  Some mathematical theories in physics justify their explanatory superiority
over earlier formalisms by the clarity of their postulates. In particular,
axiomatic reconstructions drive home the importance of the composition rule and
the continuity assumption as two pillars of quantum theory. Our approach sits
on these pillars and 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 an effective description of a
fundamental discrete theory in the critical regime.
