The Uniqueness of the Weyl Structure: Why Quantum Mechanics Is the Only Stable Realization of Pre-Coherent Non-Commutativity

The Quantum Blueprint Formalism derived the Schrödinger equation as the circulation-dominated limit of the Mother Equation on M_s (Schmieke, 2026r), depending on the Weyl Structure Postulate (A2b): [q, p] = iħ. This paper closes the gap. We prove (A2b) follows from (A2a) + (A1)–(A3) via four steps: (1) irreducibility, separability, and projection stability are established from (A1)–(A3) in pre-quantum phase-space language; (2) projection stability forces the star product to be equivalent to the Moyal product with constant deformation parameter (Theorem 6.1); (3) Stone–von Neumann uniqueness applies to the resulting CCR per Darboux chart; (4) algebraic rigidity (H² = 0) confirms stability. The value c = ħ remains empirical. The proof is local (per Darboux chart); for infinitely many degrees of freedom, unitarily inequivalent representations exist and underlie the dissipative QFT architecture. Consequence: quantum mechanics is the unique locally stable algebra for projecting pre-coherent possibility into coherent actuality.