Papers

Stochastic Portfolio Theory provides a model-free framework in which functionally generated portfolios track the market index up to two terms: a boundary term in the generating function and the time-integral of an *excess growth rate*.

We propose a finite-window temporal diagnostic for selected near-integrable Hamiltonian systems. It compares a normalized Fourier statistic of the perturbation Hessian along trajectories with a separately normalized finite-time redistribution estimator.

We present XRayBench v0.2, a seven-phase controlled benchmark for evaluating option-scoring evidence about mathematical representations in transformer language models.

Low-rank approximations scale Gaussian-process regression, but they are typically judged by kernel accuracy rather than posterior-solve safety; this paper introduces a noise-floor rule for certified low-rank GP linear solves.

An elementary representation route for sums of correlated lognormals; published with DOI and stated for review.

We define the **Latent** of a smooth system as the basis-free element of a graded Hilbert tensor algebra that completely characterizes the system's distributional, dynamic, and functional properties.

The Spectral Fenton Distribution represents a portfolio loss distribution with 128 Fourier coefficients. Under the deterministic simulated protocol reported here (5 assets, 250 trading days, seed 42), a single principal component captures 97.81\% of observed coordinate variation and three components capture 99.9996\%.

We introduce the Structured Latent Basis (SLB) framework, a perspective that compares feature engineering, meta-learning, and representation learning through a common diagnostic question: does the chosen representation make a regularized linear predi

We present a bounded verification case study for COS caplet pricing. The numerical component expands the payoff of a log-forward rate, pairs characteristic-function coefficient proxies with raw payoff integrals, and reproduces Black benchmark values in a lognormal special case.

We present a machine-checked source containing 78 named real-arithmetic declarations that occur as local steps in standard analyses of stochastic gradient descent (SGD). This declaration count includes support identities, recovery variants, and direct restatements; it is not a count of novel or publication-credit theorems.

The Birch and Swinnerton-Dyer conjecture predicts that for an elliptic curve $E/\mathbb{Q}$ the Mordell-Weil rank equals the order of vanishing of the Hasse-Weil $L$-function at $s = 1$.

We present a reusable algebra for machine-checked certificates in declared engineering models, where supplied equations, inequalities, monotonicity directions, and perturbation bounds imply an encoded safety, lifetime, stability, or performance predicate.

Saddle-point approximations replace an action by its quadratic part, but transferring a quantitative error statement between applications requires an explicit remainder estimate.

We establish conditional bounds in a stylized antitone threshold model of recursive AI self-improvement. A mode $k$ is model-learnable at budget $N$ when the stipulated predicate $N g(k)\ge 1$ holds, where $g$ is positive and antitone.

A proposed route toward finiteness of central configurations for positive masses, with formalized components and explicit assumptions.

The Z₃ Ansatz $\sqrt{m_r} = a(1 + b\cos(\theta_0 + 2\pi r/3))$ with $b^2 = 2$ is a parametrization — not a dynamical model — that encodes the Koide mass relation $Q = 2/3$.

We present an algebraic framework relating the growth of the zeta moments to Hankel-determinant structure, together with an honest account of where the framework does and does not reach the Riemann Hypothesis.

A proposed finite Latent encoding for gravitational three-body trajectories, with convergence and formalization status separated from the main claim.

This paper studies **harvestability** as a horizon object for portfolio allocation within a CRRA investor model facing Ornstein-Uhlenbeck eigenmodes.

The equity premium puzzle of Mehra and Prescott (1985) is the observation that the standard consumption-based asset pricing model, calibrated to plausible risk aversion and the observed smoothness of aggregate consumption, predicts an equity premium

We give a short conditional reduction of the Riemann Hypothesis to three classical inputs — Kronecker-Weyl equidistribution, the Bessel I₀ product identity, and Mertens' divergence theorem — plus a cited pair-correlation step.

We prove that 100% of the nontrivial zeros of $\zeta(s)$ lie on the critical line in the density sense: $N_0(T)/N(T) \to 1$ as $T \to \infty$. The proof combines two results.

Derivative pricing has a clear mathematical target: compute the discounted risk-neutral value of a payoff under a specified model. For European vanilla contracts this target is often analytic or nearly analytic.

The companion core paper establishes, and machine-checks, a single identity: a transformer's forward pass can implement one gradient-descent step on an implicit least-squares objective (the ICL=GD mechanism).

The companion core paper establishes, and machine-checks, a single identity: a transformer's forward pass can implement one gradient-descent step on an implicit least-squares objective (the ICL=GD mechanism). This satellite asks what that verified identity forces to be true about *representational capacity and scaling*.

The companion core paper establishes, and machine-checks, a single identity: a transformer's forward pass can implement one gradient-descent step on an implicit least-squares objective (the ICL=GD mechanism).

We turn the gradient-descent account of in-context learning (ICL) into machine-checked mathematics and falsifiable predictions about real transformers. The formal target is the linear-attention regression identity: a forward pass can implement one gradient-descent step on an implicit least-squares objective.

How many parameters does it take to represent a smooth probability density on a bounded domain to accuracy $\varepsilon$? We prove that for densities extending holomorphically to the Bernstein ellipse with parameter $\rho > 1$, the answer is $N = \Th

**Theorem A (Main result, conditional).** Conditional on the 20 named Tier A–D hypotheses of §7.1 — in particular the three Tier-D perturbative-QFT inputs (`tomboulis_formula`, `b_zero_from_feynman`, `beta_1_rge_def`) — we establish that Yang-Mills t

The Latent Theorem guarantees that any smooth system has a finite representation whose size depends on regularity and accuracy, not on ambient dimensionality. We extend this result to **families** of smooth systems.

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.

We present a deterministic, semi-analytical framework for computing the complete distribution of a portfolio's terminal value at horizon $T$ for correlated lognormal assets. Unlike traditional approaches, this method requires no Monte Carlo simulation.

Every formula in quantitative finance — CAPM, Markowitz, VaR, Sharpe ratio, GARCH — takes returns as input. Yet the standard definitions of return fail when prices cross zero: log-returns are undefined, and simple returns produce sign errors.

We develop a variance reduction framework for simulating rare events in correlated portfolios by exploiting the eigenvalue decomposition of the correlation matrix. The central observation is that the eigenvalue modes $Z_k$ — projections of the asset vector onto the eigenvectors of the correlation matrix — are mutually independent.

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 demonstrate that Padé resummation of Taylor-series solutions provides a practical, machine-precision representation of the full gravitational three-body problem.

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.

The CDF of a weighted sum of correlated lognormal random variables has lacked a tractable characterization since Fenton (1960). We show that eigenvalue conditioning of the correlation matrix, followed by Fourier-cosine inversion, yields an analytic, grid-free $N$-term spectral representation of that CDF: the **Spectral Lognormal Distribution**.

A speculative grade-ratio model for fundamental constants, with formalized arithmetic components and explicit physical assumptions.