The Dew-Point Anchor Hypothesis (DPAH) proposes that the troposphere is primarily regulated by the dew-point lifting condensation level (LCL) and associated latent-heat processes rather than radiative forcing alone. This deposit documents the iterative development of a Markovian state-space model (~29,160 states: surface pressure × temperature × dew point × environmental lapse rate). The framework uses a clean physics kernel (moist-adiabatic ascent to LCL followed by hydrostatic + dry-adiabatic descent) to compute stationary distributions for tropical ascent (ITCZ) and subtropical descent regimes. Results demonstrate a robust warm-moist attractor in the ascent regime (mean ~294.8 K, clear peak near 300 K). Systematic sensitivity tests to ocean-surface evaporation suppression (simulating oil films) confirm measurable shifts in the attractor. Full Python scripts (Runs 307–311), reports, and plots are included. This work provides a physics-driven stochastic testbed for mass-motion and water-cycle regulation of tropospheric structure.