The paper introduces the Time-Dependent Quantum Geometric Tensor (tQGT) as a comprehensive tool to capture the geometric properties of insulators within linear response. The tQGT describes the zero-point motion of bound electrons and acts as a generating function for generalized sum rules of electronic conductivity. It enables a systematic framework for computing various instantaneous responses of insulators, including optical mass, orbital angular momentum, and dielectric constant. The construction ensures consistent approximations across these quantities by restricting the number of occupied and unoccupied states in a low-energy description of an infinite quantum system. The authors outline how quantum geometry can be generated in periodic systems through lattice interference and examine spectral weight transfer from small frequencies to high frequencies by creating geometrically frustrated flat bands. The main results include a rewriting of the Kubo formula for conductivity in terms of the tQGT and the consequent generalized form for dissipative sum rules that tie various geometric properties of an insulating system. The paper also discusses the exact bounds on sum rules and provides insights into the dynamics of quantum geometry in materials with flat bands and geometric frustration.The paper introduces the Time-Dependent Quantum Geometric Tensor (tQGT) as a comprehensive tool to capture the geometric properties of insulators within linear response. The tQGT describes the zero-point motion of bound electrons and acts as a generating function for generalized sum rules of electronic conductivity. It enables a systematic framework for computing various instantaneous responses of insulators, including optical mass, orbital angular momentum, and dielectric constant. The construction ensures consistent approximations across these quantities by restricting the number of occupied and unoccupied states in a low-energy description of an infinite quantum system. The authors outline how quantum geometry can be generated in periodic systems through lattice interference and examine spectral weight transfer from small frequencies to high frequencies by creating geometrically frustrated flat bands. The main results include a rewriting of the Kubo formula for conductivity in terms of the tQGT and the consequent generalized form for dissipative sum rules that tie various geometric properties of an insulating system. The paper also discusses the exact bounds on sum rules and provides insights into the dynamics of quantum geometry in materials with flat bands and geometric frustration.