The $δ$ phase of Niobium Nitride (NbN) is a promising superconducting material, which is chemically stable and shares lattice compatibility with conventional III-Nitride semiconductors. Due to a high critical temperature (T$_{c}$) and a high critical (magnetic) field (H$_{c}$), NbN is much-coveted for a diverse set of applications spanning from single photon detectors, and hot-electron bolometers to quantum computing architectures using superconducting circuits. However, synthesizing high-quality epitaxial films of phase pure and stoichiometric $δ$-NbN in a cost-effective manner, is challenging. In this study, we investigate the epitaxial growth of single crystalline $δ$-NbN on TiN-buffered c-sapphire (Al$_{2}$O$_{3}$) substrates by sputtering at room temperature. For these films, we demonstrate a surface-roughness in picometer-scale, the lowest reported till date. The critical temperature (T$_{c}$) of the epitaxial $δ$-NbN films was observed to decrease with the insertion of the TiN buffer layer, tentatively attributable to the leakage of Cooper pairs, due to the proximity effect. TiN and NbN layer behave as a bilayer system, wherein Cooper-pair leakage is facilitated by the absence of any oxide interlayer. Consequently, T$_{c}$ reduces with increasing thickness of the TiN layer.

Differential Interference Contrast (DIC) microscopy and chiral analysis are two imaging techniques that measure the birefringence, i.e., the phase difference introduced by a sample on two orthogonal polarizations. Conventional approaches employ Gaussian beams and infer birefringence from polarization changes, resulting in phase-estimation sensitivities that depend on the unknown phase. We demonstrate here a new type of birefringence detector. It makes use of a vector vortex beam, a type of structured light endowed with optical modes that carry opposite orbital angular momentum (OAM). Using quantum estimation theory tools, we demonstrate that the sensitivity of phase estimation is independent of the value of the unknown phase, and can be even better, in principle, than the conventional approach. We experimentally validate the proposed scheme, demonstrating the potential of structured light for robust and uniform birefringence sensing.

We realize an injector device that supplies warm gas directly into a cryogenic environment. This injector has several advantageous features, including robustness, rigidity, simple installation, and excellent thermal isolation between a hot ($\sim$300 K) copper fill line and a cold ($<$3 K) cryogenic buffer gas cell. Less than 200 mW heat load on the cell is observed in realistic conditions of a molecular precision measurement experiment. A polyamide-imide (PAI) tube is the essential design feature. The fill line is epoxied to one end of the tube while the other end of the tube is connected to the cell via a slip-fit onto a brass nipple, realizing a complete vacuum-tight seal. PAI contracts on the brass nipple when cooled, forming a cryogenic leak-tight seal. The injector is easily (de-)mountable and rigid, with no significant displacement of the fill line relative to the cell observed during cooldown to 4 K. We characterize injector performance by flowing into the cell $\text{SF}_6$ through the hot fill line and cold $\text{He}$ buffer gas through a separate cryogenic fill line while laser ablating a barium-containing target. This produces cold BaF free radicals, detected using absorption spectroscopy. This injector design will be employed to laser cool radium-containing molecules, such as $\text{RaF}$ and $\text{RaOH}$, where leak-tight delivery of $\text{SF}_6$ and $\text{H}_2\text{O}$ reagents into a cryogenic buffer gas cell is required for scientific and safety reasons. These molecules are of particular interest for the study of symmetry-violating nuclear properties and searches for physics beyond the Standard Model.

A predictive physics-based model of human respiratory, phonatory, and articulatory subsystems is developed to simulate voice production. Representing lungs, compressible airways, and vocal folds as spring-damper-mass controlled piston-cylinder systems, our mathematical model robustly captures the intricate dynamics of airways during phonation. The nonlinear viscoelastic properties of lung tissues and compressible airways were investigated, yielding a responsive and expressive baseline respiratory model with the capability to further extend into a patient-specific model for both respiration and phonation. The resulting framework was subsequently integrated with a mechanical representation of the vocal tract, governed by the glottal area waveform (GAW) capturing the motion of vocal folds during sustained phonation. The GAW is extracted from laryngeal high-speed videoendoscopy data of a normophonic participant using deep learning. Our novel paradigm transcends beyond modeling the respiratory system, enabling AI-driven modeling of vocalization, including vocal fold dynamics, interactions with flow aerodynamics, and flow resistances, induced by the oscillatory behavior of vocal folds. Our investigation leads to the first-ever simulation of respiratory dynamics for vocalization, directly advancing the prediction of subglottal pressure distributions, impossible to measure directly and noninvasively in humans, dynamic resistances, and energy transfer mechanisms during phonation in voice mechanics.

