pith. sign in
module module high

IndisputableMonolith.Physics.AnomalousMagneticMoment

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This module derives the inverse fine-structure constant α^{-1} ≈ 137.036 from Recognition Science using the eight-tick structure and J-cost relations. Quantum electrodynamics researchers would cite it when connecting discrete recognition cycles to the anomalous magnetic moment. The argument consists of zero-sorry algebraic theorems that reduce the Schwinger term and g-factor excess directly from upstream lemmas on the 8-tick phases.

claimThe module establishes $α^{-1} ≈ 137.036$ as the Recognition Science value obtained from the eight-tick projection equality, together with the leading Schwinger correction $α/(2π)$ to the electron magnetic moment.

background

The module imports JcostCore for the J-cost function J(x) = (x + x^{-1})/2 - 1 and the EightTick module whose doc-comment states that reality operates on a discrete 8-tick cycle with phases 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4. In the Recognition Science setting these phases supply the T7 eight-tick octave that forces D = 3 and the self-similar fixed point phi. The module therefore treats α^{-1} as an emergent constant inside the interval (137.030, 137.039) generated by the forcing chain.

proof idea

The module organises its content as a chain of theorems. rs_alpha_inverse applies w8_projection_equality from EightTick to obtain the numerical value. schwinger_term and schwinger_term_positive compute the leading QED correction and prove its positivity. Subsequent results bound the term below 0.002 and assemble the electron g-factor excess. All steps are algebraic reductions that invoke only the imported J-cost identities and the eight-tick phase sum.

why it matters in Recognition Science

The module supplies the RS-native α^{-1} that lies inside the predicted band and feeds the electron_g_factor and g_exceeds_dirac declarations. It thereby closes the link from the T7 eight-tick octave to an observable QED parameter, confirming the framework's claim that the anomalous magnetic moment is fixed by the discrete recognition clock.

scope and limits

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (14)