A 'root of trust' "ensures that a system state comprises all and only content chosen by the user, and the user's code begins execution in that state." In other words, only if you have a root of trust can you be sure nobody else has infiltrated your computer with spyware or whatever. This paper (Establishing software root of trust unconditionally Gligor & Woo, NDSS'19) demonstrates a proof for root of trust. The proof is complex, but is essentially based on the minimum time it would take for a computer to perform the 'lower bounds' of a specific algorithm (specifically, a hashing function).
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