Universal Relations in the G→X→Q→N Cycle: Five Quantitative Invariants Derived from Möbius Bundle Topology Across Physical, Biological, and Cognitive Systems

The G→X→Q→N generative cycle has been shown to instantiate across physical, biological, and cognitive systems. The present paper addresses a more specific question: are the quantitative parameters of these instantiations independent, or are they related by formal structures derivable from the cycle's topology? Five universal quantitative relations — all derivable from the Möbius bundle topology generated by the involutive property X² = −Id — are demonstrated across fourteen independent instantiations spanning twenty-two orders of magnitude in energy scale, with zero free parameters. The five relations are: (R1) the stable Q amplitude relation |φQ|² = m²/g, verified in DNA supercoiling, neuronal threshold dynamics, and the Higgs vacuum expectation value; (R2) the half-period consolidation τ₀ = T/2, verified across four independent biological tissue renewal systems with deviations 0–4. 1%; (R3) the critical crystallization threshold λc = g₀/ (4K̂²ρQ), verified in traumatic memory crystallization and holistic field stability, with Alzheimer's disease as the complementary hypodissolutive regime; (R4) the quadratic self-composition law A², instantiated in mitosis, Type II topoisomerase action, the REK memory kernel, and the non-Markovian dispersion relation; and (R5) the bundle closure condition generalizing R1–R4 as aspects of the topological requirement that the Möbius bundle closes with integer quantisation imposed by X² = −Id. A cross-domain parameter translation table is derived. Three verifiable predictions are formulated: quadratic scaling of PTSD vulnerability with hippocampal volume (R3), cross-domain τ₀ ratio test in haematological systems (R2), and non-linear A² therapeutic dose-response signature (R4). Explicit falsifiability conditions are stated for each relation.