The paper discusses the development of a new one-loop algorithm for scattering amplitude calculations, particularly relevant for theoretical simulations at the Large Hadron Collider (LHC). The authors address the challenges of handling high particle multiplicities and complex one-loop amplitudes, which can lead to numerical instabilities and large algebraic expressions. They introduce an open-loop approach that combines tensor integrals with a one-loop Dyson-Schwinger recursion, allowing for efficient and numerically stable computation of multi-gluon amplitudes. This method is fully general and can be combined with both tensor-integral and OPP (Ossola-Papadopoulos-Pittau) reductions. The open-loop approach is designed to maximize speed and flexibility while maintaining numerical stability, making it suitable for a wide range of high-energy collider processes, from 2→2 scattering to multi-particle processes with up to O(10^5) diagrams. The authors demonstrate the efficiency and correctness of their method through various tests, including comparisons with tensor-integral and OPP reductions, and show that it significantly reduces CPU time and improves numerical stability compared to traditional methods.The paper discusses the development of a new one-loop algorithm for scattering amplitude calculations, particularly relevant for theoretical simulations at the Large Hadron Collider (LHC). The authors address the challenges of handling high particle multiplicities and complex one-loop amplitudes, which can lead to numerical instabilities and large algebraic expressions. They introduce an open-loop approach that combines tensor integrals with a one-loop Dyson-Schwinger recursion, allowing for efficient and numerically stable computation of multi-gluon amplitudes. This method is fully general and can be combined with both tensor-integral and OPP (Ossola-Papadopoulos-Pittau) reductions. The open-loop approach is designed to maximize speed and flexibility while maintaining numerical stability, making it suitable for a wide range of high-energy collider processes, from 2→2 scattering to multi-particle processes with up to O(10^5) diagrams. The authors demonstrate the efficiency and correctness of their method through various tests, including comparisons with tensor-integral and OPP reductions, and show that it significantly reduces CPU time and improves numerical stability compared to traditional methods.