Physics Gates

NTX uses explicit physics gates so that validation claims are tied to the actual model scope.

These gates separate five different questions:

is the monoenergetic solver algebra correct?
is the database handoff to the closure workflow correct?
does the imported integrated workflow transfer cleanly?
do differentiable geometry and boundary-control workflows match centered finite differences on their claimed scope?
where does the reduced closure model pass as a total-current stress diagnostic, and where does it still stop matching fuller collisional tools?

That separation matters. Without it, a closure-model gap can be mistaken for a solver bug, or a benchmark-specific fit can be mistaken for production physics.

Gate Families

1. Analytical Identities

These are hard structural checks:

Monoenergetic validation summary: the committed validation_summary.json artifact is now a release gate. The maximum of the DKES-style and VMEC finest plotted N_\xi convergence errors must stay below 2.5e-1 against the finest plotted reference. This keeps the promoted methods figure tied to a machine-checked convergence metric.
Onsager symmetry: |D13 + D31| must remain small on converged solves.
Owned-surface coefficient convergence: on the repository-owned analytic Boozer surface, the fast test suite now checks that the D11, D31, and D33 Legendre-resolution errors decrease from N_\xi=6 to N_\xi=8 relative to the N_\xi=10 reference, that the finest fast-lane error remains bounded, and that the same coefficients transfer between the 5x5 and 7x7 angular grids within the current release tolerance.
Constant-field symmetric limit: when B is constant on the Boozer surface, the magnetic-drift source vanishes. The fast test suite therefore requires D11, D31, and D13 to vanish while the parallel-conductivity channel remains positive and equal to the Spitzer branch reported as D33_spitzer.
Spitzer inverse-collisionality normalization: in the same constant-field limit, the fast test suite checks that D33_spitzer scales as 1 / nu_hat. This catches drift-kinetic normalization regressions without needing an external benchmark file.
Constant-field radial-electric-field invariance: in the constant-field limit, sweeping er_hat must not create radial transport or change the parallel-conductivity branch. This guards the radial-electric-field advection term against producing unphysical transport when the magnetic-drift drive is absent.
Boozer Jacobian identity: the Boozer geometry projection must preserve \mathcal J B^2 = B_\zeta + \iota B_\theta together with B^\theta \mathcal J = \iota and B^\zeta \mathcal J = 1 on owned surfaces. This anchors the field normalization used by the drift source, parallel streaming, and imported geometry handoff before any benchmark coefficient is interpreted.
Finite Legendre source projection: the magnetic-drift drive must populate only the k=0 and k=2 source rows with the runtime 2/3 and 1/3 weights, and the parallel-conductivity source must populate only the k=1 row as the physical B. This protects the equation-to-code map before any solve or closure post-processing is involved.
Imported Boozer handedness: VMEC-to-Boozer helper paths must choose the same right-handed Boozer convention as the file-backed loader, so B_\zeta + \iota B_\theta >= 0 before the geometry Jacobian \mathcal J = |B_\zeta + \iota B_\theta| / B^2 is consumed by the solver or imported closure workflow. This protects the sign convention without fitting any transport coefficient.
Operator parameter-derivative consistency: the hand-coded dD_k/dnu_hat and dD_k/depsi_hat blocks used by the implicit-adjoint path must match JAX differentiation of the assembled Legendre-space operator. This catches collisionality and radial-electric-field normalization regressions before they can contaminate sensitivity, inverse-design, or uncertainty-quantification workflows.
Profile interpolant derivative consistency: the imported profile interpolants must give D33 sensitivities with respect to electric-field basis parameters that agree with centered finite differences on a controlled coefficient table. This protects the interpolation layer used by profile inverse design and uncertainty propagation.
