Physical transport processes organize through local interactions that redistribute imbalance while preserving conservation. Classical solvers enforce this organization by applying fixed discrete operators on rigid grids. We introduce the Hebbian Physics Network (HPN), a computational framework that replaces this rigid scaffolding with a plastic transport geometry. An HPN is a coupled dynamical system of physical states on nodes and constitutive weights on edges in a graph. Residuals--local violations of continuity, momentum balance, or energy conservation--act as thermodynamic forces that drive the joint evolution of both the state and the operator (i.e. the adaptive weights). The weights adapt through a three-factor Hebbian rule, which we prove constitutes a strictly local gradient descent on the residual energy. This mechanism ensures thermodynamic stability: near equilibrium, the learned operator naturally converges to a symmetric, positive-definite form, rigorously reproducing Onsagerś reciprocal relations without explicit enforcement. Far from equilibrium, the system undergoes a self-organizing search for a transport topology that restores global coercivity. Unlike optimization-based approaches that impose physics through global loss functions, HPNs embed conservation intrinsically: transport is restored locally by the evolving operator itself, without a global Poisson solve or backpropagated objective. We demonstrate the framework on scalar diffusion and incompressible lid-driven cavity flow, showing that physically consistent transport geometries and flow structures emerge from random initial conditions solely through residual-driven local adaptation. HPNs thus reframe computation not as the solution of a fixed equation, but as a thermodynamic relaxation process where the constitutive geometry and physical state co-evolve.

Code generation is one of the most active areas of application of Large Language Models (LLMs). While LLMs lower barriers to writing code and accelerate development process, the overall quality of generated programs depends on the quality of given prompts. Specifically, functionality and quality of generated code can be sensitive to user's background and familiarity with software development. It is therefore important to quantify LLM's sensitivity to variations in the input. To this end we propose an evaluation pipeline for LLM code generation with a focus on measuring sensitivity to prompt augmentations, completely agnostic to a specific programming tasks and LLMs, and thus widely applicable. We provide extensive experimental evidence illustrating utility of our method and share our code for the benefit of the community.

Using Resistive Random Access Memory (RRAM) crossbars in Computing-in-Memory (CIM) architectures offers a promising solution to overcome the von Neumann bottleneck. Due to non-idealities like cell variability, RRAM crossbars are often operated in binary mode, utilizing only two states: Low Resistive State (LRS) and High Resistive State (HRS). Binary Neural Networks (BNNs) and Ternary Neural Networks (TNNs) are well-suited for this hardware due to their efficient mapping. Existing software projects for RRAM-based CIM typically focus on only one aspect: compilation, simulation, or Design Space Exploration (DSE). Moreover, they often rely on classical 8 bit quantization. To address these limitations, we introduce CIM-Explorer, a modular toolkit for optimizing BNN and TNN inference on RRAM crossbars. CIM-Explorer includes an end-to-end compiler stack, multiple mapping options, and simulators, enabling a DSE flow for accuracy estimation across different crossbar parameters and mappings. CIM-Explorer can accompany the entire design process, from early accuracy estimation for specific crossbar parameters, to selecting an appropriate mapping, and compiling BNNs and TNNs for a finalized crossbar chip. In DSE case studies, we demonstrate the expected accuracy for various mappings and crossbar parameters. CIM-Explorer can be found on GitHub.

In constraint learning, we use a neural network as a surrogate for part of the constraints or of the objective function of an optimization model. However, the tractability of the resulting model is heavily influenced by the size of the neural network used as a surrogate. One way to obtain a more tractable surrogate is by pruning the neural network first. In this work, we consider how to approach the setting in which the neural network is actually a given: how can we solve an optimization model embedding a large and predetermined neural network? We propose surrogating the neural network itself by pruning it, which leads to a sparse and more tractable optimization model, for which we hope to still obtain good solutions with respect to the original neural network. For network verification and function maximization models, that indeed leads to better solutions within a time limit, especially -- and surprisingly -- if we skip the standard retraining step known as finetuning. Hence, a pruned network with worse inference for lack of finetuning can be a better surrogate.

