# Erdős #336 Test Bench Flow
# Explicit Example: A = ∪(2^{2k}, 2^{2k+1}], order=2, exact_order=3

flowchart TD
    A[Start: Basis A
        k=0: {2}
        k=1: {5,6,7,8}
        k=2: {17..31}] --> B[Encode to 30-base
        L1: F(E) → bases 0-7
        L2: τ(E) → bases 8-15
        L3: δ(E) → bases 16-23
        L4: consistency → bases 24-29]
    
    B --> C{Run Verification}
    
    C -->|Pass| D[DISCRETE Cycle
        Propagate constraints
        I1-I6 check]
    
    C -->|High-Gap| E[CONTINUOUS Mode
        + Kirchhoff validation]
    
    D --> F{Fixed Point?}
    
    F -->|Yes ≤20 iter| G[Decode Layout
        Extract: order
        Extract: exact_order
        Extract: basis A]
    
    F -->|No| H[Fail: Divergence
        Constraint logic error]
    
    E --> F
    
    G --> I{Verify Results}
    
    I -->|order==2
       exact==3
       I1-6 pass| J[✅ SUCCESS
        Erdős #336 test passed]
    
    I -->|Mismatch| K[❌ FAIL
        Encoding error]
    
    %% Style definitions
    classDef success fill:#90EE90,stroke:#333,stroke-width:2px
    classDef fail fill:#FFB6C1,stroke:#333,stroke-width:2px
    classDef process fill:#87CEEB,stroke:#333,stroke-width:2px
    classDef decision fill:#FFD700,stroke:#333,stroke-width:2px
    
    class A,B process
    class C,F,I decision
    class D,E process
    class G process
    class J success
    class H,K fail