Changbal Theory
of Emergent Solvability

This paper presents a theoretical and experimental framework that goes beyond modeling the nonlinear emergence of solvability in NP-complete problems to actively controlling it. Building upon prior studies that identified the Changbal Point and defined the Changbal Function and Changbal Region, this work proposes a novel model that enables intelligent intervention in problem structure to control both the direction and steepness of solvability transitions.

This control is formalized through the Changbal Jump Function, a structural mechanism incorporating an external intervention variable J, which serves as an AI-guided operator that visualizes and expands the latent solvability of a given problem space. Rather than a simple modifier, this variable functions as a guide for emergent jumps, actively shaping the problem’s resolution trajectory.

Through experiments using various AI models—including Graph Neural Networks (GNNs), Generative Adversarial Networks (GANs), Transformers, and Deep Reinforcement Learning (DRL)—we demonstrate that targeted structural adjustments can shift or widen the Changbal Region and modulate the slope of the transition curve. In particular, we show that adaptive structural changes in the model architecture significantly impact solvability, indicating that the Changbal Jump Function is not merely a mathematical function but an adaptive dynamic control mechanism.

This research extends beyond theoretical modeling by collecting real-world data, training applicable algorithms, and implementing a live platform capable of visualizing emergent transitions in real time across practical optimization tasks.

Through this integrated perspective connecting computational complexity, artificial intelligence, and structural optimization, we formally establish the mathematical foundation and applied potential of the proposed Changbal Theory.