Redefinition of the LG Operator: A Covariant Spiral Geometry of Time

This component presents the theoretical foundation of LG Time–Flow Theory through a covariant redefinition of the LG operator. Earlier formulations of LG Theory modeled spiral temporal behavior using a phenomenological spiral Laplacian. While conceptually effective, that representation was not fully covariant. In this work, the derivative structure itself is modified, leading to the definition of a new geometric wave operator: □_LG = D_μ D^μ where the LG covariant derivative encodes spiral time-flow directly into the geometry of temporal evolution. Importantly, this reformulation does not alter the physical assumptions or the universal spiral law of LG Theory. Instead, it provides a coordinate-independent and mathematically consistent framework in which spiral time evolution arises naturally from the operator structure. This component establishes the formal operator-level basis of LG Theory. Applications