Lopsidedness is common in disk galaxies, yet its origin and evolution remain unclear. Previous studies typically examined stellar and gas asymmetries separately, but a combined analysis offers a stronger probe of the mechanisms driving lopsidedness, recent galaxy evolution, and environment. We analyze the density and kinematics of stellar and atomic hydrogen (HI) components in nine Milky Way type galaxies from the Auriga Superstars cosmological zoom-in simulations. The high stellar mass resolution improves the visibility of disk features while reducing noise, enabling a detailed study of dynamical processes in a cosmological context. Morphological and kinematical lopsidedness are quantified using the first Fourier mode (m=1) of the face-on mass distribution and radial velocity maps, measured consistently for stars and gas between 0.5 and 1 stellar optical radius. At z=0, morphological lopsidedness in old stars (>0.5Gyr) strongly correlates with HI, tracing distortions in the global gravitational potential. In contrast, young stars (<0.5Gyr) trace asymmetric star formation along spiral arms. Stellar morphological and kinematical lopsidedness are strongly correlated, whereas HI shows a weaker correlation, with kinematic asymmetries dominating. We also find an anti-correlation between stellar lopsidedness and bar strength. Strongly barred galaxies tend to host more symmetric disks and higher central stellar mass densities. Tracing lopsidedness evolution over time, tidal interactions with massive satellites (mass ratio >1:50) induce coherent lopsidedness in both stars and HI. In contrast, smooth gas accretion mainly affects HI and young stars, leaving the total stellar component largely symmetric. Overall, these results demonstrate that lopsidedness is a powerful diagnostic of internal disk evolution, gas accretion, and environmental interactions across cosmic time.

Large surveys of galaxies in the local and high-redshift Universe have, traditionally, relied on the intensity of rest-optical emission lines from metal ions in the Interstellar Medium (ISM) to indirectly estimate the O/H abundance in the gas. However, these optical strong line diagnostics are also sensitive to the electron gas temperature ($T_e$), resulting in large systematic uncertainties that inherently limit their utility as metallicity tracers, especially in dust-obscured and metal-rich environments. To this end, we provide the first empirical calibration of Ne$_{23}$, a novel abundance diagnostic using the mid-infrared (MIR) $T_e$-insensitive [Ne II]$λ$12.81$μ$m and [Ne III]$λ$15.56$μ$m fine-structure lines. We present new JWST/MIRI MRS observations of ten H II regions with optical measurements of $T_e$ and O/H from the CHAOS project, and we analyze MIRI observations of eight low-metallicity galaxies with similarly high-fidelity direct O/H. We measure Ne$_{23}$ from 1D MIR spectra extracted from apertures matched to the ground-based spectroscopy used to obtain O/H, a method that is unfeasible from MIR spectra acquired on prior space-based observatories. From these nebulae, Ne$_{23}$ is strongly correlated with O/H over 1.5 dex in 12+log(O/H). We calibrate the O/H-Ne$_{23}$ relation from the empirical data, finding a scatter of just 0.06 dex in O/H at fixed Ne$_{23}$. The O/H-Ne$_{23}$ relation presented here provides a means to reliably estimate 12+log(O/H) from JWST/MIRI MRS observations of ionized nebulae out to z$\approx$0.8, enabling new chemical abundance surveys of highly-attenuated regions and in the metal-rich ISM.

Nonlocal magic quantifies the irreducible nonstabilizerness of a bipartite quantum state after optimizing over local basis changes. We study nonlocal magic for pure fermionic Gaussian states, and derive a simple closed-form entanglement spectrum bound in terms of the singular values of the subsystem-restricted covariance matrix. We benchmark our result against simulated annealing over local Gaussian unitary transformations, which supports optimality along the full local Gaussian orbit. For states drawn from the Gaussian Haar ensemble, we show that the average nonlocal magic is extensive and determine its thermodynamic limit using random matrix theory for the appropriate circular unitary ensemble. We also study Gaussian ground states, focusing on the Kitaev chain, and find that nonlocal magic is suppressed deep in both trivial and topological phases and peaks near the critical points. Finally, we investigate Gaussian evolution via random circuits and in quenches with the XY chain. For random circuits, we find that nonlocal magic grows diffusively, while in the XY chain the XX limit reveals a striking separation between nonlocal magic and entanglement.

