Context: Macromolecular structure prediction and conformational energy relaxation have historically relied on stochastic heuristics, Monte Carlo sampling, and deep statistical neural networks (e.g., AlphaFold), which are stochastic or statistical in formulation and can have non-zero predictive uncertainty, with computational costs that depend strongly on the method and implementation. Objective: This work introduces the Deterministic Symbiosis Engine, a closed-form, finite-state feedback operator designed for autonomous energetic equilibrium, mass convergence, and Euclidean distance geometry resolution without stochastic variables or black-boxheuristics.Method: The state operator T : (E,M) →(Eu2032,Mu2032)acts as a non-linear piecewise dead-band contractor over a designated energy interval Isymb = [Eopt−ϵ,Eopt + ϵ]. We generalize T into an N-dimensional tensorial map incorporating angular momentum tensors J and local hydrodynamic dissipation matrices Γ. Results: We prove that for 2ϵ≥max(∆Einc,∆Edec), limit cycles are strictly precluded, yielding exact closed-form convergence in Ki steps. For a benchmark suite of 7 heterogeneous molecular subunits, the maximum individual convergence horizon is Ktotal = 4 under the stated parameters, with ∆dev = 0 in the fixed implementation. The perturbation test returns to the dead-band in Kpert = 2 cycles under the stated benchmark conditions. Conclusion: Bymembedding T within Euclidean Distance Matrix (EDM)completion via semidefinite algebraic constraints, thisframework demonstrates O(N) computational complex-ity for uncoupled systems and a conditional Lyapunov analysis for the coupled consensus dynamics, establishing a deterministic foundation for computational structural biophysics.Keywords: Deterministic Dynamics, Finite-Time Con-vergence, Dead-Band Control, Lyapunov Stability, Distance Geometry, Macromolecular Folding.