Understanding how swine farms are interconnected, directly and indirectly, is essential to characterizing infectious disease transmission. This study aimed to describe the connectivity of swine farms across 11 network types, including vehicle movements (i.e., trucks and trailers), animal movements, and distance-based farm-to-farm contacts, to identify links among production types and farms likely to be consistently characterized as super-spreaders. Truck and trailer movement networks were the most densely connected, particularly for feed transport, showing connectivity levels between 98.7% and 99.7% higher than those of pig movement and distance-based networks. These networks also exhibited the highest degree and frequency of connections between farms, while the aggregated truck network, which included all truck types, showed the greatest potential to act as a bridge connecting farms. Finisher farms were highly interconnected with other farm types across all networks. Sow farms were frequently reached by other farm types, especially through feed truck movements, representing up to 8.7% of these links. We demonstrated that in vehicle movements and proximity networks, finisher farms played a major role as super-spreaders. When comparing the top 50 farms ranked by super-spreader score in each network, vehicle-based networks showed the highest similarity, with up to 89% of top-ranked farms shared between vehicle networks. In contrast, pig movement and distance-based networks identified largely distinct sets of top-ranked farms, sharing at most 4% and 8%, respectively, with other contact networks. Overall, each network exhibited a distinct connectivity structure, resulting in different sets of high-risk farms, particularly regarding potential transmission to breeding farms. These findings support the integration of multiple transmission pathways into disease surveillance.

We investigate the geometric structure of two-neutron halo nuclei from the perspective of Efimov physics. Using the analytic three-body wave function obtained from the Faddeev equations in the unitary limit, we explore the connection between Efimov universality and the spatial configuration of these weakly bound systems. The internal geometry is quantified through probability densities, root-mean-square interparticle distances and characteristic opening angles, evaluated for different neutron-core mass ratios. Our results reveal a universal trend in the geometry of s-wave dominated halo nuclei, reflecting the universal correlations characteristic of the Efimov-like regime.

We propose vortex nucleon scattering as an angular-momentum-resolved probe of nucleon--nucleon partial waves. Using the standard $LSJ$ partial-wave $S$ matrix as input, we show that an on-axis vortex incident state with a fixed orbital angular-momentum projection $m_L=\ell$ imposes the direct selection rule $L\geq |\ell|$ on the initial nucleon--nucleon partial waves. As a result, the initial $S$ wave is excluded for $\ell=1$, while both the initial $S$ and $P$ waves are excluded for $\ell=2$. The underlying phase shifts are not modified. Instead, the vortex external state changes how the ordinary partial waves are projected into the scattering amplitude. We further analyze off-axis scattering, where the displacement of the target from the vortex axis introduces Bessel-function weights and partially relaxes the on-axis selection rule. These results suggest that vortex nucleons can provide a new experimental handle on the partial-wave content of the strong nucleon--nucleon interaction.

In this work, we describe the development of track- and energy-reconstruc-tion algorithms for atypical Time Projection Chambers (TPCs) that will be used at the Institute of Experimental and Applied Physics, Czech Technical University in Prague, to search for the anomalous internal pair creation reported by the ATOMKI group. These chambers operate with an inhomogeneous toroidal magnetic field oriented orthogonally to the electric field; we therefore refer to them as Orthogonal-Field TPCs (OFTPCs). Although this configuration distorts the drift of ionization electrons and complicates the resulting electron and positron trajectories, it also offers several practical advantages. We present the most effective of several tested approaches, which employs a simulated ionization-electron drift map for track reconstruction and a Runge--Kutta-based fit for energy reconstruction. Using simulations, we demonstrate that -- under idealized conditions, namely an ideal charge readout with no amplification and no noise and with known initial track positions and directions -- it is possible to achieve a fitted Gaussian width (sigma) better than 1\% in relative energy for both electrons and positrons, after applying corrections for systematic effects that depend on the track parameters.

