On the Wave-Kinematic Interpretation of Fermat's Last Theorem: The Problem of Phase Blockage within the Ullerian Formalism

This paper proposes a fundamental paradigm shift for Fermat's Last Theorem by approaching the problem through the lens of continuum mechanics and wave kinematics as established by Karl Uller, rather than using the traditional number-theoretic framework. Within this model, the discrete powers of the equation are mapped onto the amplitudes of coupled oscillatory domains. The analysis demonstrates that for the second power, the system remains hysteresis-free in the Ullerian sense, establishing a perfect resonance within the principal position. However, for higher geometric dimensions, the underlying structural topology inherently enforces a non-zero hysteresis coefficient. This induced cyclic hysteresis leads to a kinematic phase blockage: the boundaries of the oscillatory fields shift relative to one another in such a manner that a closed, stable attractor cannot exist within the discrete lattice of integers.