Daopological Structural Annealing (DSA): A Gradient-Free Discrete Topological Computing Paradigm Beyond the Calculus Constraint

The two pillars of modern computational intelligence—deep learning and molecular dynamics simulation—share a common calculus premise: the state space must be continuous and differentiable, and optimization must proceed along gradients. On non-convex problems this premise produces a structural paradox: small step sizes converge slowly and trap in local minima, while large step sizes are unstable and may diverge. This paper proposes Daopological Structural Annealing (DSA), a discrete topological computing paradigm that does not rely on gradients, does not require differentiability, and does not aim at continuous function fitting. DSA maps problem states onto discrete topological lattices, searches the lattice space through structural operators (Permutation, Inversion, Mutation), and drives the system toward the ground state of an energy landscape via the Metropolis criterion and a cooling schedule from statistical physics. Unlike classical simulated annealing, DSA’s search unit is a topologically meaningful structural event rather than an isolated parameter, and its energy function is a multi-objective Hamiltonian rather than a single scalar objective. We give an axiomatic formalization, discuss convergence conditions, and report consistent behavior across three completed cross-domain benchmarks: transient signal detection, peptide conformational sampling, and real-time logistics scheduling. DSA is not an improvement upon gradient methods; it opens a third path whose first principle is discrete structural search rather than calculus.