Recursive Incompleteness Framework: Truth Eigenstates, Phase Stability, and Dynamic Coherence

This publication extends the Recursive Incompleteness Theorem — originally proposed as a formal extension to Gödel’s incompleteness results — into a fully articulated dynamic framework. It introduces the concept of truth eigenstates, showing that recursive logical systems stabilize around coherent attractors rather than collapse under contradiction. Truth is modeled as a recursive, phase-relative structure, evolving through contradiction absorption, phase transitions, and internal coherence reorganization. Key contributions include: The definition and emergence of truth eigenstates as fixed points of recursive extension, The dynamic behavior of eigenstates: stabilization, drift, and collapse, The mapping of phase landscapes and coherence basins in recursive truth spaces, The identification of internal geometric structures (spherical, toroidal, polygonal, fractal) within truth eigenstates, A unified synthesis describing truth as a dynamic, living coherence architecture, not a static absolute. This work is a structural elaboration of the original Recursive Incompleteness Theorem and positions recursive logic as a natural evolution of formal logical systems under self-referential pressure.