Record coupled convergence results, virial limitations and validated model slices

experiments/COUPLED_CONVERGENCE_STUDY_2026-09-19.md

@@ -1,5 +1,32 @@
 # Coupled harmonic-surface convergence study
 
+The clearest measured improvement is the existing gravity-Schur inverse:
+at matched saved states and a checked full linear tolerance of .003, total
+construction/solve/check cost falls from 53.31 to 31.17 seconds for n=3,J=0,
+and from 118.62 to 82.31 seconds for n=1.5,J=.1. These are frozen linear
+improvements, not demonstrated complete-model speedups. The new surface/scalar
+Schur correction is algebraically effective but is not the best total-cost
+candidate in these tests and can worsen finite-step behavior.
+
+The live rotating n=3 comparison also gives a substantive improvement:
+existing stellar LDU with gravity refinement reaches a 12.687-times smaller
+residual than gravity refinement alone after ten updates, at 14.593% more
+Newton time. The energy h-pressure virial improves from 7.184e-5 to 1.811e-5,
+but the full virial milestone is still unmet and small-step stagnation returns.
+Density remains independent and no positivity enforcement is introduced.
+
+Nonlinear progress is limited by more than Krylov accuracy. The n=2 control
+stalls with positive sampled density and both virials below 1e-5. Its gravity
+trial-path correction buys an initial improvement but no durable recovery.
+At n=3, measured weak coupled direction differences are dominated by changes
+in the surface monopole compensated by interior fields. Better treatment of
+this coupled response is a stronger next hypothesis than positivity repair.
+
+Physical xz/xy slices are implemented, exported from unchanged saved fields,
+checked at two display resolutions and visually inspected. The rotating
+n=1.5 model is smoothly oblate but remains unconverged and misses the virial
+milestone. Images, linear histories, raw results and audits are linked below.
+
 The user has deferred positivity enforcement. This study keeps density an
 independent Q2 field and retains the simultaneous all-m degree-four harmonic
 surface/interior system. The primary milestones are useful convergence at
@@ -29,7 +56,7 @@ claims require independently applied full-J residuals; nonlinear claims use
 common stopping thresholds plus physical diagnostics, not residual alone.
 Report scalar-border forcing separately from the unbordered equations.
 
-The slice feature will evaluate physical geometry and independent fields,
+The slice feature evaluates physical geometry and independent fields,
 show the material surface at true scale, retain signed density, and separate
 outside-domain points from valid interior samples. It must not silently turn a
 reference-coordinate cut into a physical planar cut.
@@ -37,10 +64,10 @@ reference-coordinate cut into a physical planar cut.
 Builds and expensive numerical cases run serially. The existing campaign
 runner records exact source, binary, mesh, arguments, saved states and output
 hashes. Initial evidence directory:
-`../../diagnostics/coupled_convergence_2026-09-19/screen_v1`.
+`../../../diagnostics/coupled_convergence_2026-09-19/screen_v1`.
 
-Results and any adaptive extensions will be recorded below before finalizing
+Results and the specifications written before each adaptive extension are
-the study. Defaults and the physics-facing API are unchanged.
+recorded below. Defaults and the physics-facing API are unchanged.
 
 ## Completed nonlinear controls
 
@@ -296,7 +323,7 @@ Our inference from this bound and the isolated steady virial identity is:
 at M=M_LE(K), W+3 integral(P)>=0, while nonzero angular momentum at finite
 moment of inertia requires T>=J^2/(2I)>0. Thus 2T+W+3 integral(P)=0 is
 impossible. A rotating n=3 family needs M>M_LE(K); at fixed M=1 this means
-K below the driver's nonrotating critical value. This necessary condition
+K below the exact continuum nonrotating critical value. This necessary condition
 does not itself construct a rotating equilibrium or choose its rotation rate.
 Fixing an additional central density cannot repair incompatible physical
 specifications; a central artificial force could instead mask them.
