Fix: LOGOS Log Polar Cone Topology (mod 10 rings, 1/3/7/9 lanes)

app.py

@@ -120,37 +120,97 @@ def run_mtl_demo() -> str:
         return f"Demo Error: {str(e)}"
 
 # --- PHYSICS VISUALIZERS ---
-def get_prime_topology(max_n=1000):
-    """Generates the Prime Spiral Visualization."""
+def get_prime_topology(max_n=500):
+    """
+    LOGOS Concentric Log Polar Cone Topology.
+    - Each ring = mod 10 (decade layer)
+    - Special lanes: mod 1, 3, 7, 9 (prime-generating residues)
+    """
+    import math
     fig = go.Figure()
     
-    primes = [n for n in range(2, max_n) if sympy.isprime(n)]
-    r = [n for n in primes]
-    theta = [n * 2.39996 for n in primes]  # Golden Angle
+    # Generate numbers and categorize by mod 10
+    all_nums = list(range(1, max_n))
     
-    fig.add_trace(go.Scatterpolar(
-        r=r, theta=theta, mode='markers',
-        marker=dict(
-            color=r, 
-            colorscale='Viridis', 
-            size=[5 + (n%5) for n in primes],
-            line=dict(color='white', width=0.5)
-        ),
-        name='Primes'
-    ))
+    # Color by mod 10 residue class
+    residue_colors = {
+        1: '#00ffea',  # Cyan - Prime lane
+        3: '#ff00ff',  # Magenta - Prime lane
+        7: '#ffff00',  # Yellow - Prime lane
+        9: '#00ff00',  # Green - Prime lane
+        0: '#333333',  # Gray - Even decade
+        2: '#333333', 4: '#333333', 5: '#333333', 
+        6: '#333333', 8: '#333333'
+    }
+    
+    # Build traces for each residue class
+    for residue in [1, 3, 7, 9]:  # Prime-generating lanes only
+        nums_in_class = [n for n in all_nums if n % 10 == residue]
+        
+        # Log polar coordinates
+        # r = log10(n) gives concentric rings per decade
+        # theta = (n mod 10) * 36 degrees + offset for spread
+        r = [math.log10(n) if n > 0 else 0 for n in nums_in_class]
+        theta = [(n % 100) * 3.6 for n in nums_in_class]  # Spread within decade
+        
+        # Mark primes
+        is_prime = [sympy.isprime(n) for n in nums_in_class]
+        sizes = [12 if p else 4 for p in is_prime]
+        colors = [residue_colors[residue] if p else '#555555' for p in is_prime]
+        
+        fig.add_trace(go.Scatterpolar(
+            r=r, 
+            theta=theta, 
+            mode='markers',
+            marker=dict(
+                color=colors,
+                size=sizes,
+                line=dict(color='white', width=0.3),
+                opacity=0.8
+            ),
+            text=[f"{n} (mod10={residue})" for n in nums_in_class],
+            hoverinfo='text',
+            name=f'Mod {residue}'
+        ))
+    
+    # Add ring labels for decades
+    for decade in [10, 100]:
+        r_ring = math.log10(decade)
+        theta_ring = list(range(0, 360, 10))
+        fig.add_trace(go.Scatterpolar(
+            r=[r_ring] * len(theta_ring),
+            theta=theta_ring,
+            mode='lines',
+            line=dict(color='rgba(255,255,255,0.2)', width=1, dash='dot'),
+            showlegend=False
+        ))
     
     fig.update_layout(
         template="plotly_dark",
         paper_bgcolor='rgba(0,0,0,0)',
         plot_bgcolor='rgba(0,0,0,0)',
-        showlegend=False,
+        showlegend=True,
+        legend=dict(font=dict(color='white')),
         polar=dict(
-            radialaxis=dict(visible=False),
-            angularaxis=dict(visible=False),
-            bgcolor='rgba(11,15,25,0.8)'
+            radialaxis=dict(
+                visible=True,
+                range=[0, 3],
+                ticktext=['1', '10', '100', '1000'],
+                tickvals=[0, 1, 2, 3],
+                gridcolor='rgba(255,255,255,0.1)'
+            ),
+            angularaxis=dict(
+                visible=True,
+                gridcolor='rgba(255,255,255,0.1)'
+            ),
+            bgcolor='rgba(11,15,25,0.9)'
         ),
-        margin=dict(l=20, r=20, t=20, b=20),
-        height=500
+        margin=dict(l=40, r=40, t=40, b=40),
+        height=550,
+        title=dict(
+            text="LOGOS Log Polar Cone (Mod 10 Rings)",
+            font=dict(color='white')
+        )
     )
     return fig
 
@@ -312,17 +372,20 @@ with gr.Blocks(theme=gr.themes.Soft(), css=load_css(), title="LOGOS: Arithmetic
         with gr.Tab("Prime Topology"):
             with gr.Row():
                 with gr.Column():
-                    prime_plot = gr.Plot(value=get_prime_topology(), label="The Prime Field")
+                    prime_plot = gr.Plot(value=get_prime_topology(), label="Log Polar Cone")
                 with gr.Column():
                     gr.Markdown("""
-                    ### Prime Spiral (Golden Angle)
+                    ### LOGOS Log Polar Cone Topology
+                    
+                    **Concentric rings = Mod 10 decades**
                     
-                    Each prime is plotted at its value with golden angle rotation.
+                    **Prime Lanes (Mod 10 residues):**
+                    - **Cyan (1)**: Numbers ending in 1
+                    - **Magenta (3)**: Numbers ending in 3
+                    - **Yellow (7)**: Numbers ending in 7
+                    - **Green (9)**: Numbers ending in 9
                     
-                    **Patterns reveal:**
-                    - Ulam spiral structures
-                    - Twin prime clustering
-                    - Gap distribution
+                    Large dots = **Primes** (only end in 1,3,7,9)
                     
                     *Arithmetic is Architecture.*
                     """)