Hydrogen 1s Orbital from Stochastic Collapse Testing the Quantum Measurement Problem via the Fine-Structure Constant

We test a recently proposed algebraic resolution of the quantum measurement problem by deriving the fine-structure constant from the same dissipative collapse dynamics, and by verifying that the resulting stochastic collapse reproduces the Schrödinger distribution for the hydrogen 1s orbital. Working within the Jordan-Clifford immersive framework on the 14-dimensional operational subspace H = C¹⁴ associated with the Fano incidence geometry, we show that the stochastic collapse equation dcᵢ = -1/2γ cᵢ(1 - 2pᵢ + ∑ⱼ pⱼ²)dt + √ᵢ(dWᵢ - ∑ⱼ pⱼ dWⱼ) contains the decoherence rate γ = √λgraphon, where λgraphon = Λ₁/Λ₀ ≈ 1.99765 is the spectral gap of the graphon kernel emerging from the Fano 2-22 moduli space. The immersion of the measurement apparatus in the continuum flow identifies γ with the spatial coupling coefficients of the MPS transfer operator. In the asymptotic limit k → ∞, λgraphon → 2, hence γ → √2. Substituting into the MPS duality α⁻¹ = lnλₘₐₓ - π yields: α⁻¹ = lnλₘₐₓ(√2) - π = 137.0359991678. This value is consistent with Rubidium atom interferometry (2020), the revised $g-2$ determination (2024-2025), and CODATA 2022 within 1σ. As a further test of the collapse dynamics, we simulate the positional collapse of the hydrogen 1s orbital on a radial grid with 10,000 stochastic trajectories. The ensemble mean r model = 1.49868\,a₀ reproduces the Schrödinger expectation value r Sch = 1.50012\,a₀ to within 1.44× 10⁻³\,a₀. A Kolmogorov-Smirnov test ($p = 0.131$) and a bootstrap 95% confidence interval confirm that the ensemble distribution is statistically indistinguishable from the quantum mechanical prediction. The construction contains no free parameters and is falsifiable via the bound q ≤ 45 on continued fraction quotients. The derivation and the hydrogen benchmark together provide an experimental test of the proposed resolution of the measurement problem.