Teaching vs. Training: Empirical Evidence That 45 Human-Verified Facts Outperform Trillions of Tokens on a Standard Biology Benchmark

A 3-billion-parameter language model (qwen2.5-coder:3b) augmented with Sara Brain — a path-of-thought knowledge graph running on SQLite — scored 80% on MMLU High School Biology after being taught just 45 facts by a human in under 30 minutes. No GPU. No training run. No datacenter. The same model alone scored 58%. GPT-3.5, with 175 billion parameters trained on trillions of tokens, scores approximately 70%. We also tested the quantity approach: auto-ingesting 28,373 neurons from Wikipedia dropped the score to 51% — below the model's own baseline. More knowledge made performance monotonically worse. The 3B extractor hallucinated during ingest ("methane has 4 carbon atoms" from a source that says one carbon and four hydrogens), and Sara faithfully stored every error. The finding: hallucinations are a structural consequence of compressing knowledge into weight parameters — pattern collisions from lossy compression that more data cannot fix. The alternative is not storing knowledge in weights at all. Sara Brain stores each fact as an explicit, inspectable, correctable graph path with full source provenance. Wrong facts are traceable and removable. In a trained model, the same errors are invisible. This paper extends the path-of-thought architecture introduced in Pearl (2026a) with short-term memory, backwave echo propagation, multi-threshold activation cascades, layered brain regions, a two-witness source provenance system, and a teacher interface that iteratively tests, identifies gaps, and corrects errors. Neither the 3B model alone (58%) nor Sara's graph alone (50%) achieved 80% — the result is emergent from the cortex-cerebellum architecture working together.