Recursive Structure in Quantum Quadratic Gravity: The Law of Recursion at the Planck Scale

We demonstrate that the quantum quadratic gravity (QQG) inflationary scenario recently proposed by Liu, Quintin & Afshordi (2026) instantiates the seven-node topology and rewriting principle of the Law of Recursion at the Planck scale. The renormalization group flow of the QQG couplings ξ and λ constitutes recursive traversal through parameter space, with each energy scale rewriting the effective theory for subsequent scales. The three-phase cosmological evolution (Euclidean tunneling → slow-roll inflation → kination/reheating) maps onto the three-traversal handshake (signal → response → coupling). The tachyon divide and strong-coupling threshold function as selective membranes governing phase transitions. The emergence of General Relativity as an effective field theory in the infrared represents substrate rewriting at the deepest level. This analysis establishes that recursive architecture operates not only in biological, chemical, and astrophysical systems but at the fundamental level of quantum gravity itself. Three falsifiable predictions are derived from this structural correspondence. Keywords: Law of Recursion, quantum quadratic gravity, renormalization group, inflationary cosmology, UV completion, recursive architecture, Planck scale