Technology

Technology

Core

• Stack: Next.js 15 (App Router), React 19, TypeScript 5.
• Styling: Zero-runtime CSS variables. No Tailwind.
• Typography: EB Garamond (Variable), self-hosted.

Architecture

Content Pipeline

• Unified Backend: lib/content.ts acts as a type-safe filesystem CMS.
• Custom Compiler: remark-lemma plugin traverses the AST at build time to auto-link glossary terms.
• Academic Ops: <Theorem>, <Proof>, and <BibTex> components for rigorous mathematical writing.

Signal Engine (Recommendation)

• Vector Space: Client-side cosine similarity engine.
• Observer: Scroll-depth and dwell-time tracking in localStorage.
• Visualization: Force-directed D3 graph (SignalMap) of semantic relationships.

Lemma System (Footnotes)

• Context Stack: Bidirectional linking. Inline terms stack into a persistent UI container (LemmaStack).
• Responsive: Hybrid sidenote/modal behavior based on viewport width.

Weather Engine

• Heliotrope: Real-time solar position calculator (lib/solar.ts). Drives the site’s “Solar Sync” circadian lighting.
• Weather: Local Chapel Hill weather synchronization via Open-Meteo (lib/weather.ts).
• Phases: ASTRO_DAWN, GOLDEN_HOUR, BLUE_HOUR states derived from solar elevation.

Simulation Engine

• Physics Core: useCanvas hook with requestAnimationFrame decoupling and off-thread rendering.
• Chaotic Systems:
  • Lorenz: RK4 integration of 3D chaotic attractors.
  • Double Pendulum: Hamiltonian mechanics solver (Lagrangian dynamics).
• Stochastic Processes:
  • Monte Carlo 404: Ornstein-Uhlenbeck process with mean reversion, simulating hypothesis rejection.
  • Wiener Process: Real-time random walk with spring physics damping (Heartbeat).
  • Galton Board: Binomial distribution simulation via physics engine.
  • Ising Model: Metropolis-Hastings algorithm for ferromagnetic phase transitions.
• Vector Fields:
  • Perlin Flow: Interactive particle system driven by Simplex noise and mouse repulsion.
  • Reaction Diffusion: Gray-Scott algorithm with Laplacian convolution.
• L-Systems: Recursive string re-writing system for fractal generation.

Identity

• Digital Signature: “Refined Graphite” shader. FNV-1a hash seeding. Gaussian envelope.

Utilities

• Command Palette: Cmd+K global search with fuzzy filtering.
• Course Explorer: Recursive filesystem tree renderer.
• RSS: Automated feed generation during next build.