Profile-control linear response: scalar and radial-basis profile controls must be identity maps at zero control and exactly linear in their prescribed response matrices. This protects the profile optimization, sensitivity, and uncertainty workflows from hidden nonlinearities in the control-to-force map.
VMEC-JAX boundary edge transfer: the traced fixed-boundary Fourier edge arrays must be forwarded to both the implicit VMEC residual solve and the explicit relaxation solve. This protects boundary-to-output derivatives from accidentally following stale non-differentiated boundary data.
VMEC-JAX to NEOPAX radial metric transfer: the imported field builder must preserve the rho = sqrt(s) radial mapping, axis regularization, enclosed-volume scale, edge major-radius scale, and toroidal-flux normalization before any bootstrap-current or boundary-derivative workflow consumes the field.
NTX-to-NEOPAX field-channel normalization: scan assembly must preserve E_r = E_s * transport_psi_scale while checking the rho, drds, and electric-field table shapes before the monoenergetic coefficients are handed to the imported closure workflow.
Primitive profile force reconstruction: the profile workflow must recover A3 = d ln T / dr and A1 = d ln n / dr - 3 d ln T / (2 dr) + C_E Z E_r before those forces are used in particle-flux or reduced bootstrap-current response calculations.
Charge-symmetric ambipolar cancellation: the profile workflow must return zero charge-weighted particle-flux residual for equal particle-flux responses with opposite charges. This is the local implementation gate for the quasineutral ambipolarity condition sum_s Z_s Gamma_s(E_r) = 0, which sets the stellarator radial electric field outside intrinsically ambipolar symmetry limits.
Primitive transport positivity floor: explicit primitive-profile updates must keep density and temperature finite and positive. The update uses exponential relaxation plus a small floor, so large transport mismatches cannot create unphysical negative thermodynamic state variables.
Prepared derivative-path consistency: the committed derivative-path benchmark must keep the prepared custom-VJP electric-field derivative within 1e-4 relative mismatch of direct reverse-mode on the same prepared surface. The speedup remains reported, but agreement is the release gate.
Exact P=2 recovery: the generated Sonine/Hankel projection must recover the current three-moment closure exactly at P=2.
Low-order collision-block recovery: the active low-order momentum-conserving collisional blocks must be reproducible from the standard low-order moment equations, with only the runtime heat-flow basis sign convention differing from the canonical notation.
Fixed observable map: for the present Sonine basis, the corrected parallel-flow observable remains U_parallel = n c_0.
Source-channel superposition: for a frozen finite-beta stress-radius momentum-restoring matrix, the density/electric, effective temperature, and parallel-electric one-channel solves must reconstruct the full corrected current to roundoff before the dominant channel is interpreted physically.
Intrinsic ambipolarity in symmetric limits: finite-order closure work must preserve the symmetric-limit ambipolar structure emphasized by the Sugama–Nishimura formulation.
Momentum-conservation null mode: the collisional blocks must retain a common-flow null mode so that total parallel momentum is conserved.
Particle conservation: the projected collisional operator must preserve the density invariant and must not generate a spurious source term.
Energy conservation: the projected collisional operator must preserve the energy invariant in the same finite basis used for the closure.
Weighted self-adjointness: the finite-order collision operator should preserve the self-adjoint structure of the linearized Coulomb problem under the appropriate weighted inner product.
Non-negative entropy production: the symmetric collisional form must remain positive semidefinite, following the finite-order constraints emphasized by Sugama–Horton.

