Odd-parity altermagnetism(ALM) extends compensated collinear magnetism beyond the even-parity spin splitting of conventional altermagnets, but its role in correlated topological phases remains largely unexplored. Using the cluster slave-spin method, we show that the odd-parity ALM appearing in the ALM Chern-insulating phase of Haldane-Hubbard model significantly reconstructs the local topology in the conventional Chern-insulating phase, while the total Chern number remains unchanged compared to the Chern-insulating phase. The Berry curvature becomes spin and valley selective; zigzag ribbons develop chiral-symmetry-breaking edge states; while armchair ribbons remain inversion symmetric. The optical response mirrors this separation between the local reconstruction and the global topology: low-energy spectra are governed by quasiparticles near the gap, whereas the low-frequency Hall conductivity stays quantized, $σ_{\rm T\uparrow}(Ω\to 0)=σ_{\rm T\downarrow}(Ω\to 0)=e^2/h$. These results establish the Haldane-Hubbard model as a minimal correlated platform for odd-parity altermagnetic topology.

In this work, we developed analytic asymptotic methods for computing the Fourier modes of gravitational waves from post-Newtonian binary systems in the quasi-Keplerian parametrization in the high eccentricity regime. We have also derived the large-eccentricity asymptotic expansion of the eccentricity enhancement function appearing in the tail contributions to the radiation. Furthermore, based on these results, we constructed an endpoint-constrained analytic approximation that significantly accelerate the computation of the Fourier modes at large eccentricity.The overall error of this analytic approximation is controlled within $10^{-3}$, and it remains valid for Fourier modes with $p\le200$. This approach provides an analytic building blocks for modeling frequency-domain gravitational wave from highly eccentric binaries.

A generalization of the Sherrington-Kirkpatrick (SK) model for spin glasses is considered, in which the interaction matrix is endowed with a variance profile that has no particular structure an may be sparse. In the first part of this paper, an asymptotic equivalent of the free energy is derived at sufficiently high temperatures, regardless of the signature of the variance profile matrix. In the second part, the mean of the spin vector under the Gibbs measure is estimated using an Approximate Message Passing algorithm based on the Thouless-Anderson-Palmer equations. The dynamical approach of Adhikari et.al. (J. Stat. Phys., 2021), originally developed for the classical SK model, is adapted to the present setting to obtain these results.

We present a general and systematic framework to quantify uncertainties arising from imperfectly known systematic correlations in data combinations. Formulated at the level of the combined data, the method enables controlled variation of the correlation structure, leading to the construction of covariance matrices directly on the resulting combination and thus providing a robust and systematic estimate of correlation-induced uncertainties. We apply the method to $e^+e^- \to \mathrm{hadrons}$ cross section data, with the resulting covariance matrices propagated to derived observables, including dispersive determinations of the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, $a_μ^\mathrm{HVP}$. We find that uncertainties from systematic correlation assumptions are generally subdominant but non-negligible, and do not fully account for differences between existing $e^+e^- \to \mathrm{hadrons}$ data combinations. The framework is broadly applicable to correlated data combinations in precision measurements and constitutes a new component of the upcoming KNTW data combination for $a_μ^\mathrm{HVP}$.

Semiconductor spin qubits are a promising platform for large-scale quantum computing, but have yet to take full advantage of the broad class of quantum low-density parity check (QLDPC) codes, which promise high encoding rates and efficient logic but require nonlocal connectivity between physical qubits. In this work, we investigate the implementation of QLDPC codes on a tileable, shuttling-based spin qubit architecture. By tailoring syndrome extraction circuits to the shuttling noise model, we significantly improve on previous surface code proposals and extend the feasible shuttling range of the architecture by 5-10x, enabling the implementation of more complex codes with long-range interactions. Taking inspiration from the field of robotics, we develop a coordinated shuttle scheduling algorithm that supports arbitrary codes and use it to benchmark the logical performance of a variety of promising code families. We find that the optimized schedules are up to 86% faster than hand-optimized schedules for certain code families. Through detailed circuit-level simulations, we identify specific QLDPC codes that improve upon prior surface code implementations by orders of magnitude, increasing encoding efficiency and reducing logical error rates. This work demonstrates the potential of shuttling-based spin qubit hardware platforms for scalable and efficient fault-tolerant quantum computation.

