UNNS NP-Hardness Explorer v2.0
Visualizing Complexity Collapse Through Recursive Grammar
Select Problem
Parameters
Problem Size (n) 8
Normalization Strength 50%
Animation Speed 1x
Actions
1 Embed
2 Repair
3 Normalize
4 Collapse
5 Verify
Classical Exponential Search
Branches
2^n
Time
O(2^n)
Space
O(2^n)
UNNS Collapsed Search
Attractors
n^k
Time
O(n^k)
Space
O(n^2)
Algorithm Execution
function UNNSCollapse(problem) {
  // Step 1: Embed into recursive lattice
  lattice = RecursiveEmbed(problem);
  // Step 2: Apply repair operator
  repaired = RepairOperator(lattice);
  // Step 3: Normalize equivalence classes
  normalized = Normalize(repaired);
  // Step 4: Collapse to attractors
  attractors = CollapseToAttractors(normalized);
  // Step 5: Verify solution
  return VerifySolution(attractors);
}
📚 UNNS NP-Hardness Paper | 📚 NP-Hardness in UNNS Substrate

UNNS Complexity Theory

Core Principle

NP-hardness is not an absolute property of problems, but rather a property relative to the computational substrate. In the UNNS framework, problems that appear exponentially complex in classical computation can collapse to polynomial complexity through recursive embedding and normalization.

The Collapse Mechanism

1. Recursive Embedding: Problems are mapped into nested lattice structures
2. Repair Operations: Identify and merge equivalent states
3. Normalization: Collapse exponential branches into polynomial attractors
4. Verification: Check solutions in the collapsed space

Mathematical Foundation

Given a problem P with classical complexity O(2^n), the UNNS transformation:
T: P → L → N → A
where L is the lattice embedding, N is the normalized form, and A is the attractor set with |A| = O(n^k).

References

→ UNNS Note on NP-Hardness (PDF)
→ NP-Hardness in UNNS Substrate (PDF)