We introduce Effective Field Neural Networks (EFNNs), a new architecture based on continued functions -- mathematical tools used in renormalization to handle divergent perturbative series. Our key insight is that neural networks can implement these continued functions directly, providing a principled approach to many-body interactions. Testing on three systems (a classical 3-spin infinite- range model, a continuous classical Heisenberg spin system, and a quantum double exchange model), we find that EFNN outperforms standard deep networks, ResNet, and DenseNet. Most striking is EFNN's generalization: trained on $10 \times 10$ lattices, it accurately predicts behavior on systems up to $40\times 40$ with no additional training -- and the accuracy improves with system size, with a computational time speed-up of $10^{3}$ compared to ED for $40\times 40$ lattice. This demonstrates that EFNN captures the underlying physics rather than merely fitting data, making it valuable beyond many-body problems to any field where renormalization ideas apply.

Causal discovery methods based on the PC algorithm are proven to be sound if all structural assumptions are fulfilled and all conditional independence tests are correct. This idealized setting is rarely given in real data. In this work, we first analyze how local errors can propagate throughout the output graph of a PC-based method, highlighting how consequential seemingly innocuous errors can become. Next, we introduce coherency scores to find assumption violations and small sample errors in the absence of a ground truth. These scores do not require statistical tests beyond those already executed by the causal discovery algorithm. Errors detected by our approach extend the set of errors that can be detected by comparable existing methods. We place our computationally cheap global error detection and quantification scores as a bridge between computationally expensive global answer-set-programming-based methods and less expensive local error detection methods. The scores are analyzed on simulated and real-world datasets.

Large Language Models (LLMs) can solve previously intractable tasks given only natural-language instructions and a few examples, but they remain difficult to steer precisely and lack a key capability for building reliable software at scale: the modular composition of computations under enforceable contracts. As a result, they are often embedded in larger software pipelines that use domain-specific knowledge to decompose tasks and improve reliability through validation and search. Yet the complexity of writing, tuning, and maintaining such pipelines has so far limited their sophistication. We propose oracular programming: a foundational paradigm for integrating traditional, explicit computations with inductive oracles such as LLMs. It rests on two directing principles: the full separation of core and search logic (allowing the latter to freely evolve without breaking the former), and the treatment of few-shot examples as grounded and evolvable program components. Within this paradigm, programmers express high-level problem-solving strategies as programs with unresolved choice points. These choice points are resolved at runtime by LLMs, which generalize from user-provided examples of correct and incorrect decisions. An oracular program is composed of three orthogonal components: a strategy that consists of a nondeterministic program with choice points that can be reified into a search tree, a policy that specifies how to navigate this tree with the help of LLM oracles, and a set of demonstrations that describe successful and unsuccessful tree navigation scenarios across diverse problem instances. Each component is expressed in a dedicated programming language. We address the key programming language design challenges of modularly composing oracular programs and enforcing consistency between their components as they evolve.

Deep learning models for pulmonary disease screening from Computed Tomography (CT) scans promise to alleviate the immense workload on radiologists. Still, their high computational cost, stemming from processing entire 3D volumes, remains a major barrier to widespread clinical adoption. Current sub-sampling techniques often compromise diagnostic integrity by introducing artifacts or discarding critical information. To overcome these limitations, we propose an Efficient and Reliable Framework (ERF) that fundamentally improves the practicality of automated CT analysis. Our framework introduces two core innovations: (1) A Cluster-based Sub-Sampling (CSS) method that efficiently selects a compact yet comprehensive subset of CT slices by optimizing for both representativeness and diversity. By integrating an efficient k-nearest neighbor search with an iterative refinement process, CSS bypasses the computational bottlenecks of previous methods while preserving vital diagnostic features. (2) An Ambiguity-aware Uncertainty Quantification (AUQ) mechanism, which enhances reliability by specifically targeting data ambiguity arising from subtle lesions and artifacts. Unlike standard uncertainty measures, AUQ leverages the predictive discrepancy between auxiliary classifiers to construct a specialized ambiguity score. By maximizing this discrepancy during training, the system effectively flags ambiguous samples where the model lacks confidence due to visual noise or intricate pathologies. Validated on two public datasets with 2,654 CT volumes across diagnostic tasks for 3 pulmonary diseases, ERF achieves diagnostic performance comparable to the full-volume analysis (over 90% accuracy and recall) while reducing processing time by more than 60%. This work represents a significant step towards deploying fast, accurate, and trustworthy AI-powered screening tools in time-sensitive clinical settings.

