Rust

March 17, 2026

Price as Geometry: Resolution, Coarse-Graining, and the Structure of Market Noise

A rigorous tour through stationary and non-stationary models of price evolution, with geometric analysis at the forefront. From the random walk null and Black-Scholes as flat geometry, through mean reversion as curved Riemannian diffusion, wavelets, geometric harmonics, and information geometry, anchored throughout by empirical evidence from BTC/ETH millisecond data.

March 9, 2026

BTC/ETH Lead-Lag: Resolution-Dependent Direction Reversal on Binance Spot

Resolution-dependent direction reversal in BTC/ETH lead-lag on Binance spot: ETH leads at 1ms, BTC leads at 100ms, crossover at 15–20ms. January and full year 2025.

Pathwise

High-performance SDE simulation toolkit. Rust core with Python bindings via PyO3. Supports Brownian motion, GBM, Ornstein-Uhlenbeck, and custom processes with rayon-parallelised Monte Carlo.

Cartan

Riemannian geometry on smooth manifolds. Connection forms, parallel transport, holonomy groups, and geodesic flows. Documentation at cartan.sotofranco.dev.

Volterra

Covariant active nematics solver built on Cartan. Dimensionally agnostic: any type implementing cartan_core::Manifold serves as the simulation domain. Beris-Edwards equations on arbitrary Riemannian geometries via discrete exterior calculus.

von Karman

Multi-precision pseudospectral Navier-Stokes solver. ETD-RK4 time integration with Kassam-Trefethen contour integral, dealiased 3/2 cross product, adaptive CFL. Five initial conditions, energy spectrum diagnostics, HDF5 snapshots, Parquet time series.

Elworthy

JIT compiler that specialises Bismut-Elworthy-Li formulas into SIMD kernels for unbiased Monte Carlo Greeks on non-stationary SDEs. Symbolic AST, Cranelift lowering (scalar and 2-lane F64X2), multi-dimensional Heston driver, pathwise and likelihood-ratio Malliavin parameter Greeks (machine-checked with SymPy). European call price and BEL delta cross-validated against Black-Scholes closed form and the independent blackscholes crate; both agree within four Monte Carlo standard errors. About 22x over a tree-walking interpreter on GBM paths.

Kloeden

Hand-written SIMD C++ vs Rust (LLVM + Cranelift) benchmark companion to pathwise and elworthy. Same Brownian-increment fixture across four impls; single-thread pinned-core throughput on scalar Euler / Milstein / Taylor 1.5 on GBM, plus a digital-delta correctness table showing naive pathwise silently returns 0 in both languages while the Bismut-Elworthy-Li constant-flow weight matches analytic within 4 Monte Carlo standard errors (bitwise-identical between hand-rolled C++, hand-rolled Rust, and elworthy_rt::from_paths). Named after Peter Kloeden.

Mermin

k-atic alignment analysis of fluorescence microscopy. Minkowski tensor shape descriptors, multiscale structure tensor fields, topological defect detection via cartan-geo SO(3) holonomy, persistent homology, spatial statistics, and Landau-de Gennes parameter fitting. Outputs calibrated parameters for forward simulation in volterra. 7 crates on crates.io, Python bindings on PyPI.

inferCNAsc

Copy number variation and ascertainment bias inference for single-cell genomics. Rust compute core with Python bindings via PyO3/maturin. Published on PyPI.