Feature: Replace Sankey with Factorization Tree (Sunburst) visualization

app.py

@@ -55,34 +55,77 @@ def get_gpf(n):
             n //= i
     return n
 
-def visualize_potentiality_flow():
+def get_prime_factors(n):
+    """Returns list of prime factors."""
+    factors = []
+    d = 2
+    while d * d <= n:
+        while n % d == 0:
+            factors.append(d)
+            n //= d
+        d += 1
+    if n > 1:
+        factors.append(n)
+    return factors
+
+def visualize_factorization_tree(max_n=60):
     """
-    Tab 1: Directed Graph (Sankey) showing Digit Constraints.
+    Factorization Tree: Primes are roots, composites branch from their smallest prime factor.
+    Uses Plotly Sunburst for hierarchical visualization.
     """
-    labels = ["Integer Stream"] + [f"Ends in {i}" for i in range(10)] + ["Composite Sink", "Prime Potential (P_n)"]
-    sources, targets, values, colors = [], [], [], []
-
-    # Layer 1: Stream -> Digits
-    for i in range(10):
-        sources.append(0); targets.append(i+1); values.append(10); colors.append("#444")
-
-    # Layer 2: Digits -> Destination
-    prime_lanes = [1, 3, 7, 9]
-    for i in range(10):
-        sources.append(i+1)
-        if i in prime_lanes:
-            targets.append(12) # Prime Potential
-            colors.append("#00ffea") # Cyan
-        else:
-            targets.append(11) # Sink
-            colors.append("#ff0055") # Red
-        values.append(10)
-
-    fig = go.Figure(data=[go.Sankey(
-        node=dict(pad=15, thickness=20, line=dict(color="black", width=0.5), label=labels, color=["white"]+["#333"]*10+["#ff0055", "#00ffea"]),
-        link=dict(source=sources, target=targets, value=values, color=colors)
-    )])
-    fig.update_layout(title="Prime Potentiality Flow (Mod 10 Constraints)", template="plotly_dark", height=600)
+    ids = ["Root"]
+    labels = ["ℤ"]
+    parents = [""]
+    values = [0]
+    colors = ["#1a1a2e"]
+    
+    # Collect primes first
+    primes = [n for n in range(2, max_n + 1) if sympy.isprime(n)]
+    
+    # Add primes as children of root
+    for p in primes:
+        ids.append(f"p_{p}")
+        labels.append(f"P({p})")
+        parents.append("Root")
+        values.append(1)
+        colors.append("#00ffea")  # Cyan for primes
+    
+    # Add composites as children of their smallest prime factor
+    for n in range(4, max_n + 1):
+        if not sympy.isprime(n):
+            factors = get_prime_factors(n)
+            smallest_prime = factors[0]
+            
+            ids.append(f"c_{n}")
+            labels.append(f"{n}")
+            parents.append(f"p_{smallest_prime}")
+            values.append(1)
+            
+            # Color by abundance (sum of divisors)
+            divisor_sum = sum(d for d in range(1, n) if n % d == 0)
+            if divisor_sum > n:
+                colors.append("#ff6b35")  # Orange for Abundant
+            elif divisor_sum < n:
+                colors.append("#ff0055")  # Red for Deficient
+            else:
+                colors.append("#9d4edd")  # Purple for Perfect
+    
+    fig = go.Figure(go.Sunburst(
+        ids=ids,
+        labels=labels,
+        parents=parents,
+        values=values,
+        branchvalues="total",
+        marker=dict(colors=colors, line=dict(color="#000", width=1)),
+        hovertemplate="<b>%{label}</b><br>Parent: %{parent}<extra></extra>"
+    ))
+    
+    fig.update_layout(
+        title="Prime Factorization Tree (Composites inherit from smallest prime factor)",
+        template="plotly_dark",
+        height=600,
+        margin=dict(t=50, l=10, r=10, b=10)
+    )
     return fig
 
 def visualize_prime_network(max_integer, show_links):
@@ -237,12 +280,12 @@ with gr.Blocks(theme=gr.themes.Monochrome(), title="LOGOS SPCW Protocol") as dem
             
             with gr.Row():
                 with gr.Column():
-                    plot_flow = gr.Plot(label="Potentiality Flow")
+                    plot_flow = gr.Plot(label="Factorization Tree")
                 with gr.Column():
                     plot_counts = gr.Plot(label="Composite Density")
             
             btn_viz.click(visualize_prime_network, [max_int, show_links], plot_radial)
-            btn_viz.click(visualize_potentiality_flow, None, plot_flow)
+            btn_viz.click(visualize_factorization_tree, None, plot_flow)
             btn_viz.click(visualize_gpf_counts, [max_int], plot_counts)
 
         with gr.Tab("The Machine Shop (DSP Bridge)"):