  The integrated luminosity of the TP-AGB phase is a major uncertainty in
stellar population synthesis models. We use the white dwarf initial final mass
relation and stellar interiors models to demonstrate that a significant
fraction of the core mass growth for intermediate (1.5 < Msun < 6) mass stars
takes place during the TP-AGB phase. We find evidence that the peak fractional
core mass contribution for TP-AGB stars is ~20% and occurs for stars between 2
Msun and 3.5 Msun. Using a simple fuel consumption argument we couple this core
mass increase to a lower limit on the TP-AGB phase energy output. Roughly half
of the energy released in models of TP-AGB stars can be directly accounted for
by this core growth; while the remainder is predominantly the stellar yield of
He. A robust measurement of the emitted light in this phase will therefore set
strong constraints on helium enrichment from TP-AGB stars, and we estimate the
yields predicted by current models as a function of initial mass. Implications
for stellar population studies and prospects for improvements are discussed.
