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To show this, we consider a semi-device-independent randomness generation scheme where one of two spatial rotations is performed on an otherwise uncharacterized preparation device, and one of two possible measurement outcomes is subsequently obtained. An upper bound on a theory-independent notion of spin is assumed for the transmitted physical system. It turns out that this determines the set of quantum correlations and the amount of certifiable randomness in this setup exactly. Interestingly, this yields the basis of a theory-independent protocol for the secure generation of random numbers. Our results support the conjecture that the symmetries of space and time determine at least part of the probabilistic structure of quantum theory.<\/jats:p>","DOI":"10.22331\/q-2026-01-16-1966","type":"journal-article","created":{"date-parts":[[2026,1,16]],"date-time":"2026-01-16T13:08:03Z","timestamp":1768568883000},"page":"1966","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Theory-independent randomness generation from spatial symmetries"],"prefix":"10.22331","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-2445-6001","authenticated-orcid":false,"given":"Caroline L.","family":"Jones","sequence":"first","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria"},{"name":"Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7259-1327","authenticated-orcid":false,"given":"Stefan L.","family":"Ludescher","sequence":"additional","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria"},{"name":"Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1401-0184","authenticated-orcid":false,"given":"Albert","family":"Aloy","sequence":"additional","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria"},{"name":"Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8086-5586","authenticated-orcid":false,"given":"Markus P.","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria"},{"name":"Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria"},{"name":"Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2026,1,16]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"L. 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