In 2005, the Radioisotopes and the Age of The Earth (RATE) research initiative published compelling evidence for at least one episode of past radioactive decay which was accelerated by orders of magnitude compared with the rates measured in recent years. Constancy of radioactive decay rates is a central assumption in radiometric dating. Accelerated nuclear decay (AND) causes systematic change in the results of radiometric dating beyond the in situ above normal accumulation of daughter products. This includes relaxation of magma reservoirs to equilibrium and excessive inheritance arising from disequilibrium excesses of daughter products of greater order than crystal-melt partition ratios. Uncertainties associated with these mechanisms are shown to disproportionately affect old magma reservoirs and magmatic systems that persist after the end of the accelerated nuclear decay epoch. This paper continues the RATE research by developing a mathematical formalism and deriving several significant equations covering nuclear decay acceleration factors, primordial signature, inheritance, mixing, relaxation to equilibrium, sampling, and measurement which are different from the equivalent relations under the standard assumptions of constant decay rates. These derivations provide a mathematical basis for the assumed modeling approach used by the RATE authors and provide a foundation for further model development. I use this formalism to establish the form for corrected absolute dating within a young earth framework and propose a model for magma reservoir relaxation following AND. The reservoir relaxation mechanism has the potential to easily explain post-AND radiometric measurements including old Pleistocene dates and occasional persistently high radiometric dates of modern lava flows. When properly constructed from comparisons between radiometric and geologic observations, a model of acceleration factors over time enables the recovery of absolute dates from isotopic analysis under certain circumstances. I also discuss the appropriate conditions and usage for corrected absolute radiometric dating, relatively accurate dating, and data required for constraining accelerated nuclear decay histories within and across radioisotope systems. I identify a location with appropriate geological context and some existing radiometric dates to test the predictions of this model.
