IndisputableMonolith.Physics.AnomalousMagneticMoment
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
- Does not incorporate QED corrections beyond the leading Schwinger term.
- Does not derive the numerical value of phi or the mass ladder.
- Does not perform renormalization or running of the coupling.
- Does not compare the derived α^{-1} against experimental data tables.
depends on (2)
declarations in this module (14)
-
abbrev
rs_alpha_inverse -
def
schwinger_term -
theorem
schwinger_term_positive -
theorem
schwinger_is_alpha_over_2pi -
theorem
eight_tick_sum -
theorem
vacuum_phase_one -
def
ae_leading -
theorem
ae_leading_positive -
theorem
schwinger_lt_002 -
theorem
schwinger_in_range -
def
electron_g_factor -
theorem
g_exceeds_dirac -
def
known_ae_coeffs -
theorem
c1_half