The Kármán constant κκ in the logarithmic law of wall turbulence is a universal constant whose accepted value is approximately 0.41, yet for more than a century it has generally been treated as an empirical parameter. In the framework of global realism, we derive κκ from first principles by starting from the topological-soliton structure of matter in the spacetime vacuum, passing through the corrected Boltzmann equation and the memory-extended Navier–Stokes equation, and closing the argument with a wall-constrained geometric optimization of macroscopic memory vortices. The derivation proceeds in four theoretical layers. (i) The Hopf-soliton model determines the effective topological complexity of molecules and their coupling to the vacuum substrate. (ii) A Chapman–Enskog analysis of the corrected Boltzmann equation relates the macroscopic memory parameters to microscopic molecular properties. (iii) A singular-perturbation analysis of the memory-extended Navier–Stokes equation in channel flow yields the structural relation between κκ, a memory-coupling number ββ, and a geometric factor CκCκ. (iv) The optimal geometry of wall-constrained macroscopic memory vortices fixes this geometric factor and provides the irreducible numerical contribution ∫0∞dt/1+t4=Γ(1/4)2/(4π)∫0∞dt/1+t4=Γ(1/4)2/(4π). The paper states explicitly that the full axiomatization of chemistry has not yet been completed; a minimal set of provisional chemical axioms and closure hypotheses is therefore introduced where needed to define stable molecular carriers and their transport-relevant invariants. Across all layers every parameter is assigned an explicit physical origin, no experimental fitting to the target value is introduced, and the provisional status of the chemical bridge is stated rather than concealed. The resulting prediction is κ≈0.409κ≈0.409, in close agreement with the commonly accepted experimental range 0.41±0.020.41±0.02.
Jianming Wang (Fri,) studied this question.