{
  "cases": [
    {
      "aspect_final": 4.999998728306325,
      "case_id": "qa_baseline_scipy",
      "diagnostic_gate_passed": true,
      "gate_blockers": [],
      "gate_passed": true,
      "iota_final": 0.4102000063210299,
      "iota_shortfall": 0.0,
      "label": "QA baseline scipy",
      "message": "`xtol` termination condition is satisfied.",
      "nfev": 48,
      "objective_final": 8.911810817152997e-06,
      "objective_initial": 1682.6412678151564,
      "objective_reduction_fraction": 0.9999999947036775,
      "optimizer_method": "scipy",
      "qs_final": 8.911808800393997e-06,
      "spectrax_weight": 0.05,
      "transport_kind": "nonlinear_window_heat_flux",
      "transport_metric_final": NaN
    },
    {
      "aspect_final": 5.004308467177267,
      "case_id": "growth_from_strict_baseline",
      "diagnostic_gate_passed": true,
      "gate_blockers": [
        "mean_iota"
      ],
      "gate_passed": false,
      "iota_final": 0.40997669004694615,
      "iota_shortfall": 2.3309953053829435e-05,
      "label": "growth from strict QA",
      "message": "scalar trust-region radius became too small",
      "nfev": 16,
      "objective_final": 0.0005337804397439096,
      "objective_initial": 0.018258286623189304,
      "objective_reduction_fraction": 0.9707650312014506,
      "optimizer_method": "scalar_trust",
      "qs_final": 0.0005097840112125825,
      "spectrax_weight": 0.1,
      "transport_kind": "growth",
      "transport_metric_final": 0.06974835426425598
    },
    {
      "aspect_final": 5.004321533731939,
      "case_id": "quasilinear_from_strict_baseline",
      "diagnostic_gate_passed": true,
      "gate_blockers": [
        "mean_iota"
      ],
      "gate_passed": false,
      "iota_final": 0.4099789731090947,
      "iota_shortfall": 2.1026890905273543e-05,
      "label": "QL flux from strict QA",
      "message": "`ftol` termination condition is satisfied.",
      "nfev": 22,
      "objective_final": 0.0007155621870566978,
      "objective_initial": 0.018444942892736252,
      "objective_reduction_fraction": 0.9612055081320696,
      "optimizer_method": "scalar_trust",
      "qs_final": 0.0006924652318489914,
      "spectrax_weight": 0.1,
      "transport_kind": "quasilinear_flux",
      "transport_metric_final": 0.081787646664499
    },
    {
      "aspect_final": 5.004339789413262,
      "case_id": "nonlinear_window_from_strict_baseline",
      "diagnostic_gate_passed": true,
      "gate_blockers": [
        "mean_iota"
      ],
      "gate_passed": false,
      "iota_final": 0.4099940357439537,
      "iota_shortfall": 5.964256046264715e-06,
      "label": "NL-window from strict QA",
      "message": "`ftol` termination condition is satisfied.",
      "nfev": 39,
      "objective_final": 0.0004615233544219823,
      "objective_initial": 0.018178508010602126,
      "objective_reduction_fraction": 0.9746115933082731,
      "optimizer_method": "scalar_trust",
      "qs_final": 0.0004423338587686629,
      "spectrax_weight": 0.1,
      "transport_kind": "nonlinear_window_heat_flux",
      "transport_metric_final": 0.06364721463489577
    }
  ],
  "claim_scope": "Optimizer-strategy evidence and campaign design. The RBC(1,1) sweep is a landscape/noise/convergence diagnostic, not an admission source for optimized QA stellarators and not a promoted nonlinear turbulent-flux optimization claim.",
  "gates": {
    "deterministic_transport_rows_all_strict_gates_pass": false,
    "has_admitted_long_window_landscape": false,
    "has_converged_long_window_landscape": true,
    "has_material_landscape_reduction_direction": true,
    "nonlinear_absolute_optimization_promoted": false
  },
  "kind": "vmec_jax_qa_optimizer_strategy_report",
  "landscape": {
    "baseline_point": {
      "coefficient_value": 0.12662450813837142,