Barrett reduction is the nonlinear core of every practical NTT-based post-quantum cryptography implementation. Existing composition frameworks (ISW, t-SNI, PINI, DOM) address Boolean masking over GF(2); none provides a machine-checked characterization of Barrett's leakage under first-order arithmetic masking and the first-order probing model over prime fields. Building on our prior series, QANARY [15], partial-NTT-masking margins [14], algebraic foundations [16], and butterfly composition [18], we close this gap. We prove a trichotomy: for any $q > 0$ and shift $s$, the Barrett internal wire map $f_x(m) = ((x + 2^s - m) \bmod 2^s) \bmod q$ has preimage cardinality in $\{0, 1, 2\}$, never more. We call this the 1-Bit Barrier: max-multiplicity 2 implies at most 1 bit of min-entropy loss per internal wire, universal over all moduli. The count-zero cases, unreachable output values, reveal that actual leakage is often strictly less than 1 bit, making the bound conservative. We introduce PF-PINI (Prime-Field PINI): Barrett satisfies PF-PINI(2); the Cooley-Tukey butterfly satisfies PF-PINI(1). We observe (not yet proved) that with fresh inter-stage masking, the composed pipeline has max-multiplicity $\max(k_1, k_2)$, so the 1-Bit Barrier propagates. The trichotomy, the PF-PINI instantiations, and cardinality results are machine-checked in Lean 4 with Mathlib: 12 proved results, zero sorry, universal over all $q > 0$ (the min-entropy bound follows by standard definitions). Adams Bridge lacks fresh inter-stage masking, violating PF-PINI composition and explaining why Papers 1 [15] and 2 [14] found vulnerabilities. NIST IR 8547 recommends formal methods for PQC implementation validation. The 1-Bit Barrier provides the first universal machine-checked cardinality bound for masked Barrett reduction in ML-KEM (FIPS 203) and ML-DSA (FIPS 204), with a corresponding 1-bit leakage interpretation.

Cosmological analyses using the latest set of type Ia SNe data weakly favor an evolving dark energy (EDE) model without strongly disfavoring the standard LCDM paradigm. Nonparametric reconstructions of the expansion history may reveal signal features potentially missed by a parametric LCDM model without laying out a specific functional form for the evolution of dark energy. Information field theory (IFT) is a Bayesian framework for optimal, nonparametric reconstruction algorithms. In this work, we present charm2, the successor to charm1, a previous IFT-based code to reconstruct the cosmic energy density's redshift evolution from SNe Ia. We apply our reconstruction algorithm to the Union2.1, Pantheon+, DESY5 and DESY5-Dovekie data sets to investigate the agreement between the nonparametric reconstruction and the signal suggested by a parametric, flat LCDM model. To enable an accurate Gaussian approximation, we employ geometric variational inference, which finds a coordinate transformation through which a curved posterior gets "flattened". The redshift evolution of the energy density can then be traced on a double-logarithmic scale, which, after de-trending, is well described by a stationary Gaussian process. The nonparametric charm2 reconstructions using the Union2.1 and Pantheon+ data sets are consistent with flat LCDM signal fields. The DESY5 and DESY5-Dovekie reconstructions deviate from flat LCDM comparison fields and are compatible with an evolving dark energy signal. However, using the evidence lower bound (ELBO) measure for model selection, we find no conclusive evidence supporting a preference for non-flat-LCDM features in any of the data sets. We note that at current DESY5 noise levels, the ELBO tends to favor flat LCDM over our nonparametric model although the latter better recovers the ground truth in synthetic EDE data; a trend reversing only at ~7x lower noise covariance.

Heinsohn and Steiger's "Eigentum, Zins und Geld" (1996) proposes the property premium as the foundational determinant of interest, replacing time preference. This paper examines whether the replacement succeeds. It does not. The two arguments against time preference, the savings-inelasticity claim after Hahn and the portfolio-shift claim after Keynes, both fail on standard microeconomic grounds. With time preference intact, the property premium sits within the standard decomposition of the interest rate. In ordinary collateralized credit it coincides with the risk premium. Only when the lender is a money-issuing bank with a real redemption obligation does a third term enter the decomposition that standard asset-pricing theory does not articulate. That third term is Heinsohn and Steiger's genuine contribution. The paper discusses its apparent disappearance or disguised operation after 2008, and the circularity of a property anchor measured in money.

