A Third Law of Biology: Gradient Descent on the Unique Reciprocal Cost, Across Evolution, Development, and Cognition

Biology has had two laws that generalise across all life: Darwinian selection and Mendelian inheritance. Everything since 1900 has been mechanism, not law. We propose a third: every trajectory of every living, cognitive, and evolutionary process is gradient descent on the reciprocal-symmetric cost functional J(x) = ½(x + x⁻¹) − 1, uniquely forced by the Recognition Composition Law, computed on the D = 3 causal lattice, subject to heritable boundary conditions and bounded external energy throughput. Life, cognition, and evolution are three timescales of one variational principle. We decompose the claim into six propositions, fifteen named corollaries, and five empirical falsifiers. Each proposition is stated and proved. The law is packaged as a single master theorem: every biological trajectory satisfies a cost-accounting inequality, structural cost is monotonically non-increasing without energy input, and the alive/dead demarcation reduces to three independent conditions with three named failure modes.