@@ -307,7 +334,7 @@ negative density, gravity approximation and central forcing can bypass its
 assumptions. Numerical Lane–Emden integration also makes the driver's K only
 approximately critical. Independent Lane–Emden integration gives
 M_LE=0.9999999918534539 for the recorded K, allowing only
-T/|W| <= 2.7155e-9 under those continuum assumptions. Thus the actual rounded
+T/|W| <= 2.7155e-9 under those continuum assumptions. Thus the recorded numerical
 parameters permit negligible, rather than literally zero, rotational support.
 A small discrete virial in such a case would require careful interpretation.
 
@@ -317,3 +344,333 @@ and isolated on `research/n3-compatible-family-20260919`: reduce K by one
 percent, leave M=1, omit the central border and prescribe J=.035. This tests
 a necessary physical compatibility condition, not a preconditioner speedup
 or a guarantee of equilibrium or a particular fraction of critical rotation.
+
+## Completed frozen linear comparisons
+
+All eleven retained-artifact audits pass, including independent arithmetic
+checks of saved corrections, fresh full-J actions and endpoint defects.
+This does not independently reassemble J or certify every recurrence norm.
+
+Each arrow is independent baseline → candidate at the same frozen state and requested tolerance within that case. The true relative defect is ‖Jp+F‖/‖F‖, from the fresh endpoint check. The ordinary relative tolerance is 0.003; the explicitly marked tight case requests 1e−7. A speedup is reported only when both endpoints pass the requested true gate. Times are seconds, with rounding only for display.
+
+| Case | Iterations B→C | True relative defect B→C | True gate B/C | Total seconds B→C | Candidate construction | Full J calls B→C | Equal-gate speedup |
+|---|---:|---:|:---:|---:|---:|---:|---:|
+| `n2_late_gravity` | 105→83 | 2.62169821e-03→2.53227246e-03 | pass/pass | 51.1251→50.2194 | 1.7656 | 106→84 | 1.018× |
+| `n2_late_surface` | 105→300 | 2.62169821e-03→5.67029124e-03 | pass/fail | 51.6185→244.6878 | 21.2548 | 106→657 | not applicable |
+| `n2_late_combined` | 105→109 | 2.62169821e-03→2.60837250e-03 | pass/pass | 51.4773→117.3489 | 24.4227 | 106→273 | 0.439× |
+| `n2_late_tight_combined` | 300→300 | 1.87757546e-04→1.21976551e-04 | fail/fail | 145.5541→283.3130 | 24.7723 | 303→657 | not applicable |
+| `n3_late_combined` | 99→41 | 2.82583089e-03→2.77409778e-03 | pass/pass | 53.1688→65.6294 | 27.7166 | 100→139 | 0.810× |
+| `n1_rotating_late_combined` | 63→28 | 2.97251190e-03→2.02497346e-03 | pass/pass | 29.9344→44.3827 | 22.3112 | 64→111 | 0.674× |
+| `n1p5_rotating_late_combined` | 246→95 | 2.99226031e-03→2.99968978e-03 | pass/pass | 117.9250→101.7603 | 23.2647 | 248→245 | 1.159× |
+| `n2_late_ldu_gravity` | 105→78 | 2.62169821e-03→2.80557346e-03 | pass/pass | 51.4910→60.0450 | 2.0900 | 106→79 | 0.858× |
+| `n3_late_ldu_gravity` | 99→41 | 2.82583089e-03→2.65862364e-03 | pass/pass | 53.1904→35.2005 | 2.6098 | 100→42 | 1.511× |
+| `n3_late_gravity` | 99→46 | 2.82583089e-03→2.59308753e-03 | pass/pass | 53.3147→31.1652 | 2.1394 | 100→47 | 1.711× |
+| `n1p5_rotating_late_gravity` | 246→137 | 2.99226031e-03→1.99325392e-03 | pass/pass | 118.6171→82.3113 | 1.7997 | 248→138 | 1.441× |
+
+`gravity` means gravity-Schur on the independent base; `surface` means surface/border Schur on the independent base; `combined` means surface/border Schur on the gravity-Schur base; `ldu_gravity` means stellar LDU plus gravity Schur. The rotating cases are identified by their input case names; this note does not reconstruct their physical metadata from external artifacts.