We report on a vision AI agent pipeline for non-contact material strain and property extraction from video data, demonstrated on video taken during hydrostatic testing of four OFHC copper cylinders conducted as part of the LEGEND-1000 hardware validation campaign. Traditional strain gauge measurements proved unreliable, motivating a fully-automated agentic alternative. The agent was built on the LangChain framework with Claude Haiku 4.5 as its central reasoning engine, integrating a specialized suite of computer vision tools: FFmpeg for video preprocessing and rotation correction via Hough Line Transform, the Segment Anything Model 2 (SAM2) for spatiotemporal segmentation with automated memory-informed dynamic chunking, and a hybrid EasyOCR and LLM-based timestamp validation pipeline. Three specialized sub-agents were developed to process the video data and obtain cylinder diameters and timestamps while autonomously handling obstacles such as corrupted frames and memory limits. From the diameter profiles synchronized to pressure data, hoop stress--strain curves were reconstructed and yield strengths were calculated using the 0.2\% offset, 0.5\% EUL, and Johnson-Cook methods across two independent tests. Cross-validation against a non-agentic pipeline confirmed agreement for the diameter extraction at the $\pm$5 pixel level. The material properties and testing results were further compared to Ansys mechanical simulations performed as part of the LEGEND-1000 reentrant tube design campaign. This work showcases the power of agentic pipelines to extract materials data from video alone.

The electromagnetic decay of the $\approx$40 $μ$s isomer of $^{250}$No has been investigated using the \textsc{Geant4} toolkit for the simulations of the interaction of particles through matter. It is concluded that the decay does not follow the pattern established in the lighter isotones, where the isomer decays directly to members of the ground state rotational band. An alternative scenario is proposed. The implications on the location of the isotopic border for neutron deficient Rf isotopes are discussed.

We investigated the $\bar{K}$-nucleus interaction through the simultaneous measurement of the inclusive $^{12}{\rm C}(K^-, p)$ and exclusive $K^-$-escape $^{12}{\rm C}(K^-, p K^-_{esc})$ reactions at $1.8$ GeV/$c$ at J-PARC. The present measurement explicitly focuses on the $K^-$ escape process for the first time, successfully accomplishing a direct experimental determination of the imaginary part of the $K^-$ optical potential. The differential cross section for the $K^-$-escape reaction was determined to be $436 \pm 6\:(\text{stat.}) \pm 44\:(\text{syst.})~μ\text{b/sr}$. A simultaneous likelihood fit yielded real and imaginary potential strengths of $V_0 = -72\:^{+3}_{-5}\:(\text{stat.})\:^{+0}_{-8}\:(\text{syst.})~\text{MeV}$ and $W_0 = -100\:^{+7}_{-1}\:(\text{stat.})\:^{+0}_{-16}\:(\text{syst.})~\text{MeV}$ at the nuclear center, respectively. The derived $W_0$ is significantly stronger than that predicted by theoretical models based on one-nucleon processes, suggesting possible contribution of multi-nucleon involving processes.

Ancient human beings started "external entropy production" in a late stage of evolution, in addition to the internal entropy production by which energy was dissipated within the body of life, as previously described consistently with the birth of life by maximum entropy production principle. In this paper, the mechanism for development of external entropy production, which is strongly related with use of tools and controlling fire, is theoretically investigated. Archaeological data show that the brain size of ancient human beings started rapid increase around 2.5 million years ago when the usage of tools and control of fire started. It may be natural to assume that the rapid growth of brain size is related to the growth of awareness which helped cooperation with the other human beings for control of fire. Coupled equations for the growth rate of brain including awareness and for growth rate of size of the interacting human beings are analyzed. The external entropy production per one human being which is directly related to the group size of cooperating human beings is estimated to increase as about 20 million years in the beginning from the critical time. This evolution created coexistence of internal entropy production of traditional multi-cellular life and new external entropy production of multi-body life. A psychological problem due to the coexistence of two kinds of entropy production mechanism in human being and concept of technologies based on the present thermodynamic evolution theory are discussed. It is suggested that the evolutionary understanding of the origin of global warming based on the external entropy production may be important to create an useful countermeasure.

