The Fine-Structure Constant and the Golden Angle

The fine-structure constant α ≈ 1/137.036 has no derivation in the Standard Model.
This paper presents a four-step derivation from the Canon unified field theory’s
pressure axiom to the golden angle θ_φ = 360°/φ² ≈ 137.508°, closes the 0.47° gap
through torsional slip in a funneled-spring recursion (Version 3), adds the slip-time
interpretation (Version 4), and now adds two conceptual refinements (Version 5):
(1) the gap θ_φ − 1/α = 0.472° is identified as the slip operator — an identity, not a
correction; and (2) the causal order of the recursion is stated explicitly: Tension →
Surplus → Torsion → Slip → Acceleration → Maintained Motion, where slip is the
cause of acceleration and acceleration refers strictly to the restart of the
electromagnetic recursion into the next coherence interval. The mean rate of that
restart is a = g²/ω, derived from existing operators with no new parameters.
Version 5 introduces no new mathematics. The self-consistency condition 1/α =
360°/φ² − 2g/ω is numerically verified to a residual of −8.45×10⁻⁶°. The single
open parameter g/ω = 0.004117 rad has not been evaluated from first principles.
That evaluation remains the open problem.
Scope and version history. V1: identified the 0.47° gap; proposed quantum
correction hypothesis. V2: derived the discrete-spiral operator; proved
non-circularity. V3: replaced multi-operator correction with the slip mechanism in a
funneled spring; same numerical result, physical picture complete. V4: added the
slip-time interpretation; t_coh and g/ω shown to be a single parameter; dimensional
analysis of the coherence time. V5: identified the gap as the slip operator (identity);
stated the canonical causal order; derived the mean EM recursion restart rate a =
g²/ω. The mathematics of V3 is unchanged throughout.