+
+**Cost scope.** Total = preconditioner construction + normalization binding + Krylov setup + Krylov solve + one fresh true-residual check. Construction includes coarse-Schur setup. Internal Schur Jacobian work is already included in inverse/Krylov time and must not be added again. Total excludes initial model/context setup, separate diagnostic inverse/Jacobian action checks, nonlinear trial sampling, and output observers. These are cold one-right-hand-side measurements, so they do not establish a benefit from future cache reuse or amortization. The independent baselines were freshly timed for each pair; variation across those timings is visible, but there are no statistical repeats or confidence intervals.
+
+Full J calls count outer Krylov actions + coarse-Schur setup actions + full J actions inside Schur inverse applications + the fresh endpoint check. They exclude separate diagnostic checks and lower-level component operator work. Therefore they are a useful work counter, not a replacement for elapsed time. Restart bookkeeping can make outer J actions exceed the iteration count.
+
+
+Gravity-only saves 41.54% for n=3 and 30.61% for rotating n=1.5. The n=2
+saving is only 1.77%, too small for a robust timing claim from one pair.
+LDU improves n=3 over default but is slower than gravity-only. The new coarse
+wrapper pays 20-26 seconds of setup and an additional full J per inverse
+application. Fewer outer iterations can therefore cost substantially more.
+
+The tight n=2 endpoints improve within the budget, but neither passes 1e-7.
+All n=2 directions with raw-trial samples have the same largest sampled
+passing alpha=1/256; approximately
+90.18% of the small-step squared Taylor remainder is Poisson. Its measured
+quadratic scaling supports finite curvature over that range. More accurate
+linear solutions have not enlarged the sampled usable step range. These
+finite-budget endpoints are not demonstrated residual floors.
+
+The rotating n=1 candidate leaves the pressure-preparation restriction
+unchanged. The rotating n=1.5 candidate leaves its largest sampled acceptable
+alpha at 1/16. Gravity-only n=3/n=1.5 followups omit raw trials and establish
+linear cost benefits only. Full cost, gate, setup and trial tables are in
+[FINAL_INTERPRETATION.md](../../../diagnostics/coupled_convergence_2026-09-19/linear_analysis/FINAL_INTERPRETATION.md).
+The [linear histories](../../../diagnostics/coupled_convergence_2026-09-19/figures/linear_rates/frozen_linear_rates.pdf)
+distinguish reported recurrence histories from checked endpoint defects.
+
+## Measured weak coupled response
+
+At the common n=3 frozen state, baseline, combined and LDU directions all
+pass eta=.003 and have merit slopes within 8e-6 relative of -||F||^2. Nevertheless,
+combined increases the normalized surface-direction norm from .0681146 to
+.113440 and reduces the largest sampled passing alpha from 1/4 to 1/16.
+LDU reduces that norm to .0287899, retains alpha=1/4 and improves its trial
+residual ratio from .702686 to .674223. Full-step ratios are 7.42157,
+14.7443 and 2.77979, respectively.
+
+Saved-vector analysis measures complete direction differences of 58.44% and
+61.89% of baseline norm but action differences of only .3197% and .3364%
+of ||F||. Response per unit difference norm is 183-184 times smaller than
+along the baseline direction, in the same normalized metric. This measures
+two weak directions, not a condition number or an exact nullspace.
+
+Roughly 43% of each squared normalized difference is surface, 34% potential
+and 14% density. Of the surface difference alone, 97.67% and 96.77% are l=0.
+The signed monopole is -.057083 for baseline, -.104359 for combined and
+-.00681011 for LDU. This is a coupled radial-size/field response, not mainly
+translation or high-degree roughness. Freezing the monopole is premature:
+radius is physical and this control already has a central phase constraint.
