Letter While Lattice QCD simulations require millions of CPU hours to estimate the proton spin partition, we present an instantaneous, parameter-free derivation based on Spectral Graph Theory. Unlike Lattice QCD simulations, which consume millions of CPU hours (Cray, IBM Summit, etc. ) and months of supercomputing time, we present an analytical solution that is computationally instantaneous. By reducing the problem to its fundamental topological constraints, we derive the quark spin fraction (Δ Σ = 1/3) in real-time and without free parameters. The validity of this approach is confirmed by replicating decades of experimental results (HERMES, COMPASS) with 0. 72α precision, demonstrating that spectral geometry offers the same accuracy as numerical brute force, but at zero cost. The "Proton Spin Crisis" remains one of the most persistent puzzles in hadronic physics, referring to the experimental finding that quark spins contribute only ≈ 30 % to the proton's total spin, contradicting naive constituent quark models. We present a parameter-free derivation of this partition based on Spectral Graph Theory. Modeling the proton as a complete graph K₃ governed by the Fiedler eigenvalue λ₂=3, we demonstrate that the quark spin fraction is inversely proportional to the spectral rigidity: ∆σ = 1/λ₂ = 1/3 = 0. 333. This prediction achieves 0. 72 σ agreement with weighted experimental data from HERMES, COMPASS, and Lattice QCD (∆ Σ obs = 0. 317 ± 0. 023). We conclude that the "missing spin" is not lost but topologically sequestered in gluon field connectivity required to maintain the mass gap. This represents the first geometric explanation of the quark spin contribution without free parameters. Please send Feedback to andrespirolo@gmail. com
Andrés Sebastián Pirolo (Sat,) studied this question.