Quantum–AI Earth-System Intelligence for Climate-Risk Discovery, Natural-Capital Valuation and Planetary Investment Decision Systems

Abstract: Climate-risk discovery and sustainable capital allocation increasingly require a common analytical language for physical hazards, ecological degradation, carbon integrity, financial contagion and distributional outcomes. This paper develops a model-based framework for Quantum-AI Earth-System Intelligence that connects geospatial observations, Earth-system digital twins, topological and network structure, probabilistic machine learning, natural-capital valuation and planetary investment optimisation. The proposed QESI-PID framework treats climate, ecological, infrastructure and financial conditions as a partially observed dynamic state vector. Remote-sensing and administrative data update the twin; persistent and graph-based features identify structural regimes; quantum-AI components are positioned as optional computational accelerators for high-dimensional inference and optimisation; and an investment layer evaluates projects using risk-adjusted natural-capital, resilience, carbon and inclusion objectives. The methodology combines state-space modelling, matrix coupling, differential dynamics, network risk, discounted ecosystem-value proxies, multi-objective optimisation and an illustrative 0-10 scoring model. The demonstration produces a baseline integrated capability score of 7.674 and a risk-adjusted score of 6.931 under a moderate penalty parameter, while sensitivity analysis shows that valuation uncertainty and climate-transition risk can materially alter investment rankings. These values are illustrative and are not empirical findings. The paper contributes a transparent architecture for linking Earth-system science to investment decision systems without collapsing ecological value into a single financial price. It also specifies validation requirements for remote-sensing calibration, model uncertainty, distributional fairness, scenario robustness and decision auditability before real-world use. Keywords: quantum-AI; Earth-system intelligence; climate risk; natural capital; digital twins; geospatial analytics; topological data analysis; systemic risk; climate finance; carbon integrity; ecosystem services; risk-adjusted valuation; sustainable investment; planetary resilience; decision intelligence