+
+Combined lowers its final surface/scalar defect/||F|| from 4.64933e-4 to
+1.07519e-6 while worsening trials. LDU permits 9.45535e-4 there but has the
+better quarter-step result. Per-application coarse recovery alone does not
+select a good finite Krylov direction. The n=3 combined coarse matrix's
+reported reciprocal condition is 1.31320e-9, not the conditioning of full J.
+These coarse validation scalars are producer FEM observations, separate from
+the independently audited endpoint vectors.
+
+For e_i=Jp_i+F, the common gate bounds ||J(p_c-p_b)|| by ||e_c||+||e_b||;
+it does not bound ||p_c-p_b|| without inverse information. This motivates
+coupled step control and a better approximate field response. The measured
+weak directions come from the centrally constrained nonrotating control;
+their magnitude and modal structure must be rechecked in the unbordered
+rotating family before treating them as its demonstrated mechanism. Full identities,
+modes and provenance are in the
+[direction comparison](../../../diagnostics/coupled_convergence_2026-09-19/n3_direction_difference/README.md).
+
+## Physical slices and display refinement
+
+The optional diagnostic exports physical xz/xy cuts, independent density and
+enthalpy, and the actual deformed material boundary. Other planes and offsets
+are available. Element-owned triangles preserve DG traces; exterior points
+remain masked. Deformation is not exaggerated and signed values are retained.
+[MODEL_SLICES.md](MODEL_SLICES.md) documents use and geometric limitations.
+
+Four replay cases export final n=2,J=0 and n=1.5,J=.1 states at four/eight
+subdivisions. All four retained-artifact audits pass, including source-state
+provenance and unchanged source fields. Both planes were rendered at common
+axes/color ranges on a 512-by-512 scalar raster and inspected visually.
+
+| Model / plane | Area change | Signed 2D density integral change | Signed 2D h integral change | Boundary length change |
+|---|---:|---:|---:|---:|
+| n=2 / xz | .12333% | .07667% | .07036% | .03065% |
+| n=2 / xy | .12333% | .07667% | .07036% | .03065% |
+| n=1.5, J=.1 / xz | .12495% | .00319% | .08797% | .03165% |
+| n=1.5, J=.1 / xy | .12395% | .01249% | .07838% | .03088% |
+
+These relative absolute changes concern displayed straight triangles, including
+any overlaps, not exact curved-FEM integrals or 3D mass/virials. Sampled chord
+errors decrease about fourfold; axial surface extents agree. Broad shape and
+central concentration are stable. Small seams from independently triangulated
+curved faces remain a documented display limitation.
+
+The rotating meridional cut has equatorial extent approximately +/-1.12084
+and polar extents -.988807 and +.988480. It is smoothly oblate; the equatorial
+cut is approximately circular. The north/south difference is retained.
+Its refined meridional sampled density minimum is -8.59e-4, without clipping.
+The n=2 outline is near spherical at radius 1.0049. Neither image establishes
+equilibrium; only n=2 meets the recorded virial milestone. Exact comparisons
+are in [SLICE_REFINEMENT_SUMMARY.json](../../../diagnostics/coupled_convergence_2026-09-19/SLICE_REFINEMENT_SUMMARY.json).
+
+
+## Completed rotating n=3 field-feedback comparison
+
+Both compatible-family runs complete ten accepted updates and pass the
+retained-artifact audit. They share n=3, J=.035, K factor=.99, no central
+constraint, all-m L4/Q2, the gravity-curvature trial path and eta=.03. The
+initial completed residual is .101333855231 and the nonlinear target is
+1e-12. Only the inverse differs. Neither converges to that target.