The LHCb collaboration has recently observed the rare hyperon decay $Σ^+\to pμ^+μ^-$. It can also measure the corresponding antihyperon channel with comparable precision and is thus in a position to extract information on $CP$ violation in this mode. Interestingly, the long-distance contributions that dominate it within the standard model provide large absorptive phases that could drive substantial $CP$ violation through interference with potential new-physics contributions. Here we explore this possibility, finding that the decay rate asymmetry is currently allowed to be as high as tens of percent, which can be probed by LHCb in the near future. We additionally consider the same with regard to the dielectron mode $Σ^+\to pe^+e^-$ as well as the related radiative one $Σ^+\to pγ$.

Prediction markets are widely treated as forecasting devices that reveal collective expectations about uncertain futures. This article argues that under specifiable conditions they also function as coordination mechanisms: public probabilities that organize the behavior of voters, donors, journalists, traders, and institutions in ways that can be self-fulfilling or self-defeating. Most existing work asks whether prediction markets forecast accurately; this paper asks whether accurate forecasting is even the right criterion for a market that has become a public coordination device. Drawing on transaction-level evidence from the 2024 U.S. presidential election, we show that the social force of a market signal depends less on its size than on its persistence, the breadth of responding trader types, and cross-platform consensus. We introduce a Signal Credibility Index (SCI) -- combining the variance ratio VR(6), a two-sidedness diagnostic, and a trader-concentration adjustment -- as a microstructure-grounded criterion for predicting when price moves acquire behavioral traction. Applied to three major 2024 political shocks, the framework reveals that superficially similar events generated qualitatively distinct signal types with different implications for elite coordination. A cross-platform comparison establishes a systematic decoupling of social authority from epistemic robustness: the most visible market produced the least accurate forecasts. The framework carries direct implications for regulating prediction markets as democratic information infrastructure.

We present a novel architecture-aware transpilation method for exact general unitary gate synthesis on superconducting quantum hardware. Our approach is tightly integrated with the optimized block-ZXZ decomposition, exploiting its recursive structure to make hardware-aware decisions at each level of the recursion rather than treating transpilation as an independent post-processing step. The method introduces three key techniques: a greedy qubit mapping strategy that minimizes pairwise distances between physical qubits, an adaptive Gray code selection combined with qubit swapping that optimizes the construction of uniformly controlled Rz gates for the target topology, and a heuristic for reducing CNOT gates by exploiting the structure of long-range CNOT ladders. We benchmark our method against TKet, Qiskit, and Pennylane on the 20-qubit IQM Garnet (square lattice) and the 156-qubit IBM Marrakesh (heavy-hex) architectures with qubit counts ranging from 3 to 11. Our method achieves CNOT count reductions of up to 36 percent on the IQM Garnet and up to 34 percent on the IBM Marrakesh compared to the best competing transpiler, while simultaneously achieving transpilation speedups of up to 553x. Furthermore, our method is the only one capable of transpiling circuits beyond 10 qubits within a 30-minute time limit across both architectures.

We study lattice point visibility along polynomial lines of sight and prove the Visibility Density Conjecture of Chaubey and Pandey for a large class of polynomials.

Debugging nondeterministic programs is inherently difficult, particularly in microcontroller environments where execution paths can diverge unpredictably due to external sensor inputs. Traditional debugging techniques often fail to capture or reproduce this nondeterministic behavior effectively. Multiverse debugging has emerged as a compelling technique to debug nondeterministic programs, allowing developers to systematically explore all possible execution paths. Unfortunately, current multiverse debuggers are snapshot-based and most operate over a model of the program, limiting their use for debugging resource-constrained microcontrollers. Additionally, current multiverse debuggers, even ones specifically designed for microcontrollers suffer from state explosion making the state space overwhelming during debugging. To address these challenges, we introduce a trace-based multiverse debugger with a novel state-space reduction technique based on concolic execution. Our approach interleaves concolic analysis with live debugging to identify input values that define unique program paths. This hybrid technique efficiently prunes redundant paths from the state space while ensuring full code coverage. Unlike MIO, a recently published multiverse debugger for microcontrollers that focuses on IO consistency, our approach directly targets state explosion by leveraging concolic execution and uses a trace-based approach, significantly reducing the memory and communication overhead. We implemented a prototype using the WARDuino WebAssembly VM, demonstrating the feasibility and efficiency of our approach in real-world scenarios. Our results highlight substantial reductions in the state space compared to traditional multiverse debugging. This makes multiverse debugging more accessible and efficient for developers working with complex, nondeterministic programs running on microcontrollers.

