Deriving the Canonical Pillars of Modern Physics UCL

We present a fully explicit, non-ambiguous deployment of the Universal Correlational Lattice (UCL) as a closed foundational framework from which the canonical structural pillars of modern physics are derived as emergent limits. Starting from a purely correlational, pre-geometric, and non-temporal base defined by a self-adjoint correlational operator acting on an abstract site-indexed Hilbert space, we fix a canonical class of admissible operators, equivalence relations, and coarse-graining maps.