+
+| Quantity | Gravity-Schur | Stellar LDU + gravity-Schur |
+|---|---:|---:|
+| Final normalized residual | 1.64730591e-4 | 1.29842469e-5 |
+| Newton seconds | 918.881 | 1052.972 |
+| Linear seconds / iterations | 348.441 / 534 | 335.399 / 410 |
+| Trial preparation seconds | 477.771 | 621.957 |
+| Final accepted alpha | 1/16 | 1/64 |
+| Energy h-pressure virial | 7.18429e-5 | 1.81141e-5 |
+| Force h-pressure virial | 5.23757e-5 | 2.90028e-6 |
+| Energy density-pressure virial | 6.96335e-5 | 3.51558e-5 |
+| Force density-pressure virial | 5.01663e-5 | 1.41415e-5 |
+| Absolute mass error | 5.45536e-5 | 3.37148e-6 |
+| EOS density RMS / sampled density scale | 3.99773e-4 | 4.00529e-4 |
+| Bernoulli RMS / sampled h scale | .00408345 | .00372207 |
+| Hydrostatic-gradient RMS (model units) | .656446 | .588702 |
+| T/abs(W) | .00497575 | .00497421 |
+
+LDU produces a 12.687-fold lower residual after the same update budget, at
+14.593% more Newton time. Total linear time decreases 3.743%, while trial
+preparation rises 30.179%. These are evolving trajectories, not a speedup
+to a common converged model. Every reported full linear gate passes. All
+rejected trials fail sufficient decrease; neither run has a pressure or
+geometry rejection. q18 sampled density remains positive in both, without
+any positivity repair. This is not a global positivity certificate.
+
+The LDU trajectory makes its major gain by update seven, reaching
+1.30261014e-5 with a full step. Three further updates reduce that only .3213%,
+at alpha=1/64. Its final squared residual is 36.500% Poisson, 34.432%
+hydrostatic, 20.234% surface and 6.742% mass. The gravity-only endpoint is
+80.254% hydrostatic and 10.967% mass. Field feedback is a useful live
+improvement in this configuration, but does not remove the small-step stall.
+
+The q14/q18 energy h-pressure virials differ by less than 8e-14 in both
+runs; this is a quadrature check, not a mesh-convergence result.
+
+The LDU force h-pressure virial passes 1e-5, but **the model does not meet the
+virial milestone overall**: energy h-pressure and both density-pressure
+virials fail. Its signed h-force result is -2.90028e-6; signed h-energy is
++1.81141e-5. Their gap is about 2.10144e-5, consistent with the separately
+reported gravity-energy discrepancy. Changing from h-pressure to
+rho-pressure shifts the signed virials by about +1.70418e-5. Reporting only
+the passing force/h diagnostic would conceal these consistency errors.
+
+The gravity-energy discrepancy remains about 2e-5 in both trajectories,
+and EOS density RMS barely changes despite the large algebraic improvement.
+This motivates separate checks of gravity/pressure consistency and spatial
+discretization after improving the coupled solve. It does not prove a mesh
+error floor: neither state solves the discrete equations, and this pair does
+not vary mesh or field order. The finite-element closure tests a projected
+EOS relation; a small algebraic closure norm alone is not pointwise EOS
+accuracy. No exterior-only cause is inferred from these energy diagnostics.
+
+At fixed density, gravity and rotation, any pressure-only change shifts both
+signed virials equally. Their 2.10144e-5 separation therefore implies a best
+possible maximum absolute error of at least 1.05072e-5 under such a shift.
+Pressure repair alone cannot make both diagnostics pass in this frozen state.
+This is not a bound on a newly solved or refined model.
+
+A useful pressure-consistency identity for the present polytrope is
+P(rho)-P(h)=(h/n)[rho-rho_EOS(h)]+D, with D>=0 for nonnegative fields.
+Current DGQ2 closure tests do not generally contain the H1Q3 h field, so even
+zero weak closure does not cancel the linear integrated pressure term.
+Compatible test-space inclusion would cancel it under the same quadrature,
+but the convex remainder, quadrature difference and finite residual remain;
+near vacuum that remainder is not uniformly quadratic. This is an untested
+consistency hypothesis, not evidence for a particular order change or a
+reason to derive density from h. The derivation and scope are in the
+[pressure-moment note](../../../diagnostics/coupled_convergence_2026-09-19/PRESSURE_MOMENT_NOTE.md).