We introduce multiplicative Ehresmann connections on surjective submersions of Lie groupoids, extending both the classical notion of Ehresmann connections on fibre bundles and the more recent notion of multiplicative connections on Lie groupoid extensions. We investigate the existence of such connections, showing that, in general, they may fail to exist even for proper Lie groupoids. In contrast, positive results hold for Morita submersions, uniform Lie groupoid fibrations, locally trivial families of Lie groupoids, and proper families of Lie groupoids. Our main results concern completeness. For Lie groupoid fibrations, we prove that the completeness of a multiplicative connection is governed by the induced connection on the kernel bundle and, under connectivity assumptions, by the base connection. For families of source-proper Lie groupoids, we prove the equivalence between local triviality and the existence of complete multiplicative Ehresmann connections.

Stochastic field theories are often constructed phenomenologically, without a systematic assessment of thermodynamic consistency or local detailed balance. This may hinder a physical description of irreversibility at the field-theoretic level beyond the standard statistical formulation of stochastic thermodynamics. Here, we develop a variational formulation for thermodynamically consistent stochastic field theories by extending Hamilton's principle of classical field theory. Introducing the second law as an axiom yields a consistent local thermodynamic structure in which novel fluctuationdissipation relations emerge naturally, ensuring local detailed balance. Remarkably, the resulting entropy production takes the same form as in standard stochastic thermodynamics, up to a reformulation in an extended phase space incorporating both configurational and thermal variables. This correspondence extends key results, including individual trajectory-level thermodynamics and fluctuation theorems. The construction is formulated within a unified geometric framework based on a generalized Lagrange-d'Alembert principle, providing a top-down connection between phenomenological modeling and thermodynamic consistency. Potential applications include thermodynamically consistent modeling of complex fluids, Lagrangian reduction by symmetry in continuum systems, and structure-preserving numerical schemes for stochastic partial differential equations.

An explicit positronium (Ps) source model was implemented in Geant4 to provide direct event-level control over annihilation channel selection, decay timing, and photon emission topology. The implementation supports direct annihilation, para-positronium (p-Ps), and ortho-positronium (o-Ps) branches with user-defined fractions, explicit routing of o-Ps events to two-photon (2-gamma) or three-photon (3-gamma) decay, exponential or fixed delay sampling, optional prompt-photon emission, and optional positron-range displacement. Event-level truth metadata were retained to support downstream validation and analysis. The implementation was evaluated in controlled Geant4 studies using native reference configurations, explicit branch-fraction sweeps, lifetime sweeps, timing benchmarks, and a frozen point-source downstream test harness. Observed 2-gamma and 3-gamma fractions followed the requested control parameters with the expected linear behavior, and measured mean delays reproduced the prescribed lifetime settings with near one-to-one agreement. Computational cost scaled linearly with event count, with modest overhead relative to native Geant4 operation. A minimal downstream validation framework was used to verify branch-consistent handling of pure and mixed datasets, including expected method-source compatibility and recovery of valid events under unified 2-gamma and 3-gamma routing. These results establish a practical and internally consistent code framework for explicit positronium modeling in Geant4 and provide a simple pathway for PET researchers to incorporate controlled Ps generation into existing simulation pipelines.