Incorporating learning-based models, such as artificial neural networks or Gaussian processes, into model predictive control (MPC) strategies can significantly improve control performance and online adaptation capabilities for real-world applications. Still, enabling state-of-the-art implementations of learning-based models for MPC is complicated by the challenge of interfacing machine learning frameworks with real-time optimal control software. This work aims at filling this gap by incorporating external sensitivities in sequential quadratic programming solvers for nonlinear optimal control. To this end, we provide L4acados, a general framework for incorporating Python-based dynamics models in the real-time optimal control software acados. By computing external sensitivities via a user-defined Python module, L4acados enables the implementation of MPC controllers with learning-based residual models in acados, while supporting parallelization of sensitivity computations when preparing the quadratic subproblems. We demonstrate significant speed-ups and superior scaling properties of L4acados compared to available software using a neural-network-based control example. Last, we provide an efficient and modular real-time implementation of Gaussian process-based MPC using L4acados, which is applied to two hardware examples: autonomous miniature racing, as well as motion control of a full-scale autonomous vehicle for an ISO lane change maneuver.

Quantum computing offers exciting opportunities for simulating complex quantum systems and optimizing large scale combinatorial problems, but its practical use is limited by device noise and constrained connectivity. Designing quantum circuits, which are fundamental to quantum algorithms, is therefore a central challenge in current quantum hardware. Existing reinforcement learning based methods for circuit design lose accuracy when restricted to hardware native gates and device level compilation. Here, we introduce gadget reinforcement learning (GRL), which combines learning with program synthesis to automatically construct composite gates that expand the action space while respecting hardware constraints. We show that this approach improves accuracy, hardware compatibility, and scalability for transverse-field Ising and quantum chemistry problems, reaching systems of up to ten qubits within realistic computational budgets. This framework demonstrates how learned, reusable circuit building blocks can guide the co-design of algorithms and hardware for quantum processors.

We prove Ehrenborg's conjecture that every connected bipartite graph $G$ with parts of size $m$ and $n$ has at most $\frac{1}{mn}\prod_{v\in V(G)} \operatorname{deg}(v)$ spanning trees, and that equality holds if and only if $G$ is a Ferrers graph. The proof is fully formalized in Lean 4.

Linear limit continuation was recently developed as a systematic and effective method for constructing numerically exact solitary waves from their respective linear limits. In this work, we apply the technique to two typical anisotropic harmonic traps in two-dimensional Bose-Einstein condensates to further establish the method and also to find more solitary waves. Many wave patterns are identified in the near-linear regime and they are subsequently continued into the Thomas-Fermi regime, and then they are further continued into the isotropic trap if possible. Finally, the parametric connectivity of the pertinent solitary waves is also discussed.

We revisit the flipped standard model where a $U(1)_N$ gauge group is added, determining a dark charge through the weak isospin such as $D=T_3+N$, analogous to the electric charge and hypercharge relation. We find %discover that neutrino masses are appropriately generated by a radiative inverse seesaw mechanism mediated by dark fields. Dark matter candidate is a naturally light fermion with the mass radiatively induced at the keV scale. The residual $Z_2$ parity arising from $U(1)_N$ symmetry breaking both stabilizes the dark matter candidate and prevents its potential mixing with neutrinos. Such residual $Z_2$ parity also guarantees the radiative nature of the inverse seesaw mechanism responsible for light active neutrino mass generation. It is noted that the keV dark matter may be thermally produced in the early Universe as decoupled but being still relativistic and typically overpopulated due to $U(1)_N$ portal interactions. To achieve the correct abundance, the excessive thermal production is counterbalanced by sufficient late-time entropy generation from the decay of long-lived particles. The parameter space under consideration can simultaneously accommodate the observational data from cosmic inflation and keV dark matter.

