Crypto Existence?

Can anyone display evidence that the solution to a math problem has a claim to existence?

An algorithm is an iterative approach to solving a math problem in which an input array is passed through some sort of filter to produce an output array. This output array is then incorporated into the input array and the action is repeated ad infinitum or until some stable results are achieved.

Crypto is "mined" by such a system.

Ones and zeros are not commodities. They are symbols. Symbols don't exist. They are markers for things that do exist.

A FRN is a symbol too (although one that doesn't claim to represent anything). Yet crypto is valued in FRNs. A case of a symbol representing another symbol? Or the Matrix being expanded?