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The Fine-Structure Constant and the Golden Angle

Funneled-Spring Recursion, the Slip Operator, and the Slip-Time Interpretation
Authors: Gilbert, Dexter;

The Fine-Structure Constant and the Golden Angle

Abstract

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’spressure axiom to the golden angle θ_φ = 360°/φ² ≈ 137.508°, closes the 0.47° gapthrough torsional slip in a funneled-spring recursion (Version 3), adds the slip-timeinterpretation (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 acorrection; and (2) the causal order of the recursion is stated explicitly: Tension →Surplus → Torsion → Slip → Acceleration → Maintained Motion, where slip is thecause of acceleration and acceleration refers strictly to the restart of theelectromagnetic recursion into the next coherence interval. The mean rate of thatrestart 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 singleopen 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 quantumcorrection hypothesis. V2: derived the discrete-spiral operator; provednon-circularity. V3: replaced multi-operator correction with the slip mechanism in afunneled spring; same numerical result, physical picture complete. V4: added theslip-time interpretation; t_coh and g/ω shown to be a single parameter; dimensionalanalysis 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.

Keywords

Ontology, Physics, Mathematical physics, Physics/methods, Quantum physics, Nuclear physics, Particle physics, Physics/standards, Theoretical physics, Atomic physics

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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