Every tokamak detects the L–H transition the same way it has since 1982: watch the Dα light drop. This paper asks a different question — not how bright the edge emission is, but how spectrally complex it is. A Hankel embedding of the raw Dα signal produces a Gram matrix whose eigenvalue distribution follows the Baik–Ben Arous–Péché spiked model: coherent turbulent modes create spectral outliers above the Marchenko-Pastur bulk, and E×B shear suppression at the L-H transition merges them back in. The Lanczos spectral complexity σ² measures how much coherent structure survives — and it drops by a median of 64% at the confinement transition in 10 of 11 MAST discharges, confirmed by an out-of-sample validation on 60 additional shots (combined N = 49, 69. 8% median drop). The transition turns out to be geometrically simple. In the 44-dimensional Lanczos fingerprint space, correlation-PCA recovers 90–96% of the variance along a single principal direction in L-mode, H-mode, and transition segments — and those directions are parallel to within 8° across phases. The plasma is not crossing a new axis at the transition; it is translating along an axis of turbulent-mode variability already present in both confinement states, with E×B shear acting as the parameter that moves it. The plasma spends almost no time in intermediate states: instead it switches stochastically between two discrete spectral configurations with telegraph-like dynamics over an ~8 ms coexistence window, consistent with first-order phenomenology. Combining σ² with a skewness channel derived from Ritz eigenvalue spacings — which probes independent spectral information — raises the detection rate to 65% across 458 MAST discharges (82% sign consistency), substantially exceeding either channel alone. A companion result: the Lanczos fingerprint compresses to 3–5 effective dimensions out of 44 at 99% explained variance, an order of magnitude tighter than the D*/d ≈ 0. 5–0. 7 typical of generic chaotic attractors — suggesting that L-H turbulence lives on a structured low-rank manifold rather than a generic strange attractor. The method requires no equilibrium reconstruction, no plasma model, and no machine-specific calibration. Its sole hardware requirement is a single Dα photomultiplier at ≥ 50 kHz. Validated on MAST (aspect ratio ~1. 3) via the public FAIR-MAST archive; cross-machine validation remains open. Part of the ICP series on the information geometry of chaos: Paper Role DOI The Instability Compression Principle ICP empirical foundation: β → compression scaling across 30 chaotic systems 10. 5281/zenodo. 18099118 The Compressibility of Chaos (Ordo ab Chao) ICP theoretical derivation: scaling coefficient α₀ = 5π² 10. 5281/zenodo. 18834609 Variance Excess ε (β) formula, one-point/two-point divide at βc = π 10. 5281/zenodo. 18650473 Information Geometry of the Brody Distribution Fisher metric, spectral duality theorem, effective dimension 10. 5281/zenodo. 18879754 The α-Connection Structure of the Brody Manifold Amari–Chentsov tensor, orbit-universal connection 10. 5281/zenodo. 19151206 Dual Symmetries of the Brody Statistical Manifold Z₂×Z₂ symmetry group, GOE=GUE orbit-equivalence 10. 5281/zenodo. 19239285 The Duality Web of the Brody Statistical Manifold Conjugation-singularity theorem, certified interval arithmetic 10. 5281/zenodo. 19389065 Spiked Random Matrix Signatures of the L-H Transition First experimental application: Lanczos spectral complexity in tokamak plasmas this paper The Spectral Geoid Convergent mode structure of Wigner surmise residuals; two-point layer 10. 5281/zenodo. 19518426
Jon Wiberg (Sat,) studied this question.