SystemsNo. 002
Rust, from first principles
Types, ownership, operational semantics, async, and the FFI bridge: a graduate-level treatment of Rust from mathematical first principles.
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Contents
01Reservoir Geometry: Riemannian Manifolds in Oil and Gas02Rust, from first principles03Maxwell's Equations and Gauge Theory: Electromagnetism as a Principal Bundle04Navier–Stokes: Derivation in and on a Riemannian Manifold05Price as Geometry: Resolution, Coarse-Graining, and the Structure of Market Noise06Diffusion on Curved Spaces07Manifolds: The Language of Modern Geometry08Kuramoto: How Order Emerges from Chaos09BTC/ETH Lead-Lag: Resolution-Dependent Direction Reversal on Binance Spot
Lead ArticleNo. 001
Physics
Reservoir Geometry: Riemannian Manifolds in Oil and Gas
Darcy's law recast as geodesic flow on a Riemannian manifold , pressure diffusion as the Laplace–Beltrami equation, and permeability tensor interpolation via geodesics, with Rust for embedded well-site monitoring.
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All Articles
PhysicsNo. 003
Maxwell's Equations and Gauge Theory: Electromagnetism as a Principal Bundle
Four languages for one theory: vector calculus, differential forms, spacetime algebra, and principal fiber bundles. From the classical field equations to gauge invariance, the Aharonov-Bohm effect, Yang-Mills theory, and Dirac monopoles.
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AnalysisNo. 004
Navier–Stokes: Derivation in and on a Riemannian Manifold
An end-to-end derivation of the incompressible Navier–Stokes equations from continuum mechanics axioms, geometric reformulation via differential forms, coordinate-free lift to a Riemannian manifold, the Millennium Prize problem, functional analysis, and geometric algebra.
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FinanceNo. 005
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.
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AnalysisNo. 006
Diffusion on Curved Spaces
From the Gaussian heat kernel on to the Laplace-Beltrami operator on Riemannian manifolds, with the short-time heat kernel expansion and spectral theory.
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GeometryNo. 007
Manifolds: The Language of Modern Geometry
A rigorous construction of smooth manifolds from first principles: charts, tangent spaces, Riemannian metrics, curvature tensors, and geometric flows.
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ProbabilityNo. 008
Kuramoto: How Order Emerges from Chaos
Fireflies, neurons, power grids: all governed by the same equation. A tour through the Kuramoto model, its order parameter, and the phase transition that turns noise into rhythm.
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FinanceNo. 009
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.
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