Long-run evidence

This page records nonlinear evidence available through commit adcc714, including 30-minute-budget long runs, double-Harris validation promotion/convergence bundles, and deliberately skeptical interpretation. These runs validate long integration, checkpointing, media, nonlinear budget gates, and bounded current-sheet response diagnostics. The latest GPU campaign closes the Rutherford production-promotion response gate, but it does not yet demonstrate Rutherford algebraic scaling across amplitudes or plasmoid onset.

Production automation lane

The current production-campaign lane is generated, not launched, by default:

python tools/run_nonlinear_production_campaign.py \
  --outdir outputs/campaigns/nonlinear_production_campaign \
  --dry-run

This writes production_campaign_manifest.json and run_commands.sh with exact Rutherford and double-Harris commands for the duration, convergence, seed-QI, sheet-width/aspect, eta/Lundquist, fixed-scale movie, and promotion gates. The manifest itself is validation-level planning evidence only. Running the lane requires the explicit --execute flag plus timeout controls, and production wording remains blocked unless the Rutherford target completes, the promotion report passes, and the final --allow-production-claim --max-steps 0 refresh command succeeds. The 2026-05-25 GPU campaign satisfied those Rutherford promotion gates for commit adcc714.

Latest passing Rutherford production-promotion run:

outputs/campaigns/release_long_gpu_20260525_203421_n128_t240_periodic_rutherford_adcc714

Key promotion metrics from the run:

• target duration: t_end = 240.0, terminal_step = 12000, target_step = 12000;

• history samples: 123;

• reconnecting-flux amplification: 8.359281934515764;

• Rutherford-width amplification: 2.8912422822232937;

• promotion reports: rutherford/validation.json, rutherford/promotion/validation.json, and production_campaign_manifest.json all pass.

Reproducible command sequence

The completed duration run used the restartable production executor:

mhx campaign rutherford-plan-production \
  --outdir outputs/long_runs/rutherford_96_dt005_full_20260512 \
  --nx 96 --ny 96 --dt 0.05 --target-saved-frames 200 \
  --max-walltime-hours 0.5 \
  --seconds-per-step-estimate 0.04 \
  --checkpoint-interval-minutes 5 \
  --preemption-margin-minutes 2

mhx campaign rutherford-execute \
  outputs/long_runs/rutherford_96_dt005_full_20260512 \
  --max-steps 45802 --movies \
  --max-relative-energy-growth 1e-6 \
  --max-divergence-linf 1e-8

The active nonlinear-budget run used the multi-mode reduced-MHD state from nonlinear.py:

from mhx.benchmarks.nonlinear import write_nonlinear_energy_budget_validation

write_nonlinear_energy_budget_validation(
    "outputs/long_runs/nonlinear_budget_96_dt005_steps20000_20260512",
    shape=(96, 96),
    resistivity=2e-2,
    viscosity=2e-2,
    dt=5e-3,
    steps=20000,
    save_every=50,
    max_budget_residual=5e-4,
    max_relative_energy_growth=1e-8,
)

The current-sheet long replay uses the periodic double-Harris initializer from equilibria.py and the scalable base-vs-seeded benchmark in current_sheet.py:

mhx benchmark double-harris-long-run \
  --outdir outputs/long_runs/periodic_double_harris_seeded_128_t100_20260512 \
  --nx 128 --ny 128 --t-end 100 --save-every 200 --fit-stop 10 --no-movies

Rutherford-duration executor run

The 96×96 Rutherford-duration executor run completed the configured duration target under the executor schema available when it was generated. It remains a validation-level bundle unless rerun or upgraded with current history keys and a passing promotion-readiness report.

Quantity	Value
RK4 steps	45,802
final time	2290.1
saved samples	202
policy e-folds	30
elapsed walltime	888.6 s
executor gates	passed; promotion gates not claimed
final/initial reconnecting-flux proxy	2.73e-6
final/initial island-width proxy	1.65e-3
final/initial total energy	1.03e-2
max kinetic energy	5.85e-9

The fixed-scale movies show the same conclusion visually: the periodic cosine field diffuses away rather than forming growing islands.

