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GALAXY BRAIN COLLECTIVE - GSM8K FINAL RESULTS
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Streams:
  FUZZY:        MathBERT (symbolic), T5 (linguistic)
  DETERMINISTIC: Eigenspectrum, Cayley-Menger, Symbolic Calc, Fractal

| Epoch | Collective | MathBERT | T5 | Eigen | Cayley | Symbolic | Fractal | ρ |
|-------|------------|----------|-----|-------|--------|----------|---------|-------|
| 1 | 8.9% | 10.4% | 13.0% | 5.4% | 5.4% | 5.7% | 6.7% | 0.686 |
| 2 | 9.6% | 8.9% | 13.0% | 6.5% | 6.5% | 4.6% | 6.1% | 0.738 |
| 3 | 9.9% | 9.6% | 13.6% | 5.8% | 5.8% | 4.5% | 5.8% | 0.728 |
| 4 | 8.3% | 10.1% | 13.3% | 6.1% | 4.5% | 4.8% | 4.5% | 0.619 |
| 5 | 9.0% | 11.1% | 14.6% | 4.5% | 4.6% | 5.0% | 5.9% | 0.620 |

✓ Best epoch: 3 with collective accuracy 9.9%
✓ All checkpoints available at: https://huggingface.co/AbstractPhil/math_collective

┌─────────────────────────────────────────────────────────────┐
│                    GALAXY BRAIN COLLECTIVE                   │
├─────────────────────────────────────────────────────────────┤
│  FUZZY STREAMS (learned representations)                    │
│  ├── MathBERT (frozen) → Head A → "symbolic understanding"  │
│  └── T5-base (frozen)  → Head B → "linguistic reasoning"    │
│                                                             │
│  DETERMINISTIC STREAMS (pure computation)                   │
│  ├── Eigenspectrum    → Head C → "covariance geometry"      │
│  ├── Cayley-Menger    → Head D → "distance geometry"        │
│  ├── Symbolic Calc    → Head E → "actual arithmetic"        │
│  └── Fractal Dim      → Head F → "complexity measure"       │
│                                                             │
│  All 6 streams → Fusion → Classifier                        │
└─────────────────────────────────────────────────────────────┘

ρ = collective_accuracy / max(individual_accuracies)

ρ > 1.0 = emergence (collective outperforms best individual)