+
+Angular velocities are .401764 and .401388 in model units. Neither is a
+calibrated fraction of critical rotation. The compatible physical inputs
+make this a meaningful rotating test; changing K and removing the central
+border are shared by both runs and are not counted as a preconditioner gain
+against the earlier n=3,J=0 screen.
+
+Final xz/xy slices were rendered and inspected for both runs. They show strong
+central concentration and modest oblateness. These n=3 exports use four
+subdivisions only; the separate n=2/n=1.5 display-refinement check must not be
+misrepresented as a refinement test of these n=3 images. The complete results,
+trial accounting, states and physical metrics are in
+[N3_COMPATIBLE_RESULTS.md](../../../diagnostics/coupled_convergence_2026-09-19/N3_COMPATIBLE_RESULTS.md)
+and its adjacent JSON.
+
+## Architecture and interpretation for the next investigation
+
+The library fields, orders, all-m L4 surface, normalization and physics-facing
+API remain unchanged. No clipping, logarithmic density, derived-density
+replacement or new positivity acceptance gate was introduced. The new coarse
+inverse is an experiment-only frozen policy. It uses generated row/column
+partitions and an explicitly unbordered base inverse; compile-time concepts
+check structural contracts, while generation/dimension/rank checks guard facts
+known only after preparation. Changed Jacobians require reconstruction.
+
+Checked restart support is separated from read-only diagnostic observation.
+The context's explicit diagnostic initializer validates compatible finite
+physical coordinates, prepares and refreshes before commit, clears stale
+warm starts and rolls back on failure. An unconverged snapshot requires an
+explicit experimental override. None of this silently accepts an invalid
+model or changes the physical equations.
+
+The current evidence supports the following order of work:
+
+1. Retain gravity-Schur as the frozen linear-cost comparator and stellar
+   LDU plus gravity as the better live candidate in the tested rotating n=3
+   configuration. That live result is conditional on its gravity-curvature
+   trial path; it does not establish the best raw-Newton default. Candidate
+   iteration counts alone are insufficient. Do not promote the new surface
+   wrapper on this evidence.
+2. Investigate the weak coupled radial-size/field response and finite-step
+   curvature. A coupled trust region or regularized step with a physical
+   displacement scale is a plausible swappable experiment. Keep radius free,
+   keep surface/interior simultaneous and evaluate the full residual and both
+   virials. The data do not yet select a regularization strength or prove
+   this remedy works.
+3. Improve the approximate material response in controlled stages: exact local
+   DG density mass inversion and stronger enthalpy mass inversion are narrower
+   candidates before a more expensive EOS-aware material/gravity Schur solve.
+   The existing material inverse already includes the h-to-density derivative;
+   claiming it is missing would be incorrect. This remains an independent
+   density formulation. See [FIELD_COUPLING_REVIEW_2026-09-19.md](FIELD_COUPLING_REVIEW_2026-09-19.md).
+4. Define a compatible n=3 rotating family and calibrate dimensionless rotation
+   before targeting 50% critical. At fixed M and K, n=3 homology changes J with
+   scale; changing input J alone is not a calibration of critical fraction.
+   This physical parameter issue is separate from the n=2 numerical stall.
+
+A projected surface-equipotential equation and native lower harmonic degree
+were reviewed as possible future operator studies but were not implemented
+or tested here. They change the discrete system. In particular, a surface
+potential derivative must respect the actual ALE pullback/field transport;
+substituting an effective-gravity derivative without that analysis would not
+be sound. The present mechanical surface equation and pressure-query guards
+are retained.
+
+
+## Validation, artifacts and reproduction
+
+Release builds of the diagnostic and targeted test executables pass. The
+new coarse inverse passes 70 assertions in nine cases, including typed
+normalization/partition behavior and algebraic recovery. The transactional
+initializer passes 71 assertions in three real-FEM cases. Pure slice geometry
+controls pass; all 14 slice plotting/comparison tests pass, including after
+the final label/bounds fixes. The artifact auditor passes 11 controls, and
+both convergence plotters pass 11 tests each with actual rendering enabled.