Skeptical interpretation

This is strong evidence for the restartable production-executor path, not for a promotion-ready production physics claim:

• the full target step count is completed in one restartable bundle;

• checkpoint state, checkpoint metadata, resume plan, manifest hashes, fixed-scale movies, and history schema are written;

• finite-history, energy, divergence, checkpoint, and movie gates all pass for that execution bundle.

• the archived history predates the newer current-sheet geometry and refined X/O-count promotion keys, so it is not sufficient for today’s promotion gate.

It is not evidence for Rutherford growth. The reconnecting-flux proxy, island-width proxy, current, and total energy all decay, and the kinetic energy stays nearly zero. The current periodic cosine initial condition is therefore a long dissipative integration test, not a tearing-growth experiment.

Current-schema Rutherford executor rerun

A current-schema 96×96, dt=0.05 rerun was executed with the same duration target so the long-run bundle includes the newer current-sheet geometry and refined critical-point count histories:

mhx campaign rutherford-plan-production \
  --outdir outputs/campaigns/rutherford_current_schema_96_dt005_20260517_161235 \
  --nx 96 --ny 96 --dt 0.05 --target-saved-frames 200 \
  --max-walltime-hours 0.5 \
  --seconds-per-step-estimate 0.04 \
  --checkpoint-interval-minutes 5 \
  --preemption-margin-minutes 2

mhx campaign rutherford-execute \
  outputs/campaigns/rutherford_current_schema_96_dt005_20260517_161235 \
  --max-steps 45802 --movies \
  --max-relative-energy-growth 1e-6 \
  --max-divergence-linf 1e-8

mhx campaign rutherford-promotion-check \
  outputs/campaigns/rutherford_current_schema_96_dt005_20260517_161235 \
  --convergence-dir outputs/campaigns/rutherford_current_schema_96_dt005_20260517_161235/evidence_20260517_response_gate/convergence_n16_24 \
  --convergence-dir outputs/campaigns/rutherford_current_schema_96_dt005_20260517_161235/evidence_20260517_response_gate/convergence_n18_26 \
  --seed-qi-dir outputs/campaigns/rutherford_current_schema_96_dt005_20260517_161235/evidence_20260517_response_gate/seed_robust_qi_n16 || true

Quantity	Value
RK4 steps	45,802
final time	2290.1
saved samples	202
execution gates	passed
promotion gates	failed: no positive reconnecting-flux/island-width response
convergence evidence	two small validation bundles passed and were checksummed
seed-QI evidence	one small validation bundle passed
reconnecting-flux amplification	1.00 versus required 1.05
island-width amplification	1.00 versus required 1.05
max X/O counts	2 / 1
current-sheet aspect proxy	0.667
final/initial total energy	1.03e-2
max energy-budget residual	0

The important result is negative but useful: the executor now writes every history key required by the current promotion gate. The promotion gate also requires positive reconnecting-flux and island-width amplification, so this purely dissipative duration-complete run remains validation evidence even after convergence and seed-QI bundles are attached.

Active nonlinear energy-budget run

The second run uses a genuinely nonlinear multi-mode initial condition with a large ideal-to-full RHS ratio. It checks the periodic reduced-MHD budget

\[ \frac{dE}{dt} = -\eta \langle j^2 \rangle - \nu \langle \omega^2 \rangle, \qquad E = \frac{1}{2}\langle |\nabla\psi|^2 + |\nabla\phi|^2\rangle . \]

Quantity	Value
grid	96×96
RK4 steps	20,000
final time	100.0
saved samples	401
nonlinear RHS ratio	0.994
relative energy drop	0.985
max relative budget residual	3.65e-5
gates	passed

This is good evidence that nonlinear Poisson brackets, spectral current, dissipation signs, and RK4 integration remain coherent over a substantially longer run than the FAST CI defaults.

