  Popular wisdom suggests that measuring the tensor to scalar ratio $r$ on CMB
scales is a "proof of inflation" since one generic prediction is a
scale-invariant tensor spectrum while alternatives predict $r$ that is many
orders of magnitude below the sensitivity of future experiments. A bouncing
Universe with sourced fluctuations allows for nearly scale-invariant spectra of
both scalar and tensor perturbations challenging this point of view. Past works
have analyzed the model until the bounce, under the assumption that the bounce
will not change the final predictions. In this work, we discard this
assumption. We explicitly follow the evolution of the Universe and fluctuations
across the bounce until reheating. The evolution is stable, and the existence
of the sourced fluctuations does not destroy the bounce. The bounce enhances
the scalar spectrum while leaving the tensor spectrum unchanged. The
enhancement depends on the duration of the bounce - a shorter bounce implies a
larger enhancement. The model matches current observations and predicts any
viable tensor-to-scalar ratio $r\lesssim 10^{-2}$, which may be observed in
upcoming CMB experiments. Hence, a measurement of $r$ will no longer be a
"proof of inflation'', and a Sourced Bounce is a viable paradigm with distinct
predictions.