These are not benchmark fits. They come directly from the model derivation and from the present closure basis.

2. Differentiability Artifact Gates

These gates protect the end-to-end JAX workflows without overstating their geometry breadth:

Owned analytic geometry-control derivatives: direct AD must match centered finite differences below 2e-4 on the committed three-harmonic analytic-surface audit.
File-backed geometry-control derivatives: the same direct AD/finite difference comparison must stay below 5e-4 on the repository-owned Boozer and VMEC sample surfaces.
Same-coordinate Boozer-file round trip: generated boozmn surfaces must reload on the VMEC half grid and reproduce the in-memory vmec_jax -> booz_xform_jax -> NTX transport coefficients below 1e-6. This protects the radial-coordinate convention used by packed Boozer spectra.
Finite-beta finalized-wout Boozer transfer: optimized finite-beta wout files whose input current-profile representation cannot yet be re-evaluated by the optional differentiable state path must still transform through the finalized VMEC magnetic channels and reload through the direct boozmn backend below 1e-6 transport mismatch. This is a file-backed transfer gate, not a claim of differentiable finite-beta equilibrium-state sensitivities.
Boundary-projected current derivatives: forward-mode derivatives through the optional JAX geometry backends, NTX coefficients, and the integrated current objective must stay below 1e-5 on the committed sample input.
Explicit-relaxed boundary-to-current derivatives: the self-consistent forward-mode QA/QH family must stay below 1e-4; the artifact also reports the ordinary-vs-explicit-relaxed volume agreement so the derivative check is not hiding a branch mismatch.
Implicit-equilibrium derivatives: this remains a monitored stress lane, not a passing gate. The current artifact validates the equilibrium-volume derivative but leaves the Boozer-space and NTX transport observables open.
Bootstrap-current optimization gain: the committed science/application artifact must keep the optimized weighted-current response at least equal to the baseline before the manuscript cites the gain. This is a stress gate, not a broad optimization-design claim.

3. Independent-Code Comparison Gates

These are trust-building comparisons against independent workflows:

Precise-QS Redl vs archived SFINCS: on the interior benchmark window, the Redl reconstruction should stay below 1e-1 maximum relative error.
Fixed-field transport-matrix audits: the archive-backed RHSMode=3 and RHSMode=2 comparisons against SFINCS-JAX are used to localize normalization and closure differences.
Owned finite-beta same-grid coefficients: the finite-beta QA ladder now has a passing normalization-side gate. The maximum same-grid L13/L31/L33 relative difference is required to stay below 1e-1 before any finite-beta profile-current result is interpreted. This is not by itself a current-parity gate when the net current is cancellation-conditioned.
Owned finite-beta RHSMode=1 profile current: direct SFINCS-JAX profile-current decks now use the same finite-beta VMEC wout and analytic profile contract as Redl and NTX+NEOPAX. The committed artifact is a monitored convergence and normalization diagnostic, not a parity gate, until pitch, velocity, radial, and collisionality-normalization ladders pass.
Owned finite-beta source-channel reconstruction: the finite-beta source decomposition is a stress gate on the linear momentum-restoring system: one-channel solves must reconstruct the full corrected current below 1e-8. The resulting dominant-channel statement is diagnostic, not a fitted current correction.
Owned finite-beta temperature-source response: the source-channel sidecar also stores the Redl density and temperature target terms on the same current observable. The high-order Redl/NTX effective-temperature response ratio is a monitored stress metric, not an acceptance gate and not a runtime fit.
Owned finite-beta profile source-response: the source-response sidecar extends the effective-temperature channel measurement over the finite-beta profile. Its radial response span and correlations with Redl collisionality, trapped fraction, epsilon, and L32 are monitored diagnostics for a future physics-derived closure, not fitted correction factors.
Owned finite-beta closure-target driver audit: the closure-target sidecar ranks local neoclassical drivers for the measured temperature-source response before any runtime model is proposed. The current artifact selects the Redl geometry factor epsilon as the strongest single driver and records that diagnostic regressions are not applied as production corrections.
Owned finite-beta profile-current observable: the finite-beta bootstrap-current profile remains a monitored stress diagnostic, not a parity gate. The current artifacts keep the net-current residual, the applied-versus-needed momentum correction, and the species-correction cancellation scale visible because the stress radius is dominated by electron/ion cancellation.
Owned finite-beta current conditioning: the coefficient ladder is also compared with the species-current L1 scale. The current artifact reports that the stress-radius net current needs about 1.1e-3 coefficient precision for a 1e-1 current gate, while the completed coefficient ladder is order 2e-2.
Owned finite-beta resolution floor: the stress-radius point has also been rerun at 35 x 43 x 48 and with a tighter VMEC harmonic cutoff. The coefficient floor stays near 2.05e-2, so angular resolution and harmonic truncation are not treated as the closure fix.
Owned finite-beta production ladder: the six production same-grid radius/collisionality points all stay below 2.07e-2 coefficient difference. The current-conditioned precision gap remains larger than the coefficient floor, so the coefficient-resolution lane is localized rather than a broad whole-profile failure.
Owned finite-beta closure quadrature: higher Sonine order is now monitored together with velocity quadrature. The current corrected-field artifact has zero stress-radius current-gate passes; the best stress point remains above 1e-1, so this remains a reduced-closure stress diagnostic. This keeps the next physics step honest: profile-current diagnostics must tighten the conditioned uncertainty before a new reduced-closure term is promoted.

