Circular Astronomy

Tag: structure-transformation duality

  • A New Understanding of P vs NP Through Structure and Transformation

    Beyond the Millennium Statement: A Dual Structure–Transformation Reformulation of P versus NP Perhaps the central question is not only whether solutions can be found as efficiently as they can be checked, but whether the structure of a problem and the transformations used to solve it are fundamentally interchangeable. Introduction The P versus NP problem is…

  • Reformulating the Yang-Mills Mass Gap via Dual Representations

    Beyond the Millennium Statement: A Dual Structure–Transformation Reformulation of the Yang–Mills Mass Gap Problem “Perhaps some mathematical problems remain difficult not because their statements are incomplete, but because they are represented from only one side.” Introduction The Clay Millennium Prize Problems are among the most carefully formulated open problems in mathematics. They are not vague…