We prove that the Dimension Conjecture implies the Jacobi Bound Conjecture.

We prove the Strong Jacobi Bound Conjecture for generically reduced components of differential schemes.

In the presence of qubit losses, the building blocks of fault-tolerant error correction (FTEC) must be revisited. Existing loss-tolerant approaches are mainly architecture-specific, and little attention has been given to optimizing the syndrome measurement sequences under loss. Schemes designed for the standard Pauli error model are not directly applicable because the syndrome patterns differ when both Pauli errors and erasures can occur. Based on recent advances in loss detection units and loss-tolerant syndrome extraction gadgets, we extend the study of adaptive Shor-style measurement sequences to the mixed error model. We begin by discussing how to adaptively convert correctable erasures into located errors. The minimal overhead is quantified by the number of stabilizer measurements, which can be reduced to a subgroup dimension problem for erasures arising in any FTEC circuit for qubits and prime-dimensional qudits. As a byproduct, we provide the construction of the canonical generating set with respect to a given bipartite partition for a stabilizer group on qudits of composite dimension. We then generalize both the weak and strong FTEC conditions. Finally, we present adaptive syndrome-measurement protocols for the mixed error model, generalizing the adaptive protocols for the standard Pauli error model.

There is increasing evidence for multiple binary black hole~(BBH) subpopulations in the cumulative gravitational wave catalog by the LIGO-Virgo-KAGRA Collaboration. The astrophysical interpretation of this complex underlying population is subject to theoretical uncertainties in treatments of binary stellar evolution, core collapse, and host environments. In this \textit{Letter}, using parametrized mixture models, we show that the BBH detection sample comprises three astrophysical subpopulations that are likely dominated by specific formation channels. In particular, we show that the $10M_{\odot}$ peak and the $35M_{\odot}$ feature in the BBH mass spectrum correspond to distinct mass-ratio, spin alignment, spin precession, and redshift evolution properties. We show that mass-based transitions reported in the distribution of BBH parameters naturally emerge from our inferred distributions without explicit modeling. Our results are consistent with the current observed population arising from specific relative abundances of isolated binary evolution, dynamical formation in globular clusters, and higher-generation BBH mergers. Under this interpretation, we constrain the relative underlying fraction of these channels to be $79.0^{+11.5}_{-10.9}\%$, $14.5^{+11.6}_{-8.0}\%$, and, $2.5^{+5.5}_{-1.8}\%$, respectively, and find these relative fractions to be evolving over cosmic time with more than $1σ$ confidence. Our interpretation relies on simple theoretical predictions that are mostly robust against uncertainties in BBH formation, with more definite conclusions expected in the near future.

We consider the dynamics of an expanding superfluid modeled by Mueller-Israel-Stewart theory coupled to a complex scalar field with a $U(1)$ symmetry that is spontaneously broken. This is a manageable theoretical setting for explorations of the chiral phase transition of expanding quark-gluon plasma. We study the late proper-time behavior of Bjorken flow in this physical system and find that asymptotic solutions can be expressed as a transseries of a novel form, which contains factors like $τ^{-a\ln τ}$. This transseries describes how the information encoded in the initial data is diluted in the course of dissipative evolution. These solutions retain memory of the symmetry-breaking transition and describe two qualitatively different late-time behaviors of the dynamical variables, depending on condensate relaxation rate: either a purely damped fall-off or damped oscillations. The possibility that such oscillations could be imprinted in the observed outcomes of heavy ion collision experiments is the main physical insight that follows from our analysis.

