Validation

NTX validation is organized around four layers:

1. unit and regression tests in tests/

2. workflow and convergence examples in examples/

3. CPU/GPU runtime checks

4. downstream database and profile checks through NEOPAX

The gate hierarchy behind those layers is now documented explicitly in physics-gates.md. In short:

• analytical identities and exact P=2 recovery are hard gates,

• independent-code comparisons are trust-building physics gates,

• the rebuilt integrated W7-X raw branch is the main transfer gate,

• the precise-QS fixed-field NTX+NEOPAX current benchmark is a scoped total-current closure stress gate rather than a monoenergetic parity requirement or a species-current parity claim.

The maintained benchmark matrix in benchmark-matrix.md maps each promoted claim and monitored stress lane to its scripts, tests, artifacts, manuscript figures, and non-promoted future work.

Validation Philosophy

NTX is validated as a standalone solver. The repository therefore emphasizes:

• internal numerical consistency

• convergence behavior

• trustworthy geometry loading

• end-to-end workflow checks

• imported JAX workflows

• CPU/GPU execution stability

Independent comparisons are useful, but they are treated as trust-building studies rather than as the definition of NTX itself.

Owned Dataset Discipline

External reference datasets remain useful transfer checks, but they are not interchangeable. In particular, the W7-X imported-workflow comparison exercises the NTX-to-NEOPAX handoff against an existing external workflow; it is not a SFINCS parity statement. Promoted SFINCS/Redl/NTX+NEOPAX bootstrap-current figures must be generated from the same geometry, profile family, collisionality grid, radial-electric-field grid, interpolation convention, and normalization map.

The owned provenance lane is:

python examples/owned_geometry_neopax_dataset.py
python examples/owned_finite_beta_sfincs_jax_inputs.py
python examples/owned_finite_beta_sfincs_jax_production_ladder_audit.py
python examples/owned_finite_beta_sfincs_jax_profile_current_audit.py
python examples/owned_finite_beta_bootstrap_comparison.py
python examples/owned_finite_beta_closure_localization.py
python examples/owned_finite_beta_profile_current_observable_audit.py
python examples/owned_finite_beta_current_conditioning_audit.py
python examples/owned_finite_beta_closure_quadrature_audit.py
python examples/owned_finite_beta_source_channel_audit.py
python examples/owned_finite_beta_source_response_profile_audit.py
python examples/owned_finite_beta_closure_target_audit.py
python examples/owned_finite_beta_radial_interpolation_audit.py --rebuild-matched
python examples/owned_finite_beta_closure_quadrature_audit.py \
  --bootstrap-json docs/_static/owned_finite_beta_field_radius_matched_bootstrap_comparison.json \
  --x-values 10 18 --n-orders 10 12 14 18 \
  --output-prefix docs/_static/owned_finite_beta_field_radius_matched_closure_quadrature_audit \
  --output-dir examples/outputs/owned_finite_beta_field_radius_matched_quadrature_probe
python examples/owned_finite_beta_source_channel_audit.py \
  --bootstrap-json docs/_static/owned_finite_beta_field_radius_matched_bootstrap_comparison.json \
  --settings 10:12 10:18 18:18 \
  --output-prefix docs/_static/owned_finite_beta_field_radius_matched_source_channel_audit \
  --output-dir examples/outputs/owned_finite_beta_field_radius_matched_quadrature_probe

The NTX/NEOPAX script now prioritizes local finite-beta stellarator input/wout pairs from the single-stage finite-beta checkout. The finite-beta QA pressure/current case runs through the vmec_jax -> booz_xform_jax -> NTX path, passes the physical VMEC edge toroidal flux divided by 2*pi as the Boozer-surface psi_p, writes NEOPAX-style scan tables, stores compact profile flux/current proxies from those same scan tables, and audits the direct VMEC-harmonic interpolation path on the same radial and collisionality grid. This removed the earlier order-of-magnitude Boozer-path normalization error: the current artifact has a maximum Boozer-vs-direct path coefficient difference of about 1.4e-1 instead of an order-unity hidden path mismatch. Optimized finite-beta QH/QI cases are retained as direct wout-harmonic stress cases until the JAX geometry stack supports their cubic-spline current-profile input representation. That blocker is recorded in the JSON sidecar rather than hidden behind a parity plot.

The direct boozmn backend now has a separate same-coordinate round-trip gate. The loader uses VMEC half-grid metadata (s_in, s_b, or jlist = compute_surfs + 2) for Boozer spectra and radial profiles; it does not use the full-grid phi_b profile as the packed-mode interpolation grid. The artifact below generates a Boozer file from a VMEC wout, reloads the same half-grid surfaces, and compares geometry metadata plus D11/D31/D13/D33 with the in-memory vmec_jax -> booz_xform_jax -> NTX path. This closes the direct loader radial-coordinate mismatch while leaving VMEC-harmonic versus Boozer-coordinate comparisons as representation audits.

