Spectral Chain Quantum Gravity C: Gravitational Wave Spectroscopy and High-Energy Quantum Observations — An Experimental Decoding Framework for Quantum Gravity Effects

This paper establishes a systematic methodology for inferring the microscopicstructure of quantum spacetime from multi-messenger astronomical data. The coreinnovation lies in developing a “spectral template matching” algorithm that unifies the dimensional reduction features in gravitational waveforms from black hole mergers, the Lorentz-violating dispersion in high-energy photon propagation, andthe fine structure of the cosmological constant into constraints on the parametersof finite spectral chains. We construct a Bayesian inference framework and demonstrate that the combined sensitivity of next-generation gravitational wave detectors(Einstein Telescope) and gamma-ray observatories (CTA/LHAASO) is sufficientto distinguish quantum gravity corrections from classical post-Newtonian effectsat the 5σ confidence level. Furthermore, we develop an open-source data analysisplatform, Spectral-Manifold Observatory (SMO), enabling end-to-end processingfrom raw detector data to posterior distributions of spectral chain parameters. Allmethodologies are validated for statistical rigor and provide an actionable technicalroadmap for quantum gravity observations in the coming decade.