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There are real challenges involved in identifying the organic residues that suggest the processing of alcoholic beverages. As you observed, fermentation is a natural process and would be expected to occur in a number of vessels at random. So how do we know that the alcohol was deliberately produced?
The short answer is consistency. For example, chemical signatures consistent with honey, and organic compounds associated with fermentation are routinely found in beaker vessels - it could still be there by chance, but the frequency with which it has been found suggests that the probability of it being intentional is high.
Some of the evidence for the early production of beer in Britain and Northern Europe is currently less compelling, but the analysis techniques used for residue analysis are improving all the time.
However, we don't always have to rely solely on the evidence provided by residue analysis. There is also often supporting evidence in the form of the wear on the pottery vessel itself. It may sound strange, but fermentation actually causes what is known as "nonabrasive attrition" of the vessel in the form of spalling [Skibo, 2015, p194]. Repeated use of the vessel exacerbates the effect, and this would indicate that the fermentation was non-accidental in nature.
The fact that the same evidence has been found in contexts from around the world adds further support to the idea that the fermentation was deliberate. In Ancient Egypt, we have multiple strands of evidence that a range of alcoholic drinks were prepared, including mead made from honey. In the case of Ancient Egypt, we have texts, images painted on tomb walls, and the pottery vessels themselves. Interestingly, the vessels used to produce mead in Ancient Egypt appear to present with exactly the same evidence for fermentation that we see in Bronze Age beakers from the UK and Northern Europe [Dietler, 2006].
I know that this answer has just skimmed the surface of the subject. I hope that I've given enough information to answer your question, without getting too bogged down in the details. A complete answer would take a book (and several have been written on the subject!).
If you're interested in gaining a better understanding of the theory behind archaeological residue analysis, and some of the practical considerations involved in obtaining suitable samples for analysis (particularly trying to avoid contamination of samples), the volume Theory and Practice of Archaeological Residue Analysis in the British Archaeological Reports International Series is a good place to start. As one of my tutors said, "It may not have all the answers, but it will provide enough background to ask the right questions ...".
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