We propose a superconducting circuit hosting $d$ low-lying states, well separated from the rest of the spectrum, that naturally realizes a qudit system protected from leakage errors. The system represents a generalization of the fluxonium and the low-energy states are constituted by fractional fluxon states, that we call {\it fraxons}, localized in the minima of a suitably designed Josephson potential. The latter is tailored through a Fourier engineering approach, that employs multi-harmonic Josephson building block elements composed by a Josephson junction and an inductance connected in series. We present the spectrum of a $d=4$ and a $d=5$ qudit system and study in detail the qutrit case. We analyze the dipole matrix elements for coupling to radiation and propose a non-Abelian, stimulated Raman adiabatic passage (STIRAP) protocol for single-qutrit gates, that is particularly suited for the present system. The proposed platform opens novel perspectives in circuit engineering and quantum computing beyond the qubit paradigm.

We introduce a modular silicon-photonic Fabry-Perot resonator lattice based on cascaded tunable Sagnac loop reflectors. Each SLR is controlled by a single directional-coupler cross-coupling coefficient, enabling modular control of the effective lattice hoppings. As a representative example, alternating two SLR types maps the lattice onto the Su-Schrieffer-Heeger model in the weak-coupling limit. We derive the Bloch dispersion via a transfer-matrix formulation and obtain an effective tight-binding Hamiltonian in the weak-coupling limit. S-parameter simulations of a 20-site lattice show an isolated midgap resonance with edge-localized power profiles in the topological phase, and disorder tests show robustness against symmetry-preserving hopping perturbations. Our results establish SLR-based FP lattices as a complementary platform for on-chip topological photonics.

We explicitly describe the set of gaps and the Weierstrass semigroup at a totally ramified place of degree one on a Kummer extension defined by the affine equation $y^m = f(x)$ over $K$, an algebraic extension of $\mathbb{F}_q$, where $f(x)\in K(x)$. Our description takes a unified form for distinct totally ramified places of degree one. We then provide a necessary and sufficient condition for the Weierstrass semigroup at a totally ramified place of degree one to be symmetric. Furthermore, we investigate the minimal generating set of the Weierstrass semigroups at many totally ramified places of degree one. We not only explicitly describe the minimal generating set, but also construct functions whose pole divisors have coefficients lying in the set. Finally, we apply our results to specific Kummer extensions, including function fields of GGS curves and subcovers of the BM curve.

The parametric amplification enabled by two-photon driving constitutes a versatile platform for advanced quantum technologies. We present an optimized scheme for implementing quantum batteries (QBs) based on a superconducting circuit system, where a two-photon-driven LC resonator serves as the charger and an array of transmon qubits functions as the battery. Our results show that two-photon parametric driving exponentially enhances the effective cavity-qubit coupling, which in turn gives rise to near-degenerate energy-level structures and highly entangled quantum states. This significantly enhances the charging power and enables rapid energy transfer from the charger to the battery. Moreover, the engineered squeezed cavity mode and the associated quantum correlations effectively suppress environmentally induced decoherence, thereby delaying energy leakage and facilitating stable energy storage. The proposed scheme remains robust against practical experimental imperfections, such as parameter disorder and environmental noise, preserving its performance advantages. The work provides a feasible platform for realizing high-power, high-stability QBs and highlights the potential of parametric control in quantum energy technologies.

We study the linearized scattering of dilaton-graviton waves from a thin brane in three-dimensional spacetime. Holographically, the setup models scattering from an interface in a family of strongly coupled theories related to dimensional reductions of higher-dimensional $AdS_{d+2}$ gravity. Unlike the pure $AdS_3$ case, for $d>1$ the physical bulk mode allows incident radiation to be redistributed into reflected, transmitted, and evanescent components. For the $d=2$ background, we obtain a controlled solution in which the interface acts like a rough translucent window, producing diffuse angular scattering and absorption into surface modes. From the dual perspective, the scattering process is suggestive of dissipative flow toward the infrared. For $d=4$, the same analysis reveals a sensitivity to the infrared boundary condition, suggesting that the singular zero-temperature geometry must be regulated in order to have a well-defined scattering process. The structure of the equations nevertheless suggests that a regulated $d=4$ problem may exhibit the same qualitative redistribution of incident flux.