The same backend issue has now been checked on the finite-beta QA wout used by the owned stellarator lane. That input uses an optimized current-profile form that the optional differentiable VMEC-state reconstruction path does not yet support. NTX therefore treats profile_source="wout" as the correct file-backed transfer route for this case: it transforms the finalized VMEC magnetic channels, reloads the generated Boozer file on the same half-grid surfaces, and compares D11/D31/D13/D33. The committed artifact closes the transport mismatch to about 8e-14. This removes the Boozer radial-selection and finalized-channel ambiguity for finite-beta file-backed runs while keeping fully differentiable finite-beta state sensitivities out of shipping claims.

The SFINCS-JAX generation script writes RHSMode=3, geometryScheme=5 namelists for the same finite-beta wout, rho, collisionality, electric-field, and resolution grids. Add --run-sfincs-jax only when the local SFINCS-JAX checkout should execute those inputs. The committed artifact now ingests a six-point same-grid coefficient ladder on the finite-beta QA case, including the profile-current stress neighborhood, using the reported nu_n normalization and a coefficient-level NTX bridge comparison. The current max L13/L31/L33 relative difference is about 2.1e-2 after enforcing exact radial interpolation, the pitch-angle-scattering nuD frequency bridge, and the RHSMode=3 flow-row normalization. This localizes the remaining finite-beta bootstrap-current mismatch downstream of the monoenergetic coefficient solve. These artifacts are deliberately scoped as smoke-resolution same-grid generation control, not independent-code bootstrap-current parity. The same generator can also emit bounded RHSMode=2 row-3 diagnostic decks with explicit electron/ion species selection. In that mode, the input axis is written as SFINCS nu_n rather than using the RHSMode=3 nuPrime overwrite, and an optional profile-contract switch writes nHats=n/10^20 and THats=T/(1 keV) from the same analytic finite-beta profiles used by the Redl/NTX+NEOPAX stress audit. These RHSMode=2 decks are source-row diagnostics only; they are not used to promote a finite-beta current parity claim until the collisionality/profile-current normalization is closed.

The owned RHSMode=1 profile-current diagnostic writes direct profile-current SFINCS-JAX decks on the same finite-beta VMEC wout and analytic profile contract used by the Redl and NTX+NEOPAX stress audit. The committed low-resolution artifact completes three radii with the optimized SFINCS-JAX 1.1.0 main branch and shows that direct profile-current amplitudes need their own pitch, velocity, radial, and collisionality-normalization ladder before they can be used as a finite-beta current reference. A 17 x 21 x 12, Nx=5 inner-radius rerun now completes the HDF5 output on local CPU, moving the SFINCS-JAX-vs-Redl current gap from about 8.5e-1 on the smoke grid to about 5.6e-1, but the reported linear residual remains 1.88e-2 against a 1.09e-9 target. The office one-GPU rerun reaches the same fallback residual and then fails with a CUDA illegal-address error in JAX GMRES. This keeps the current comparison explicit rather than folding an unconverged direct-profile observable into a promoted parity claim.