      "label": "0",
      "mean": 11.009004455010071,
      "metrics": {
        "growth": 0.00032901121102689,
        "quasilinear_flux_absolute_growth_mixing_length": 0.0024377204608587795,
        "quasilinear_flux_lapillonne_2011": 0.0024377204608587795,
        "quasilinear_flux_linear_weight": 1.3607083812623606,
        "quasilinear_flux_mixing_length": 0.0024377204608587795,
        "quasilinear_flux_shape_aware_power_law": 1.4004462693129638
      },
      "relative_fraction": 0.0,
      "sem": 0.16644554696572134
    },
    "best_point": {
      "coefficient_value": 0.17727431139372,
      "label": "p0p4",
      "mean": 7.106718769073449,
      "metrics": {
        "growth": 0.0047690101274776445,
        "quasilinear_flux_absolute_growth_mixing_length": 0.022637717468361795,
        "quasilinear_flux_lapillonne_2011": 0.022637717468361795,
        "quasilinear_flux_linear_weight": 1.7974227149853979,
        "quasilinear_flux_mixing_length": 0.022637717468361795,
        "quasilinear_flux_shape_aware_power_law": 1.8419045990364096
      },
      "relative_fraction": 0.4,
      "sem": 0.14279109245892385
    },
    "best_reduction_fraction_vs_baseline": 0.35446308536651894,
    "metric_correlations": [
      {
        "metric": "growth",
        "pearson_with_nonlinear_q": -0.20011870188122882,
        "spearman_with_nonlinear_q": 0.06173913043478261
      },
      {
        "metric": "quasilinear_flux_absolute_growth_mixing_length",
        "pearson_with_nonlinear_q": -0.20503358305618766,
        "spearman_with_nonlinear_q": -0.03130434782608696
      },
      {
        "metric": "quasilinear_flux_lapillonne_2011",
        "pearson_with_nonlinear_q": -0.20503358305618766,
        "spearman_with_nonlinear_q": -0.03130434782608696
      },
      {
        "metric": "quasilinear_flux_linear_weight",
        "pearson_with_nonlinear_q": -0.5700632542073908,
        "spearman_with_nonlinear_q": -0.7069565217391305
      },
      {
        "metric": "quasilinear_flux_mixing_length",
        "pearson_with_nonlinear_q": -0.20503358305618766,
        "spearman_with_nonlinear_q": -0.03130434782608696
      },
      {
        "metric": "quasilinear_flux_shape_aware_power_law",
        "pearson_with_nonlinear_q": -0.5702269092065192,
        "spearman_with_nonlinear_q": -0.7069565217391305
      }
    ],
    "n_admitted_nonlinear_points": 24,
    "n_converged_nonlinear_points": 24,
    "nonlinear_points": [
      {
        "coefficient_value": 0.031656127034592856,
        "label": "m0p75",
        "mean": 18.571735657056582,
        "metrics": {
          "growth": 0.000993144991151871,
          "quasilinear_flux_absolute_growth_mixing_length": 0.003674003708200363,
          "quasilinear_flux_lapillonne_2011": 0.003674003708200363,
          "quasilinear_flux_linear_weight": 1.2630572416367416,
          "quasilinear_flux_mixing_length": 0.003674003708200363,
          "quasilinear_flux_shape_aware_power_law": 1.301415644412736
        },
        "relative_fraction": -0.75,
        "sem": 0.237515147475319
      },
      {
        "coefficient_value": 0.037987352441511434,
        "label": "m0p7",
        "mean": 15.585753262044335,
        "metrics": {
          "growth": 0.0009709076398181523,
          "quasilinear_flux_absolute_growth_mixing_length": 0.004259293116358383,
          "quasilinear_flux_lapillonne_2011": 0.004259293116358383,
          "quasilinear_flux_linear_weight": 1.2505830044592705,
          "quasilinear_flux_mixing_length": 0.004259293116358383,
          "quasilinear_flux_shape_aware_power_law": 1.28875513956657
        },
        "relative_fraction": -0.7,
        "sem": 0.645342891826938
      },
      {
        "coefficient_value": 0.04431857784843,
        "label": "m0p65",