This paper investigates the mechanisms underlying scientific stratification in the era of transition from elite to mass science. Existing scholarship has largely examined scientific stratification through the Matthew effect framework at the individual, institutional, and lineage levels, but this theoretical lens has grown limited in today's academic landscape, where mass, team-based, and lab-centered research has become the dominant mode of knowledge production. As scientists increasingly share institutional and lineage backgrounds, considerable variation within these units remains unexplained. We propose a new framework that integrates concepts and methodological tools from demography into the social study of science. Drawing on the parallel between biological families and scholarly lineages as fundamental units of reproduction, we adapt the concept of birth order to examine how the sequence of doctoral students within a lineage shapes their career trajectories. Using data on more than one million U.S. doctoral graduates, our analysis shows that, much like in biological families, later students systematically perform worse than earlier ones across multiple dimensions of academic achievement, both short and long term. Examining the underlying mechanisms, we find that later students receive less cognitive stimulation from mature scholars and instead more from peers, and specialize in narrower intellectual domains as senior siblings occupy adjacent territories. These factors constrain their intellectual development as independent scholars. By introducing a demographic framework into the study of science, this paper offers a new perspective on scientific stratification and demonstrates how demographic concepts can be fruitfully extended to analyze broader social and epistemic systems.

Quantum linear system solvers typically realize the inverse map as a polynomial transformation of the spectrum, so their practical cost hinges on implementing this transformation at a low polynomial degree. We introduce constrained optimal polynomials as a framework for this task, drawing on classical Krylov subspace theory. Within this framework, we develop two classes of solvers. Constrained Uniform Polynomial (CUP) solvers optimize the tradeoff between approximation accuracy and block encoding normalization under a uniform spectral model consistent with the available bounds. Constrained Adaptive Polynomial (CAP) solvers retain this structure but replace the uniform model with a probability measure reconstructed from spectral moments via a maximum entropy ansatz, where the moments are extracted from QSVT measurements. Numerical experiments under hardware and stochastic noise show that these methods achieve lower error than standard QSVT-based and Chebyshev-iteration-type solvers, particularly in noise-limited regimes. CUP offers robust performance under generic spectra, while CAP provides further improvement when the spectral structure can be exploited.

Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often established via the Banach fixed point theorem, provided that a suitable contraction property can be verified. However, such conditions are typically too restrictive for more complex nonlinear equations that lack key structural features such as monotonicity or convexity. In this paper, we develop a general framework for the weak convergence of fixed point iterations based on asymptotic bounds. In particular, we introduce and exploit a weak sequential non-expansiveness property, which is significantly weaker than the global Lipschitz assumptions commonly employed in this context. This approach permits to extend classical convergence results to a broader class of mappings in general (reflexive) Opial spaces, without relying on additional geometric assumptions such as uniform convexity.

Electroencephalography (EEG) source imaging aims to infer brain activity from electrical potentials measured on the scalp. This is a difficult problem because many different source patterns can explain the same measurements. The result depends strongly on two things: the forward model and the inverse method. In this work, we study how these two parts work together. We focus not only on where the activity is located, but also on how the reconstructed activity is distributed in space. We suggest that different source models create different signatures in the reconstructed activity. We use realistic head models and compute forward solutions with the finite element method using Zeffiro Interface and DUNEuro. We test different source models, including 2 implementations of a divergence-conforming model, and one implementation of Local subtraction approach. For inverse methods, we use advanced methods such as standardized hierarchical adaptive L1 regression (SHAL1R), standardized Kalman filtering (SKF), and classical dipole scanning. To understand the complex interplay between the forward and inverse approaches, we analyze the inverse source localization results using distributional quantitative measures, including Earth Mover's Distance and depth bias scatter plot, and qualitatively assess the amplitude distribution and focality. The results show that there is a strong dependence between the choice of source model and the success rate of a given inverse method: a source model that corresponds well with a single point-like source is a good match with an inverse method that presupposes such a source.

Postmarketing safety surveillance relies on data from spontaneous reporting systems (SRS) such as FAERS, EudraVigilance and VigiBase, and commonly uses SRS data mining methods to assess the associations between drugs and adverse events (AEs). Traditionally, these analyses have focused on signal detection framed as a binary decision problem, whereas more recent work has emphasized more nuanced inference involving signal strength estimation and uncertainty quantification. In this paper, we review contemporary SRS data mining approaches and their statistical underpinnings for safety assessment using data from major pharmacovigilance databases worldwide. In addition to methodological review, we provide practical guidance on data preprocessing for such analysis, including construction of SRS contingency tables using only aggregated AE-drug counts, as are publicly available from databases such as VigiBase and EudraVigilance. We illustrate the guidance via opioid-related datasets obtained from FAERS and VigiBase, complied with subsequent downstream SRS data analyses.

