Some mathematical theories in physics have claimed explanatory superiority even in the absence of new predictions. This was justified by the clarity of their postulates. In particular, mathematical derivations drive home the importance of the composition rule and the continuity assumption as two pillars of quantum theory. Our approach sits on these pillars but it combines new mathematics with a testable prediction. If the observer is defined by a limit on string complexity, information dynamics leads to an emergent continuous model in the critical regime. Restricting it to a family of binary codes describing `bipartite systems,' we find strong evidence of an upper bound on bipartite correlations equal to $2.82537$. This is measurably different from the Tsirelson bound. The Hilbert space formalism emerges from this mathematical investigation as but an effective description of a fundamental discrete theory in the critical regime.
Alexei Grinbaum