What question did this study set out to answer?

The aim is to show that the Weyl Structure Postulate leads to the unique stability of quantum mechanics.

February 13, 2026Open Access

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

Key Points

The aim is to show that the Weyl Structure Postulate leads to the unique stability of quantum mechanics.
Derived the Schrödinger equation from the Mother Equation on M_s.
Established irreducibility, separability, and projection stability using pre-quantum phase-space concepts.
Showed equivalence of the star and Moyal products under projection stability.
Applied Stone–von Neumann uniqueness in the context of the CCR.
Confirmed that quantum mechanics is the only locally stable algebra for projecting pre-coherent states into reality.
Found that constant deformation parameters lead to significant implications in quantum field theory.
Proved that algebraic rigidity supports the empirical value of ħ, solidifying its relevance.

Abstract

The Quantum Blueprint Formalism derived the Schrödinger equation as the circulation-dominated limit of the Mother Equation on Mₛ (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.

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

Key Points

Abstract

Cite This Study