The finite-beta bootstrap-current script now runs Redl and NTX+NEOPAX on the same finite-beta QA pressure/current wout, Boozer transform, analytic profile contract, radial grid, adaptive physical nu/v support, and current normalization. It also fixes two user-facing normalization issues: current conversion uses exactly one elementary-charge factor, and the file-backed Boozer-field path evaluates the B00 coefficient on normalized radius rho with dB00/dr = (dB00/d rho)/a_b, rather than evaluating a normalized-radius profile on physical minor radius. The current artifact uses the explicit D33_spitzer audit branch and records a Sonine-order convergence sidecar. The production-resolution QA ladder uses a 25 x 31 x 24 NTX grid, 15 NEOPAX field radii, 17 adaptive physical nu/v support points, and Pmax 12; its total-current max/RMS relative differences against Redl are now about 2.2e-1/1.4e-1 with unit sign agreement. This remains a mismatch-localization diagnostic rather than a README/manuscript parity claim because the full profile is still above the 1e-1 current gate. The closure-localization sidecar makes this split explicit: at the current stress radius, the nearest same-grid coefficient difference is about 1.3e-2, the profile-current difference is about 2.2e-1, and the current/coefficient error ratio is about 17. The maximum same-grid coefficient difference remains about 2.1e-2, so the non-promoted follow-up is scoped to the reduced momentum/profile-current observable and production profile-current closure. The profile-current observable audit then shows that the stress-radius momentum correction has the correct sign but overshoots the Redl target correction by about a factor 2.1 at the current stress radius. The remaining residual is only about 2.5e-3 of the species momentum-correction L1 scale, so the net current is cancellation-sensitive even when the absolute species-flow residual is small. The Pmax sidecar is monitored rather than promoted because the stress error is not monotone in the current finite-order/quadrature sweep. The current-conditioning audit adds the matching precision statement: the most cancellation-sensitive radius has a species-flow L1 scale divided by the Redl net current of about 1.45e2. A 1e-1 net-current gate therefore requires same-grid coefficient precision near 1e-3 at sensitive radii, tighter than the completed coefficient ladders. The production stress probe and six-point radial/collisionality ladder keep the same-grid finite-beta coefficient differences near 2.1e-2. That closes the production coefficient ladder as a broad numerical failure and scopes the non-promoted finite-beta parity work to the profile-current closure layer. The production radial/collisionality ladder then runs the six same-grid finite-beta QA SFINCS-JAX points at 35 x 43 x 48. The optimized SFINCS-JAX main-branch refresh leaves all completed points below 2.07e-2 coefficient difference; the maximum precision gap is still the inner rho=1/7, nuPrime=1e-2 point. That closes the production coefficient ladder as a broad numerical failure and scopes the non-promoted finite-beta parity work to the profile-current closure and converged RHSMode=1 profile-current layers. The closure-quadrature audit then varies only the momentum-closure Sonine order and velocity quadrature while holding the finite-beta scan, profiles, Redl observable, and normalization fixed. After the Boozer-field radius fix, the accepted quadrature-stable pass count is still zero, the best stress value is about 1.16e-1, and the highest-quadrature largest-order stress error is about 1.27e-1. This keeps the quadrature/Pmax lane open without allowing an under-integrated apparent pass into the runtime. Any future finite-beta profile-current claim must pass the current gate and the velocity-quadrature stability gate simultaneously. The source-channel audit then freezes the same stress-radius matrix and solves the density/electric, effective temperature-gradient, and parallel-electric source columns separately. Those one-channel solves reconstruct the full corrected current to roundoff. At the quadrature-stable high-order setting the dominant corrected source channel is the density/electric channel, the effective temperature channel carries about 42% of the corrected response, and the parallel-electric channel is zero for this profile contract. The Redl density and temperature terms are stored on the same observable, so the audit measures source-response ratios rather than fitting a profile-dependent bridge; the Redl effective-temperature target is about 1.35 times the frozen corrected temperature response at this stress point. The profile source-response audit extends that same one-channel solve over all 13 finite-beta profile radii at X=18, P=18. The temperature response multiplier spans 0.765 to 1.349, has median 1.040, preserves temperature source sign agreement over the profile, and records the high-order stress at rho=0.143. The JSON sidecar records correlations with Redl collisionality, trapped fraction, epsilon, and L32; these are diagnostics for a future physics-derived closure term, not runtime corrections. The closure-target audit then reads that source-response sidecar and ranks local neoclassical drivers before any closure implementation is attempted. The current artifact selects the Redl geometry factor epsilon as the strongest single driver with absolute Pearson correlation 0.970; an epsilon-only leave-one-out diagnostic model has RMSE 5.58e-2, about 3.68x smaller than a constant-response model. This is still a design diagnostic: it records that no runtime correction is applied and that any future closure change must preserve the fixed-field QA/QH total-current stress gate, the W7-X transfer gate, the source-channel reconstruction gate, and the same-grid finite-beta coefficient gate. The radial-interpolation audit then removes one sparse-radius interpolation layer by rebuilding the database on the field radii. It does not reduce the full-profile maximum below the 1e-1 current gate: the sparse and matched profile maxima are about 2.19e-1 and 2.27e-1, respectively. The matched-radius quadrature audit keeps the same rebuilt database and repeats the Sonine/quadrature sweep: the best stress value is about 1.30e-1, the quadrature-stable pass count is still zero, and the X=18, P=18 stress is about 1.44e-1. This closes the interpolation-only and Pmax-only explanations without promoting a runtime closure change. The matched-radius source-channel sidecar reconstructs the corrected current to 1.82e-14 and keeps the accepted physics interpretation unchanged: the quadrature-stable response remains a finite-beta reduced-closure stress with no runtime correction applied. These scripts write:

• docs/_static/owned_geometry_neopax_dataset.png

• docs/_static/owned_geometry_neopax_dataset.pdf

• docs/_static/owned_geometry_neopax_dataset.json

• docs/_static/owned_geometry_neopax_database/*.h5

• docs/_static/owned_finite_beta_sfincs_jax_inputs.png

• docs/_static/owned_finite_beta_sfincs_jax_inputs.pdf

• docs/_static/owned_finite_beta_sfincs_jax_inputs.json

• examples/outputs/owned_finite_beta_sfincs_jax_inputs/**/input.namelist

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_audit.png

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_audit.pdf

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_audit.json

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_resolution_audit.png

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_resolution_audit.pdf

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_resolution_audit.json

• docs/_static/owned_finite_beta_bootstrap_comparison.png

• docs/_static/owned_finite_beta_bootstrap_comparison.pdf

• docs/_static/owned_finite_beta_bootstrap_comparison.json

• docs/_static/owned_finite_beta_closure_localization.png

• docs/_static/owned_finite_beta_closure_localization.pdf

• docs/_static/owned_finite_beta_closure_localization.json

• docs/_static/owned_finite_beta_profile_current_observable_audit.png

• docs/_static/owned_finite_beta_profile_current_observable_audit.pdf

• docs/_static/owned_finite_beta_profile_current_observable_audit.json

• docs/_static/owned_finite_beta_current_conditioning_audit.png

• docs/_static/owned_finite_beta_current_conditioning_audit.pdf

• docs/_static/owned_finite_beta_current_conditioning_audit.json

• docs/_static/owned_finite_beta_closure_quadrature_audit.png

• docs/_static/owned_finite_beta_closure_quadrature_audit.pdf

• docs/_static/owned_finite_beta_closure_quadrature_audit.json

• docs/_static/owned_finite_beta_source_channel_audit.png

• docs/_static/owned_finite_beta_source_channel_audit.pdf

• docs/_static/owned_finite_beta_source_channel_audit.json

• docs/_static/owned_finite_beta_source_response_profile_audit.png

• docs/_static/owned_finite_beta_source_response_profile_audit.pdf

• docs/_static/owned_finite_beta_source_response_profile_audit.json

• docs/_static/owned_finite_beta_closure_target_audit.png

• docs/_static/owned_finite_beta_closure_target_audit.pdf

• docs/_static/owned_finite_beta_closure_target_audit.json

• docs/_static/owned_finite_beta_radial_interpolation_audit.png

• docs/_static/owned_finite_beta_radial_interpolation_audit.pdf

• docs/_static/owned_finite_beta_radial_interpolation_audit.json

• docs/_static/owned_finite_beta_field_radius_matched_closure_quadrature_audit.png

• docs/_static/owned_finite_beta_field_radius_matched_closure_quadrature_audit.pdf

• docs/_static/owned_finite_beta_field_radius_matched_closure_quadrature_audit.json

• docs/_static/owned_finite_beta_field_radius_matched_source_channel_audit.png

• docs/_static/owned_finite_beta_field_radius_matched_source_channel_audit.pdf

• docs/_static/owned_finite_beta_field_radius_matched_source_channel_audit.json

• docs/_static/owned_finite_beta_sfincs_jax_resolution_audit.png

• docs/_static/owned_finite_beta_sfincs_jax_resolution_audit.pdf

• docs/_static/owned_finite_beta_sfincs_jax_resolution_audit.json

• docs/_static/owned_finite_beta_sfincs_jax_production_ladder.png

• docs/_static/owned_finite_beta_sfincs_jax_production_ladder.pdf

• docs/_static/owned_finite_beta_sfincs_jax_production_ladder.json

• docs/_static/owned_finite_beta_sfincs_jax_production_ladder_audit.png

• docs/_static/owned_finite_beta_sfincs_jax_production_ladder_audit.pdf

• docs/_static/owned_finite_beta_sfincs_jax_production_ladder_audit.json

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_audit.png

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_audit.pdf

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_audit.json

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_prod_17x21x12.png

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_prod_17x21x12.pdf

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_prod_17x21x12.json

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_prod_25x31x17.png

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_prod_25x31x17.pdf

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_prod_25x31x17.json

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_resolution_audit.png

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_resolution_audit.pdf

• docs/_static/owned_finite_beta_sfincs_jax_profile_current_resolution_audit.json

• examples/outputs/owned_finite_beta_bootstrap_comparison/*.h5

The updated SFINCS-JAX sparse-PC branch closes the old RHSMode=1 residual blocker: the 17 x 21 x 12, Nx=5 point now completes in seconds with a passing true-residual gate, and the 25 x 31 x 17, Nx=11 three-radius production ladder also passes solver metadata gates. The finite-beta pitch-resolution stress lane is accepted with a high-order even/odd tail gap of 1.323e-1, below the current 1.5e-1 reduced-closure tolerance. The full-collision RHSMode=1 branch remains a non-shipping feasibility diagnostic, not a release blocker or a fitted runtime correction.

What Is Covered

The maintained suite covers:

• Fourier-series evaluation and flux-surface averages

• operator assembly and nullspace handling

• dense block-tridiagonal solves

• scan helpers and prepared-solver reuse

• autodiff inverse and profile-analysis workflows

• DKES-style, VMEC, and Boozer file loaders

• TOML input parsing and NetCDF/NPZ/HDF5 output writing

• imported NEOPAX-array and HDF5 mapping helpers

• vmec_jax and booz_xform_jax integration points

• serial versus parallel-scan equivalence

• example and publication-figure regeneration

Core Physics Checks

Onsager Closure

Every solve reports:

\[|D_{13} + D_{31}|\]

This is the main scalar physics sanity check exposed directly by NTX.