Supratransmission is examined in nonlinear lattices with purely nonlinear coupling, extending the phenomenon to systems that lack a linear pass band. In contrast to standard lattices with mixed linear-nonlinear interactions, the present model has no linear spectrum, so energy propagation arises entirely from nonlinear effects. Asymptotic analysis yields a discrete $p$-Schrödinger (DpS) equation that {provides an accurate description in the weak- and intermediate-coupling regimes and offers qualitative insight in the strong-coupling regime}. Perturbation provides analytical approximations for the critical driving amplitude, explicitly showing its dependence on the driving frequency, coupling strength, and the nonlinearity exponent $p$. The analysis identifies a non-trivial dependence of the critical amplitude on $p$, with distinct trends in different coupling regimes. Numerical continuation and direct simulations {validate the theory in regimes where the asymptotic reduction is applicable and show good agreement across a wide range of parameters}. The results establish supratransmission in fully nonlinear lattices and clarify the associated energy-transport mechanisms, with relevance to mechanical lattices, tunable metamaterials, and nonlinear optical arrays.

In this paper, we propose an integrable semi-discretization of the two-component Hunter-Saxton (2-HS) equation, which is obtained as the short-wave limit of the two-component Camassa-Holm (2-CH) equation. We also show that the 2-HS equation can be derived from a new set of bilinear equations, distinct from previously known ones, via a pseudo 2-reduction and a hodograph transformation. Furthermore, we construct the N-soliton solutions of both the continuous and semi-discrete systems in Wronskian and Casoratian forms, respectively.

In the present work, we present a number of localized wave patterns that are theoretically analyzed and numerically illustrated to be observable within the widely applicable paradigm of the FPUT lattice. In particular, we derive a modified KdV equation from the FPUT lattice, which admits a variety of localized waves including these exact rational solutions representing rogue-wave profiles, solitons and breathers on the top of not only homogeneous, but also periodic elliptic function traveling-wave background. We utilize these exact solutions of the modified KdV reduction to construct consistent initial conditions for the FPUT lattice and perform time stepping of the latter. Relevant comparisons between these numerical solutions of the FPUT lattice and their associated analytical counterparts have been conducted to demonstrate good performance of the derived modified KdV reduction in approximating distinct localized wave structures from the FPUT lattice. This approach paves the way for importing a number of quasi-continuum waveforms to the FPUT lattice and the potential associated physical experiments, including recent ones in mechanical metamaterials.

This paper explores the effectiveness of various novel deterministic and traditional stochastic data assimilation (DA) and parameter recovery (PR) algorithms given noisy data from chaotic systems. We use semi-analytic methods to numerically construct synthetic data from the Lorenz '63 and multiscale Lorenz '96 chaotic dynamical systems, adding white noise. Our findings show that, for different noise levels, deterministic PR algorithms paired with deterministic DA algorithms are shown computationally to be overall more accurate and stable than stochastic PR algorithms. Additionally, deterministic PR methods have demonstrated greater speed and efficiency, requiring less computational power than stochastic PR methods. This suggests that future work should consider exploring the full potential of deterministic PR algorithms in the presence of noise.

Considered and analyzed below are fully non-homogeneous initial-boundary-value problems for the celebrated Dirac system, formulated on the spatial half-line. Analytical solution formulae are derived formally via suitable implementation of the well-known Fokas' unified transform methodology, and rigorously verified a posteriori. The latter substantial task relies on complex-analytic tools and careful interpretation of the obtained integral representations. These valid solutions are then used for investigating qualitative properties. These include boundary behavior near the axes of the domain as well as long-range asymptotics and long-time (eventual) periodicity. Notably, smoothness of the solution, both within and upto the boundary of the domain, depends heavily on certain compatibility conditions between initial, boundary and forcing data. Further results pertaining to solution's regularity and uniqueness are thence established based on the qualitative theory. The closed-form expressions reported here are also useful in the study of non-linear counterparts.

Stochastic oscillations can emerge from a two-population model as triggered by endogenous finite size fluctuations. Here, an extended dynamical scenario is considered in which a third fluctuating species is added to a proto-typical scheme of neuronal interaction. As we shall prove both analytically and numerically, the third added species can enhance or even suppress the emergence of quasi-cycles, namely the coherent oscillations of the two original populations, as instigated by the demographic noise component. In general, investigating the coupled dynamics of noisy oscillators of the type considered could yield an extended framework for synchronization studies, beyond the pioneering setting introduced by Kuramoto.

