TRIDENT Mini Case Card — Deep Interior Volatile Partitioning: Hydrogen in Earth's Core (GEO-CORE-H-RES-001.v1)

This technical note applies the TRIDENT-Z0 diagnostic framework to the claim that Earth's metallic core contains 0.07–0.36 wt% hydrogen, equivalent to ~9–45 present-day oceans expressed as water-mass. The claim is evaluated through four gates: Bulk Lock (G1), Boundary Flow (G2), Constraint Field (G3), and Coherence Dependency (G4). G1 and G2 pass on the basis of high-pressure experimental evidence and standard differentiation partitioning mechanisms. G3 passes as non-exclusive — hydrogen is a plausible contributor to the core's density deficit without displacing other light elements (Si, O, S, C). G4 is held open pending joint seismic density/velocity closure, cosmochemical D/H isotopic mass-balance, and agreement across independent EOS datasets and thermodynamic models spanning the relevant P–T range. A corrected quantitative sanity band resolves an internal tension between the reported range and prior density/velocity-compatible modelling envelopes: the lower half of the reported range (0.07–0.3 wt%) is compositionally plausible but insufficient to account for a major share of the density deficit; only the upper overlap band (~0.3–0.36 wt%) approaches contribution levels suggested in earlier analyses. Three hard falsifiers are specified. The case is placed within the SHRF band for extreme-boundary thermodynamic partitioning. Produced under the Sympathetic Harmonic Resonance Framework (SHRF) evidence-bound analysis protocol. Corpus node: GEO. Keywords TRIDENT; SHRF; core composition; hydrogen partitioning; volatile sequestration; deep Earth; light elements; iron alloy; seismic constraints; PREM; density deficit; D/H isotopes; EOS; metal–silicate partitioning; planetary formation; core formation; magma ocean; falsifiability; boundary dynamics; diagnostic framework; technical note