Now by “application” we mean: another abstract or mathematical problem that is solved by our tools. This is how the word “application” is used in mathematics and theoretical computer science; and a bit at-odds with how the word “application” is commonly used. In particular: it implies no claim of practicality at real-world scales.
Screening for strong pesticides/poisons
Strong pesticides or poisons likely have the “union property” (a mixture has the property if and only if one of the components of the mixture has the property). So looking for strong poisons pesticides meets the spicy soup un-stirring criteria.
Trying Apple Group Facetime
Apple Facetime is a video calling system that claims to allow multiple party video calls if:
iOS 12.1.4 or later, or iPadOS on one of these devices: iPhone 6s or later, iPad Pro or later, iPad Air 2 or later, iPad mini 4 or later, iPad (5th generation) or later, or iPod touch (7th generation).
This fits the spicy soup un-stir criteria: a group call can not be placed if one or more of the participants have poison iPhones or iPads (wrong version numbers of device and/or operating system). So under the, obviously false, assumption that out of date operating systems are rare we could use the spicy soup un-stirring design to design up a small set of group calls to find and isolate the iPhones or iPads ruining the attempted group video call.
However in practice it is going to be better to use an online method instead of a batch method: add and remove callers one by one observing which callers break the group call ability. Or use a web-service that doesn’t require owning a specific brand of device.
Bulk screening for a rare disease
Another application would be batch screening for a rare disease using DNA amplification methods.
In amplification based tests: a test sample is checked for the presence of a marker by reproducing the maker in the sample up to detectable levels. This amplification step makes it impractical to determine how much of the marker was in the original sample.
So if one were screening for a rare disease (for instance something like Polio, but unfortunately probably not something like COVID-19) with an amplification style test that had a long turn-around time, then it might make sense to use a batch design such as the spicy soup un-stirring procedure. The long turn-around time making the follow-up tests needed in interactive re-checking impractical.
However this is itself possibly not practical, as the diseases we are currently facing are not rare and combining medical samples is possibly not a safe and effective procedure.
Chemical or biological assays where the detection depends on a counter-agent being consumed may also be viable spicy soup un-stirring candidates. If most of the test reagents don’t bind with the detector, then the detector being bound to a high degree is some evidence one of the candidates in the mixture may be effective.
Again, this depends on the assumptions that success is rare and there are no interactions (test reagents don’t inhibit or promote each other).
Screening mixtures can in fact be relevant to combinatorial chemistry.