Recent proposals suggest that a notion of generalized complexity, analogous to generalized entropy, may be necessary for understanding the dynamics of holographic complexity in settings where quantum effects are non-negligible, such as evaporating black holes. Beginning with a notion of generalized complexity, we introduce a complexity-based quantum expansion for timelike geodesic congruences, and investigate the consequence of a timelike quantum focusing conjecture. We find that for a suitable class of codimension-0 field theory complexity measures the timelike focusing condition implies a complexity-based quantum strong energy condition as well as a complexity bound which is analogous to the covariant entropy bound.

Topological entanglement entropy (TEE) is a key diagnostic of long-range entanglement in two-dimensional gapped phases of matter, but it can suffer from spurious contributions that overestimate the total quantum dimension of the underlying topological order. In this work, we identify the microscopic origin of spurious TEE and introduce a concave partition for computing the Levin-Wen TEE of translation-invariant stabilizer codes of prime-dimensional qudits. We rigorously prove that this prescription is free of spurious contributions. As a complementary probe, we study bivariate bicycle codes on a bipartite cylinder and show that the entanglement entropy depends sensitively on the cylinder circumference, revealing topological frustration of the underlying anyons.

Neural network field theory (NNFT) represents fields as neural networks and samples field configurations by drawing network parameters from a probability distribution. We identify a previously unexplored architectural freedom in NNFT, parameterized by $α$, that leaves the infinite-width theory invariant but dramatically affects finite-width errors in the calculation of correlation functions. For a massive scalar field, we show that $α=0$, corresponding to propagator-weighted neuron momenta and constant neuron amplitudes, is optimal: it minimizes finite-width variance and uniquely removes IR-sensitive corrections in the interacting theory. Even at $α=0$, relative errors from both bias and variance grow exponentially with distance beyond the correlation length. The bias can be removed by extrapolating to infinite width, which we demonstrate numerically, while the variance imposes a fundamental bound on the achievable signal-to-noise ratio as in lattice field theory. These results chart a path toward developing NNFT into a practical tool for the numerical study of field theories.

Entanglement and magic are fundamental resources that capture the complexity of quantum many-body systems. Non-local magic isolates the irreducible nonstabilizerness intrinsically tied to entanglement. However, evaluating this quantity generally requires a prohibitive minimization over the full Hilbert space, making it computationally inaccessible beyond a few qubits. Here, we overcome this bottleneck by suggesting a closed-form expression for the non-local stabilizer entropies of fermionic Gaussian states over local Gaussian unitaries, which can be evaluated in polynomial time directly from the eigenvalues of the reduced Majorana covariance matrix. We apply this framework to characterize fermionic non-local magic across diverse physical regimes: we derive an exact Page-like curve for typical random states, reveal logarithmic scaling at the quantum critical point of the XY model, and establish a quasiparticle picture for magic generation during out-of-equilibrium quantum quenches. Crucially, because our result relies solely on two-point correlation functions, it provides a scalable route for the experimental estimation of fermionic non-local magic in large-scale quantum processors via fermionic shadow tomography.

We investigate the resilience of spinon quasiparticles in the $J_1$-$J_2$ zig-zag spin chain ($J_2>0$) from the viewpoint of momentum-space entanglement. For small $J_2$, we show that deconfined spinons survive well past the liquid-dimer transition before eventually collapsing towards the Majumdar-Ghosh point. In the highly frustrated zig-zag regime ($J_2 \gg |J_1|$), we model the system as two coupled Heisenberg chains and by Fourier transforming each subchain individually, a framework we dub the double-spinon description. While continuum field theories predict that this decoupled phase is strictly unstable to any finite inter-chain coupling, our analysis reveals that the double-spinon description remains robust over an extensive parameter regime. Notably, we find a stark asymmetry in spinon stability reflecting the underlying renormalization group flow: ferromagnetic coupling ($J_{1} < 0$) is marginally irrelevant and sustains fractionalization deep into the spiral phase, whereas antiferromagnetic coupling ($J_{1} > 0$) is marginally relevant and drives confinement much earlier. The ultimate breakdown of this fractionalized description is driven by a continuum of inter-chain excitations which manifests itself as a sharp ground-state momentum shift distinct from macroscopic thermodynamic phase boundaries. Our results establish momentum cut entanglement analysis as a tool to trace the quasiparticle resilience of spinons, as we show that treating the zig-zag Heisenberg chain as two coupled SU(2)$_1$ Wess-Zumino-Witten models provides a theoretical framework for strongly frustrated quantum magnets applicable beyond the decoupled limit.

