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Physics Draft DOI

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

Formal Verification Working Paper DOI

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

Formal Verification Working Paper Lean DOI

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

Formal Verification Draft Lean DOI

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

Mathematics Working Paper Lean DOI

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.

Mathematics Working Paper DOI

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.

Quantitative Finance Draft Lean DOI

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.

machine_learning Short Draft Lean DOI

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).

machine_learning Short Draft Lean DOI

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…

machine_learning Short Draft Lean DOI

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).

machine_learning Draft Lean DOI

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 impl…

Formal Verification Working Paper Lean DOI

Formal Verification Draft Lean DOI

**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

Machine Learning Draft Lean DOI

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.

Core Theory Draft Lean DOI

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.

Quantitative Finance Working Paper Lean DOI

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

Quantitative Finance Working Paper Lean DOI

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.

Quantitative Finance Draft Lean DOI

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.

Quantitative Finance Draft Lean DOI

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.

Quantitative Finance Working Paper DOI

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 o…

number_theory Short Draft Lean DOI

Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh [BGST23] proved the first unconditional asymptotic for Montgomery's pair-correlation function $F(\alpha, T)$, with error $O(1/\sqrt{\log T})$ uniformly for $\alpha \in [0,1]$.

Mathematics Draft Lean DOI

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.

Formal Verification Short Draft Lean DOI

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 $Q = 2/3$.

Physics Short Draft Lean DOI

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

Physics Working Paper DOI

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.

Physics Working Paper DOI

Quantitative Finance Draft Lean DOI

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 re…

Physics Draft Lean DOI

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