        "mean": 15.227092487811793,
        "metrics": {
          "growth": 0.002017120157719241,
          "quasilinear_flux_absolute_growth_mixing_length": 0.012441804279466426,
          "quasilinear_flux_lapillonne_2011": 0.012441804279466426,
          "quasilinear_flux_linear_weight": 1.2579002715801593,
          "quasilinear_flux_mixing_length": 0.012441804279466426,
          "quasilinear_flux_shape_aware_power_law": 1.296181955336438
        },
        "relative_fraction": -0.65,
        "sem": 0.4440268731604115
      },
      {
        "coefficient_value": 0.05064980325534857,
        "label": "m0p6",
        "mean": 16.900027563967665,
        "metrics": {
          "growth": 0.0014936450464151,
          "quasilinear_flux_absolute_growth_mixing_length": 0.008626474043715303,
          "quasilinear_flux_lapillonne_2011": 0.008626474043715303,
          "quasilinear_flux_linear_weight": 1.2479170800532722,
          "quasilinear_flux_mixing_length": 0.008626474043715303,
          "quasilinear_flux_shape_aware_power_law": 1.2860491002869399
        },
        "relative_fraction": -0.6,
        "sem": 0.38710505576725995
      },
      {
        "coefficient_value": 0.05698102866226713,
        "label": "m0p55",
        "mean": 14.69577073335671,
        "metrics": {
          "growth": 0.000661770965123888,
          "quasilinear_flux_absolute_growth_mixing_length": 0.0022204431328622224,
          "quasilinear_flux_lapillonne_2011": 0.0022204431328622224,
          "quasilinear_flux_linear_weight": 1.2039209047690058,
          "quasilinear_flux_mixing_length": 0.0022204431328622224,
          "quasilinear_flux_shape_aware_power_law": 1.24137497778536
        },
        "relative_fraction": -0.55,
        "sem": 0.3262986745162938
      },
      {
        "coefficient_value": 0.06331225406918571,
        "label": "m0p5",
        "mean": 12.515966314870541,
        "metrics": {
          "growth": 0.0009964343976027834,
          "quasilinear_flux_absolute_growth_mixing_length": 0.005559987908342155,
          "quasilinear_flux_lapillonne_2011": 0.005559987908342155,
          "quasilinear_flux_linear_weight": 1.1766325406139888,
          "quasilinear_flux_mixing_length": 0.005559987908342155,
          "quasilinear_flux_shape_aware_power_law": 1.2136506421908335
        },
        "relative_fraction": -0.5,
        "sem": 0.24250864687970408
      },
      {
        "coefficient_value": 0.06964347947610429,
        "label": "m0p45",
        "mean": 7.2053161970772335,
        "metrics": {
          "growth": 0.0017445614007757838,
          "quasilinear_flux_absolute_growth_mixing_length": 0.011335842247998489,
          "quasilinear_flux_lapillonne_2011": 0.011335842247998489,
          "quasilinear_flux_linear_weight": 1.2525755865727883,
          "quasilinear_flux_mixing_length": 0.011335842247998489,
          "quasilinear_flux_shape_aware_power_law": 1.290777633785366
        },
        "relative_fraction": -0.45,
        "sem": 0.11280897495543846
      },
      {
        "coefficient_value": 0.07597470488302285,
        "label": "m0p4",
        "mean": 11.721893398366376,
        "metrics": {
          "growth": 0.0007992719654525291,
          "quasilinear_flux_absolute_growth_mixing_length": 0.003867000427468336,
          "quasilinear_flux_lapillonne_2011": 0.003867000427468336,
          "quasilinear_flux_linear_weight": 1.2848555390487506,
          "quasilinear_flux_mixing_length": 0.003867000427468336,
          "quasilinear_flux_shape_aware_power_law": 1.3235338311441913
        },
        "relative_fraction": -0.4,
        "sem": 0.2301553680852536
      },
      {
        "coefficient_value": 0.08230593028994143,
        "label": "m0p35",
        "mean": 10.77958378473808,
        "metrics": {
