G - 2 Without Infinities: A Geometric Approximation

The magnetic moment of the electron exceeds the value predicted by Dirac's equation by about one part in a thousand, a number now measured to thirteen significant digits and reproduced by quantum electrodynamics with legendary precision. This article reopens the file in two voices. A chronicler first gathers the record: the measurements, from Zeeman to the single-electron Penning traps, the history of the anomaly from Stern and Gerlach to Schwinger's $\alpha/2\pi$, the four premises behind Dirac's round number, and the present state of the theory, including the tension between the determinations of the fine-structure constant. A detective then questions the electron itself. Read as a structured partiwave, an almost point-like knotter within two counter-rotating vortices, the electron answers the facts that a dimensionless point carries with difficulty: orientation, the $720^\circ$ closure, finite energy and wave behaviour. The anomaly appears as a stratified record, with geometry in its leading term, anatomy in the next, and scale, atomic company and apparatus in its last digits; two witnesses suggest structural routes to $\alpha/2\pi$. In the grammar of cardinal fields, the size of the electron becomes a boundary declared by a criterion, the virtual cloud a boundary-band seen through the lens of a point, and $\alpha$ a declared quantity with a persistent core. The bivortical reading argues only with the dimensionless point: combined with quantum electrodynamics, it would keep every measured success, turn the infinities into a finite calibration and give the theory's cutoff an owner. Experimental tests and theoretical debts are stated with their criteria.