Deep Carbon Transport and Recycling in Uranus: An Audited, Falsifiable Framework for Testing Carbon Redistribution in an Incompletely Constrained Ice-Giant Interior

This preprint presents an audited, falsifiable framework for investigating the possibility of deep carbon transport and recycling inside Uranus. The study examines two broad mechanisms: gravitational segregation of carbon-bearing phases and the alternative possibility that carbon remains dissolved or fluid-associated and is redistributed through slow advective-diffusive transport. Previous simplified numerical estimates are reconstructed and subjected to mathematical and computational checks. The audit identifies important limitations in the earlier formulation, including uncertainties in high-pressure material properties and numerical implementation. Rather than claiming detection of a carbon cycle, the study defines quantitative conditions under which such a cycle could or could not operate over geological timescales. The resulting framework is intended as a testable hypothesis and as a basis for future laboratory measurements and planetary-interior simulations.