Ontology of Differences: The Binary Hypercube

This work eliminates the membership relation (∈) from the foundations, replacing it with binary distinction. On this basis, a hypercubic ontology is constructed which: 1) provides a direct computational semantics for dependent type theory, 2) explicitly constructs the continuum as a quotient space, localizing the source of non-constructiveness, 3) provides a tool for translating constructive fragments of classical mathematics (from ZFC to analysis) into the language of finite specifications. This is proposed as a unified metalanguage for an explicit, algorithmic rethinking of mathematical foundations.