Observer Consensus as Fixed Points in Local Algebra Categories: Categorification of Modular Inclusions, Conditional Expectations, and Unified Time Scales

In the algebraic quantum theory and quantum information perspective, ``observer consensus'' is usually taken as a prior assumption: predictions of different observers eventually agree in overlapping accessible regions. This paper proposes a purely structural characterization: we model observers and their accessible information as local algebra objects with states, with morphisms given by modular inclusions compatible with Tomita--Takesaki modular flow, and construct a ``synchronization operator'