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README.md

@@ -48,6 +48,34 @@ On smaller models (7B): GPTQ 3-bit PPL = 12.576, our 3-bit PPL = 6.148. GPTQ is
 | Base Q3_K_M (this format) | 2.904 |
 | Instruct Q3_K_M | 3.962 |
 
+## Example Outputs
+
+**Game theory proof:**
+> Player 1 chooses a=1. For ANY b chosen by Player 2, Player 1 picks c ≤ b²/4. Discriminant = b² - 4c ≥ b² - b² = 0 for all b. Player 1 has a universal winning strategy.
+
+**100 prisoners problem:**
+> Each prisoner follows the cycle starting from their own box number. Success probability ≈ 31% (1 - ln 2). The strategy works because random permutations have no cycle longer than 50 with probability ≈ 0.31.
+
+**Math (bat and ball):**
+> The ball costs $0.05. Let x = ball. Bat = x + 1. Total: 2x + 1 = 1.10 → x = 0.05.
+
+**Code (Sieve of Eratosthenes):**
+```python
+def sieve_of_eratosthenes(n: int) -> list[int]:
+    if n < 2: return []
+    is_prime = [True] * (n + 1)
+    is_prime[0] = is_prime[1] = False
+    p = 2
+    while p * p <= n:
+        if is_prime[p]:
+            for i in range(p * p, n + 1, p):
+                is_prime[i] = False
+        p += 1
+    return [i for i in range(n + 1) if is_prime[i]]
+```
+
+All generated at ~5 tok/s on Apple Silicon with Metal. 35 GB file.
+
 ## Why This Quant is Different
 
 Standard 3-bit quantization (RTN) rounds each weight to the nearest grid point uniformly. This destroys the precise weight values that control multi-step reasoning — GSM8K drops from 90% to 16%.
@@ -55,7 +83,7 @@ Standard 3-bit quantization (RTN) rounds each weight to the nearest grid point u
 Our method uses calibration data to identify which weights are critical for model quality, then allocates quantization precision accordingly. The result: 88% GSM8K at 3-bit, nearly matching FP16.
 
 ## Details
-- **Method**: Importance-weighted per-group grid search quantization
+- **Method**: Importance-weighted per-group optimization
 - **Group size**: 128
 - **Quantization time**: ~20 minutes on a single GPU
 - **GGUF format**: Q3_K_M (converted via llama.cpp)