Volume 8, Issue 3, pages 231-240
The Schrödinger equation is derived, completely and with every step displayed, from the rotor platform: a medium described by a density ρ and a phase S, whose combination ψ = √ρ e^(iS/ħ) is the rotor field written in the polar coordinates of its own fiber. The derivation rests on one demand, two inputs, and four theorems, and its every identity has been verified symbolically by machine to exact zero. The demand — logged openly, in exact parallel to the Hurwitz demand that built the ladder — is that the dynamics respect the linearity of the fiber: the fiber (the plane carrying the quarter-turn) hosts all phase directions at once, superposition is vector addition in that plane prior to any dynamics, and the platform’s intrinsic superposition is the requirement that time evolution treat every direction alike. The central new result, the Superposition Selection Theorem — a selection theorem, taking the fiber’s linearity as input rather than deriving it — shows this demand is not decorative: among all possible internal stresses of the medium, exactly one — the Bohm–Madelung gradient stiffness — produces a linear shadow equation, so the demand forces the stress uniquely, and with it the Schrödinger equation in its exact form. The famously missing ingredient of every hydrodynamic derivation, Wallstrom’s quantization condition, is supplied on this platform as a theorem: it is the same winding quantization, π₁(S¹) = Z, that quantizes electric charge. Two readings of the equation follow directly from the derivation and are noted: it is first-order in time because a stationary state turns at a single rate, and it is linear because linearity was the selection principle. A further interpretive reading — that the equation is the abelian projection of a richer fiber structure, with spin appearing at the spinor level — is offered in Section 7 as a tentative suggestion only, and is not a conclusion of the derivation; the present result does not extend to spin. What remains input is the value of ħ — the medium’s circulation quantum — the mass m, and the external potential; everything else is theorem, and every theorem is checkable in minutes.
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