We study at zero temperature a microscopic quantum spin-1 model on the fuzzy sphere that realizes the $O(2)$ Wilson-Fisher conformal field theory (CFT) in $(2+1)$-dimensional spacetime at a quantum critical point. Here, we use the fuzzy-sphere regularization as it preserves the full spatial $SO(3)$ rotational symmetry of the CFT, enabling the state-operator correspondence that maps energy eigenstates directly to CFT operators. Using exact diagonalization (ED) and matrix product state (MPS) techniques combined with conformal perturbation theory (CPT), we extract conformal data including scaling dimensions and operator product expansion (OPE) coefficients. We identify 32 primary operators and their descendants, organized by the conserved $O(2)$ charge $S^{z}$ and spatial angular momentum $L$. Our numerical results for the scaling dimensions of the lowest primary operators show good agreement with conformal bootstrap predictions. We verify predictions from the large charge expansion, which provides systematic predictions for operators carrying large $U(1)$ charge, connecting the Goldstone mode physics in the ordered phase to phonon primaries at the critical point.

We provide a simple and direct proof of a strong-type unique continuation principle for the fractional $p$-Laplacian $(-Δ_p)^s$ for a range of $s$ and $p$. The result extends to strong solutions of the fractional nonlinear Schrödinger equation. We adapt the recent proofs of the weak UCP by Berger, Schilling and Prasad.

Historical photographic plate archives anchor a growing body of time-domain astronomy, but time-domain claims drawn from them are vulnerable to plate-sensitivity variations correlated with environmental modulators that can mimic real astrophysical signals. We present a simple, broadly applicable protocol for testing such artifact hypotheses: regress catalog-aggregate reference-population metrics (stellar detection counts or plate limiting magnitudes) against the suspected modulator. Under the artifact hypothesis, the reference metric varies systematically; under the null hypothesis, it does not. We apply the protocol to test whether geomagnetic storm activity, measured by the planetary Kp index, modulates plate sensitivity at two independent observatories. At Harvard College Observatory, the DASCH DR7 archive provides limiting magnitudes for 12,510 exposures across 500 sky positions: no significant trend across Kp bins (Spearman rho = -0.011, p = 0.234). At Palomar, the MAPS Catalog of POSS-I records stellar detection counts for 638 fields: no significant trend (Spearman rho = 0.017, p = 0.673). Plate sensitivity is invariant across the full range of geomagnetic activity at both sites. The principal airglow-based artifact objection to recent claims of Kp-dependent transient suppression in the POSS-I archive is directly falsified at two observatories.

We present a first study of the scattering process $e^+ e^-\toπ^+π^-γ$ beyond next-to-leading order, aimed at providing preliminary insights required for future NNLO predictions for radiative return processes. A complete four-dimensional tensor decomposition of the amplitude is developed, and the associated one-loop polarised amplitudes are evaluated analytically to higher orders in the dimensional regulator, as required for NNLO accuracy. The calculation is complemented by an efficient numerical framework for the evaluation of the resulting five-point Feynman integrals, enabling stable and fast evaluations across the physical production region with evaluation times of a few hundreds of milliseconds. These results are suitable for implementation in Monte Carlo event generators.

In this paper, we study the regularity of the free boundary for minimizers of the Alt-Phillips functional with negative powers \[\mathcal{E}_γ(u)=\int_Ω\frac{1}{2}|\nabla u|^2+\frac{1}γu^{-γ}χ_{\{u>0\}}dx,\quadγ\in(0,2).\] We proved that the free boundaries are $C^{\infty}$ at regular points. A key technical tool is the linearized operator for the PDE satisfied by the partial derivatives of a solution to the Alt-Phillips Euler-Lagrange equation in the negative power case. For this operator we establish a comparison principle, which may have further applications to the Alt-Phillips problem with negative powers.