In a multiple testing task, finding an appropriate estimator of the proportion $π_0$ of non-signal in the data to boost power of false discovery rate (FDR) controlling procedures is a long-standing research theme, sometimes referred to as 'adaptive FDR control'. The interest in this theme has been reinforced in the recent years with conformal novelty detection, for which it turns out that similar tools can be used in combination with any 'blackbox' machine learning algorithm. Nevertheless, perhaps surprisingly, finding a solution for 'adaptive FDR control' that is optimal in a broad sense is still an open problem. This paper fills this gap by introducing new $π_0$-estimators, referred to as min-Storey (MS) and interval-min-Storey (IMS), which are built upon the so-called 'Storey estimator'. Plugging these estimators in the adaptive Benjamini-Hochberg (BH) procedure is shown to deliver FDR control both in the independent and conformal settings. In addition, these methods satisfy an optimal power property over any (regular) alternative distribution. The excellent behaviors of the new adaptive procedures are illustrated with numerical experiments both in the independent and conformal models for various distribution structures.

We consider random walk polynomial sequences $(P_n(x))_{n\in\mathbb{N}_0}\subseteq\mathbb{R}[x]$ given by recurrence relations of the form $P_0(x)=1$, $P_1(x)=x$ and $x P_n(x)=a_n P_{n+1}(x)+c_n P_{n-1}(x)\;(n\in\mathbb{N})$, where $a_n$ and $c_n$ are positive and sum up to $1$. $(P_n(x))_{n\in\mathbb{N}_0}$ is said to satisfy nonnegative linearization of products if the product of any two polynomials $P_m(x)$, $P_n(x)$ is a convex combination of $P_{|m-n|}(x),\ldots,P_{m+n}(x)$. This property gives rise to a hypergroup structure and a sophisticated harmonic analysis. We are interested in examples such that both the original sequence $(P_n(x))_{n\in\mathbb{N}_0}$ and the sequence $(\widetilde{P_n}(x))_{n\in\mathbb{N}_0}$ which corresponds to switched roles of $(a_n)_{n\in\mathbb{N}}$ and $(c_n)_{n\in\mathbb{N}}$ satisfy nonnegative linearization of products. Such considerations were recently started by Lasser and Obermaier and can be motivated from a harmonic analytic, combinatorial or probabilistic point of view. However, Lasser and Obermaier left open the question whether examples besides the trivial example of the Chebyshev polynomials of the first kind $(T_n(x))_{n\in\mathbb{N}_0}$ (with $a_n\equiv c_n\equiv1/2$) actually exist. We provide a sufficient criterion and explicitly construct such nontrivial examples. Moreover, we provide characterizations of $(T_n(x))_{n\in\mathbb{N}_0}$ by additionally involving properties of the duals and Haar measures. Our criterion also enables us to solve open problems concerning the Haar measure of polynomial hypergroups stated by Kahler and Szwarc.

We consider a multi-commodity Dynamic Traffic Assignment (DTA) problem formulated as a network flow control problem on the Cell Transmission Model (CTM). The objective is to design optimal control policies using variable speed limits, ramp metering, and dynamic routing to regulate traffic evolution over time on a given limited-capacity transportation network. Even simple instances of DTA problems on the CTM are known to give rise to non-convex optimal control formulations. Nevertheless, a single-commodity DTA formulation has recently been proposed that admits a tight convex relaxation, thereby enabling tractable optimal control synthesis. The single-commodity formulation, however, is structurally restrictive, as it effectively allows only a single destination. To address this limitation, we develop a multi-commodity CTM model in which each commodity is associated with potentially distinct sets of off-ramps. By extending the convexification approach developed for the single-commodity case, we establish a tight convex relaxation of the multi-commodity DTA problem on the CTM model. This relaxation relies on concave, commodity-specific demand functions and concave aggregate supply functions for every cell, which ensure convexity of the resulting optimal control problem. Our proposed formulation requires commodity-dependent implementation of variable speed limits and dynamic routing policies.

Hypergeometric motives are family of motives associated to hypergeometric local systems. Their special features, in particular their rigidity, makes them more tractable than general motives. In the present article we prove most of the properties that they are expected to satisfy in the rank $2$ case.

