Amanollahi Continuous SAT Solver

We present the Amanollahi Continuous SAT Solver, a novel continuous optimization framework for Boolean satisfiability problems. The method introduces a multiplicative tanh-based energy function together with a deterministic κ-annealing schedule and restart-based search, forming a simple yet effective continuous-time analogue of SAT solving. Unlike classical CDCL solvers or physics-inspired ODE systems, the Amanollahi method relies solely on bounded gradient-based minimization (L-BFGS-B) without clause learning, heuristics, or auxiliary boost mechanisms.

Using only standard Google Colab CPU resources, we experimentally verify:(1) UF125_01 (SAT) — the energy consistently descends to zero, yielding a valid satisfying assignment;(2) UUF250_01 (UNSAT) — the energy stabilizes at a strictly positive minimum under all 100 randomized restarts, providing strong empirical evidence of UNSAT within this continuous formulation.

These results demonstrate that the proposed κ-driven smooth landscape successfully separates satisfiable and unsatisfiable random benchmarks and offers a new optimization-based perspective on SAT and UNSAT detection.