We explore the interdiffusion of oppositely labeled triblock polystyrene chains, HDH/DHD, during welding in the melt using dynamic secondary ion mass spectroscopy (DSIMS) and specular neutron reflectivity (SNR). The HDH chains have the central portion of the chain deuterated (D) similar to 50% while the two ends (H) each have similar to 25% protonation; the DHD is oppositely labeled, but each set of chains contains about 50% deuteration. During welding, the deuterium depth profile exhibits "ripples" whose characteristic features, such as the time and molecular weight dependent shape, amplitude, and position, are very sensitive to the microscopic details of the polymer dynamics. The ripple experiment is especially sensitive to the presence, or absence, of topological constraints and anisotropic motion of chains. The current work significantly extends the molecular weight range up to 400 000. This allows greater separation of the six key ripple features used in deciphering the correct polymer dynamics model at the polymer-polymer interface. The DSIMS and SNR experimental results are compared to theoretical predictions and ripple simulations for Rouse, polymer mode-coupling, reptation (with and without tube broadening), and other phenomenological dynamics models. The six ripple characteristics were found to be perfectly correlated and convincingly consistent with the predictions of the reptation dynamics model. The ripple results are in significant disagreement with the polymer mode-coupling model proposed by Schweizer and other tubeless models. We conclude that the reptation model, proposed by DeGennes in 1971 with parallel developments by Edwards, is the correct model to describe the dynamics of polymer interdiffusion.