The photomolecular effect has been hypothesized to enhance evaporation of water at visible wavelengths. This study develops a measurement technique to investigate its presence and magnitude at the liquid-vapor interface of water. The experiment detects surface absorptance by comparing polarized reflectance for substrates with and without a water layer. The reflectance ratio is used as an indicator of interfacial absorptance or attenuation. Lightly doped silicon and platinum were used as dielectric and metal substrates, and their pseudo-optical properties were measured using ellipsometry. Experimental results were compared to a multilayer reflectance model to determine theoretical sensitivity and guide angle selection. Measurements showed close agreement with a classical model assuming zero surface absorptance. The model was then extended to include surface absorptance using a spectral response based on Lorentzian-distributed Feibelman parameters derived from a recent estimate of 0.84% interfacial absorption. Although this model predicted a 1-2% reduction in reflectance near resonant frequencies, no such spectral features were observed experimentally. These results suggest that under ambient conditions, interfacial absorption is well below 1%, indicating that the optical signature of the photomolecular effect is either much weaker than previously reported or strongly dependent on conditions not present in this experiment.

High-mass stars, with their powerful winds and intense radiation fields, are fundamental in regulating galactic dynamics and evolution; however, despite their great relevance, the mechanisms involved in their formation are still not fully understood. In this context, molecular outflows, which are essential for removing angular momentum and allowing accretion onto the central object, are a crucial phenomenon for characterizing their formation. Previous studies reveal a discrepancy in the masses of outflows associated with high-mass clumps between works conducted at the clump scale ($\sim$ pc) and those at the core scale ($\sim$ subpc). This suggests that the high-mass outflow activity observed at the clump scale might be the result of the contribution from several lower-mass outflows linked to individual molecular cores. This work presents a study of the molecular gas toward a high-mass clump associated with an Extended Green Object (EGO). EGOs are indicators of jets associated with high-mass protostars. Employing high angular resolution data from the Atacama Large Millimeter/submillimeter Array (ALMA), the presence of several hot cores with outflow activity was observed in the source. A characterization of the outflows at the core scale is presented within the context of the physical parameters of the molecular clumps.

Berry curvature fundamentally dictates the topological ground state, anomalous transport and optical properties of quantum materials. However, directly mapping its momentum-space distribution in real materials remains an outstanding experimental challenge. Here, we present an inverse method for reconstructing the abelian Berry curvature of a single band using angle-resolved measurements of the transverse conductance. Our inversion relies on a symmetry-constrained statistical model with two hyperparameters that can be inferred directly from the nonlinear Hall conductance, yielding a parameter-free inversion method. We demonstrate the feasibility of our method using simulated measurements of tight-binding models of WSe$_2$ and $ABC$-stacked trilayer graphene.

We report the discovery and characterization of two compact galaxies, Pelias and Neleus, at z ~ 0.71 and z ~ 0.75, identified in MACS J0416.1-2403 and GOODS-North. Both exhibit unusual spectral energy distributions (SEDs), with very blue rest-frame UV-optical emission and a steep rise toward near- and mid-infrared wavelengths. JWST/NIRISS and JWST/NIRSpec spectroscopy show strong rest-frame optical lines ([O III] 4959,5007 and Halpha) with extreme equivalent widths (>= 1000 Angstrom), indicating young burst-dominated populations with low metallicities (Z ~ 0.1-0.4 Zsun), low dust attenuation (Av ~ 0.2 mag), and stellar masses of Mstar ~ 10^7 Msun. Nonetheless, JWST/MIRI photometry reveals a strong mid-infrared excess that cannot be explained by stellar populations or star-formation-heated dust alone, requiring a hot-dust component most naturally associated with a deeply embedded active galactic nucleus (AGN). SED modelling yields log10(Lbol [erg/s]) ~ 43.7-44.0, implying black hole masses of log10(MBH [Msun]) ~ 5.7-6.7 under the assumption of Eddington-limited accretion. Given the very low stellar masses of the hosts, this corresponds to black-hole-to-stellar mass ratios of about 6-60%, well above the extrapolation of local scaling relations. The lack of X-ray detections suggests that the accretion may be either heavily obscured or intrinsically X-ray weak. Their SEDs also resemble those of Blue Excess Hot Dust Obscured Galaxies and show the characteristic V-shaped continuum seen in Little Red Dots, although with the inflection occurring at redder wavelengths.