The current tracked artifact-backed gates can be summarized locally with:

python scripts/check_physics_gates.py

Resolution Convergence

The repository-wide monoenergetic convergence benchmark is:

python examples/validation_summary.py

It combines:

• collisionality scans of D11, D13, and D33,

• Onsager residual tracking,

• and N_xi convergence on representative DKES-style and VMEC surfaces.

It writes:

• docs/_static/validation_summary.png

• docs/_static/validation_summary.pdf

• docs/_static/validation_summary.json

This is the recommended literature-anchored numerical benchmark for the NTX methods paper. The JSON sidecar freezes the transport curves, low-collisionality tail slopes, and convergence metrics for reuse in tests and manuscript artifacts. The sidecar is also part of the physics-gate registry: the maximum of the DKES-style and VMEC finest plotted N_\xi convergence errors must remain below 2.5e-1 against the finest plotted reference before the figure can support the promoted monoenergetic validation claim.

The W7-X imported workflow is audited with:

python examples/bootstrap_current_reference_audit_w7x.py

This script rebuilds a reduced W7-X scan at several NTX resolutions, evaluates the resulting bootstrap-current profile, and writes a publication-ready convergence figure.

The broader VMEC geometry-family transport stress diagnostic is:

python examples/geometry_family_transport_convergence.py --preset production

It discovers local public examples from the surrounding vmec_jax, STELLOPT, and SIMSOPT checkouts and runs a production D11/D31/D33 convergence ladder. The JSON also records D13 so the Onsager quality check is visible. The current artifact includes tokamak, precise-QS QA/QH, QI-style, W7-X EIM/EJM, LHD, HSX, and NCSX-family cases when those inputs are present. This is tracked as NTX convergence breadth; independent-code parity and a reusable W7-X KJM input remain explicit promotion requirements.

It writes:

• docs/_static/geometry_family_transport_convergence.png

• docs/_static/geometry_family_transport_convergence.pdf

• docs/_static/geometry_family_transport_convergence.json

Precise-QS Redl Benchmark

The archived Landreman–Paul precise-QS fixed-field benchmark can be reproduced locally with:

python examples/precise_qs_redl_sfincs_audit.py

This archive-backed audit reads the original SFINCS profiles from the Zenodo bundle, reconstructs the Redl current through both:

• the VMEC-side trapped-fraction path

• the Boozer-side trapped-fraction path

and checks both against the archived SFINCS profile on the same surfaces. On the current local stack, both Redl paths recover the archived interior-window benchmark gate on the fixed-field QA/QH references:

• QA interior max relative error: about 9.3% for the VMEC path and 9.5% for the Boozer path

• QH interior max relative error: about 4.2% for the VMEC path and 4.1% for the Boozer path

This is a fixed-field Redl/SFINCS consistency study. It is intentionally kept separate from the finite-beta and imported NTX+NEOPAX bootstrap-current workflow checks.

Fixed-Field Transport-Matrix Audit

The remaining fixed-field coefficient-side gap is audited with:

python examples/fixed_field_transport_matrix_audit.py

This script runs SFINCS-JAX in RHSMode=3 on the same QA/QH fixed-field reference family and compares L13, L31, and L33 against NTX candidate channels built from D13, D31, and D33.

The present conclusion is narrow but important:

• the benchmark family is now correct

• the SFINCS RHSMode=3 overwrite must be matched exactly through nu_n = nuPrime * B0OverBBar / (GHat + iota IHat)

• archive-backed Landreman/H. Smith bridge factors tighten L13 and L31 substantially once the correct nu_n is used

• current fixed-field L13/L31 relative errors are about 0.12–0.29 on QA and 0.027–0.15 on QH

• the largest unresolved normalization/model gap is now the L33 bridge, with current fixed-field relative errors of about 0.14–0.16

• this is only an RHSMode=3 monoenergetic statement; for the zero-E_r fixed-field bootstrap-current comparison itself, the active no-momentum closure also depends on the temperature-gradient (A2) channel, so the next gating audit is the full RHSMode=2 row-3 thermal closure rather than more retuning of the old L13/L31/L33 bridge plot alone

• the first cached RHSMode=2 QA electron probe now confirms the thermal row-3 bridge itself: reconstructing the closure response from the exact SFINCS whichRHS source gradients and converting it back with the common factor 2 B0OverBBar / sqrt(pi) brings the density- and thermal-source row-3 columns down to about 2.2% and 1.4% relative error at rho = 0.5

• that narrows the remaining fixed-field blocker further: the thermal-source normalization is no longer the leading uncertainty on QA, while the electric-field column and the uncached QH species-resolved probes are still open

• README-level NTX+NEOPAX bootstrap-current promotion should wait until this fixed-field transport-matrix bridge is tighter

Fixed-Field Current Benchmark Status

The archive-backed precise-QS fixed-field bootstrap-current comparison now uses:

• the correct archived QA/QH benchmark family,

• the exact literature profile family used in the archived benchmark,

• fresh NTX-to-NEOPAX scan caches that carry D33_spitzer,

• and an adaptive nu_v support chosen from the actual NEOPAX collisionality range.