Inflationary models that contain a transient ultra-slow-roll phase can exhibit strong non-perturbative dynamics, making the usual perturbative treatment of cosmological fluctuations incomplete. In such regimes, quantum diffusion and the nonlinear gravitational response of the background can both play important roles, motivating a framework that treats them systematically within quantum field theory in curved spacetime. In this work, we derive the first-order stochastic equations in quasi-de Sitter spacetime from the Schwinger-Keldysh formalism and develop a practical procedure to obtain compact stochastic equations that consistently incorporate metric perturbations via the classical Arnowitt-Deser-Misner equations. Our approach systematically captures classical non-perturbative effects while retaining the leading first-order quantum diffusion. We apply the formalism to two inflationary scenarios with an ultra-slow-roll phase, namely the Starobinsky piecewise-linear model and critical Higgs inflation. For the Starobinsky model, numerical lattice simulations validate the stochastic description and agree well with analytical results. For critical Higgs inflation, we find that the dynamics lead to a minor suppression of the power spectrum with an additional oscillation feature. Throughout, our analysis is restricted to the regime of small metric perturbations, ensuring the self-consistency of the perturbative stochastic treatment. These results establish a concrete bridge between first-principles quantum field theory in curved spacetime and the stochastic-$δN$ formalism for investigating non-perturbative inflationary dynamics.

We study the time it takes for all states of a finite quantum system to return simultaneously to their original configuration. In particular, we define the recurrence time for a quantum system to be the time at which all time-evolved states are close to their initial configuration, and at least one state has deviated significantly during this interval. Considering finite-dimensional quantum systems evolving unitarily, we find bounds on this notion of recurrence time, for continuous time and discrete time, by using Dirichlet's approximation theorem. We show how the problem of finding a bound on recurrence time can be related to approximating the difference of real numbers by rationals. We present a mathematical result on the latter, which we then use to obtain tighter bounds on recurrence time.

This paper extends and analyzes the high-order kernel regularization framework of Beale & Tlupova (arXiv:2510.13639) to all four on-surface boundary integral operators of the Helmholtz Calderon calculus in three dimensions: the single-layer, double-layer, adjoint double-layer, and hypersingular operators. To the best of our knowledge, this work provides the first high-order kernel regularization of the hypersingular operator for both the Helmholtz and Laplace equations in three dimensions. The regularization replaces each singular kernel with a smooth modification constructed from error functions together with a polynomial correction whose coefficients are determined through moment conditions. Alongside the derivation of the regularizing functions, the paper provides a unified error analysis of the combined regularization and quadrature discretization procedure. By coupling the regularization parameter to the mesh size, the two error contributions can be balanced, leading to explicit overall convergence rates that depend jointly on the order of the regularization and the degree of exactness of the surface quadrature rule. A key practical feature of the method is its implementation simplicity. Once the regularizing functions are determined, the numerical task reduces entirely to the evaluation of smooth surface integrals using standard quadrature, without the need for element-local solves, singularity-specific precomputations, or specialized quadrature rules. Although the modified kernel is generally incompatible with kernel-specific fast methods, this limitation is addressed through H-matrix acceleration, applicable in a black-box manner. Numerical examples -- including verification of the predicted convergence rates and solution of sound-soft and sound-hard scattering problems by smooth obstacles -- demonstrate the accuracy and practicality of the proposed methodology.

Heat transport exhibits distinct regimes ranging from ballistic propagation to diffusive relaxation, traditionally described by disparate theoretical frameworks. Here, we introduce a unified first-order operator formulation in which temperature and heat flux are treated as a coupled state vector, yielding a minimal dynamical closure of heat transport. The resulting generator is intrinsically non-Hermitian and gives rise to a spectral structure governed by an exceptional point that separates overdamped diffusion from underdamped wave-like propagation. In this framework, Fourier law emerges as a singular limit of a hyperbolic dissipative system, while the Cattaneo equation arises naturally as the minimal hydrodynamic closure of kinetic theory. We show that the exceptional point induces nonanalytic spectral transitions, nonmodal transient dynamics, and a breakdown of conventional modal decomposition. The theory further generalizes to anisotropic media, where direction-dependent exceptional surfaces enable intrinsic steering of heat flow. Our results establish a unified non-Hermitian dynamical framework for heat transport and reveal exceptional-point physics as a fundamental organizing principle underlying thermal dynamics across scales.