UCM Paper 50: The Substrate as a Stage for Quantum Field Theory — Seven Structural Results from the UCM Lattice

We identify seven structural results that the UCM substrate forces — without postulating any quantum-field-theoretic input — and that together constitute a complete stage on which standard QFT can operate: (1) canonical commutation relations from the quadratic substrate action (Stone–von Neumann) ; (2) the Feynman path integral from the substrate partition function; (3) quantum entanglement and Bell correlations from the membrane phase network; (4) the su (2) Lie algebra on every lattice link from the Schwinger construction; (5) local gauge invariance from the plaquette structure; (6) an accidental U (1) symmetry of the transverse bulk field; (7) emergent Lorentz invariance from the RG attractor. Each result is proved from one postulate (κₘem >> κcell) and one empirical input (the substrate fluctuates). The paper draws a sharp boundary between what the UCM provides (the stage) and what QFT computes (the physics on the stage). This paper supersedes earlier versions of Papers 50 and 51 in the UCM series.