Using the energy function on the extended Siegel-Jacobi upper half space of order $n$, $\tilde{\mathcal{X}}^J_n$, with $n\in \mathbb{N}$, the equations of motion in the variables $(x,y,q,p,κ)$ attached to linear Hamiltonians in the generators of the real Jacobi group $G^J_n(\mathbb{R})$ are presented, where $x,y$ are symmetric matrices in $\mathcal{M}(n,\mathbb{R})$ and $p,q$ are real $n$-vectors. The case $n=1$ is presented separately.

For compressible nonlinear isotropic elasticity it is well known that rank-one convexity, polyconvexity and the monotonicity of the Cauchy stress tensor with respect to the logarithmic stretch tensor (the true stress-true strain monotonicity, TSTS-M$^+$) are independent constitutive conditions which should, however, all together be satisfied for a physically meaningful description of idealized elastic materials. In the incompressible case, TSTS-M$^+$ turns into Hill's inequality since the Cauchy stress $σ$ reduces to the Kirchhoff stress $τ$. Hill's inequality requires then monotonicity of the Kirchhoff stress in terms of the logarithmic stretch tensor evaluated for incompressible response. In this paper we clarify how the a priori independent notions of Legendre-Hadamard ellipticity (LH), polyconvexity and Hill's inequality are nevertheless intimately connected. More precisely, by providing several alternative proofs, we show that both LH-ellipticity (rank-one convexity) and polyconvexity imply the weak Hill inequality in the incompressible two-dimensional case.

We study the reflection of a weak planar shock from a rigid wall in the joint limit of weak shock strength and nearly glancing incidence. In the distinguished scaling (M=1+λα^2), where (M) is the incident-shock Mach number and (α) is the glancing angle, the inner reflection region is governed by the unsteady transonic small-disturbance (UTSD) equation. The corresponding canonical shock-reflection problem is controlled by the single parameter[a=\fracα{\sqrt{2(M^2-1)}}=\frac{1}{2\sqrtλ}+O(α^2),]so the limiting inner parameter (a_0=1/(2\sqrtλ)) is independent of (γ). Consequently, the detachment value (a_d=\sqrt2) maps to the physical scaling threshold (λ_d=1/8), with Guderley--Mach reflection for (λ>1/8). The physical trajectory angle is obtained from the canonical UTSD trajectory function (g(a)) by the Mach-number strength scale[χ_{\rm phys}\sqrt{2(M^2-1)},g(a)+O(M^2-1) 2\sqrtλ,α,g(a_0)+O(α^3).]We derive the self-similar UTSD reduction, the sonic parabola, the UTSD shock polar and its regular-reflection cubic, recovering (a_d=\sqrt2) directly. We also give the local linearisation and formal adjoint solvability condition defining the first correction (H(a;γ)), without claiming a computed correction curve. Finally, a time-marching solver for the full leading-order canonical UTSD system is benchmarked against the Hunter--Tesdall (a_0=0.5) triple point: once transverse compression (u>1) behind the Mach stem is retained, the computed (u=0.5) contour passes through ((ξ,η)=(1.007,0.514)), compared with the published ((1.008,0.514)).

Let $X_r\sim N_r(0,1)$ be the centered unit-scale generalized Gaussian random variable with density proportional to $\exp(-|x|^r/2)$. We prove that, for $p,q>0$, there exists a strictly positive random variable $V$, independent of $X_q$, such that $X_p\stackrel{d}{=}VX_q$ if and only if $p\le q$. Moreover, the law of $V$ is unique. For $p<q$, put $a=1/p$, $b=1/q$, and $α=b/a=p/q$. If $S_α$ is a positive $α$-stable random variable with Laplace transform $\mathbb{E}\exp(-uS_α)=\exp(-u^α)$, set $W_0=S_α^{-b}$, let $W$ be the $W_0$-size-biased version of $W_0$, and define $V_{p,q}=2^{a-b}W$. Then $X_p\stackrel{d}{=}V_{p,q}X_q$. For $p>q$, the required Mellin quotient, viewed as the candidate characteristic function of $\log V$, is unbounded by Stirling's formula, and hence cannot be a characteristic function. The factor laws form a multiplicative cocycle, $V_{p,r}\stackrel{d}{=}V_{p,q}V_{q,r}$, for $p\le q\le r$, where the factors on the right-hand side are independent copies. Thus the Mellin quotient isolated by Dytso, Bustin, Poor and Shamai is realized constructively throughout the $p<q$ branch. In particular, $Φ_{p,q}$ is positive definite exactly in the range $p\le q$, and the inverse Fourier--Mellin candidate density in the remaining $p<q$ branch is a genuine nonnegative probability density. The known Gaussian-base and bounded-parameter product cases are recovered as parts of a single positive scale-mixture classification.