This paper presents a general framework for calculating the dimension of spline spaces over arbitrary rectilinear partitions using the smoothing cofactor method. The approach extends existing dimension theory for polynomial splines over T-meshes by introducing the concept of TE-connected components, reducing the problem to the rank computation of explicitly constructible conformality matrices. Furthermore, a new class of rectilinear partitions, termed partitions with disjoint truncated l-edges, is introduced. It is proven that under specific conditions, the dimension of the corresponding spline space attains Schumaker's lower bound. This shows that the lower bound is attainable for arbitrary degree d and smoothness order mu in certain partition configurations. Numerical examples, including the Morgan-Scott and Yuan-Stillman partitions, validate the effectiveness and generality of the framework for both triangular and non-triangular rectilinear partitions.

Poroelastic wave simulations are important for many applications relating fluid flow and wave characteristics in porous rock formations. Reciprocity is a key physical property of wave propagation in porous media that is important for such applications, even when viscous dissipation is present. However, numerical poroelastic simulations often fail to reproduce reciprocal responses because the discretization does not preserve the balance between reversible wave dynamics and irreversible fluid-solid drag. To address this, we formulate the Biot equations in terms of a continuous evolution operator split into a reversible (skew-adjoint) wave part and an irreversible (self-adjoint, non-positive) Darcy part, including the leading-order Johnson-Koplik-Dashen correction. This structure clarifies why reciprocity holds in the continuous equations and how it is easily broken in discrete form. Guided by this interpretation, we construct a symmetric second-order Strang-splitting scheme with half-step source injection. The method conserves energy in the reversible subsystem, treats Darcy dissipation unconditionally stably, and retains Courant limits similar to elastic solvers. Using a staggered pseudo-spectral discretization, we model multimode propagation in 2D VTI media and obtain cross-component reciprocity with a relative L2 misfit approaching machine precision, demonstrating that the discrete scheme inherits the symmetry properties of the continuous evolution operator.

The aim of this study is to empirically investigate the existence of a sectoral asset price channel of monetary policy in the region of the six republics of former Yugoslavia. The study constructs sectoral indices for the entire region, building on the idea that one regional stock exchange may provide more efficiency for the listed companies in the region, while monetary policy relevance for it may be sector-specific. We employ panel vector autoregressive model to observe impulse responses of sectoral indices to innovations in monetary policy, while then disentangle the long- from the short-run relationships per index through a Pooled Mean Group estimation. Overall, we document presence of the asset price channel in the finance and telecom sectors, likely driven by the established multinational corporate networks fostering sub-market regionalization. Yet, this is not the case for the manufacturing and electricity sectors, which may imply that local stock markets are yet too fragmented and space for a more efficient regional stock market, either in the true sense of the word or, more realistically, though enhanced regional cooperation of the stock exchanges certainly exists.

We use normal-turn estimates for McShane--Rivin norm balls to prove that, for every complete finite-area hyperbolic once-punctured torus $X$, the number of simple closed geodesics of length exactly $L\geq 2$ is at most $C_X(\log L)^2$. For the modular torus, this gives $$ \#λ_M^{-1}(m)\leq C(\log\log(3m))^2 $$ for every Markoff number $m$, improving the previous logarithmic Markoff-fiber bounds. These estimates also give new quantitative information on the local geometry of McShane--Rivin norm balls, including obstructions to infinite-order flatness at certain irrational directions.

Black-hole formation is expected, via holography, to correspond to thermalization in the boundary theory. For open quantum systems, an initial pure state generically evolves into a mixed state irreversibly, suggesting that horizon formation in the bulk should arise. In this paper, we extend the holographic Lindblad prescription to a non-Markovian setting and apply it to JT gravity coupled to a scalar field. Using numerical simulations in the semiclassical and high-temperature regime, we demonstrate the dynamical formation of black holes.

