EQUIL - BUGFIX - Fix ideal Δ′ non-convergence on the auto psi-grid

[logan-nc]

What & why

The two-pass auto psi-grid (grid_type = "auto") produced a non-convergent ideal Δ′: as
psi_accuracy tightened, the Δ′ diagonal oscillated erratically (dpm[1,1] ≈ 7.2–10.1 on the
DIII-D-like case) instead of converging to the fixed-grid reference.

Root cause. The grid pinned a knot on each rational surface. The Δ′ asymptotic matching
stencil [ψ_s ± singfac_min/|n·q′|] then straddled that knot, so the cubic 3rd derivative the
singular extraction samples was inconsistent across the crossing. Confirmed by a clean in-run
natural experiment: surfaces whose knot happened to fall outside the stencil (e.g. q=4) were
rock-stable, while those straddling it (q=2/3/6) were erratic.

The fix (grid layer only)

• bracket_mandatory_nodes — center each rational between a knot pair (never on a knot),
  blended to half the local spacing, so the matching stencil lies in one clean, locally-uniform
  spline segment and q‴ is single-valued across it.
• Fixed-width (τ-independent) near-rational resolution patch — Δ′ accuracy is a property of
  the rational surface, so its local resolution must not scale with the global accuracy target
  psi_accuracy (that only sizes the pedestal/edge grid). This is what makes the default
  psi_accuracy = 1e-3 land on the converged value.
• enforce_min_spacing floor on the auto refined grid and the fixed ldp/pow1 grids, so no
  grid packs its edge below the field-line-integration noise scale at high mpsi.

Result

dpm[1,1] now converges τ-independently to ~9.2 (matching the uniform mpsi ladder), default
psi_accuracy=1e-3 included, vs the prior erratic 7.2–10.1. Equilibrium scalars are unchanged
(q95, β_n = 0.00%) — this is grid placement only.

	develop (erratic)	this PR
dpm[1,1] @ τ=1e‑3	9.05 (lucky)	9.199 (converged)
dpm[1,1] across τ	7.2–10.1	9.2–9.3 (τ-independent)

Regression (diiid_n1, develop vs this branch)

Equilibrium scalars unchanged. Δ′-dependent quantities changed as intended: Δ′ diagonal
(dpm[1,1] 9.05 → 9.199), island half-widths (7.5%), Chirikov (21%), resonant field (14%). Runtime
+13% (within budget). These changes need reviewer sign-off — the harness is a live develop-vs-local
diff, so develop becomes the new baseline on merge.

Scope / follow-ups

• The accuracy-driven density remains grid-dependent near the separatrix (a real q/geometry
  singularity; the default converges to the uniform reference, ~3% above the ldp reference).
  That is out of scope here and tracked in Auto psi-grid: accuracy-driven density is grid-dependent — pursue a self-consistent / one-pass construction #349 (self-consistent / one-pass grid redesign).
• Not yet done: a kinetic_factor > 0 spot-check (the ideal deck has kinetic_factor = 0,
  and the near-rational knots' rationale is the kinetic-MHD path).
• Orthogonal grid change — cleanly cherry-pickable onto feature/tearing-growthrates (Feature: add SLAYER and GGJ tearing growth rates #238)
  if approved.

⚠️ Human review is mandatory

Do not merge without a third-party human reviewer's approval, and please confirm the regression
changes above are acceptable.

Closes/relates: #349 (deferred grid-invariance redesign)

🤖 Generated with Claude Code

https://claude.ai/code/session_0125dY2qbGtm3gky8TPv7vh6