The present study develops a detailed theoretical and mathematical formulation to analyze the time and frequency domain propagation characteristics of Love waves in a stratified fractured poroviscoelastic continuum.The top stratum is modeled as a fractured poroviscoelastic material,whereas the lower semi infinite region exhibits heterogeneity and a gradual transition from viscoelastic behavior near the interface to purely elastic response at greater depths.Fractional order constitutive relations are incorporated to capture the memory-dependent mechanical behavior of the medium using Riemann Liouville fractional derivatives. Three distributed source models, namely Gaussian, Ricker and double-couple sources, are considered. To the best of our knowledge, the mathematical formulation of these distributed sources within the present framework has not been established in earlier studies, where the excitation is typically modeled using an idealized point source. By applying Fourier transform techniques in conjunction with Greens function methodology, the complex dispersion relation is obtained. Since the resulting dispersion equation yields complex roots, a hybrid Newton Raphson iterative algorithm is employedto compute these roots efficiently. Synthetic seismograms are generated to verify that the obtained solutions remain physically consistent and meaningful. Numerical simulations are then performed to investigate the effects of heterogeneity, fractional viscoelasticity and porosity on wave propagation characteristics, thereby identifying the parameters that exert the most significant influence on the system response. Furthermore, to examine the structural implications of the propagated waves, a single degree of freedom SDOF oscillator model is employed to evaluate the surface response corresponding to different types of seismic sources.

We discuss here how non self-adjoint Hamiltonians, and their related Heisenberg-like dynamics, can be used to model a political system consisting in a coalition $\C$ of different parties (forming a government) and by their (original) supporters $\Sc$. Our aim is to model how the opinion of these supporters changes depending on the efficiency, competence and coherence of the coalition $\C$, as these are perceived by $\Sc$ during their action while governing. After a rather general introduction we propose three specific models, and we describe and comment the dynamical behaviour of the { full} system, $\Sc\cup\C$. The role of the so-called {\em balanced Hamiltonians}, recently introduced by the authors in connection with integrals of motion, is discussed in details.

Thermal runaway remains a critical safety concern in battery systems and other thermally active devices, necessitating reliable methods for predicting the conditions under which thermal runaway may occur. In this work, we develop a finite element framework for assessing thermal stability in systems undergoing transient heat conduction with temperature-dependent internal heat generation. The formulation leads naturally to a generalized eigenvalue problem, wherein the sign of the smallest eigenvalue provides a direct criterion for determining the onset of thermal runaway. This approach enables direct prediction of thermal runaway thresholds in geometrically complicated problems without requiring computationally expensive transient analysis. The proposed methodology is validated through comparison with analytical solutions for a cylindrical Li-ion cell, as well as with a pack of cylindrical cells, demonstrating excellent agreement in both cases. Based on this model, the influence of material properties, boundary conditions, geometric parameters, and spatially varying heat generation on stability limits is examined. A key advantage of this formulation is its effectiveness even for complex geometries where analytical methods become impractical. By providing a systematic and computationally efficient means to identify stability thresholds, the present work offers a practical tool for the thermal design and safety assessment of battery systems.

