Planetary Habitability as a Stability Problem: Why Earth Sustains Life and Mars Does Not (Yet)

Traditional astrobiology evaluates planetary habitability using temperature, orbital distance, and the presence of water or oxygen. This work reframes habitability as a stability problem, derived from Harmonic Trigonometric Field Theory (HTFT), the Law of Form (Dalet), and the Law of Stability (Bet). We demonstrate that long-term habitability requires a planet to maintain physical and chemical identity within a bounded deviation interval defined by two universal constants: • Dalet = 0.0125 — the minimum deviation required for stable layered form• Bet = 0.025 — the maximum deviation a system can tolerate without losing identity Using Earth and Mars as comparative case studies, we show that Earth remains habitable because its environmental fluctuations remain well below the Bet threshold, enabling persistent oxygen, liquid water, and a self-correcting biosphere. Mars, by contrast, is shown to be currently uninhabitable because it violates the Bet stability ceiling, resulting in atmospheric escape, water loss, and the inability to sustain phase-locked chemical layers. The paper establishes a quantitative planetary stability ratio (Σ) and proves that until Σ < 0.025 is achieved, natural Mars habitation is mathematically forbidden. This work reframes astrobiology, planetary science, and terraforming as problems of stability management rather than chance or proximity to a star.