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2025
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| Acceso en línea: | https://doi.org/10.5281/zenodo.16790004 |
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- <p><strong> On the Geometric Origin of Spin and Mass</strong></p> <p> </p> <p> ∆ngular Theory </p> <p> </p> <p> ***</p> <p> </p> <p> White Paper</p> <p> </p> <p> ***</p> <p> </p> <p>David Souday</p> <p>Theoretical Physics, </p> <p> </p> <p>Paris, France</p> <p> </p> <p>August 2025</p> <p dir="ltr"> </p> <p dir="ltr"> Abstract</p> <p dir="ltr">We present a purely angular model where spin-½ behaviour emerges from a π spinor closure on the ∆Graph₃ (fixing Δθ₀ = π/3).</p> <p> </p> <p dir="ltr">A parameter-free equilibrium on the loop’s SU(2) holonomy equates the scalar class invariant a := (1/2)Tr A with the generated spinor phase Φ_s, yielding the transcendental equation cos t = t (with t := Φ_s; unique fixed point in (0, π/2)).</p> <p> </p> <p dir="ltr">Its unique solution t* ≈ 0.739085 (the Dottie constant), defines the first stable massive state.</p> <p> </p> <p dir="ltr">Open paths, with trivial holonomy (A = I), structurally account for the massless sector.</p> <p dir="ltr">In this paper “mass” denotes a dimensionless holonomy parameter, m̂ := (Δθ₀/π)·Φ_s; conversion to physical units is deferred to subsequent work. (“Photon-like” is an interpretive label; phenomenology will be addressed elsewhere).</p> <p dir="ltr"> </p> <p dir="ltr"> ***</p>