The thermoresponsive behavior of Pluronic F127 solutions is governed by temperature-dependent micellization and complex self-assembly of these micelles. This study investigates the effect of thermal stimuli on the kinetics of phase transition of Pluronic systems during heating and cooling cycles. We employ Differential Scanning Calorimetry measurements to investigate the dependence of the micellization temperature on thermal stimuli, revealing that both the micellization temperature and the peak intensity vary systematically with the applied thermal ramp rate. Furthermore, we employ rheological characterization which reveals a sharp sol to soft-solid transition upon heating. Interestingly, we observe a novel multi-step transition during the cooling phase, indicating a more complex reorganization pathway with intermediate metastable states than typically assumed for reversible micellization. Our findings indicate that the characteristic multi-step cooling transition is transient, gradually weakening with successive thermal cycles. We also present a comprehensive mathematical model which accurately captures the kinetics and multiple step transition in viscoelastic parameters. Significantly, the distinct peaks in Small-Angle X-ray Scattering (SAXS) measurements clearly reveal the evolution from a disordered unimers/micelles state at low temperatures to a highly ordered lattice with long-range spatial correlation at elevated temperatures. We also present a comprehensive phase diagram highlighting the critical role of thermal stimuli and pathways in defining the phase behavior of Pluronic system. This work, therefore, offers essential experimental and theoretical insights into the thermally driven self-assembly, transition kinetics, and microstructural evolution of thermoreversible Pluronic solution.

DNA methylation is usually treated as an epigenetic memory mark: transcriptional history is written into regulatory DNA and later stabilizes a chosen cell identity. This picture explains persistence, but it makes memory passive. Here we show that the same promoter-level coupling required for methylation memory can instead turn methylation into an internal control variable for regulatory dynamics. Transcription-factor occupancy protects regulatory DNA from methylation, while methylation shifts later transcription-factor binding thresholds. Under time-scale separation, this reciprocal loop separates into fast expression dynamics conditioned on methylation and a slow methylation flow written by expression. Minimal promoter, self-activation, and fate-toggle models show that this feedback does more than preserve a past state: it autonomously reshapes the expression landscape. In a methylation-coupled toggle, the preferred expression state can move continuously through single-well drift, allowing commitment without first entering a multiwell regime. Stochastic simulations further show that evolving methylation reduces fate reversals relative to a frozen landscape, making weak early expression bias more predictive of later fate. These results recast DNA methylation from a downstream stabilizer of cell identity into a slow dynamical coordinate that can help determine how regulatory states are chosen.

Dirac-Weyl semimetals host both Dirac and Weyl fermions and the exploration of material candidates with tunable topological properties is essential to realize topological spintronic devices. In this work, we propose CaAgBi as a Dirac-Weyl semimetal with tunable type-I and type-II Weyl points based on first-principle calculations. In addition to the three pairs of Dirac points located along the rotational axis as previously reported, our calculations reveal 18 additional pairs of dual-type Weyl points distributed across three distinct planes: type-I in the $k_z=0$ plane and type-II in the $k_z= \pm 0.0698\,\frac{2π}{c}$ planes. The topological features are further confirmed through chirality of the Weyl points as well as the existence of surface Fermi arcs. Moreover, we find that the position and annihilation of Dirac and Weyl points are tunable by the alloy engineering and external strains. The alloy engineering is employed to modulate the positions of Weyl points, revealing different annihilation concentrations for type-I and type-II Weyl points, potentially offering novel experimental strategies for Weyl point manipulation. Under tensile biaxial strain, the Weyl points in the $k_{z}=0$ plane annihilate along the $Γ$--$\mathrm{M}$ path at $2.1\%$ strain, whereas the Weyl points in the $k_{z}\neq 0$ planes remain robust within $6\%$ strain. This work provides a versatile platform for manipulating Dirac/Weyl interactions, with spin-orbit coupling (SOC) driven alloy control and strain-selective engineering opening avenues for topological electronics.