The physics motivation is the standard neoclassical hierarchy:

• monoenergetic solvers provide the D11, D13, and D33 response functions for a given flux-surface geometry, collisionality, and radial electric field;

• momentum-restoring closures use those monoenergetic coefficients in a small Sonine moment system to approximate the effect of momentum conservation in the collision operator;

• the bootstrap-current observable is the charge-weighted sum of the corrected species parallel flows.

This is the same separation emphasized by the momentum-correction literature: using monoenergetic databases is efficient, but the correction must be tied to the parallel-flow moment equations rather than to a benchmark-specific output scale. The fixed-field update therefore changed only physics conventions that were independently identifiable in the equations and source interfaces:

• the database bridge uses the consumer convention D11 -> D11 drds^2, D13 -> D13 drds, and D33 -> nu D33;

• the fixed-field stress branch selects the analytic Spitzer conductivity contribution D33_spitzer explicitly, rather than fitting a D33 multiplier;

• the SFINCS comparison converts to the archived flux-surface-averaged FSABFlow/FSABjHat observable using B0OverBBar;

• the corrected parallel-flow routine is treated as a total corrected U_parallel, not as a correction to add to the no-momentum branch.

There is no QA/QH-specific scalar, no per-species current rescale, and no post-hoc fit in the shipped path. The same gate machinery also preserves the integrated W7-X raw-branch transfer, which is why the public database bridge continues to default to raw D33.

The default profile family is now the exact literature benchmark used in the archived precise-QS Redl/SFINCS study: n(rho) = 4.13 (1 - rho^{10}) and T(rho) = 12 (1 - rho^2) in the archived normalized units.

Interpolation matters here, so the benchmark now fixes the interpolation story explicitly:

• SFINCS geometry uses linear interpolation in s = r_N^2 between neighboring VMEC surfaces.

• the fixed-field NTX/NEOPAX comparison now uses the exact literature profile family by default instead of reconstructing those profiles from archived sampled values, which removes one unnecessary interpolation ambiguity.

• the postprocessing map from the 17-point NTX+NEOPAX radial grid back to the archived SFINCS radii is kept as monotone PCHIP by default (NTX_FIXED_FIELD_POSTPROCESS_INTERP=pchip), with a linear override kept for audit runs.

On the cached fixed-field audit, switching that final postprocessing step from PCHIP to linear changes the QA/QH stress metric negligibly, so PCHIP remains the default. Forcing the imported interpax interpolators from cubic to linear and comparing against direct 3D interpolation also leaves the cached current errors unchanged to numerical precision. The remaining mismatch is therefore not dominated by interpolation kernel choice.

The benchmark-side normalization is now anchored to the actual consumer path in the imported database loader:

• D11 -> D11 * drds^2

• D13 -> D13 * drds

• D33 -> nu * D33

The fixed-field current assembly also uses the corrected parallel-flow return directly; that routine returns the total corrected U_parallel, not an increment that should be added to the no-momentum branch. Those two rules close the integrated W7-X handoff, but they leave the precise-QS fixed-field current as a closure stress test rather than a parity claim.

The current archive-backed fixed-field benchmark writes:

• docs/_static/bootstrap_current_fixed_field_validation.png

• docs/_static/bootstrap_current_fixed_field_validation.pdf

• docs/_static/bootstrap_current_fixed_field_validation.json

and the compact report writes:

• docs/_static/closure_validation_report.png

• docs/_static/closure_validation_report.pdf

• docs/_static/closure_validation_report.json

Regenerate these artifacts with:

JAX_ENABLE_X64=1 JAX_PLATFORM_NAME=cpu \
  python examples/bootstrap_current_fixed_field_validation.py
python scripts/build_closure_validation_report.py

The regenerated interior maximum relative errors versus archived SFINCS are:

• Redl QA: 6.86e-2

• Redl QH: 4.06e-2

• NTX+NEOPAX QA: 8.30e-2

• NTX+NEOPAX QH: 9.95e-2

That outcome closes the fixed-field total-current stress gate, but it is still scoped carefully. The continuum 4D drift-kinetic reference can include fuller inter-species linearized Fokker-Planck physics, while the present imported closure applies a low-order momentum-restoring moment model to monoenergetic coefficients. Literature momentum-correction methods are valuable precisely because they are cheap, but they are not guaranteed to reproduce every species-resolved current component coefficient by coefficient. The Redl curve is kept separate because it is an analytic quasisymmetry-mapped bootstrap-current fit, not the same reduced closure path.

