Hartmann Time-Source Density (HTSD): Formal Operator Construction and Renormalization Framework

This technical note provides the complete operator-level definition of the renormalized Hartmann Time-Source Density (HTSD) within curved-spacetime quantum field theory. It formalizes HTSD as a local, covariant, renormalizable scalar composite operator constructed from vacuum, entropy-production, information-flow and torsion-related terms. The document establishes the renormalization group structure, operator mixing, and gravitational contribution of HTSD while complementing the previously published conceptual HTSD preprint. This file serves as a timestamped, citable reference defining the precise mathematical and physical content of HTSD.