Is thst possible, in general? If someone published an open source app to Play, could I compare the Play downloaded app to a local build, and set config appropriately, and get a match?
(Deterministic|reproducible) (compilation|builds) are a fairly recent endeavor; though they're not yet common they are technically feasible. The two efforts I'm aware of are Debian[1] and Chromium[2], though I'm not sure what state they're currently in. From their site, Chromium appears to include Android builds.
There may be Android-specific concerts w.r.t the JVM's JIT, but if you can't trust the onboard runtime, you've already lost IMO.
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[1] https://wiki.debian.org/ReproducibleBuilds
[2] https://www.chromium.org/developers/testing/isolated-testing...
[3] https://f-droid.org/wiki/page/Deterministic,_Reproducible_Bu...
https://github.com/bitcoin/bitcoin/blob/master/doc/gitian-bu...
https://trac.torproject.org/projects/tor/wiki/doc/TorBrowser...
https://blog.torproject.org/blog/deterministic-builds-part-t...