EQUIL - BUGFIX - Sample knot midpoints so the round-trip check can see spline ringing

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The bug

The efit_by_inversion round-trip check measures (psi,theta) -> (R,Z) -> psi only at psi knots:

https://github.com/OpenFUSIONToolkit/GPEC/blob/develop/src/Equilibrium/DirectEquilibriumByInversion.jl#L694-L716

The rzphi cubic splines interpolate exactly at their own knots. So the residual is near zero
there no matter how badly the splines behave in between — inter-knot ringing is invisible to this
measurement by construction, and the check reports a clean edge while the reconstruction is unusable.

Evidence

DIII-D-like deck, fixed mpsi=512, pushing psihigh toward 1:

psihigh	on-knot	midpoint	ratio	resulting et[1]
0.995	4.10e-06	5.02e-06	1.2	+0.80
0.999	3.57e-06	4.19e-06	1.2	+0.81
0.9999	1.14e-05	1.29e-03	113.1	+4.70
0.99999	2.65e-05	2.18e-02	823.2	−47707

The on-knot column is flat across the whole ladder while the stability energies collapse by six
orders of magnitude. The midpoint residual tracks the degradation.

Provenance, so nobody is misled by a single table: the three residual columns were re-measured
today through the shipped code path. The et[1] column is from the earlier instrumented ladder that
ran ForceFreeStates; today's script does not. The correlation claim — on-knot flat while the energies
collapse — was established on that earlier run, where both were measured together. The two runs also
used different sampling density, so the residual magnitudes are not directly comparable rung-by-rung
with that earlier table; the ordering and the separation are what reproduce.

The fix

Measure the residual at the knots and at the knot midpoints, and report both plus their ratio.
The ratio is the usable signal: dimensionless, so it needs no per-grid calibration, and good/bad sit
two orders of magnitude either side of a threshold of 10.

Two details that are load-bearing, both settled by measurement rather than taste:

• An absolute tolerance alone is not enough. At psihigh=0.9999 the midpoint residual is
  1.29e-3, under the existing 2e-3. Only the ratio catches that rung.
• The ratio alone is not enough either. On a clean grid both residuals sit at the rounding floor
  and their ratio is noise. So the ratio is consulted only once the midpoint residual clears
  ROUNDTRIP_TOL/20.

Sampling widened from two fixed knots to every knot and midpoint in the outer ROUNDTRIP_EDGE_FRAC
(0.9) of the grid — the region the check is named for and where the failure lives. This window
matters: I first tried the minimal version that keeps the two existing knots and adds only their
neighbouring midpoints. It reads ratio 1.0 at psihigh=0.99999 and misses the worst rung
entirely, because the ringing lives in an interval those two samples don't touch. The band variant
catches every bad rung. (Widening further, to 0.75, pulls in coarser interior knots whose ordinary
interpolation error inflates the healthy baseline from 1.2 to 7.3 against a threshold of 10 — too
little margin, hence 0.9.)

A pre-existing defect this surfaces

On test_data/CHEASE_test_data/EQDSK_COCOS_02 at psihigh=0.994, knot i=128 (psi=0.99385) traces to
(R=3.32, Z=3.91) on a machine with ro=7.04 — a badly mis-located surface. The residual there is
0.517.

This deck already warns on develop: develop's outermost sample reads 0.048, well over 2e-3. So
this is not introduced here — the warning just gets louder (0.517) and now names where the problem is.
I have deliberately not tried to fix the tracing defect in this PR. Flagging it for whoever owns
that path.

Separately, psihigh=0.95 and 0.97 on that same deck die in an unrelated pre-existing
DomainError (sqrt of a negative) in equilibrium_global_parameters! at Equilibrium.jl:371.
Also not touched here.

Verification

• test/runtests_equil.jl — 286/286 pass, including a new false-positive control asserting a
  cleanly traced deck still reports at Info with both residuals and the ratio in the message.

• Ladder above re-measured through the shipped code path, not a replica.

• Regression harness, diiid_n1, --refs develop,local against develop @ 4e430f170:
  47 quantities, all unchanged.

  Being straight about what that does and doesn't show: diiid_n1 uses eq_type = "efit", so it
  does not execute the changed code at all. It confirms no leakage into other paths — the change is
  log output only — but it is not coverage of this fix. No regression case currently uses
  eq_type = "efit_by_inversion", which looks like a real gap worth closing separately; I'd rather
  propose that than bolt a new pinned case onto a small bugfix.

Scope

Equilibrium only; no SLAYER/Tearing code touched. Split out of the FKR-width work as an
independent fix. Stacks cleanly alongside #442 (different files).

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⚠️ NO MERGE WITHOUT THIRD-PARTY HUMAN REVIEW — NON-NEGOTIABLE ⚠️

🤖 Generated with Claude Code

https://claude.ai/code/session_01PSrf6JCViFfVzqzkQ66o6b