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DISCIPLINED EVOLUTION OPERATOR FOR SECOND-ORDER DIFFERENTIAL SYSTEMS (DEO-2)

This paper introduces DEO-2 – the Disciplined Evolution Operator for Second-Order Differential Systems, combining Tuy’s Cut, Brauer Height-Zero, and Chernoff Evolution to form a deterministic, convergent, low-noise evolution mechanism that can be directly embedded in silicon for Operator Intelligence and sovereign AI.

Ivan Remizov -  Picture: Sputnik An Operator-Based Foundation for Solving Second-Order Differential Systems and Its Implications for AI and Operator Intelligence EXECUTIVE SUMMARY For nearly two centuries, a broad class of linear second-order differential equations has been regarded as unsolvable in the classical analytic sense, due to the non-existence of closed-form solutions expressible via elementary functions or finite algebraic operations. While numerical methods provide approximations, they often lack intrinsic guarantees of structural consistency, convergence discipline, and explainability. This whitepaper presents an operator-based approach that shifts the problem from searching for closed-form solutions to constructing a solution operator . Building on Chernoff-type approximations for time-dependent systems, the framework is extended by introducing two structural operators