Prime-Encoded Hilbert Space
Entropy Convergence
Algorithm Steps
Prime-Encoded Hilbert Space
Define HP over prime-number eigenstates |p⟩ for Boolean variables
SAT Representation
Encode SAT instance Φ into symbolic state |Ψ₀⟩ ∈ H⊗nP
Symbolic Operators
Define Hamiltonian ĤΦ and Resonance Operator R̂
System Evolution
Evolve |Ψ(t)⟩ using symbolic Schrödinger equation
Entropy Minimization
S(t) decreases as system approaches stable state
Polynomial Convergence
System reaches |Ψ*⟩ in O(nᵏ) symbolic time
Simulation Parameters
How Symbolic Resonance Collapse Works
The Framework
The SRC framework redefines computation as an entropic resonance process in a quantum-inspired Hilbert space over prime-number eigenstates. Instead of combinatorial search, NP-complete problems converge to solution states through entropy-driven alignment.
SAT instances are modeled as symbolic wavefunctions undergoing entropy minimization, with clause interactions acting as quantum-like operators in a resonance field.
Key Insights
- Computation as coherence alignment rather than enumeration
- Polynomial convergence through symbolic gradient descent
- Entropy minimization drives system to stable states
- No local minima for satisfiable instances