Informational Holonomy and the Electron g-Factor

Title: Informational Holonomy and the Electron g-Factor 
Subtitle: A Derivation within Super Information Theory
Version 6

Informational Holonomy and the Electron g-Factor develops a Super Information Theory (SIT) account of why the electron’s tree-level gyromagnetic ratio is g = 2 in the decohered, low-energy regime where SIT reduces to the Dirac–Maxwell sector. In this framing, electromagnetism is the holonomy of a coherence-phase U(1) principal bundle equipped with a genuine connection A, and matter couples via minimal coupling through the covariant derivative. The relevant phase transport is encoded by the Wilson line U[γ] = exp(iq/ℏ ∮_γ A). Under the same assumptions that guarantee the SIT action reduces to standard Dirac–Maxwell in the decohered limit (locality, Lorentz invariance, first-order spinor dynamics, and phase-only entry through Dμ), the nonrelativistic reduction yields the Pauli Zeeman interaction −(q/m) S·B and therefore the standard Dirac value g = 2.

What is not new: the numerical value g = 2 matches the usual Dirac prediction.
What is new: (i) a geometric interpretation of minimal coupling in terms of informational holonomy (including the role of spinor 4π periodicity versus U(1) 2π phase); (ii) a precise phase-only entry hypothesis that forbids dimension ≤ 4 dipole operators (so no tree-level Pauli term of the form ψ̄σμνψ Fμν); and (iii) an EFT map showing where SIT-specific, environment-dependent deviations could appear through gradients of the time-density ρₜ and coherence ratio R_coh, while remaining compatible with the QED anomaly aₑ = (g − 2)/2 in decohered regimes.

Previously: Version 5 incorporated earlier feedback by explicitly fixing the “connection ≠ gradient” pitfall: A is a bona fide connection 1-form with curvature F = dA, while writing A = (ℏ/e) dθ is only valid on a pure-gauge patch with F = 0 (and does not hold globally, even when local fields vanish but holonomy persists in non-simply-connected regions). This version also adds explicit Foldy–Wouthuysen and Gordon-decomposition derivations to g = 2, clarifies conventions, repairs cross-references, and includes global bundle remarks and figure-ready caption text.