I derive the regularized formula for glue scalar density (gluon condensate) in terms of Dirac spectral density [arXiv:2509.03509], and elaborate on its uses and meaning. Particular attention is given to understanding of what this new formula reveals about the relation between glue and quark scalar densities, how it relates to IR phase, how it clarifies the distinction between anomalous and spontaneous ways of breaking symmetries, and what it says about the relation between UV and IR in QCD.

CSLib is an emerging Lean 4 library for computer-science formalization, but its premise-retrieval behavior is not well represented by broad mathematical theorem-proving benchmarks. We introduce CSLibPremiseBench, a reproducible CSLib-specific benchmark and empirical study for source-visible premise retrieval over Lean 4 theorem and lemma declarations. The benchmark pins CSLib v4.29.0 at commit 0d37cc7fcc985cfc53b155e7eef2453f846c6da2, builds with Lean 4.29.0, and evaluates a strict import/source-order task set with 801 proxy-labelable tasks and 1875 CSLib candidate declarations. The labels are source-visible CSLib proof-reference proxies, not elaborated Lean dependency traces. We audit label robustness using stricter source-visible matching and a 300-task Lean environment expression probe, then compare BM25, symbol/name overlap, namespace/module and import-graph heuristics, PageRank-style module priors, fixed hybrids, and CSG-Rerank, a structure-guided graph-lexical reranker. CSG-Rerank gives a modest early-rank MRR gain over lexical BM25 under the strict policy, but does not reliably outperform BM25+symbol and does not improve Recall@10. A context-packet audit similarly finds stronger module/family concentration without reliable top-k proxy-gold coverage or token-utility gains. We position CSLibPremiseBench as a benchmark and audit paper: repository structure and candidate-policy design materially shape CSLib premise retrieval, proxy labels require explicit caveats, and proof-generation or proof-repair performance is not claimed.

Chudnovsky, Cook, Davies, and Oum introduced the notion of Pollyanna graph classes: a class $\mathcal{C}$ is Pollyanna if for every $χ$-bounded class $\mathcal{F}$, the intersection $\mathcal{C} \cap \mathcal{F}$ is polynomially $χ$-bounded. They further defined $\mathcal{C}$ to be strongly Pollyanna if it is $k$-strongly Pollyanna for some integer $k$, meaning that $\mathcal{C} \cap \mathcal{F}$ is polynomially $χ$-bounded for every $k$-good class $\mathcal{F}$. They asked whether there are Pollyanna graph classes that are not strongly Pollyanna. In this note we answer this question affirmatively, under the literal interpretation that graph classes are not required to be hereditary. We construct a class $\mathcal{C}$ that is Pollyanna but, for every $k \ge 1$, is not $k$-strongly Pollyanna; in particular $\mathcal{C}$ is not strongly Pollyanna.

This work explores the static and dynamic magnetic properties of weakly antiferromagnetically coupled Fe/Ti superlattices, emphasizing the link between magnetic behavior and structural characteristics. HRTEM and XRD analyses confirm alternating Fe and Ti layers with rough interfaces, especially in upper layers. Magnetic measurements reveal two-step hysteresis loops and a temperature and thickness-dependent interlayer exchange coupling (IEC). A macrospin model incorporating bilinear and biquadratic coupling reproduces the experimental data and supports a phase diagram analysis identifying non-collinear configurations. The results underscore the impact of structural imperfections and highlight the crucial role of biquadratic exchange in Fe/Ti/Fe multilayers.

In this work, we investigate the cosmological dynamics of a spatially flat Friedmann--Lemaître--Robertson--Walker Universe in the framework of generalized \( \mathcal{F}(\mathcal{R},Σ,\mathcal{T}) \) gravity by incorporating gravitationally induced particle creation together with the variable generalized Chaplygin gas scenario. The modified gravitational action depends explicitly on the Ricci scalar \( \mathcal{R} \), the matter-coupling scalar \( Σ\), and the trace of the energy--momentum tensor \( \mathcal{T} \), which collectively generate significant corrections to the standard cosmological evolution. The particle creation mechanism is introduced through an open thermodynamic description of the Universe. In addition, the dark sector is modeled using the variable generalized Chaplygin gas formalism. To examine the observational consistency of the model, the free parameters are constrained using the Pantheon\(^+\) Type Ia Supernova compilation together with the combined observational Hubble and Pantheon\(^+\) datasets through a statistical \(χ^2\)-analysis. The cosmological behavior of the model is further explored through the evolution of the cosmological parameters. Furthermore, the thermodynamic properties of the model are investigated using the apparent horizon formalism. The obtained results demonstrate that the entropy evolution remains physically consistent throughout the cosmic evolution. Hence, the present \( \mathcal{F}(\mathcal{R},Σ,\mathcal{T}) \) gravity framework with particle creation provides a viable geometrical description of the late-time accelerated Universe and remains compatible with recent cosmological observations.