+No unrelated full-suite claim is made.
+
+All 24 campaign cases pass retained-artifact verification: five initial
+nonlinear controls, two matched gravity-path restarts, eleven frozen inverse
+comparisons, four unchanged-state slice replays and two live n=3 controls.
+A passed artifact audit can describe a failed linear gate or an unconverged
+model; it certifies the stated records and accounting, not scientific success.
+The [study index](../../../diagnostics/coupled_convergence_2026-09-19/STUDY_INDEX.json)
+records producer revisions and hashes of all six audit files.
+
+Numerical campaigns and heavy builds/audits/rendering were serialized.
+Each campaign retains exact arguments, clean producer commit, private copied
+executable, build settings, mesh/input hashes, logs, saved states and output
+hashes. Source-provenance commits differ because followups were declared and
+committed as evidence accumulated. Later documentation/plotting edits do not
+change the copied numerical executables. Timings have no statistical confidence
+intervals and are not portable hardware benchmarks.
+
+The integration branch is `research/coupled-convergence-study-20260919`.
+Separate retained branches cover the linear coarse inverse, slice exporter,
+n=3 compatible family, gravity-only attribution and live field feedback.
+The original programming checkout is unchanged. The report and case manifests
+are tracked; large artifacts are outside the source checkout in the evidence
+folder. Production defaults, physical field orders and positivity handling
+remain unchanged.
+
+Campaign manifests in this directory are `convergence_screen_cases_2026-09-19.json`,
+`convergence_gravity_path_cases_2026-09-19.json`,
+`convergence_linear_cases_2026-09-19.json`,
+`convergence_linear_followup_cases_2026-09-19.json`,
+`convergence_slice_cases_2026-09-19.json` and
+`n3_compatible_family_cases_2026-09-19.json`. Run `run_plateau_campaign.py`
+from the matching clean source revision, supplying that manifest, source,
+build, mesh and a new output directory. Predecessor paths in restart/replay
+manifests must resolve to their recorded saved states. The runner deliberately
+refuses to overwrite campaigns or use modified tracked source.
+
+Review artifacts:
+
+- [Rotating n=3 meridional slice](../../../diagnostics/coupled_convergence_2026-09-19/figures_n3_v2/n3_J0p035_K0p99_ldu_xz.png)
+  and [equatorial slice](../../../diagnostics/coupled_convergence_2026-09-19/figures_n3_v2/n3_J0p035_K0p99_ldu_xy.png).
+  These are preliminary four-subdivision images of the unconverged feedback
+  model, with corresponding PDFs in the same folder.
+- [Refined n=1.5 rotating slice](../../../diagnostics/coupled_convergence_2026-09-19/figures_slices_v2/n1p5_rotating_xz_s8.png)
+  and [same-state display comparison](../../../diagnostics/coupled_convergence_2026-09-19/figures_slices_v2/n1p5_rotating_xz_s4_s8.pdf).
+- [Eleven frozen linear histories](../../../diagnostics/coupled_convergence_2026-09-19/figures/linear_rates/frozen_linear_rates.pdf),
+  [n=2 trial-path comparison](../../../diagnostics/coupled_convergence_2026-09-19/figures/convergence/n2_paired_convergence.pdf)
+  and [n=3 tolerance comparison](../../../diagnostics/coupled_convergence_2026-09-19/figures/convergence/n3_paired_convergence.pdf).
+- [Audited nonlinear controls](../../../diagnostics/coupled_convergence_2026-09-19/CONTROL_RESULTS.md),
+  [live n=3 comparison](../../../diagnostics/coupled_convergence_2026-09-19/N3_COMPATIBLE_RESULTS.md),
+  [implementation validation](../../../diagnostics/coupled_convergence_2026-09-19/validation/validation.json)
+  and [final slice test log](../../../diagnostics/coupled_convergence_2026-09-19/figures_n3_v2/slice_tests.log).