Seeded double-Harris long replay

The new periodic double-Harris run is the first long nonlinear current-sheet replay in this rebuild that shows an early instability-path response rather than pure decay of a stable cosine equilibrium. It advances a base run and a seeded run on the same grid and measures

\[ A_s(t)=\frac{\|q_s(t)-q_b(t)\|_2}{\epsilon}. \]

Quantity	Value
grid	128×128
RK4 steps	10,000
final time	100.0
saved samples	51
early fitted growth rate	0.141
early amplification	5.27×
maximum amplification	7.35×
final/initial total energy	0.351
max kinetic energy	6.13e-7
elapsed walltime	61.9 s
gates	passed

Skeptical interpretation

This result is a real improvement over the earlier Rutherford-duration cosine run because the perturbation grows for several Alfvén times before saturating and relaxing. It still does not close a paper-grade reconnection claim: the kinetic energy remains very small, the current-sheet peak decays under the chosen resistivity/viscosity, and the run has no resolution, time-step, seed, or aspect-ratio sweep. The correct conclusion is that MHX now has a scalable nonlinear current-sheet validation lane suitable for those sweeps.

GPU-assisted double-Harris response rerun

After adding explicit response diagnostics, the double-Harris lane was rerun on office with the system CUDA JAX backend (NVIDIA RTX A4000) to verify that a longer validation run records more than a norm-only perturbation history. The archived command was:

mhx benchmark double-harris-long-run \
  --outdir outputs/campaigns/growing_double_harris_gpu_96_t120_20260518_044120 \
  --nx 96 --ny 96 --t-end 120 --dt 0.01 --save-every 300 \
  --fit-stop 10 --min-max-growth-factor 2 --movies

Quantity	Value
grid	96×96
final time	120.0
saved samples	41
early fitted growth rate	0.1869
early amplification	5.72×
maximum perturbation amplification	7.35×
dominant reconnecting-flux amplification	6.47×
Rutherford-width proxy amplification	2.54×
max detected X/O counts	4 / 2
relative total-energy increase	0.0
gates	passed

The skeptical read is unchanged: this is now stronger validation evidence because the response gate is explicit and positive, but it remains below production claim level until larger convergence, seed, aspect-ratio, and Lundquist-number sweeps close.

The new machine-readable promotion boundary for this lane is:

mhx benchmark double-harris-promotion-check \
  outputs/campaigns/growing_double_harris_gpu_96_t120_20260518_044120 \
  --convergence-dir outputs/benchmarks/periodic_double_harris_convergence

It writes promotion/promotion_readiness.json, promotion/validation.json, promotion/figures/promotion_matrix.png, and an artifact manifest. The report can promote a run to convergence-backed validation media only; it deliberately cannot promote a run to production Rutherford/plasmoid evidence.

The same convergence code path was also run on a bounded GPU-assisted medium sweep (32/48/64, t_end=16, dt=0.02/0.01). It passed with fitted growth rates 0.1970–0.1978, maximum amplification 7.886–7.899, zero measured relative energy increase, 0.41% resolution growth-rate spread, and effectively zero time-step spread. This is no longer just a placeholder for a future script: it is convergence-backed validation evidence while remaining below production claim level.

Current claim boundary

These runs support:

• long-run stability of the current reduced-MHD code path;

• production-executor artifact correctness under a completed duration target;

• nonlinear energy/dissipation-budget correctness for an active nonlinear state;

• early seeded-growth response for a periodic double-Harris current-sheet replay;

• duration-complete Rutherford production-promotion response at 128×128, t_end=240;

• double-Harris promotion and convergence reports as validation-only claim boundaries.

• forced turbulent-reconnection readiness reports as validation-only proxy boundaries.

• explicit evidence that execution-level validation and production promotion are separate gates.

These runs do not yet support:

• Rutherford algebraic island-growth scaling across amplitudes;

• plasmoid onset statistics;

• Sweet-Parker reconnection-rate scaling;

• publication-grade reconnection claims.

The next required physics step is no longer scaffolding. MHX now has double-Harris promotion/convergence validation evidence and a forced turbulent-reconnection readiness gate. To promote either family to production physics, extend the existing gates to larger resolution, seed amplitude/mode, sheet width/aspect ratio, Lundquist number, and duration sweeps, then promote only the figures whose scalings survive the full campaign.

Source anchors:

• double-Harris and current-sheet validation

• forced turbulent-reconnection readiness

• critical-point diagnostics

• promotion CLI wiring