Implications of Complexity-Dependent Gravitation: A Conditional Analysis Using Circuit Complexity

Explores theoretical consequences of hypothesized coupling between gravitational mass and quantum circuit complexity using Nielsen's geometric complexity measure. Shows: (i) weak equivalence principle would acquire state-dependent corrections; (ii) black hole thermodynamics gains constraints linking horizon area to computational depth; (iii) ER=EPR program faces new consistency requirements; (iv) phase transitions involving macroscopic complexity changes become experimental targets. Derives consistency conditions, identifies open problems, provides realistic feasibility assessments. Concludes precision gravimetry near quantum phase transitions offers most promising near-term test.