
In 1982, a plasma inside the ASDEX tokamak in Germany spontaneously reorganised itself — turbulence at the edge collapsed, confinement doubled, and nobody had predicted it. That transition, now known as H-mode, has been reproduced in every major fusion device on Earth and is the operating regime that ITER — the international fusion reactor under construction in France — is designed to run in. This document applies the SFVFS™ framework to H-mode and finds not an analogy but a structural match: the H-mode pedestal is the Needle's Eye Attractor in a confined plasma, a self-organised geometric fixed point that the plasma locks to spontaneously, characterised by a cross-machine invariant (H98 ≈ 1) confirmed across JET, DIII-D, ASDEX Upgrade and JT-60U — the direct plasma equivalent of the equation of state (H₁_norm, Λ) = (1,1) confirmed across six fluids in the Navier–Stokes DNS programme. The periodic crashes that interrupt H-mode — ELMs — are not failures but the DN branch of the SFVFS™ cycle: the system expels energy, crosses the void floor, and immediately reconstitutes the same geometric attractor regardless of which crash type triggered it, confirming the Convergence Hypothesis in a living physical system. The framework issues a falsifiable structural prediction: the H-mode geometric attractor is scale-invariant, and ITER will sustain H98 ≈ 1 at full scale — testable approximately 2035.

Chen-Ning Yang (1922–) Chinese-American physicist and Nobel laureate who, with Robert Mills in 1954, developed the gauge theory framework that underlies the Standard Model of particle physics. The Yang-Mills equations describe the forces between elementary particles. Whether solutions always exist and carry a positive mass gap is the mathematical problem the Millennium Prize formalises..
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