Most Mature

**Methodological contribution.** Alongside the physics result below, this paper establishes a reproducible standard for *kernel-verified derived physics* that we argue is portable across domains in which classical analytic derivations have hardened into opaque community consensus. The standard has four requirements.

We present a machine-checked reduced transport law for ion-scale turbulent confinement in tokamak plasmas.

We prove that for any $N \geq 3$ bodies with positive masses in $\mathbb{R}^d$ ($d \geq 2$), the number of central configurations modulo similarity is finite, resolving Smale's 6th Problem in **every spatial dimension $d \geq 2$ simultaneously**.

We derive the Kolmogorov energy spectrum $E(k) \sim \varepsilon^{2/3} k^{-5/3}$ and anomalous intermittency corrections to the structure function exponents $\zeta_p$ from the Grade Equation — a universal structural decomposition theorem for analytic dynamical systems. The derivation proceeds in three steps.

Expected Shortfall backtesting under Basel III/IV suffers from an unmeasured structural weakness: Monte Carlo estimation of ES injects computational noise into the Acerbi-Székely (2014) test statistic, but the magnitude of this contamination has not

We present the Eigen-COS method, a deterministic algorithm that computes exact Value-at-Risk, closed-form Expected Shortfall, and the full CDF/PDF for weighted sums of correlated lognormal assets — without Monte Carlo simulation.

Derived-physics laws — the Rechester–Rosenbluth stochastic-field-line transport law, the Debye electrostatic screening length, the Clausius–Clapeyron integrated vapour-pressure equation, the Einstein chirp mass from the stationary-phase approximation

We introduce a grade decomposition of the Gevrey energy balance for the incompressible Navier-Stokes equations and formalize a complete three-phase regularity proof path in the Lean 4 proof assistant.

Every existing Expected Shortfall backtest evaluates a risk model at a single confidence level. This paper introduces four backtesting methods that test the entire tail distribution simultaneously — methods that are structurally impossible without exact closed-form computation of the CDF and density.

The companion methods paper (Nagy 2026a) defines the Knowledge Artifact — a portable spectral representation of trained model knowledge — and the Knowledge Algebra — exact arithmetic on compatible artifacts.

We introduce a grade decomposition of the Gevrey energy balance for the incompressible Navier-Stokes equations. The physically correct model uses $\mathbb{C}$-valued Fourier coefficients with a factor of $i$ in the advection; the real-coefficient model trivializes all grade-3 terms.

We prove the Riemann Hypothesis conditional on a single operator-theoretic hypothesis: that the Berry-Keating Hamiltonian $H = \frac{1}{2}(xp + px)$ admits a self-adjoint realization $\hat{H}$ with discrete spectrum whose eigenvalues are the imaginar

We introduce the **Latent solution** as a quantitative framework for finite-dimensional representation of PDE solutions.

We construct a low-rank arbitrage-aware volatility surface with $O(rm)$ parameters and closed-form COS reuse for pricing and Greeks. Total implied variance is expressed as a finite cosine series in log-moneyness, $w(k, T) = c(T) + \sum_j u_j(T)\cos(\omega_j k)$, with $r = 6$–$12$ modes per maturity.

This paper studies **fin_harvestability** as a horizon object for horizon-dependent allocation within a CRRA investor facing Ornstein-Uhlenbeck eigenmodes.

Neural scaling laws — the empirical observation that test loss decreases as a power law in compute budget — are the foundation of modern AI training strategy. Every major laboratory trains billion-dollar models by extrapolating scaling curves, yet *why* these power laws hold remains unexplained.

Adam (Kingma & Ba, 2015) is deep learning's most-cited optimizer, with over 100,000 citations and native implementation in every major framework: TensorFlow, PyTorch, JAX, Keras. Its original convergence proof — Theorem 4.1, published at ICLR 2015 — claimed $R_T = O(\sqrt{T})$ regret on convex problems.

We present a deterministic framework for computing Value-at-Risk, Expected Shortfall, and arbitrary spectral risk measures for portfolios of correlated lognormal assets, without Monte Carlo simulation.

We pre-register and test a spectral-error-mitigation prediction for the two-qubit gate fidelity of Quantum Inspire's Tuna-9 9-qubit transmon processor and execute it in four cryptographically timestamped stages.