In this work, we revisit black hole Love numbers from two complementary perspectives. First, we develop a manifestly gauge-invariant framework that directly integrates out the short-distance degrees of freedom of a static black hole in arbitrary spacetime dimensions. This approach yields the effective point-particle action and its associated Love numbers without relying on the standard matching procedure or on the Regge-Wheeler equation and its associated master field. Second, we investigate the role of Love numbers in black hole thermodynamics by analyzing a Schwarzschild black hole subjected to various types of external perturbations. We show that Love numbers govern the induced polarization of the black hole and control the leading corrections to its thermodynamic properties, thereby clarifying their physical significance in black hole thermodynamics.

Measurements of Higgs boson pair (HH) production in the four bottom quark (4b) final state are presented using proton-proton (pp) collision data at $\sqrt{s}$ = 13.6 TeV collected by the CMS experiment at the CERN LHC, corresponding to an integrated luminosity of 62 fb$^{-1}$. Events in which the Higgs boson decays, H$\mathrm{t\bar{t}}$, are separately reconstructed as pairs of small-radius jets (resolved), as well as those where they are reconstructed as single large-radius jets (merged), are studied exclusively. Benefiting from new methods in trigger selection, event selection, and signal extraction, the combination of analyses in the resolved and merged topologies gives an observed (expected) upper limit on the HH signal strength, $μ_\mathrm{HH}$, of 4.4 (4.4) at 95% confidence level (CL). Compared to previously published LHC results in the 4b final state, the expected limit with an equivalent integrated luminosity is improved by more than a factor of two in the resolved topology and is better in the merged topology as well. An updated analysis of the resolved topology using 138 fb$^{-1}$ of 13 TeV pp collision data yields an observed (expected) 95% CL upper limit on $μ_\mathrm{HH}$ of 10.0 (5.9), an improvement of about 25% in the expected limit compared to the published results using the same data. Results in the 4b final state with 13 and 13.6 TeV are combined, resulting in an observed (expected) 95% CL upper limit on $μ_\mathrm{HH}$ of 4.7 (2.8). The allowed ranges for the Higgs boson trilinear self-coupling and quartic coupling between two Higgs bosons and two vector bosons are also reported. These are the most stringent constraints achieved in the 4b final state to date.

Superactivation of quantum capacity is the phenomenon whereby two quantum channels, each with zero quantum capacity, can exhibit a strictly positive capacity when used in tandem. In this work, we explore superactivation in the previously unexplored non-asymptotic regime of finitely many channel uses. We give a definition of finite-blocklength superactivation and propose numerical methods that can certify it. Then, focusing on the 50% erasure and positive-partial-transpose channels considered in the original work on superactivation, we show that as few as 17 uses of the joint channel already enable qubit transmission with a fidelity unattainable by any number of uses of either channel alone, demonstrating a strong finite-blocklength form of superactivation and opening the door to experimental demonstration.

Prediction-market price moves are widely treated as informationally equivalent: a price jump is read the same way regardless of whether it reflects durable Bayesian updating, transient liquidity pressure, strategic position adjustment, or genuine disagreement. This paper formalizes the Signal Credibility Index (SCI) introduced in Nechepurenko (2026) as a stand-alone diagnostic. We make four contributions: (i) a revised persistence component using the persistence ratio PR(t,w) on logit prices, well-defined on short rolling windows; (ii) a weighted Cobb-Douglas form SCI(ααα) with flow-based concentration HHI_flow; (iii) a time-varying specification SCI(t; w) for real-time monitoring; and (iv) Monte Carlo validation including an out-of-distribution stress test, coordinated multi-wallet manipulation, and a logistic-regression benchmark. The validation establishes discrimination among designed microstructure regimes, not external evidence of downstream coordination effects. We document two failure modes consistent with the index targeting coordination credibility rather than pure information content: a Type II error on informed-but-concentrated whale repricing, and a Type I error on coordinated multi-wallet manipulation.

