aggregated bandwidth over the 31$-$275 GHz frequency range with the Yebes 40m, IRAM 30m and APEX radio telescopes. G+0.633 exhibits an exceptionally rich molecular feedstock comparable to that of the chemically rich G+0.693 cloud in the northern part of Sgr B2, establishing it as its 'astrochemical twin'. We report new robust interstellar detections of 15 astrochemically relevant species, most of prebiotic interest, previously identified only in G+0.693 or a very limited number of sources. These species include urea, $C$- and $N$-cyanomethanimine, ethanolamine, glycolamide, carbonic acid, and dimethyl sulphide. Our results reveal that the extraordinary molecular complexity observed in G+0.693 is not unique, but may instead reflect a natural outcome of shock-dominated chemistry in the Galactic Centre. The G+0.633 and G+0.693 clouds exhibit remarkably similar excitation conditions and comparable molecular abundances, establishing them as an ideal benchmarking pair for astrochemical studies. Moreover, G+0.633 offers a clear advantage for molecular observations over G+0.693 owing to the significantly narrower linewidths of its molecular line emission, nearly half as broad as those characteristic of G+0.693, making it an exceptionally powerful target for guiding the search for increasingly complex molecules in the ISM.

Validating variational quantum eigensolver (VQE) pipelines on realistic chemical systems is a critical stepping stone toward tackling classically intractable molecules. In this work, we report emulator-based validation of the VQE workflow proposed for the copper active site, executed on the LRZ Eviden Qaptiva emulator. A problem-tailored ADAPT-VQE with a full singles-doubles-triples (S+D+T) pool removes over 99% of the correlation error, reaching a stable plateau at 4.03 mEh relative to exact diagonalisation (148 selected operators). This establishes a >40x improvement over the hardware-efficient ansatz (HEA). Finally, we frame these emulator results as a robust baseline for upcoming physical quantum hardware runs on Euro-Q-Exa.