This paper presents a method that generates a hierarchical user mobility model from the analysis of the data available from Wi-Fi connections. The data obtained from the Wi-Fi infrastructure is defined in terms of the coverage areas of the access points that the users move through. These access points are recursively grouped into different levels of granularity based on their geospatial features. The track of a user is defined as a sequence of Wi-Fi access points, which is enough to simulate user mobility in, for example, fog scenarios. The hierarchical definition of the region under study is proposed to reduce the complexity of the model in high-scale scenarios and to increase the adaptability between scenarios with different geospatial features. The model creation is based on a user profiling method that uses a clustering algorithm and each user type is defined with a transition matrix between coverage areas and a time length vector for the areas. The method is applied to the case of the campus of the University of the Balearic Islands. From the analysis of the mean square error of the results, we determined that the proposed method obtains good results for the transition matrices, but that the time vector definition should be improved. The results also show lower complexity in the case of the hierarchical model, with one area for each building and three levels, in regard to a non-hierarchical model, with only one area and one level for the whole campus.

Wigner's thought experiment illustrates quantum theory's measurement problem by considering an observer who measures a quantum system inside a sealed lab, modeled unitarily by an outsider. Recent extensions of this thought experiment, referred to as extended Wigner's friend arguments, question how different observers can reason consistently about each other in quantum setups, and challenge the absoluteness of the outcome value obtained by the friend under a notion of locality. In this work, we present an argument against the absoluteness of free choices under the same notion of locality, using an extended Wigner's friend scenario based on the Pusey--Barrett--Rudolph theorem. Similar arguments based on other contextuality or nonlocality models are possible.

One of the central problems in the topology of hyperplane arrangements is determining whether the complement is a $K(π,1)$-space. In this paper, we study Manin--Schechtman arrangements, introduced as higher-dimensional analogs of the braid arrangement, and prove that their complements have non-vanishing higher homotopy groups. Consequently, these arrangements fail to be $K(π,1)$ in a broad range of cases.

Methane hydrate nucleation under nanoconfinement remains poorly understood due to the complex interplay between geometric restriction and molecular ordering. Here, we investigate the structural organization of water-methane systems confined between silica planar slit pores with widths ranging from 1 to 5 nm and temperatures between 250 and 295 K. Three-dimensional radial distribution functions reveal a clear suppression of hydrate-like ordering at strong confinement (below 2 nm), indicating frustrated nucleation. In contrast, projected two-dimensional correlations exhibit pronounced in-plane structural organization, evidencing a confinement-induced reduction in the dimensionality of molecular order.

We investigate the consistency in the thermodynamics and the approaches at the equation and action levels for the quantum-improved charged black holes with scale-dependent couplings. For the quantum-improved Reissner-Nordström black holes, we find that the thermodynamic consistency allows both the Newton and electromagnetic couplings to have arbitrary dependence on the radial coordinate. We point out a subtlety in the chemical potential with the scale-dependent electromagnetic coupling in the study of thermodynamics. We also examine the compatibility of the Einstein equations at the equation and action levels with the Bianchi identity, identifying the need for an additional quantum energy-momentum tensor. We then find that the consistency between the approaches at the equation and action levels requires that the Newton coupling satisfy certain property. Finally, we extend the analysis to cosmological solutions, suggesting that quantum-induced modifications can drive the isotropization of the early universe.

