Oxygen as Fixed Point: Wind, Blood, and the Constraint Surface of Existence

Molecular oxygen is maintained at a fixed-point concentration at every scale where chemistry operates: 98% arterial saturation in blood, 20.946% in the troposphere, and approximately 1% of all baryonic mass in the universe. This paper presents the oxygen fixed point as a cross-scale instantiation of the Banach contraction mapping, showing that the fine structure constant α enters the atmospheric chain through the Chapman cycle (σ ∝ α⁻⁴), that the Brewer-Dobson circulation is structurally isomorphic to cardiovascular circulation, that the Great Oxidation Event represents a discrete fixed-point transition, and that iron is the instrument of the oxygen fixed point at every scale from haemoglobin to the geodynamo…