EP-0120: The Algebraic Web Explorer & Interactive Visual Studio¶

Abstract¶

This proposal specifies The Algebraic Web Explorer (site/explorer/index.html), a zero-dependency, browser-native visual studio for algebrax. It complements the DearPyGui desktop lab (recipes/lab.py) with a lightweight web interface for interactively inspecting:

1. Semiring Matrix Operations: Live matrix power propagation across Standard, Tropical, Boolean, Viterbi, and Provenance semirings.
2. Simplicial Homology & Betti Barcodes: Interactive 2D/3D mesh rendering, boundary nilpotency \(D_{k-1} \circ D_k = \mathbf{0}\), and Betti number invariants \(\beta_k\).
3. Clifford Geometric Algebra: Interactive 3D vector rotor rotations \(v' = R v R^\dagger\) over \(Cl (3,0)\) multivectors.
4. Galois Finite Fields: AES \(\text{GF} (2^8)\) polynomial modulo reductions and MixColumns matrix state heatmaps.
5. Categorical Kleisli String Diagrams: Monadic morphism compositions \(g \circ_T f\) over category graphs.

Architecture & Design¶

Technology Stack¶

• Structure: Semantic HTML5 with dark-mode glassmorphism styling.
• Logic: Modern vanilla JavaScript (ES2024), modular, zero external framework overhead.
• Graphics: HTML5 Canvas 2D/3D rendering engines for real-time vector, graph, and mesh visualizations.

Web Sitemap¶

site/explorer/
├── index.html               (Main Web Explorer Layout & Tab Controller)
├── css/
│   └── explorer.css         (Theme Tokens, Dark Mode & Glassmorphism Utilities)
└── js/
    ├── core.js              (Pure JS Sparse Matrix & Semiring Arithmetic Engine)
    ├── homology.js          (Simplicial Mesh & Betti Barcode Renderer)
    ├── clifford.js          (Clifford Multivector & 3D Rotor Visualizer)
    ├── galois.js            (GF(2^8) Polynomial & AES MixColumns Heatmap)
    └── kleisli.js           (Category Graph & Monad Composition Diagrammer)

The Council Heuristic & Falsifiable Invariants¶

1. Aesthetic Excellence (The Physicist): Modern typography, vibrant dark-mode color palettes (HSL tailored), smooth micro-animations, and interactive hover tooltips.
2. Mathematical Accuracy (The Council): Identical numerical results to algebrax Python core, verified via automated browser tests.
3. Zero Magic / No Bloat (Dennis): Pure Vanilla JS and CSS without heavy framework dependencies (React, Vue, or Tailwind build steps).

Implementation Roadmap¶

• [ ] Phase 1: Core HTML5/CSS Glassmorphism Shell (site/explorer/index.html & explorer.css).
• [ ] Phase 2: Pure JS Semiring Matrix Engine (js/core.js).
• [ ] Phase 3: Simplicial Homology & Betti Barcode Renderer (js/homology.js).
• [ ] Phase 4: Clifford Rotor Visualizer & Galois MixColumns Heatmap (js/clifford.js & js/galois.js).
• [ ] Phase 5: Categorical Kleisli Monad Diagrammer (js/kleisli.js).