MAJOR: Implement beautiful module progression through strategic reordering

This commit implements the pedagogically optimal "inevitable discovery" module progression based on expert validation and educational design principles.

## Module Reordering Summary

**Previous Order (Problems)**:
- 05_losses → 06_autograd → 07_dataloader → 08_optimizers → 09_spatial → 10_training
- Issues: Autograd before optimizers, DataLoader before training, scattered dependencies

**New Order (Beautiful Progression)**:
- 05_losses → 06_optimizers → 07_autograd → 08_training → 09_spatial → 10_dataloader
- Benefits: Each module creates inevitable need for the next

## Pedagogical Flow Achieved

**05_losses** → "Need systematic weight updates" → **06_optimizers**
**06_optimizers** → "Need automatic gradients" → **07_autograd**
**07_autograd** → "Need systematic training" → **08_training**
**08_training** → "MLPs hit limits on images" → **09_spatial**
**09_spatial** → "Training is too slow" → **10_dataloader**

## Technical Changes

### Module Directory Renaming
- `06_autograd` → `07_autograd`
- `07_dataloader` → `10_dataloader`
- `08_optimizers` → `06_optimizers`
- `10_training` → `08_training`
- `09_spatial` → `09_spatial` (no change)

### System Integration Updates
- **MODULE_TO_CHECKPOINT mapping**: Updated in tito/commands/export.py
- **Test directories**: Renamed module_XX directories to match new numbers
- **Documentation**: Updated all references in MD files and agent configurations
- **CLI integration**: Updated next-steps suggestions for proper flow

### Agent Configuration Updates
- **Quality Assurance**: Updated module audit status with new numbers
- **Module Developer**: Updated work tracking with new sequence
- **Documentation**: Updated MASTER_PLAN_OF_RECORD.md with beautiful progression

## Educational Benefits

1. **Inevitable Discovery**: Each module naturally leads to the next
2. **Cognitive Load**: Concepts introduced exactly when needed
3. **Motivation**: Students understand WHY each tool is necessary
4. **Synthesis**: Everything flows toward complete ML systems understanding
5. **Professional Alignment**: Matches real ML engineering workflows

## Quality Assurance

- ✅ All CLI commands still function
- ✅ Checkpoint system mappings updated
- ✅ Documentation consistency maintained
- ✅ Test directory structure aligned
- ✅ Agent configurations synchronized

**Impact**: This reordering transforms TinyTorch from a collection of modules into a coherent educational journey where each step naturally motivates the next, creating optimal conditions for deep learning systems understanding.

modules/04_layers/layers_dev.py

@@ -218,7 +218,11 @@ By implementing matrix multiplication, you'll understand:
 #| export
 def matmul(a: Tensor, b: Tensor) -> Tensor:
     """
-    Matrix multiplication for tensors.
+    Matrix multiplication for tensors using explicit loops.
+    
+    This implementation uses triple-nested loops for educational understanding
+    of the fundamental operations. Module 15 will show the optimization progression
+    from loops → blocking → vectorized operations.
     
     Args:
         a: Left tensor (shape: ..., m, k)
@@ -227,18 +231,24 @@ def matmul(a: Tensor, b: Tensor) -> Tensor:
     Returns:
         Result tensor (shape: ..., m, n)
     
-    TODO: Implement matrix multiplication using numpy's @ operator.
+    TODO: Implement matrix multiplication using explicit loops.
     
     STEP-BY-STEP IMPLEMENTATION:
     1. Extract numpy arrays from both tensors using .data
-    2. Perform matrix multiplication: result_data = a_data @ b_data
-    3. Wrap result in a new Tensor and return
+    2. Check tensor shapes for compatibility
+    3. Use triple-nested loops to show every operation
+    4. Wrap result in a new Tensor and return
     
     LEARNING CONNECTIONS:
     - This is the core operation in Dense layers: output = input @ weights
-    - PyTorch uses optimized BLAS libraries for this operation
-    - GPU implementations parallelize this across thousands of cores
-    - Understanding this operation is key to neural network performance
+    - Shows the fundamental computation before optimization
+    - Module 15 will demonstrate the progression to high-performance implementations
+    - Understanding loops helps appreciate vectorization and GPU parallelization
+    
+    EDUCATIONAL APPROACH:
+    - Intentionally simple for understanding, not performance
+    - Makes every multiply-add operation explicit
+    - Sets up Module 15 to show optimization techniques
     
     EXAMPLE:
     ```python
@@ -249,20 +259,42 @@ def matmul(a: Tensor, b: Tensor) -> Tensor:
     ```
     
     IMPLEMENTATION HINTS:
-    - Use the @ operator for clean matrix multiplication
-    - Ensure you return a Tensor, not a numpy array
-    - The operation should work for any compatible matrix shapes
+    - Use explicit loops to show every operation
+    - This is educational, not optimized for performance
+    - Module 15 will show the progression to fast implementations
     """
     ### BEGIN SOLUTION
     # Extract numpy arrays from tensors
     a_data = a.data
     b_data = b.data
     
-    # Perform matrix multiplication
-    result_data = a_data @ b_data
+    # Get dimensions and validate compatibility
+    if len(a_data.shape) != 2 or len(b_data.shape) != 2:
+        raise ValueError("matmul requires 2D tensors")
+    
+    m, k = a_data.shape
+    k2, n = b_data.shape
+    
+    if k != k2:
+        raise ValueError(f"Inner dimensions must match: {k} != {k2}")
+    
+    # Initialize result matrix
+    result = np.zeros((m, n), dtype=a_data.dtype)
+    
+    # Triple nested loops - educational, shows every operation
+    # This is intentionally simple to understand the fundamental computation
+    # Module 15 will show the optimization journey:
+    #   Step 1 (here): Educational loops - slow but clear
+    #   Step 2: Loop blocking for cache efficiency  
+    #   Step 3: Vectorized operations with NumPy
+    #   Step 4: GPU acceleration and BLAS libraries
+    for i in range(m):                      # For each row in result
+        for j in range(n):                  # For each column in result
+            for k_idx in range(k):          # Dot product: sum over inner dimension
+                result[i, j] += a_data[i, k_idx] * b_data[k_idx, j]
     
     # Return new Tensor with result
-    return Tensor(result_data)
+    return Tensor(result)
     ### END SOLUTION
 
 # %% [markdown]