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Learning Trails
PIR-powered knowledge graphs for mastery tracking
A living knowledge graph system that maps concepts as nodes and prerequisite relationships as edges, using Prime Integer Relations (PIR) to measure whether a learner's understanding is in structural equilibrium. Unlike traditional L&D platforms that track completion percentages, Learning Trails uses Thue-Morse balance gap and pattern area to detect knowledge gaps, Ricci curvature to identify bottleneck concepts that block downstream learning, and cryptographic audit receipts to prove demonstrated mastery. Built on Next.js with SQLite-backed concept/edge/progress tables, interactive SVG graph visualization, and topological sort trail computation.
Key Highlights
- 15 seed concepts across 4 categories (foundation, core, advanced, application) with 21 typed edges
- PIR balance gap measures knowledge equilibrium — not just coverage, but structural soundness
- Ricci curvature identifies bottleneck concepts that block downstream learning paths
- Topological sort computes personalized learning trails from any starting point to any target
- Ready-to-learn recommendations: concepts with all prerequisites mastered
- Cryptographic audit receipts for verifiable mastery demonstrations (PrimeSwarm integration planned)
- Interactive SVG knowledge graph with color-coded categories and styled prerequisite edges