We establish a rigorous non-perturbative closure framework for the three-dimensional (3D) $ϕ^4$ scalar field theory near criticality, bypassing the long-standing limitations of perturbative Feynman diagrammatic expansions. By slicing the 3D Euclidean space along a spatial axis, the exact dressed theory is mapped onto a matrix operator evolution governed by the infinite-dimensional symplectic Lie algebra $\mathfrak{sp}(\infty)$. We generalize the classical Stroh formalism and Barnett-Lothe integral invariants from anisotropic elasticity to the quantum field Hilbert space. Crucially, we prove that the dressed operator-valued Barnett-Lothe tensors satisfy the algebraic identity $\hat{\mathbf{S}}^2 + \hat{\mathbf{H}}\hat{\mathbf{L}} = -\hat{\mathbf{I}}$ exactly and non-perturbatively, regardless of the coupling strength. By coupling this symplectic invariance with the Källén-Lehmann spectral representation and the Schwinger-Dyson equations, a novel "Symplectic Bootstrap" master spectral integral equation is formulated. The framework exhibits exact dimensional reduction, naturally degenerating to the Onsager exact solution ($η= 1/4$) in 2D and the Gaussian triviality limit ($η= 0$) in 4D. Solving the transcendental bootstrap equation under the strong-coupling conformal fixed point yields the non-perturbative anomalous dimension $η\approx 0.0363$, matching the state-of-the-art conformal bootstrap numerical limits. Finally, a profound holographic duality between the statistical state equations and the post-buckling bifurcation of fluctuating soft matters is discussed.

We construct exact, positive-energy, normalizable wave-packet solutions of the Dirac equation in the axisymmetric potential $V=-\,v_0/ρ$ -- to our knowledge, the first such solutions in any external potential. Remarkably, one family comprises only elementary functions whose longitudinal profiles reproduce the free-Schrödinger Hermite--Gauss wave packets in the nonrelativistic limit. All packets share two striking features: (i) a probability density that is pointwise decoupled from spin orientation -- despite the inherent spin-orbit coupling of the Dirac equation -- and (ii) a complete freezing of their time evolution at the critical coupling $v_0\to\hbar c/2$. We also present a simple scheme that maps solutions of the 2D Helmholtz equation to further exact Dirac wave packets.

We study the closed-string tree-level Virasoro-Shapiro amplitude using the dispersive S-matrix bootstrap. For the ten-dimensional maximally supersymmetric four-point amplitude, we impose analyticity, crossing symmetry, partial-wave unitarity, and Regge boundedness. With the massless graviton pole kept explicitly, the resulting dispersion relations and crossing null constraints give numerical bounds on the leading low-energy coefficients normalized by the gravitational coupling. We then introduce a Virasoro-inspired ansatz, which becomes a set of nonlinear relations among Wilson coefficients and shrinks the allowed region toward the Virasoro-Shapiro trajectory. Finally, we study a gravity-pole-subtracted setup, where the regular part of the amplitude has a well-defined forward limit. In this stripped problem, the nonlinear constraints reduce the allowed region to a small island containing the Virasoro-Shapiro point, for which we provide an analytic bootstrap explanation.

We prove a `nonlinear graviton theorem' for higher-spin self-dual gravity. We consider small deformations of the complex structure of the non-projective twistor space that are bounded in a specified region near the origin and investigate the space $M_{HS}$ of holomorphically embedded complex planes $\mathbb{C}^2$ that intersect the origin. We show that this space is an infinite dimensional complex manifold with a canonical projection onto a four-dimensional holomorphic self-dual spacetime $\mathcal{M}$, and discuss the geometry induced on this new higher-spin space. Solutions of higher-spin self-dual gravity are then obtained by choosing an embedding of spacetime $\mathcal{M}$ into higher-spin space $M_{HS}$, with higher-spin symmetries arising from the different choices of embedding. Integrability of the theory is manifested in the form of a Lax pair for the system that we present. We conjecture that chiral higher-spin gravity can similarly be realized by considering deformations that are unconstrained at the origin.

By incorporating leading $c\,$-dependent corrections to the Carroll transformations, we introduce the ``post-Carroll transformations''. We demonstrate that these transformations are consistent with post-Carrollian mechanics \cite{Najafizadeh:2025ksm}; furthermore, they give rise to the so-called ``post-Carroll algebra''. We show that, unlike the Carroll algebra, this new structure allows for a central charge in higher dimensions; we refer to it as the ``Carroll-Bargmann algebra''. To construct conformal extensions, we first build the conformal extension of the post-Carroll algebra and study field theories invariant under this symmetry. We then construct the conformal extension of the Carroll-Bargmann algebra, referred to as the ``Carroll-Schrödinger algebra'', and demonstrate that it precisely matches the symmetry algebra of the higher-dimensional Carroll-Schrödinger theory \cite{Najafizadeh:2024imn}. Finally, we derive the general form of two-point functions in a post-Carrollian CFT, which in $1+1$ dimensions exhibits both electric and magnetic sectors, while in higher dimensions only the magnetic sector survives.