The Law of Cognitive Phases (CPL): Formalizing Observer State Transitions in Subjective Physics

Version 4.0 separates the invariant Cognitive Phase Law (CPL)—defining three phases: Coherence, Fragmentation, and Reorganization—from its computational realization. Using reproducible simulations (seed = 42) with bifurcated ensemble sampling (n = 200) that avoids the intractable critical-slowing region near Hc=ln3, it validates phase-dependent hysteresis, rare discrete transitions, and deep attractor basins. Correlation analysis confirms transitions are emergent (|r| < 0.12 with noise) and structurally reflect the designed bifurcation. CPL 4.0 does not claim empirical calibration; all code, raw data, and figures are archived for full reproducibility. See also: Khomyakov (2025), Comment on Evans (2025), DOI:10.5281/zenodo.17469210