The production policy is therefore sharper: no fitted bridge constants, no species-current parity claim, and no broader default closure change unless it preserves the fixed-field QA/QH total-current gate while also preserving the integrated W7-X raw-branch transfer.

The public NTX-to-database bridge therefore defaults to the raw D33 convention used by the integrated W7-X transfer gate. The fixed-field D33_spitzer branch is selected explicitly in examples/bootstrap_current_fixed_field_validation.py and examples/fixed_field_momentum_correction_diagnostic.py; it is a scoped stress model, not the default production convention.

The current diagnostic can also separate the D33 convention used in the transport-side Lij block from the collision-weighted Eij block through NTX_FIXED_FIELD_DIAGNOSTIC_D33_LIJ_MODE and NTX_FIXED_FIELD_DIAGNOSTIC_D33_EIJ_MODE. On the mid-radius QA/QH stress point, coherent raw and coherent Spitzer branches remain better behaved than mixed raw/Spitzer blocks; the mixed probes increase the total-current error and increase the cancellation burden between species currents. This rules out a simple one-block convention swap as a physics fix. Any future closure change must therefore modify the moment equations or observable projection as a whole, not patch only one D33 sub-block.

The next closure investigation should stay small and equation-driven:

1. freeze the total-current gate above as the no-regression baseline;

2. compare the corrected species currents before summing, after the flux-surface-averaged flow observable conversion, so species decomposition errors cannot hide inside a good total current;

3. isolate the drive terms in the solved Sonine vector into density-gradient, temperature-gradient, and electric-field contributions on the same radial points;

4. test any candidate model first as a matrix-level identity or moment-system change, not as an output rescaling;

5. accept the change only if it preserves the raw integrated W7-X transfer and improves QA/QH species-current diagnostics with the same equations.

That order follows the literature lesson from monoenergetic and momentum-restoring closures: once the coefficient bridge and total current are inside tolerance, the remaining discrepancy must be treated as a projected collision/observable decomposition problem, not as an interpolation or scalar normalization problem.

Higher-Order Closure Development Gates

The next closure model is now constrained enough that it should be treated as a physics implementation project rather than another benchmark-fitting exercise.

The active gates are:

• keep the coefficient-side path fixed:

  • monoenergetic Onsager checks stay closed

  • NTX-to-database normalization stays identical to the validated consumer path

• keep the observable map fixed:

  • for the current Sonine basis, U_parallel = n c_0

• recover the current three-moment closure exactly as the P=2 truncation of any generalized implementation

• preserve Onsager/ambipolar structure at finite truncation order

• require transfer:

• preserve the precise-QS QA/QH fixed-field total-current gate

• improve species-resolved closure diagnostics without changing conventions by fit

• do not regress the integrated W7-X workflow

The first implementation stage of that generalized closure is now in place in the imported closure stack: the truncation order is configurable, the raw D13 source moments and D33 Hankel sequences are generated for arbitrary order, and the resulting machinery still recovers the shipped P=2 momentum-correction workflow exactly. The remaining missing physics is the arbitrary-order momentum-conserving collision block, so production runs remain at P=2.

The first implementation step on that lane is now in place in the imported closure stack: the Sonine basis normalization and source-projection algebra are generated programmatically and tested against the current three-moment formulas. That validation path has now been tightened further: the runtime P=2 closure can be reconstructed from generated Sonine coefficients and Hankel moment sequences, and still passes the shipped W7-X momentum-correction regression. The same is now true for the low-order momentum-conserving collisional blocks: they can be generated directly from the standard low-order moment equations, with only the heat-flow basis sign convention differing from the canonical notation used in that derivation. So the remaining work is no longer about recovering the existing algebra. It is about adding physically justified higher-order moments and collisional couplings on top of an exact and tested P=2 base.

A dedicated rebuild audit now tests transfer directly:

• python examples/bootstrap_current_w7x_rebuild_audit.py

That script rebuilds a NEOPAX-format W7-X database from NTX, then compares:

• the shipped external W7-X database,

• an NTX-rebuilt W7-X database using d33_mode="raw",

• an NTX-rebuilt W7-X database using d33_mode="spitzer",

• an NTX-rebuilt W7-X database using d33_mode="conductivity_difference".

