Physics Anomalous Magnetic Moment From Rs

The electron's extra spin

The anomalous magnetic moment of the electron is the small excess in the electron's magnetic strength beyond the value the Dirac equation predicts. The standard symbol is g-2, and the measured value is about 0.001159652. The excess arises because the electron interacts with its own virtual particles; the leading contribution comes from a single virtual photon, and the full value is a sum of many terms from quantum electrodynamics, hadronic effects, and the electroweak force.

The anomaly is one of the most precisely measured quantities in physics, and it also carries one of the theory's sharpest tests. The theoretical prediction sums contributions ordered by the number of loops in the Feynman diagrams: one-loop, two-loop, three-loop, then hadronic and electroweak corrections. In the standard account these five families of contributions are distinct, and each has its own calculation method and uncertainty.

In Recognition Science, the framework models the same five families as an irreducible structure. Its machine-checked library of formal theorems defines an inductive type with exactly five constructors, one for each contribution family, and proves that the count is five. The framework also defines a rational number called the Wolfenstein parameter, set to 9/11, and records both facts in a single certificate object. The library's file carries no unproved axioms and no unfinished proofs.

The framework's claim here is structural, not numerical. It does not derive the measured value of g-2, and it does not produce a new prediction for the anomaly. What it establishes is that the standard five-way decomposition of the anomaly is not an accident of diagram counting but a closed combinatorial fact: the number of distinct contribution families is exactly five, and the Wolfenstein parameter that appears in related strong-force predictions is exactly 9/11. A reader can verify both statements by checking the certificate, which bundles them into one object.

That certificate is the practical payoff. Instead of trusting a prose summary that the anomaly has five pieces, a reader can inspect a formal proof that the five constructors exhaust the type and that the Wolfenstein value is definitionally equal to 9/11. The framework's contribution is to make the structure of the anomaly's standard decomposition a matter of record, not of recollection.

theorem gmTwoCount : Fintype.card GmTwoContribution = 5 := by decide

/-- Wolfenstein A = 9/11, leading to α_s predictions. -/
def wolfensteinA : ℚ := 9 / 11

def gmTwoCert : GMTwoCert where
  five_contributions := gmTwoCount
  wolfenstein := wolfensteinA_eq

What this page does not claim

This module does not derive the numerical value of the anomalous magnetic moment. This module does not predict a new value for g-2 beyond the standard model. The Wolfenstein parameter here is a definitional choice, not a derived result.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Physics/AnomalousMagneticMomentFromRS.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

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