Rydberg atomic electrometry leverages the extreme sensitivity of highly excited atoms for calibration-free electric field measurements. The technique uses a non-metallic vapor cell to link properties of an RF field to a spectroscopic readout in the optical domain. Most demonstrations have so far focused on detecting linearly-polarized fields, for which the induced splitting of dressed atomic levels is rotationally invariant. Here we report on Rydberg atomic measurements of RF fields in a general state of polarization (SOP) which we map onto the Poincaré sphere through spectroscopic fingerprints. For a Stokes vector circumnavigating a Poincaré sphere meridian, we witness a continuous transformation of the atomic eigenenergy spectrum. Because the relative positions of eigenenergies are locked in place by quantization of angular momentum, the framework is universal and calibration free. We provide a specific demonstration in rubidium, which generalizes to all systems with a single valence electron.

Speech emotion recognition (SER) remains fragile in real-world conditions because emotional cues are subtle, speaker-dependent, and easily confounded by recording variability, while high-performing deep models typically rely on large and carefully curated training sets. Quantum machine learning offers an alternative way to introduce nonlinear correlation modeling with compact modules, yet existing quantum SER studies remain limited and the impact of circuit structure is not well understood. This paper presents HQTN-SER, a hybrid quantum-classical framework that investigates how quantum tensor network connectivity can support SER under small-qubit settings. HQTN-SER introduces (i) an MPS-inspired quantum tensor network module that enforces structured interactions to model correlations in speech representations with a small number of trainable parameters, and (ii) a fusion strategy that combines quantum measurement features with a learned classical latent embedding for end-to-end emotion classification. We evaluate HQTN-SER on three public benchmarks (RAVDESS, SAVEE, and MDER) under a unified preprocessing and training protocol. The proposed model achieves consistent performance across datasets, RAVDESS = 80.12%, SAVEE = 78.26% and MDER = 73.51% accuracy, with stable convergence and low qubit counts, showing that tensor network structure can be an effective and hardware-aware design choice for quantum-assisted SER. The results provide a reproducible baseline and clarify when structured quantum modules can add value to affective computing today.

Computation of observables in discrete stochastic, possibly conditioned, dynamics over large sparse networks is at the basis of a myriad of applications. The Matrix-Product Belief Propagation method allows a semi-analytical estimation of such observables with a controlled error that depends on the size of the employed matrices, called bond size. Its computational cost is linear in the time horizon and the network size for a large family of models with discrete degrees of freedom. Here, a generalization of this method to models with continuous or mixed continuous/discrete degrees of freedom is presented, using a tunable expansion in a Hilbert function basis. The computational cost of the method is linear in the network size with a prefactor that depends on the basis size and the bond size. The method's efficacy is demonstrated by employing a Fourier basis for a mixed continuous/discrete representation of the Kinetic Ising dynamics with real-valued random couplings, where intermediate ``local fields'' are treated as continuous. The accuracy of the method is verified via comparison with Monte-Carlo simulations. For this model, we calculate time auto-correlations, time evolution of energy and magnetization, and finally we estimate the large deviation function of the magnetization at a given future time.

We consider the Landau-Coulomb equation for a (hydrogen) plasma heated by an external electric field. In this setting, theoretical and experimental results in plasma physics show the emergence of so-called \emph{runaway electrons} which are linearly accelerating but only lead to a minimal increase of the plasma temperature. Runaway electrons are a major obstacle in nuclear fusion since they can overcome the confinement and damage the structure of the reactor. We rigorously prove the well-posedness of the underlying nonlinear \emph{open} Landau-Coulomb system in a perturbative setting and the conjectured growth bounds for the mean velocity and plasma temperature. We show that the mean velocity is linearly increasing in time, and capture the sharp logarithmic growth of the temperature. Furthermore, we prove that the electron distribution can be asymptotically described by a scattering-type Maxwellian. Due to the different nature of the electron-electron and electron-ion interactions, we recast the equation as a novel coupled system that allows us to isolate the dissipation structures of the two operators. For the coupled system, we perform a micro-macro decomposition to show convergence to the scattering-type Maxwellian.