Despite nation efforts to promote diversity and inclusion, women and gender minorities remain underrepresented in physics. One common approach to studying gender in physics contexts treats gender as a categorical identity variable (e.g. "man," "woman"). In contrast, approaches that center gender expression focus on the nuanced and context-dependent ways in which gender is socially enacted and interpreted. They are therefore well-suited for exploring how gender permeates the small-scale interactions that ultimately shape students' persistence and perceptions of inclusivity. In the present study, we utilized gender expression as a lens to investigate gendered patterns in introductory undergraduate physics students' sense of belonging in the discipline. Specifically, this qualitative investigation expands on our previous quantitative work to investigate why students may feel misperceived by their peers in physics and how that experience influences their belonging. Results indicated that students' sense of belonging may be impacted by perceived pressures to alter their gender expression in physics contexts. Many interviewees expressed a felt need to present themselves more "masculinely" to fit in. Contrastingly, pressure to present "femininely" was most often associated with standing out. Implications for supporting students' authentic self-ex in physics contexts are discussed.

Solid state athermal phonon calorimeters used in the search for low mass dark matter or coherent neutrino-nucleus interactions have long observed a large excess of events below several hundred eV. The relaxation of damage created by the interaction of fast cosmic ray neutrons with the detector has been proposed as a source of these excess events. By comparing neutron exposed detectors to control detectors, we report the first measurement of phonon bursts caused by damage created by fast neutrons. Differences in the spectral shape, the rate dependence on thermal history, and the observed spectral rate scaled to the neutron exposure between irradiated and control detectors suggest that our observed LEE backgrounds are not dominated by neutron damage-induced phonon bursts.

Fix a knot $K_0$ in $\mathbb{R}^3$ and consider a Lagrangian submanifold $L$ of $T^*\mathbb{R}^3$ that is isotopic to the conormal bundle of $K_0$ by a compactly supported Hamiltonian isotopy and intersects the zero section $\mathbb{R}^3$ cleanly along a knot. In this paper, using microlocal sheaf theory and some results in $3$-manifold theory, we prove that the knot type of $K_1 := L\cap \mathbb{R}^3$ in $\mathbb{R}^3$ is strictly constrained from the knot type of $K_0$. Specifically, we deduce the existence of a surjective group homomorphism $π_1(\mathbb{R}^3\setminus K_0) \to π_1(\mathbb{R}^3\setminus K_1)$ preserving the longitude and meridian with respect to the Seifert framing. Moreover, combining with a previous work by the second author, we obtain a rigidity result which was only known for the unknot: If $K_0$ is the $(2,q)$-torus knot or the figure-eight knot, $K_1$ must have the same knot type as $K_0$.

Extracting energy spectra from quantum Hamiltonians is a fundamental task for quantum simulation, yet remains challenging on noisy intermediate-scale quantum (NISQ) devices. We propose Measured Quantum Time Evolution (MQTE), an ancilla-free algorithm that estimates energy gaps by applying real-time evolution to a reference state and measuring time-resolved probabilities via repeated projective measurements. Spectral analysis of these signals reveals oscillation frequencies corresponding to eigenvalue differences. Crucially, MQTE exhibits inherent robustness to quantum hardware noise and sampling errors: these disturbances manifest as a white-noise background, which does not distort the underlying spectral structure but rather obscures the frequency information. By increasing the number of measurement samples, the intensity of the background white noise can be suppressed, thereby recovering the original spectral content. We validate the algorithm's performance via numerical simulations on one- and two-dimensional Heisenberg models, demonstrating accurate extraction of energy gaps and resilience against both sampling and circuit-level noise. Experimental implementation on the superconducting quantum processor Tianyan-176-II further confirms the practical feasibility and noise tolerance of MQTE under real hardware conditions. This work provides a robust and scalable framework for quantum spectral estimation in the NISQ era.