Pin converged Δ′ instead of a platform-dependent single-point snapshot (q=2)

[d-burg]

Summary

The pinned ideal-MHD Δ′ diagonal in test/runtests_parallel_integration.jl
(delta_prime_matrix, DIII-D-like STRIDE BVP testset) is a single-point snapshot on a
non-converged grid. For the q=2 surface it is also platform-dependent, which forced a
tolerance widening in #238 as a stopgap. This issue tracks replacing it with a converged Δ′ pin.

Observed platform spread (identical grid, inputs, and mode range)

platform	real(dpm[1,1]) (q=2)
linux x86_64, julia 1.11	6.1438
linux x86_64, julia 1.x	6.6867
macOS aarch64	7.7036

~25% end to end, and ~9% between two julia versions on the same OS. q=3 and q=4 are
reproducible across the same platforms.

Stopgap applied in #238

The q=2 pin was re-centered on the midpoint of the observed spread (6.9237) and its tolerance
widened from rtol=1e-1 to rtol=1.5e-1 to span it. q=3 and q=4 keep rtol=1e-1. This is an
explicit, deliberate loosening of an acceptance bound and should be reverted once a converged
pin exists — it is currently sitting at ~75% of its own budget, so a new platform could break it again.

Root cause

q=2 is the surface with the known Δ′ plateau problem. Per the psi_accuracy scan recorded in
docs/src/developer_notes.md ("Open problem: pinning grid-sensitive Δ′ robustly"), on the
two-pass auto grid dpm[3,3] (q=4) plateaus to ~1% over the four tightest grids, dpm[2,2] is
marginal, and dpm[1,1] (q=2) never settles — still moving ~7% between the two tightest grids
(2e-3 → 3.125e-5, a 64x range). Because q=2 sits on the steepest part of the refinement curve,
small platform differences in knot placement translate into large Δ′ differences.

Proposed fix

Pin q=2 Δ′ where it actually converges rather than where the production grid happens to land:

• On a fixed ldp grid the q=2 Δ′ converges to ≈8.91 at mpsi ≥ 1024 (γ(2/1) ≈ 214.5 Hz,
  γ/Δ′ ≈ 24.1 constant), whereas the auto grid at its default sits ~28% low. See the
  docs/development grid notes and the psi_accuracy scan table in developer_notes.md.
• Either (a) run the pinned case on a fixed ldp grid at sufficient mpsi, accepting the CI cost, or
  (b) implement the plateau criterion described in developer_notes.md — scan psi_accuracy and
  the truncation controls and pin the stationary value — so the reference is a property of the
  physics rather than of the discretization.

Option (b) is the more general fix and would also make the harness-tracked Δ′ meaningful across
grid-generator changes; option (a) is cheaper but adds a large-mpsi run to CI.

Acceptance criteria

• q=2 Δ′ pin is a converged value, reproducible across linux/macOS and julia versions
• q=2 tolerance restored to rtol=1e-1 (or tighter)
• Pin survives a grid-generator change without manual re-pinning
• developer_notes.md open-problem section updated to reflect the resolution

[d-burg]

Cross-linking related issues, since this is the third instance of one recurring pattern rather than an isolated report:

• ForceFreeStates: ex5 kinetic-damping imag(et[1]) pin (rtol=0.08) is platform-fragile (fails on macOS aarch64) #273 — ex5 kinetic-damping imag(et[1]) pin (rtol=0.08) is platform-fragile, fails on macOS aarch64. Same failure mode as this issue: a numeric pin measured on one platform that a different platform cannot satisfy. This one is q=2 Δ′ instead of et[1], but the mechanism is identical.
• auto mpsi under-resolves the edge, giving spurious dW and Delta-prime #302 — auto mpsi under-resolves the edge, giving spurious dW and Δ′. This is the upstream root cause: because the q=2 surface never plateaus under the auto grid, its Δ′ sits on the steepest part of the refinement curve, which is what turns small platform differences in knot placement into a ~25% spread.

Taken together these suggest the general problem is that the suite pins platform-sensitive quantities at tolerances they cannot support, and that fixing it per-pin (as here) is treating the symptom. A shared resolution — pinning converged/plateau values, or a documented policy for which quantities may carry numeric pins at all — would close #273 and this issue together, with #302 as the physics prerequisite.

Context: found while getting #238 green. The immediate stopgap there was re-centering the q=2 pin on the midpoint of the measured spread (6.1438 linux/1.11, 6.6867 linux/1.x, 7.7036 macOS/aarch64) and widening rtol from 1e-1 to 1.5e-1 — an explicit, deliberate loosening that should be reverted once a converged pin exists.