Angular momentum has the dimensions of action. A plane angle and a linear momentum have different physical meanings. The current source accordingly distinguishes the dimensionless invariant coefficient, its angular realization, and its momentum realization before using them in physical relationships.

The shared numerical coefficient in the adopted representation does not identify those dimensioned quantities with one another. The realization relations supply the dimensional connection. Removing that connection would turn a physical relation into a numerical resemblance.

The result is a theoretical geometric construction, not a direct observation of a universal particle spin or a new test of angular-momentum quantization. Its provenance date identifies the completed September manuscript version. The record does not assign an earlier discovery day to this particular derivation, and the illustration remains evidence of the model’s geometry rather than an experimental image.