Phase 2 Deep Dive Results for 'The Geometry of a Solution' Project

Description This dataset and its accompanying source code represent the results of Phase 2 ("Deep Dive") of an ongoing research project exploring the P vs. NP problem through the lens of information geometry and statistical mechanics. The experiment tests the hypothesis that the boundary between easy and hard problem instances in an NP-complete problem constitutes a physical-like phase transition. A "computational heat capacity" metric, defined as the variance of energy (number of unsatisfied clauses) during a stochastic random walk, was measured for random 3-SAT instances. This "deep dive" experiment builds on a preliminary biomarker test by increasing the system size to n=100 variables and refining the data acquisition process (100 instances per data point, 3000 steps per walk) across a focused range of clause densities (alpha = 4.0 to 4.8). The results show a clear and prominent peak in the heat capacity, providing a high-confidence, quantitative "biomarker" for the phase transition. This dataset serves as a foundational input for subsequent geometric analyses, such as calculating geodesic distances and scalar curvature on the problem's information manifold. The included .ipynb file contains the complete Python code used to generate the data and the final plot.