[StuartBenjamin]

Problem. With integrator = "Riccati", nzero tests crit only at chunk endpoints, about 8 per singular surface. A crossing inside a chunk is missed, and two crossings in one chunk cancel. On a DIII-D equilibrium that RDCON and Fortran STRIDE find fixed-boundary unstable at n = 1 and 2, the Riccati path reports 0 at both. The forward path, which checks every step, has a separate gap. It confirms a crit sign change with an interpolated midpoint, and that check rejects a real crossing when the smallest eigenvalue switched at the step before.

Fix.

• Riccati, inside each chunk: each chunk counts the zero crossings of its principal solution (U₁ = 0 at its start) at every ODE step, in the propagator callback. This uses the inertia of U₂ᴴU₁ from an LDLᴴ factorization; crit is evaluated only on the steps where the inertia changes.
• Riccati, at assembly: the crossings of the axis solution beyond those come from the chunk's end data alone. They are the negative eigenvalues of dir·X_sᴴP₁₂⁻¹X_e, a Morse-index split that holds for F̄ > 0.
• Riccati, outer plasma: it is still counted from its stored steps.
• Forward: a sign change of crit counts when the number of negative eigenvalues of W⁻¹ drops. With F̄ > 0, a crossing raises an eigenvalue through 0; a switch of the smallest eigenvalue or a passage through ∞ does not.

Test	Result
DIII-D equilibrium 174956 at 1715 ms (draw 12), n = 1 / 2; RDCON and Fortran STRIDE give 2 / 1	Riccati 0 / 0 before, 1 / 1 after; forward 0 / 0 before, 1 / 0 after. At n = 2 the forward solution's crit never changes sign (closest |crit| = 0.2 at ψ = 0.13, the same on develop), so there is nothing for it to count. On the previous develop (728a7e7) both paths gave 1 / 1, and Riccati matched an exact count of the code's own axis solution (eigenphases of (X + iU)(X − iU)⁻¹, 5000 steps per chunk). The remaining n = 1 gap to Fortran comes from small equilibrium differences, not the counting.
test/runtests_riccati.jl, test/runtests_eulerlagrange.jl	pass; new: oscillator (per-step count, Morse split, basis and scale independence, backward chunks), a crossing right after an eigenvalue switch (fails on develop), Solovev verdict (Riccati said stable on develop)
Full test suite	all files pass (9,662 tests after runtests_equil.jl); its one failure, "Load TokaMaker i-file" (runtests_equil.jl:312), fails on develop too
Regression harness (27 cases, develop vs this branch)	all 27 bitwise

The Solovev example is Mercier unstable at q = 2: its crossings pile up log-periodically into that surface, so their number depends on resolution, and the test compares only the verdict.

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