Perhaps you should consider this article: http://ilikekillnerds.com/2016/02/shared-state-in-aurelia/
It seems that Aurelia (and I m not aurelia dev) easily manage singleton and reactive state. Therefore, I suggest: immediately identify Store and Reducers without using Redux or MobX.
Perhaps ImmutableJS can be very useful here to define your store (mostly an object).
And don't forget, gearboxes are just pure functions. So, although you know how to write pure functions, and you know how to contact the store, you are fine.
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