Exploiting permutation invariance to reduce the exponential scaling of semidefinite programs in quantum information has emerged as a powerful computational technique. In this work, we develop a systematic framework for using this reduction via Schur-Weyl duality for optimization problems, and establish methods that allow one to work fully inside the permutation invariant subspace while performing operations such as (partially) applying channels and taking (partial) traces, or computing expressions like the quantum relative entropy. We then apply our techniques to the problem of computing efficient lower bounds on the channel fidelity over $n$ parallel uses of a quantum channel. The algorithm, which we call symmetric seesaw method, exploits permutation-invariant codes to yield improved lower bounds on the channel fidelity over $n$ uses of the depolarizing and amplitude-damping channel in the regime of tens of channel uses, and was used in [Parentin, Bergh, Datta, Wilde: Onset of superactivation of quantum capacity, arXiv: today] to demonstrate non-asymptotic superactivation of quantum capacity for $n = 17$. An implementation of our methods, aimed at being suitable for various quantum information theoretic optimization problems, is also available as an open-source Python package.

Storage ring-based steady-state microbunching (SSMB) is a promising approach for generating high-average-power coherent radiation, while the instabilities driven by coherent undulator radiation in the laser modulator (LM) is important for the ring performance. In this paper we investigate the longitudinal single-bunch multi-turn LM instability using cavity mode decomposition techniques. The evolution of the wakefield in the longitudinal beam dynamics equations are derived, and the instability growth rates are analyzed. Numerical simulations show excellent agreement with the theoretical model, validating the mode decomposition approach. These findings provide critical insights into the design and operation of SSMB storage rings, suggesting effective mitigation strategies to suppress the instability and enhance the overall performance.

This paper develops a doubly robust extension of local-projections difference-in-differences (LP-DiD) for staggered absorbing treatments. The resulting estimator, DRLPDID, preserves the LP-DiD local-stack ATT target and is consistent when either the local untreated-outcome regression or the local treatment-probability model is correctly specified. It also delivers influence-function-based inference for post-treatment summaries and multiplier-bootstrap bands for dynamic paths. In Monte Carlo designs with covariate-driven selection, DRLPDID matches regression-adjusted LP-DiD under outcome-model alignment and clearly outperforms the IPT-only variant under propensity-score misspecification. In the no-fault-divorce application, DRLPDID tracks robust staggered-adoption estimators and is less negative than unadjusted LP-DiD.

This paper investigates the properties of Choi polynomials and their fundamental role in the theory of positive linear maps between matrix algebras. By focusing on Hermitian symmetric biquadratic forms, we establish a connection between the positivity of these forms and the structure of positive maps. We specifically explore the construction of indecomposable positive maps in matrix algebras, and their application as entanglement witnesses. Our analysis extends to the detection of Positive Partial Transpose (PPT) entangled states and the classification of edge PPT states in $M_m(\mathbb{C}) \otimes M_n(\mathbb{C})$. Our results provide a refined framework for identifying non-separable states that escape the standard PPT criterion, contributing to the broader understanding of entanglement distillation and quantum information theory.

We present a hardware-native gadget framework for solving constraint satisfaction problems on Rydberg quantum computing architectures. Our approach introduces a compact $xor_1$ gadget that enforces exactly-one constraints, ubiquitous in combinatorial optimization, directly through geometric embedding and blockade interactions. A key advantage of the $xor_1$ gadget is its fixed, problem-size-independent detuning requirements: enforcing constraints through blockade interactions eliminates the need for large penalty terms, thereby substantially reducing the detuning range compared to Quadratic Unconstrained Binary Optimization (QUBO) formulations and improving experimental feasibility. By tailoring the construction to the geometric connectivity of Rydberg atom arrays, the framework bypasses the all-to-all physical couplings often assumed in logical encodings. This enables embeddings compatible with planar layouts and avoids highly connected arrangements. We develop scalable implementations that reduce atom count and connectivity overhead while avoiding extensive classical preprocessing, making them compatible with near-term neutral-atom hardware. As illustrations, we apply our framework to the gate-assignment and $N$-queens problems, highlighting its practicality, resource efficiency, and hardware compatibility. In these examples, we observe reductions in detuning range of up to $99\%$ and savings in atom count and connectivity overhead of up to $54\%$ compared to the QUBO method. These results establish a route toward implementing large-scale combinatorial optimization on Rydberg platforms beyond the limits of existing encodings.