These comparisons are useful because they check the physical bridge to well-established neoclassical calculations without redefining NTX as “whatever matches another code.”

4. Integrated-Workflow Transfer Gate

The strongest imported-workflow gate is the rebuilt W7-X bootstrap-current workflow.

The active acceptance target is:

Monoenergetic validation summary: committed validation-summary finest plotted coefficient error <= 2.5e-1 on both the DKES-style and VMEC surfaces.
Prepared derivative path: maximum prepared-vs-direct derivative mismatch <= 1e-4 on the committed derivative-path benchmark.
Differentiable geometry path: the promoted finite-difference agreement gates above must pass for the analytic, file-backed, boundary-projected, and explicit-relaxed artifacts; the implicit-equilibrium artifact is monitored separately until it closes.
Geometry-family transport convergence: the public VMEC example-family production D11/D31/D33 ladder must keep its maximum last-step relative change <= 5e-1; D13 and the normalized Onsager residual remain visible in the artifact before any broad geometry-family parity claim is promoted.
W7-X rebuilt raw branch: best observed maximum relative error <= 2e-2 against the frozen reference profile.

This gate is important because it validates the full path:

NTX monoenergetic tables -> database normalization -> imported closure workflow.

5. Closure Stress Tests

The fixed-field precise-QS NTX+NEOPAX current comparison is a scoped total-current stress gate, not a release gate for the monoenergetic solver and not an independent species-current parity claim.

The current interior QA/QH total-current errors now pass the documented 1e-1 stress tolerance after applying only physics-normalization choices that are already part of the closure model:

the archived SFINCS observable is compared through its flux-surface-averaged parallel-flow convention,
the reduced fixed-field branch uses the explicit low-order Spitzer-conductivity block,
the closure grid uses the P=2 low-order moment system.

No fitted bridge constants, benchmark-specific scale factors, or hard thresholds are used in the current fixed-field branch.

The current compact closure report records:

Redl fixed-field QA/QH maximum interior errors of 6.86e-2 and 4.06e-2
NTX+NEOPAX fixed-field QA/QH total-current stress errors of 8.30e-2 and 9.95e-2
rebuilt W7-X raw-branch integrated transfer error of 1.83e-2

Those numbers are intentionally interpreted together. The fixed-field stress case compares a reduced momentum-restoring closure built from monoenergetic coefficients against a fuller drift-kinetic reference, while the integrated W7-X transfer checks the actual database normalization and imported workflow used by NTX. The low-order Spitzer-conductivity fixed-field branch does not transfer to the imported W7-X database convention, so the W7-X release gate remains the validated raw branch. A broader closure default is promotable only if it preserves both the precise-QS total-current gate and the integrated W7-X raw-branch transfer gate.

The owned finite-beta closure lane is tracked by additional artifact gates:

same-grid finite-beta coefficient normalization: passing, with current maximum relative difference about 2.1e-2;
finite-beta profile-current observable: monitored, with current stress-radius total-current relative difference about 2.2e-1;
finite-beta Boozer-field normalization: file-backed B00 profiles are evaluated on normalized radius and converted to physical radial derivatives with the VMEC minor radius;
finite-beta species-cancellation scale: monitored, with current stress-radius residual about 2.5e-3 of the species momentum-correction L1 scale.
finite-beta production coefficient floor: monitored, with the current production stress probe still much looser than the cancellation-conditioned coefficient target.
finite-beta production radial/collisionality ladder: monitored, with all production coefficient differences below 2.07e-2 but the maximum current-conditioned precision gap still well above unity.
finite-beta RHSMode=1 profile current: the direct-profile amplitudes remain monitored, while the companion high-Nxi even/odd pitch stress gap is accepted at 1.32e-1 under the 1.5e-1 reduced-closure tolerance.
finite-beta closure quadrature: monitored, with zero current-gate passes and a highest-quadrature largest-order stress difference near 1.3e-1 at the default stress radius.
finite-beta profile source response: monitored, with the current high-order temperature response multiplier spanning 0.765 to 1.349 over the profile.
finite-beta closure-target driver ranking: monitored, with the current best single driver epsilon, absolute Pearson correlation 0.970, and no runtime correction applied.

