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QA benchmark discrepancy: spline floor of field-line |B| maxima; evaluate maxima spectrally #92

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@krystophny

Lambda_B is linear in the maxima-height differences Delta_eta = 1/B_max^loc - eta_b, so a relative field error delta at the maxima propagates as an absolute Delta_eta error of order delta/B. The resolvable coefficient floor is Lambda_floor ~ C * delta_spline with C = O(1).

With delta_spline ~ 1e-6 this floor sits at the QH signal level (coefficients ~1e-6, agreement observed, marginally above floor) and two orders above the QA signal (~1e-8, discrepancy observed). The floor reproduces the observed QH-good/QA-broken pattern with no physics error. Treat this as the default explanation until the maxima comparison falsifies it.

Fix, if confirmed: evaluate |B| and its field-line maxima spectrally (direct Fourier sum from the Boozer spectrum at the maxima search points); keep splines for radial profiles only. That moves the floor from interpolation error (~1e-6) to Fourier truncation (~1e-12). Cost is negligible next to the quadratures (~200 field lines, a few hundred evaluations each).

Acceptance: QA rerun with spectral maxima matches the NEO-2 golden record at the same tolerance as QH today. Only if it does not, re-derive the M = 1, N = 0 corner of the iota_p formula. The release paper states the floor formula with the measured delta_spline; the same evaluation rule carries over to pyrabe (interpax for radial profiles only).

A direct measurement of delta_spline (spline vs spectral maxima on the QH and QA reference wout files) is in progress and will be attached here.

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