In this paper we show that the $θ$ invariant generalizes the Rozansky-Overbay invariant.

Based on a sample of $(10087 \pm 44) \times 10^6$ $J/ψ$ events collected with the BESIII detector at BEPCII, we report the first observation of the decay $J/ψ\rightarrow K^- Σ^0 \barΞ^++c.c.$. A partial wave analysis is performed to investigate the involved excited states. In addition to the well-established $Ξ(1690)$, a new doubly-strange hyperon $Ξ(1720) $ is observed decaying to $K^- Σ^0$ with a mass of $1721.0 \pm 5.2_{\rm stat.} \pm 3.4_{\rm syst.} ~{\rm MeV}/c^2$ and a width of $31.3 \pm 18.3_{\rm stat.} \pm 15.4_{\rm syst.} ~{\rm MeV}$, with a statistical significance exceeding $10σ$. The spin-parity hypothesis testing across various quantum number configurations reveals that the spin-parity of $Ξ(1720)$ favors $J^P = {\frac{3}{2}}^+$. Furthermore, the branching fraction of $J/ψ\rightarrow K^- Σ^0 \barΞ^++c.c.$ is determined to be $(2.68 \pm 0.04_{\rm stat.} \pm 0.17_{\rm syst.}) \times 10^{-5}$.

Searches for neutrinoless double beta decay are growing larger, with tonne-scale targets in several nuclides still far from exhausting the discovery space. What's beyond ton scale? Time projection chambers (TPCs) are one option for building large (100~T or kiloton-scale) instruments, but filling them with the familiar $^{136}$Xe for a $0νββ$ search is a problem: xenon is a scarce element whose atmospheric-extraction supply chain is small and hard to grow. If future $0νββ$ searches wish to exploit TPCs' known hardware scalability, we need to fill them with non-xenon target materials. Of particular value would be a TPC that can drift electrons, rather than ions, letting us use mature readout schemes which require gas gain. In this paper, we identify a set of previously-unappreciated, affordable gases which are likely to be electropositive, allowing electron drift and gain in gas-phase TPCs sensitive to $0νββ$ with the help of track-topology background rejection. We identify candidate $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{124}$Sn, and $^{130}$Te compounds suitable for gas-phase electron-drift TPCs; some may be suitable for liquid-phase TPCs as well. Using a figure-of-merit that emphasizes the need for track topology for background rejection, we argue that 100~T and kiloton-scale gas TPCs are realistic without unprecedented underground infrastructure.

This thesis is devoted to the study of hyperbolic differential operators on globally hyperbolic manifolds, linear gauge theories and their quantisation. In the first part, we treat the Cauchy problem for symmetric hyperbolic systems and normally hyperbolic operators on globally hyperbolic manifolds from first principles. Although hyperbolic equations are usually studied with local interactions, there are strong motivations from several areas of mathematical physics to consider also nonlocal interactions. As an intermezzo, we therefore take a small deviation from the classical local theory and prove well-posedness of the Cauchy problem for symmetric hyperbolic systems coupled to a broad class of nonlocal potentials. The second part presents a detailed exposition of linear gauge theories in globally hyperbolic spacetimes. Linear gauge theories are yet another deviation from the concept of hyperbolicity: the corresponding equations of motion are generically non-hyperbolic; however, can always be reduced to a constrained hyperbolic dynamics once an appropriate gauge fixing procedure has been applied. We give a thorough analysis of their Cauchy problem and classical phase space, complemented by a detailed discussion of many examples of physical interest, and discuss their quantisation following the algebraic approach to quantum field theory. The final chapter is devoted to the quantisation of Maxwell's theory on globally hyperbolic spacetimes, with the goal of proving the existence of Hadamard states. The novelty of our approach lies in a new gauge-fixing procedure at the level of initial data, which allows us to suppress the unphysical degrees of freedom. This gauge is achieved by means of a new Hodge decomposition for differential k-forms in Sobolev spaces on complete Riemannian manifolds, while states are constructed using tools from pseudodifferential calculus.

