Add slipnet analysis: depth vs topology correlation study

Analysis shows no significant correlation between conceptual depth
and hop distance to letter nodes (r=0.281, p=0.113). Includes
Python scripts, visualizations, and LaTeX paper.

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

slipnet_analysis/compute_stats.py

@@ -0,0 +1,85 @@
+"""Compute correlation statistics for the paper (hop-based)."""
+
+import json
+import numpy as np
+from scipy import stats
+
+def main():
+    with open(r'C:\Users\alexa\copycat\slipnet_analysis\slipnet.json', 'r') as f:
+        data = json.load(f)
+
+    # Extract data points (excluding letter nodes themselves)
+    names = []
+    depths = []
+    hops = []
+    is_unreachable = []
+
+    for node in data['nodes']:
+        name = node['name']
+        depth = node['conceptualDepth']
+        path_info = node.get('minPathToLetter', {})
+        hop_count = path_info.get('hops')
+        nearest = path_info.get('nearestLetter')
+
+        # Skip letter nodes (hops 0)
+        if hop_count is not None and hop_count > 0:
+            names.append(name)
+            depths.append(depth)
+            hops.append(hop_count)
+            is_unreachable.append(nearest is None)
+
+    # Convert to numpy arrays
+    depths = np.array(depths)
+    hops = np.array(hops)
+
+    # Compute correlation
+    correlation, p_value = stats.pearsonr(depths, hops)
+    spearman_corr, spearman_p = stats.spearmanr(depths, hops)
+
+    # Linear regression
+    z = np.polyfit(depths, hops, 1)
+
+    # R-squared
+    y_pred = np.polyval(z, depths)
+    ss_res = np.sum((hops - y_pred) ** 2)
+    ss_tot = np.sum((hops - np.mean(hops)) ** 2)
+    r_squared = 1 - (ss_res / ss_tot)
+
+    num_unreachable = sum(is_unreachable)
+    print(f"Number of nodes analyzed: {len(names)}")
+    print(f"Total nodes: {data['nodeCount']}")
+    print(f"Letter nodes (excluded): 26")
+    print(f"Unreachable nodes (hops = 2*max): {num_unreachable}")
+    print()
+    print(f"Pearson correlation: r = {correlation:.4f}")
+    print(f"Pearson p-value: p = {p_value:.6f}")
+    print(f"Spearman correlation: rho = {spearman_corr:.4f}")
+    print(f"Spearman p-value: p = {spearman_p:.6f}")
+    print(f"R-squared: {r_squared:.4f}")
+    print(f"Linear regression: hops = {z[0]:.4f} * depth + {z[1]:.4f}")
+    print()
+    print(f"Depth range: {min(depths):.1f} - {max(depths):.1f}")
+    print(f"Hops range: {min(hops)} - {max(hops)}")
+    print(f"Mean depth: {np.mean(depths):.2f}")
+    print(f"Mean hops: {np.mean(hops):.2f}")
+    print(f"Std depth: {np.std(depths):.2f}")
+    print(f"Std hops: {np.std(hops):.2f}")
+    print()
+
+    # Distribution of hops
+    print("Distribution of hops:")
+    for h in sorted(set(hops)):
+        count = sum(1 for x in hops if x == h)
+        nodes_at_h = [n for n, hp in zip(names, hops) if hp == h]
+        print(f"  {h} hops: {count} nodes")
+
+    print()
+    print("Data points (sorted by hops, then depth):")
+    print(f"{'Node':<30} {'Depth':<10} {'Hops':<10} {'Reachable':<10}")
+    print("-" * 60)
+    for name, depth, hop, unreachable in sorted(zip(names, depths, hops, is_unreachable), key=lambda x: (x[2], x[1])):
+        status = "No" if unreachable else "Yes"
+        print(f"{name:<30} {depth:<10.1f} {hop:<10} {status:<10}")
+
+if __name__ == '__main__':
+    main()