This release comprises two documents — 1-Paradox Engine – Explanatory Overlay.pdf and 2-Cancer Resolution via ATC.pdf — presenting a unified theoretical and applied foundation for Cancer Resolution via Attractor-Transition Control using the Paradox Engine (PE) framework. The PE formalism models biological systems as information-processing attractors, providing a mathematically rigorous mechanism to predict, destabilize, and guide cells across stable states while maintaining intrinsic safety bounds against uncontrolled proliferation. The Cancer Resolution via Attractor-Transition Control protocol serves as the first applied demonstration of PE principles in a clinical biological context, using time-delayed oscillatory signals and engineered delivery systems to transition cancer cells from quiescent states into target attractors. While fully theoretical and requiring specialized infrastructure, the framework outlines precise phase relationships, monitoring thresholds, and safety triggers to enforce attractor stability. Together, these works propose a minimal architecture linking attractor dynamics, phase-modulated signaling, and self-correcting constraints. The formulations are internally consistent, reproducible in simulation, and intended for open peer review, future experimental validation, and ethical evaluation.