We introduce the finite-horizon first-order rank profile of a language $L \subseteq Σ^*$: the least quantifier rank needed by an $\mathrm{FO}[<]$ sentence to classify membership in $L$ correctly on all words of length at most $n$. The invariant measures quantifier depth only; formula size is deliberately not bounded. First, we prove a rank calculus that is independent of regularity. Every language satisfies $ρ_L(n) \le \lceil \log_2 n \rceil + 4$, via balanced first-order distance formulas and exact-word definitions. Moreover, $\sup_n ρ_L(n) < \infty$ holds exactly when $L$ is globally $\mathrm{FO}[<]$-definable, and the supremum equals the minimum quantifier rank of such a definition. Second, for regular languages we prove a sharp aperiodicity gap: if the syntactic monoid of $L$ is aperiodic, then $ρ_L(n) = O(1)$; otherwise $ρ_L(n) = \log_2 n + O_L(1)$. The lower bound extracts a nontrivial cyclic component from the syntactic monoid and combines it with an Ehrenfeucht-Fraisse power lemma for long repetitions of a fixed word. Thus, for full $\mathrm{FO}[<]$ quantifier rank, regular languages admit no intermediate finite-horizon growth between bounded and logarithmic rank.

We prove a low-regularity version of Hawking's singularity theorem for Lorentzian metrics in $W^{1,p}$ with Riemann curvature in $L^p$, where $p>2n$ and $n$ the dimension of spacetime. This extends previous results beyond the Lipschitz regime. Under suitable lower Ricci bounds and upper mean curvature assumptions, expressed in terms of temporal functions, we establish both the globally hyperbolic version of Hawking's theorem, in the form of an upper bound on the time separation from a spacelike Cauchy hypersurface, and the version with a compact achronal spacelike hypersurface, yielding timelike RT-geodesic incompleteness. The proof combines regularisations, based on the elliptic RT-equations, to raise the regularity of the metric by one derivative, with a refinement of the previously used manifold convolution. We introduce a new smeared-out notion of mean curvature adapted to the low metric regularity before, and the $W^{2,p}$-hypersurfaces arising after regularisation. As further consequences, we show that $W^{1,p}$-Lorentzian metrics with $L^p$-bounded curvature are causally plain, and we prove a corresponding low-regularity version of Myers's theorem in the Riemannian setting.

Financial misconceptions carry direct economic costs, from panic selling to equity market avoidance, yet they are notoriously resistant to correction. Traditional financial literacy interventions are constrained by cost, reach, and a persistent gap between knowledge and behavioral change. Across three pre-registered studies, we find that purposefully designed LLMs can durably correct financial misconceptions. Critically, two factors are necessary for this effect. First, corrective intent: LLMs prompted only to discuss a misconception produce corrections no better than unassisted self-reflection, and undirected LLM conversations can actively entrench misconceptions. Second, recipient receptivity: financial concepts are often foreign to the investors who misapply them, and LLM responses pitched below a participant's financial sophistication are judged as less credible and produce substantially weaker corrections. LLMs thus offer a scalable alternative to traditional financial literacy intervention, but only when designed with both factors in mind.

In this work, we construct a double O(3)-sigma model minimally coupled to a Maxwell field in (2+1)-dimensional spacetime and investigate the existence of self-dual magnetic vortex solutions. An analysis of the Bogomol'nyi-Prasad-Sommerfield (BPS) property reveals that both sigma fields belong to the same topological sector and that the potential assumes a periodic cosine-like form. Furthermore, the theory supports the emergence of magnetic vortices with quantized flux, described by two nonlinear O(3)-sigma sectors that effectively combine into a single topological sector in the BPS regime. In addition, we analytically verify the consistency of the BPS structure and its asymptotic behavior. Within this framework, numerical vortex solutions confirm that the field profiles are smooth and spatially localized, with both the magnetic field and the energy density remaining regular and localized.