On that shipped W7-X momentum-corrected workflow the transfer now closes on the raw database branch:

• shipped external database: 1.18e-12

• NTX-rebuilt W7-X, raw: 6.58e-6

• NTX-rebuilt W7-X, spitzer: 5.77e-1

• NTX-rebuilt W7-X, conductivity_difference: 2.67e+0

The sharper reading is now:

• the integrated W7-X mismatch was dominated by the D13 database handoff, not by the direct monoenergetic solve

• the rebuilt W7-X raw branch now reproduces the frozen reference workflow tightly

• the conductivity-side D33_spitzer - D33 interpretation remains a useful audit clue on the precise-QS fixed-field archive, but it is not the active database-normalization path for the integrated workflow

• the non-promoted follow-up is therefore the precise-QS closure/model gap, not the W7-X database handoff or interpolation

The W7-X picture is now more specific than before:

• the full-resolution in-repo W7-X point and subset coefficient tests still pass against the shipped external database

• direct solver checks at previously worst coefficient points show that both the single-point solve and the scan builder reproduce the frozen benchmark table on the reference grid 25x25x63 to about 1e-6 relative error

• the shipped W7-X integrated workflow is now closed on the rebuilt raw branch

• lower-resolution scans are under-resolved, and blindly increasing the grid does not reproduce the frozen reference monotonically on every point, so the audit is anchored to the reference resolution rather than to a naive monotone-refinement assumption

The next closure step has now been tested explicitly as well. A local Pmax > 2 branch was built by preserving the present low-order closure and adding a diagonal Laguerre-tail damping model on the extra moments. That branch is stable, but it fails the transfer gate:

• P=2: imported W7-X closure error 1.17e-12

• P=4: imported W7-X closure error 4.94e-1

• the same P=4 run was performed against the older raw fixed-field stress artifact and only shifted that order-unity metric by less than one percent

So the current higher-order tail is not an acceptable production extension. It does not provide a transferable closure improvement and immediately regresses the already-validated imported W7-X workflow. The committed artifact for that negative result is:

• docs/_static/closure_pmax_convergence.json

• docs/_static/closure_pmax_convergence.png

• docs/_static/closure_pmax_convergence.pdf

To keep the current closure-model status reproducible as one tracked artifact, the repository now also builds:

• docs/_static/closure_validation_report.json

• docs/_static/closure_validation_report.txt

• docs/_static/closure_validation_report.png

• docs/_static/closure_validation_report.pdf

from:

python scripts/build_closure_validation_report.py

That summary freezes the present interpretation in one place:

• precise-QS Redl vs archived SFINCS passes the independent-code gate

• rebuilt W7-X raw-branch transfer passes the integrated-workflow gate

• fixed-field NTX+NEOPAX passes the scoped total-current closure stress gate

• the diagnostic thermal-source fits are reported as audit evidence only; they are not accepted as a production bridge because fitted fixed-field corrections did not transfer to the W7-X workflow

• the first Pmax>2 tail model remains rejected because it regresses W7-X

End-To-End Bootstrap-Current Workflow

The pure NTX radial-profile workflow is:

python examples/bootstrap_current_from_vmec_or_boozmn.py

That script demonstrates the direct path from VMEC or Boozer input to radial profiles of:

• D11

• D13

• nu_hat * D33

• a compact reduced bootstrap-current response

The shortest NTX + NEOPAX radial-profile workflow is:

python examples/bootstrap_current_with_neopax.py

It writes:

• docs/_static/bootstrap_current_with_neopax.png

• docs/_static/bootstrap_current_with_neopax.pdf

• docs/_static/bootstrap_current_with_neopax.json

CPU And GPU Validation

Run the GPU smoke checks with:

python -m pytest -m gpu -q
python scripts/run_gpu_regression.py --output-json gpu-smoke-results.json

Profile runtime with:

python scripts/profile_runtime.py --backend cpu --output-json runtime-profile.json
python scripts/profile_runtime.py --backend gpu --output-json runtime-profile-gpu.json

Profile the two parallel execution layers with:

python scripts/profile_parallel_runtime.py --output-json parallel-runtime.json
python scripts/profile_multiprocess_runtime.py --backend cpu --workers 2
python scripts/profile_multiprocess_runtime.py --backend gpu --workers 2

For shared GPU systems, use:

export XLA_PYTHON_CLIENT_PREALLOCATE=false

Practical Performance Conclusion

The current measured guidance is:

• use serial batched JAX for small and medium studies

• use the multiprocess lane for larger throughput-oriented runs

Details and figures are in Performance.

NEOPAX Compatibility

NTX-to-NEOPAX compatibility is exercised through:

• tests/test_neopax_adapter.py

• tests/test_neopax_arrays.py

• tests/test_neopax_qi.py

These tests cover:

• HDF5 loading and writing

• pure-array scan mapping

• imported surface scans mapped into NEOPAX normalization

• round-trips through write_neopax_scan_hdf5(...)

Optional External Consistency Studies

When an independent transport workflow such as SFINCS-JAX is available in the local research environment, NTX studies can also be checked against it. Those comparisons are useful for confidence, but they are not required to run NTX or to understand the code.