This is the current physics interpretation: the coefficient-side bridge is no longer the leading suspect for the finite-beta QA stress case, and the accepted result is a reduced profile-current/source-response stress benchmark under strong species-current cancellation. Future closure work may improve that observable, but any runtime change must avoid device-specific scale factors and must not regress the fixed-field precise-QS or integrated W7-X gates.

Current Policy

The gate registry is exposed in the public API:

ntx.physics_gates.physics_gate_registry()
ntx.physics_gates.evaluate_artifact_gates(...)
ntx.validation.physics_gate_registry()
ntx.validation.evaluate_artifact_gates(...)

To inspect the tracked artifact-backed gates locally:

python scripts/check_physics_gates.py

The script reads the tracked benchmark artifacts in docs/_static/ and reports which gates are:

pass/fail acceptance gates,
test-backed analytical gates,
or monitored stress metrics.

A compact companion report is built by:

python scripts/build_closure_validation_report.py

This report packages the same tracked artifacts into one summary figure and JSON/Markdown set. It is useful when reviewing the current model-family status without rereading the individual benchmark outputs one by one.

Acceptance Rules For Closure Work

Any higher-order closure change must satisfy all of the following:

keep the monoenergetic coefficient-side invariants unchanged
keep U_parallel = n c_0
recover the present three-moment system exactly at P=2
preserve finite-order symmetry structure as far as the projected model allows
preserve the fixed-field precise-QS total-current closure stress gate
improve species-resolved fixed-field closure parity only if it also preserves the integrated W7-X workflow
show controlled convergence in Pmax on the precise-QS QA/QH family
avoid any regression in the integrated W7-X workflow when Pmax changes

That is the standard for physically defensible closure work in this repository.

Current Higher-Order Closure Status

The first higher-order validation stage is now in place in the imported closure stack:

configurable Sonine truncation order in the closure grid
generated raw D13 source-moment sequences for arbitrary order
generated raw D33 Hankel moment sequences for arbitrary order
exact recovery of the present P=2 closure
exact recovery of the active low-order momentum-conserving collision blocks from the standard moment equations

That stage is intentionally incomplete. The production runtime still stops at P=2 because the arbitrary-order momentum-conserving collision blocks have not yet been derived and validated. This is a physics boundary, not an implementation oversight.

The first higher-order tail experiment has now also been run against the committed gate set. It keeps the current low-order closure unchanged and adds a diagonal Laguerre-tail damping model on the extra moments. That branch is numerically stable, but it is not physically acceptable: the first Pmax=4 run barely moves the precise-QS stress metric while regressing the imported W7-X closure error from 1.17e-12 at P=2 to about 4.94e-1. That result is now pinned in docs/_static/closure_pmax_convergence.json and is treated as a rejected higher-order branch rather than as production physics.

Additional Literature Requirements

Beyond the existing acceptance targets, the literature imposes a few stronger requirements on any generalized closure:

the finite-order system should preserve Onsager symmetry rather than recover it only asymptotically
intrinsic ambipolarity should remain exact in symmetric limits at each truncation order
particle and energy conservation should remain exact collisional invariants of the projected system
the collisional operator must conserve momentum exactly and should not break the common-flow null space
the projected collisional form should remain self-adjoint under the weighted inner product used by the finite-order derivation
the symmetric collisional form should not generate negative entropy production
convergence in Pmax should be demonstrated on a stress-test family, not only on an integrated workflow that already closes at P=2

These are now treated as first-class design requirements for the higher-order closure lane.