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We utilize nonlinear pulsation models to reproduce the observed light andcolor curves for two samples of bump Cepheid variables, 19 from the LargeMagellanic Cloud and 9 from the Small Magellanic Cloud. This analysisdetermines the fundamental parameters mass, luminosity, effective temperature,metallicity, distance and reddening for the sample of stars. The use of lightcurve shape alone to determine metallicity is a new modelling techniqueintroduced here.  The metallicity, distance and reddening distributions for the two samples arein agreement with those of similar stellar populations in the literature. Thedistance modulus of the Large Magellanic Cloud is determined to be18.54$\pm$0.018 and the distance modulus of the Small Magellanic Cloud isdetermined to be 18.93$\pm$0.024. The mean Cepheid metallicities are $Z =0.0091\pm0.0007$ and $0.0050\pm0.0005$ for the LMC and SMC, respectively.  The masses derived from pulsation analysis are significantly less than thosepredicted by stellar evolutionary models with no or mild convective coreovershoot. We show that this discrepancy can not be accounted for byuncertainties in our input opacities or in mass-loss physics. We interpret theobserved mass discrepancy in terms of enhanced internal mixing in the vicinityof the convective core during the main-sequence lifetime and find that theovershoot parameter $\Lambda_{c}$ rises from 0.688$\pm$0.009H_p at the mean LMCmetallicity to 0.746$\pm$0.009H_p in the SMC.Comment: ApJ accepte

Bump Cepheids in the Magellanic Clouds: Metallicities, the Distances to the LMC and SMC, and the Pulsation‐Evolution Mass Discrepancy