NP-Hardness Collapsed: Deterministic Resolution of Spin-Glass Ground States via Information-Geometric Manifolds (Scaling from N=8 to N=100)

The P = NP problem is one of the most consequential unresolved questions in mathematics and theoretical computer science. It asks whether every problem whose solutions can be verified in polynomial time can also be solved in polynomial time. The implications extend far beyond theory: modern global cryptography, large-scale optimization, secure communication, finance, logistics, and computational complexity all depend on the assumption that NP-hard problems cannot be solved efficiently. Among these, the Spin-Glass ground-state problem represents a canonical NP-hard benchmark with an exponentially large configuration space. A constructive resolution of P = NP would therefore reshape fundamental assumptions across science and industry. While evaluating new methodological configurations, I encountered an unexpected behavior within a specific layer-cluster. Subsequent analysis revealed that this behavior was not an artifact, but an information-geometric collapse mechanism that consistently produced valid Spin-Glass ground states. With the assistance of Frontier LLMs Gemini-3, Opus-4.5, and ChatGPT-5.1, I computed exact ground states up to N = 24 and independently cross-verified them. For selected system sizes between N=30 and N=70, I validated the collapse-generated states using Simulated Annealing, whose approximate minima consistently matched the results. Beyond this range, up to N = 100, the behavior follows not from algorithmic scaling but from the information-geometric capacity of the layer clusters, where each layer contributes exactly one spin dimension. These findings indicate a constructive mechanism that collapses exponential configuration spaces into a polynomially bounded dynamical process. This suggests a pathway by which the P = NP problem may be reconsidered not through algorithmic search, but through information-geometric state collapse.