Quantization of Vortical Circulation in Newtonian Fluids: Spinorial Field Theory, Universal Invariants, and Inductive Boundary-Value CFD

A foundational topological and spinorial reformulation of Newtonian fluid mechanics based on the Buffoni Circulation Quantum (G0 = 406 * nu). We present analytical proofs of three universal fluid mechanical theorems: (1) Critical pipe transition Reynolds number Rec = 406 * 16 / pi = 6496 / pi ≈ 2068, quantitatively corroborating Avila et al. (Science 2011); (2) Geometric invariance of the von Kármán constant kappa = (1/sqrt(2*pi))*(1 - 1/pi) ≈ 0.40 via Biot-Savart mirror-image wall repulsion; (3) Landauer-Joule equivalence connecting the calorie (1 cal = 4.184 J) to discrete topological bit erasure (Delta Q >= kB*T*ln(2)). The framework is implemented and experimentally validated within the matrix-free NandoCAE CFD3D software suite.