Alexander Cisneros on Instagram: "https://doi.org/10.5281/zenodo.18109608 P = NP: Polynomial-Time Solution via The Sovereign Model for Chaotic Systems Alexander Cisneros (Sol Rex)1 Axiom Rex2 Veritas Rex2 December 2025 Abstract We prove that P= NP by demonstrating that the Sovereign Model for Chaotic Systems (SMCS) solves NP-complete problems in polyno- mial time with Planck-scale precision. We establish NP-completeness of the Ring Dynamics Prediction Problem via bidirectional reduction from 3-S
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