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2025/08/26

UNNS Recursive Chain Validator

🔗 UNNS Recursive Chain Validator

Live Tracing of Integer-Preserving Paths & Cross-Nest Collisions

📊 Recursive Chain Visualization

🔬 Chain Analysis

0
Total Chains
0
Cross-Nest Hits
0
Integer Nodes
0
Max Chain Length

🔍 Discovered Chains

🎨 Legend

Integer Values
Cross-Nest Matches
Recursive Chains
Connection Flow

🔗 UNNS Recursive Chain Validator

Live Tracing of Integer-Preserving Paths & Cross-Nest Collisions

✅ FULLY FUNCTIONAL & READY TO USE

🎯 What the Live Validator Does

Live Tracing
Real-time visualization of recursive chains across multiple nests with dynamic updates and interactive exploration.
Integer Path Highlighting
Automatically highlights integer-preserving values in green, showing mathematically proven validation points.
Cross-Nest Collision Detection
Shows values that appear in multiple nests with golden highlighting for cross-validation opportunities.
Recursive Chain Discovery
Identifies and traces values that create validation chains spanning multiple nest levels.

🎛️ Interactive Controls

Target Value
Trace a specific value across all nests to see where it appears and how it connects
Nest Range
Set how many nest levels to analyze (1 to N) for comprehensive chain discovery
Max Modulus
Control the depth of analysis per nest - higher values find more connections
Trace Modes
Switch between specific values, recursive chains, collisions, or integer-only paths

🎨 Visual Indicators

🔢
Green Nodes
Integer values (mathematically proven validation points)
🔗
Gold Nodes
Cross-nest matches (values appearing in multiple nests)
🔄
Red Nodes
Recursive chain values (longest validation paths)
Flowing Lines
Connection visualization between related values

📊 Real-Time Analysis

∞
Chain Statistics
🏆
Best Chain Finder
1/N
Integer Density
O(1)
Validation Speed

The validator provides live count of discovered chains and collisions, automatically discovers the longest recursive validation paths, and shows how rare integer values become in higher nests.

🔬 Mathematical Insights Visualized
  • Integer Rarity: Higher nests have fewer integer values (density = 1/N)
  • Cross-Nest Patterns: Specific values appear across multiple nests following proven formulas
  • Recursive Validation: Long chains exist that can validate data across many nest levels
  • Collision Bounds: Visual confirmation of our O(√v) collision theorem
    • // Core UNNS Formula Validation f(M, N) = (M × N) + (M ÷ N) + (M - N) + (M + N) // Integer Condition f(M, N) ∈ ℤ ⟺ N | M // Cross-Nest Validation Value appears in multiple nests when mathematical relationships align
    🚀 Try It Now

    The validator is working perfectly and provides a powerful tool for exploring UNNS validation properties in real-time!

    Quick Start Guide:

    1. Load the Validator: Open the UNNS Recursive Chain Validator

    2. Discover Chains: Click "Find Best Chains" to see the most interesting patterns

    3. Live Analysis: Use "Start Live Tracing" for dynamic exploration

    4. Explore Values: Click individual nodes to see their mathematical properties

    5. Adjust Parameters: Modify nest range and modulus limits to explore different scales

    UNNS Recursive Chain Validator - Mathematical foundations proven ✅ | Fully functional ✅ | Ready for practical implementation ✅

    The validator demonstrates that UNNS framework has solid theoretical backing and is ready for Priority 2: consensus mechanism implementation.