The open past in an indeterministic physics

Discussions on indeterminism in physics focus on the possibility of an open future, i.e. the possibility of having potential alternative future events, the realisation of one of which is not fully determined by the present state of affairs. Yet, can indeterminism affect also the past, making it open as well? We show that by upholding principles of finiteness of information one can entail such a possibility. We provide a toy model that shows how the past could be fundamentally indeterminate, while also explaining the intuitive (and observed) asymmetry between the past -- which can be remembered, at least partially -- and the future -- which is impossible to fully predict.