Formal Verification

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 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.

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 $Q = 2/3$.

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

**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

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.