Motivic Galois Structures: Quantum Decoherence and the Emergence of Classical Gravity Connection

This paper proposes a conceptual and mathematical framework connecting quantum decoherence andgravity through the language of motivic geometry and the motivic Galois group. The central idea is that quantumsuperpositions correspond to mixed motivic structures, while gravitational interaction induces a flow towardpure motives via the suppression of extension classes. In this picture, divergences in quantum path integrals arereinterpreted as artifacts of non-admissible motivic weights, and classical spacetime geometry—governed byEinstein’s equations— emerges as a stable fixed point under the combined action of gravitational dynamics andthe motivic Galois group. It is presented explicit toy numerical examples illustrating (i) the resolution ofquantum infinities via motivic periods and (ii) the emergence of classical reality through gravitationally inducedmotivic decoherence. Finally, It is discussed the advantages of this approach relative to existing methods inquantum gravity and decoherence theory.