FFS - EXPERIMENT - Phase 1 of route (a): the remap manufactures the noise, worth ~50%

Gate 1a (dtmax forcing dense saves) flips the geometry from a flat floor with
white-noise correlation to converging data with r1 -> +0.98, and cuts accepted steps
37% at mpsi=512 and 53% at mpsi=1024, dropping the per-doubling ratio 1.92x -> 1.43x.

Gate 1a's internal confound is settled from the existing etol sweep: four decades of
integration accuracy leave the geometry residuals flat, while forcing dense steps at
the same accuracy cleans them ~24x. The error is set by the spacing of the resample
abscissae, not by node accuracy -- which is why etol and abstol were both null.

Gate 1b could not run: post-refinement saves break the periodic closure. Recorded as
inconclusive, with the periodicity constraint noted for Phase 2.

src probes reverted; no source changes.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

Author: logan-nc

handoff/issue376/PREDICTIONS.md

@@ -119,3 +119,42 @@ et[1] identical to 6-7 digits across the ladder.
    Route (a) is strongly motivated. This also refutes the section 11 speculation that a good share
    of the near-axis steps might be legitimate resolution of real structure, and shows the ~20%
    ceiling was a limit of that PARTIAL repair, not of fixing the source.
+
+--- Phase 1 gates (route (a)), written before the runs ---
+
+Two candidate manufacturers of eps inside the Fill Site A trace+remap, probed one line at a time
+on the DIIID stripped decks at mpsi 512 and 1024 (baselines 3977 / 7638 accepted steps; nu
+mid-plasma residual flat at 1.51e-6 / 1.29e-6):
+
+Gate 1a "remap interpolation error": dtmax = 2pi/2000 at DirectEquilibrium.jl:294 forces >=2000
+solver steps, so ff_x_nodes get much denser and the periodic-cubic resample error (~h^4) collapses,
+with tolerances and refinement untouched.
+  - predicts, if the remap is the source: nu/offset/rcoords residuals drop by orders of magnitude
+    and start converging; accepted steps fall toward the LAR-like flat scaling.
+
+Gate 1b "pre-refinement save drift": save_positions=(true,false) -> (false,true) at line 290. The
+saved states are currently taken BEFORE refine_affect! Newton-projects them onto the flux surface,
+so every saved rfac carries the raw per-step drift off the surface.
+  - predicts, if the drift is the source: same qualitative drop, and the fix is nearly free.
+  - note reltol is already 1e-10, so the drift should be ~1e-10 relative -- too small to explain a
+    1e-6..0.19 floor. Expected to be null or minor; running it to be sure rather than assuming.
+
+If BOTH are null, the eps is manufactured by neither candidate and Phase 2 must be rethought
+before any code is written.
+
+Phase 1 RESULTS:
+  Gate 1a (dtmax=2pi/2000) FIRES. Geometry goes from flat to converging: near-axis nu residual
+  2.11e-5 / 2.12e-5 (flat, r1 -0.52/-0.74) -> 7.42e-7 / 8.22e-8 (converging, r1 +0.97/+0.98).
+  Accepted steps 3977 -> 2521 (-37%) at mpsi=512 and 7638 -> 3614 (-53%) at mpsi=1024; the
+  per-doubling ratio drops 1.92x -> 1.43x. Far beyond the section 11 "20% ceiling".
+
+  Gate 1a's internal confound (dtmax improves integration accuracy AND save density together)
+  settled for free from the existing etol sweep: at mpsi=512 mid-plasma, nu residual is 1.544e-6 /
+  1.513e-6 / 1.769e-6 for etol 1e-8 / 1e-10 / 1e-12 -- FLAT across four decades of integration
+  accuracy -- versus 6.36e-8 for gate 1a at etol 1e-10. Integration accuracy is not the lever;
+  save/step density is. That is the remap-interpolation signature.
+
+  Gate 1b DID NOT RUN: save_positions=(false,true) breaks the periodic closure (theta=0 is the
+  unrefined initial condition while theta=2pi is refined), so the PeriodicBC check rejects the
+  data. Its premise was weak anyway (drift ~reltol=1e-10, far below the observed floor). Recorded
+  as inconclusive; Phase 2 must preserve the periodic closure when choosing evaluation points.

handoff/issue376/RESULTS.md

@@ -561,6 +561,47 @@ Two things this overturns:
 **Phase 0 verdict: proceed.** The premise of route (a) is confirmed with the input, fill-site and
 grid confounds each eliminated by measurement.
 
+## 15. Phase 1 of route (a): the remap is the manufacturer, and the prize is ~50%
+
+**Gate 1a — force dense saves.** `dtmax = 2π/2000` at `DirectEquilibrium.jl:294` shrinks the
+spacing of `ff_x_nodes`, leaving tolerances and refinement untouched.
+
+| mpsi | accepted steps | near-axis `nu` resid | near-axis r1 |
+|---|---|---|---|
+| 512 stock | 3977 | 2.11e-5 (flat) | −0.515 |
+| 512 + dtmax | **2521 (−37%)** | 7.42e-7 | **+0.968** |
+| 1024 stock | 7638 | 2.12e-5 (flat) | −0.744 |
+| 1024 + dtmax | **3614 (−53%)** | 8.22e-8 | **+0.984** |
+
+The geometry flips from a flat floor with white-noise correlation to **converging** data with
+r1 → +0.98, and the per-doubling step ratio drops **1.92× → 1.43×**.
+
+**The confound inside Gate 1a is settled.** `dtmax` improves integration accuracy *and* save
+density together. The existing etol sweep separates them, at mpsi=512 mid-plasma:
+
+| variant | `nu` resid | `offset` resid |
+|---|---|---|
+| etol 1e-8 | 1.544e-06 | 9.09e-06 |
+| etol 1e-10 | 1.513e-06 | 7.93e-06 |
+| etol 1e-12 | 1.769e-06 | 7.04e-06 |
+| **etol 1e-10 + dtmax** | **6.36e-08** | **3.39e-07** |
+
+Four decades of integration accuracy move nothing; forcing dense steps at the *same* accuracy
+cleans by ~24×. **The error is set by the spacing of the resample abscissae, not by how accurately
+each node is computed** — the remap-interpolation signature, and the reason `etol` and `abstol`
+were both null.
+
+**Gate 1b did not run.** `save_positions=(true,false) → (false,true)` breaks the periodic closure
+— θ=0 is the unrefined initial condition while θ=2π is refined — and the `PeriodicBC` check
+rejects it. Its premise was weak regardless (drift ~ reltol = 1e-10, orders below the observed
+floor). Recorded as inconclusive, with a constraint for Phase 2: **whatever points are evaluated,
+the periodic closure must be preserved.**
+
+**Phase 1 verdict: proceed.** `dtmax` is a brute-force proxy — it forces 2000 steps per surface and
+still leaves finite resample error. The Phase 2 fix evaluates *exactly* at the target abscissae, so
+the resample error at the output nodes is zero rather than merely small, and it does not force
+extra steps.
+
 ## Implications / ranked follow-ups
 
 1. **Use the two-pass auto grid** (`mpsi=0`, `psi_accuracy`) — already the example default; it