In living cells, proteins involved in specialized biochemical functions are often spatially organized within biomolecular condensates. Increasing evidence suggests that some of these condensates, including DNA repair condensates, emerge through liquid-liquid phase separation (LLPS). In the nucleus, however, condensates form within a highly heterogeneous environment composed of chromatin fibers, RNA, and additional protein scaffolds such as PAR chains, all of which may interact with phase-separating proteins. Moreover, condensate formation is frequently associated with specific chromatin conformations; for instance, loop extrusion has been proposed as a mechanism promoting DNA repair condensates. Here, we investigate how the surrounding fibrous environment controls the morphology and spatial organization of phase-separated condensates. Using Brownian dynamics simulations of minimal models combining Lennard-Jones particles with fixed fibrous substrates, we examine the respective roles of local fiber geometry and large-scale network organization, reflecting the multiscale architecture of chromatin. We show that protein-fiber interactions strongly influence droplet positioning relative to the substrate, in a manner analogous to wetting transitions in soft condensed matter systems. Both local geometric constraints and global network organization markedly affect droplet size, morphology, and multiplicity. In addition, large-scale asymmetries in fiber organization can induce robust spatial localization of the dense phase. Our results thus highlight how multiscale structural heterogeneity of the nuclear environment can regulate the emergence and organization of biomolecular condensates.

Entanglement can hide in two fundamentally different ways. First, multi-copy correlations can carry information that no single-copy measurement on an unknown state is able to access. Second, bound entangled states possess a positive partial transpose, which makes them invisible to the Peres-Horodecki criterion and all moment inequalities that depend on it. Here we show that the moment difference between the partial transpose and purity decomposes exactly as a chirality-chirality correlator, where the relevant operator is the scalar spin chirality -- the same quantity that governs chiral spin liquids and the topological Hall effect. This decomposition identifies the specific physical structure that multi-copy entanglement detection probes. Using the same controlled-SWAP circuits, we develop a multi-channel spectral classifier for bound entanglement. The classifier combines realignment spectral features with chirality corrections and achieves 99.9% recall at zero false positives across all three known 3x3 bound entangled families, compared with ~40% for the CCNR criterion alone. We also introduce a marginal-noise construction that produces CCNR-invisible bound entangled states, which the classifier detects but which remain invisible to all single-parameter criteria. We validate our approach experimentally on three IBM Quantum processors and demonstrate negativity reconstruction with mean errors of 0.002-0.027, chirality detection for pure and mixed entangled states, and bound entanglement detection across two structurally distinct families (Horodecki and chessboard) on a single gate-based superconducting processor.

Large Language Models (LLMs) deployed in high-stakes applications must simultaneously manage multiple risks, yet existing defenses are almost exclusively evaluated in isolation under a one-shot deployment assumption. In practice, providers patch models incrementally throughout their lifecycle-responding to newly exposed vulnerabilities or targeted data-removal requests without retraining from scratch. This raises a fundamental but underexplored question: does a later defense preserve the protections established by an earlier one? We present the first systematic study of cross-defense interactions under sequential deployment. Evaluating 144 ordered sequences across three risk dimensions and three model families, we find that 38.9% exhibit measurable risk exacerbation on the originally defended dimension. These interactions are highly asymmetric and order-dependent. To explain these phenomena, we conduct a mechanistic analysis on representative deployment sequences. Using layer-wise representational divergence and activation patching, we localize each defense to a compact set of critical layers. In conflicting sequences, the overlapping critical layers exhibit strongly anti-aligned parameter updates, whereas benign orderings maintain near-orthogonal updates. PCA trajectory analysis reveals that defense collapse stems from activation pattern reversals in these shared layers. We further introduce a layer-wise conflict score that quantifies the geometric tension between defense-induced activation subspaces, offering mechanistic insight into the observed reversals. Guided by this diagnosis, we propose conflict-guided layer freezing, a lightweight mitigation that selectively freezes high-conflict layers during sequential deployment, preserving prior protections without degrading secondary defense performance.