In this thesis, we study the collective modes induced by the chirality of elementary particles in magnetized media and their implications for neutron star phenomenology. We theoretically predict that the chiral magnetic wave can arise in quark matter inside neutron stars, resulting in the emergence of novel types of seismic oscillations and associated gravitational waves in the context of asteroseismology. We also investigate the response to dynamical electromagnetic fields and find that a dynamical screening, distinct from the conventional Landau damping, occurs due to the chiral anomaly.

In this article, we derive a rigorous lower bound on the ground-state energy for a class of one-dimensional quantum systems in deformed space with minimal coordinate and momentum uncertainties, representing the absolute minimum energy that is physically attainable. We consider a harmonic oscillator in such a space and calculate its ground state energy. We generalized the problem to an arbitrary potential, deriving an equation for the coordinate uncertainty corresponding to the minimal energy, which can be solved numerically. Using a linear approximation in the deformation parameters, we obtained a general expression for the ground-state energy. We determined the domain of existence of solutions for the anharmonic oscillator potential with respect to the deformation parameters.

We show that in a self-consistent preon model, where Standard Model quarks and leptons are three-body composites confined at a metacolor scale Lambda_cr ~ 10^14 GeV, both leptoquarks and the Standard Model gauge group SU(3)_c x SU(2)_L x U(1)_Y emerge as structural predictions rather than inputs. Combining the preon content of a quark with that of a lepton gives exactly four distinct six-body bosonic leptoquark composites per generation, with electric charges Q = +2/3, -1/3, -1/3, -4/3 and a universal B-L = -2/3 fixed by the preon charge assignments. Their mass is of order Lambda_cr rather than of order the SM fermion masses, because the dynamical near-cancellation that produces light fermion masses is specific to three-body fermionic composites and does not extend to six-body bosonic ones. The fractional B-L = -2/3 forbids proton decay via single leptoquark exchange, requiring a dimension-12 operator and giving tau(p -> e+ pi0) ~ 10^58 years, consistent with the experimental bound > 2.4 x 10^34 years. It is shown that the SM gauge group emerges as a low-energy symmetry consistent with the Planck-scale boundary condition, and leptoquarks are required -- not merely permitted -- by the matching. The anomaly-matching argument extends to a tower of 3n-body composites, each level imposing consistency conditions on the next; we call this the vertical bootstrap and advance it as the organizing principle of the preon program.

The Barcelona Zetascale Lab (BZL) project aims to strengthening Europe's capacity in the design and manufacture of RISC-V based high-performance computing chips. In this context, we present a holistic pre-silicon verification and validation (V&V) methodology targeting highly robust RISC-V chip designs. This paper provides an overview of BZL's V&V approach, which integrates three complementary platforms: (1) a UVM-based verification environment to thoroughly validate RTL functionality; (2) an FPGA-based validation platform that enables system-level pre-silicon hardware-software RTL validation; and (3) a CI/CD flow that continuously automates build, deployment, and tests across these domains. By embedding these platforms into an industrial-grade V&V loop and exploiting large-scale CPU and FPGA hardware infrastructures, the BZL project enables continuous evolution of reliable hardware development and software integration. We believe that the BZL's V&V flow represents a robust and scalable foundation for ensuring the pre-silicon functional correctness and system level validation of RISC-V chip designs, and can serve as a key enabler for strategic initiatives in Europe, such as EPI and DARE, and beyond.

FPGA-level emulation is a key step in pre-silicon chip design validation. However, emulating large-scale multi-core systems increasingly exceed the hardware resource capacity of a single FPGA, limiting the feasibility of full-system emulation. To address this challenge, we introduce EMiX, a scalable multi-FPGA framework that enables distributed emulation of multi-core RISC-V architectures beyond single-FPGA resource limits. EMiX systematically partitions a monolithic multi-core design into multiple components and deploys them across multiple interconnected FPGAs, effectively exploiting inter-FPGA interconnects to balance scalability and performance without requiring fundamental RTL redesign. We prototype EMiX with a 64-core architecture across eight interconnected Alveo U55c FPGAs (scalable on core and FPGA counts), successfully demonstrating full-system execution including Linux boot. EMiX will be released as an open-source platform.