Topological Geophysics and Earth-System Physics: A Three-Axiom Framework for the Solid Earth, Atmosphere, Oceans, Hydrology, Cryosphere, Climate, and Natural Hazards

Earth is formulated as a finite, rotating, self-gravitating, electromagnetically active, chemically differentiated, multiphase system. The framework retains exactly three physical axioms: microscopic ontic definiteness with finite localization, the physical reality of the spacetime–vacuum substrate, and persistent causal delayed source–response coupling. Established theories of mechanics, thermodynamics, continua, fluids, waves, electromagnetism, plasma physics, gravitation, statistical mechanics, and nonlinear dynamics are incorporated through typed interfaces. The complete Earth state includes geometry, solid deformation, core and surface fluids, atmosphere, ocean, terrestrial water, ice, electromagnetic fields, chemical and biological inventories, causal-history variables, and moving interfaces. Conservation laws, constitutive relations, interface conditions, and controlled reductions connect this state to models of seismology, geodesy, geodynamics, the geodynamo, atmospheric and oceanic circulation, hydrology, cryosphere dynamics, climate, and natural hazards. A single-ownership ledger prevents the double counting of energy, mass, chemistry, radiation, viscoelasticity, turbulence, reservoir storage, and historical response across coupled subsystems. The framework distinguishes physical states from statistical representations, inverse solutions, data-assimilation states, and machine-learning surrogates. It further specifies reproducible benchmarks, observation-lineage requirements, uncertainty accounting, standard-model-first residual tests, and quantitative rejection criteria. The resulting construction is an auditable mathematical architecture for coupled geophysics and Earth-system physics, rather than a claim of exact earthquake, climate, or geomagnetic-reversal prediction. Keywords Geophysics; Earth-system physics; solid Earth; seismology; geodesy; geodynamics; geomagnetism; atmosphere–ocean coupling; hydrology; cryosphere; climate dynamics; natural hazards; multiphysics coupling; inverse problems; data assimilation.