Dissipative Mixed Hodge Modules and Weight Filtered Spectroscopy

Addressing the fundamental challenges of decoherence and instability in open quantum hardware, this project introduces the theory of Dissipative Mixed Hodge Modules (DMHM) to rigorously classify topological phases in gapless, non-Hermitian systems. 

By characterizing open quantum systems as Regular Holonomic D-Modules, we analyze the underlying mixed Hodge structure of spectral singularities. 
 

A core physical outcome of this framework is the formulation of Weight Filtered Spectroscopy, a spectroscopic protocol that utilizes "Weight Filtration" to certify topological protection directly at Exceptional Points, mathematically isolating classical decay channels from quantum superpositions.