          "growth": 0.00036324999420497145,
          "quasilinear_flux_absolute_growth_mixing_length": 0.001721375495376055,
          "quasilinear_flux_lapillonne_2011": 0.001721375495376055,
          "quasilinear_flux_linear_weight": 1.316003379468946,
          "quasilinear_flux_mixing_length": 0.001721375495376055,
          "quasilinear_flux_shape_aware_power_law": 1.3551266621918572
        },
        "relative_fraction": -0.35,
        "sem": 0.17065470471898825
      },
      {
        "coefficient_value": 0.08863715569686,
        "label": "m0p3",
        "mean": 11.529562663236282,
        "metrics": {
          "growth": 0.00035977600813323385,
          "quasilinear_flux_absolute_growth_mixing_length": 0.0015413912910698577,
          "quasilinear_flux_lapillonne_2011": 0.0015413912910698577,
          "quasilinear_flux_linear_weight": 1.2881145456779914,
          "quasilinear_flux_mixing_length": 0.0015413912910698577,
          "quasilinear_flux_shape_aware_power_law": 1.3268400585542846
        },
        "relative_fraction": -0.3,
        "sem": 0.18601815043882974
      },
      {
        "coefficient_value": 0.09496838110377856,
        "label": "m0p25",
        "mean": 10.50694545388174,
        "metrics": {
          "growth": 0.00045224089130219873,
          "quasilinear_flux_absolute_growth_mixing_length": 0.0020040425667256227,
          "quasilinear_flux_lapillonne_2011": 0.0020040425667256227,
          "quasilinear_flux_linear_weight": 1.3110672253795992,
          "quasilinear_flux_mixing_length": 0.0020040425667256227,
          "quasilinear_flux_shape_aware_power_law": 1.3501209222093165
        },
        "relative_fraction": -0.25,
        "sem": 0.15191536506516262
      },
      {
        "coefficient_value": 0.10129960651069714,
        "label": "m0p2",
        "mean": 9.996700754563774,
        "metrics": {
          "growth": 0.00029434398108973834,
          "quasilinear_flux_absolute_growth_mixing_length": 0.001376731254302939,
          "quasilinear_flux_lapillonne_2011": 0.001376731254302939,
          "quasilinear_flux_linear_weight": 1.3092844151359402,
          "quasilinear_flux_mixing_length": 0.001376731254302939,
          "quasilinear_flux_shape_aware_power_law": 1.348312893606461
        },
        "relative_fraction": -0.2,
        "sem": 0.17028963055879517
      },
      {
        "coefficient_value": 0.1076308319176157,
        "label": "m0p15",
        "mean": 10.150795456172139,
        "metrics": {
          "growth": 0.0005698955266109517,
          "quasilinear_flux_absolute_growth_mixing_length": 0.0036689857633075518,
          "quasilinear_flux_lapillonne_2011": 0.0036689857633075518,
          "quasilinear_flux_linear_weight": 1.2704925411243473,
          "quasilinear_flux_mixing_length": 0.0036689857633075518,
          "quasilinear_flux_shape_aware_power_law": 1.3089608527134984
        },
        "relative_fraction": -0.15,
        "sem": 0.1393522479360177
      },
      {
        "coefficient_value": 0.11396205732453428,
        "label": "m0p1",
        "mean": 12.04502573450325,
        "metrics": {
          "growth": 0.0003351270591256402,
          "quasilinear_flux_absolute_growth_mixing_length": 0.002076875416909513,
          "quasilinear_flux_lapillonne_2011": 0.002076875416909513,
          "quasilinear_flux_linear_weight": 1.2944020915203387,
          "quasilinear_flux_mixing_length": 0.002076875416909513,
          "quasilinear_flux_shape_aware_power_law": 1.333218266681435
        },
        "relative_fraction": -0.1,
        "sem": 0.17592842769884576
      },
      {
        "coefficient_value": 0.12029328273145284,
        "label": "m0p05",
        "mean": 11.002428053617473,
        "metrics": {
          "growth": 0.0002630344386202458,
          "quasilinear_flux_absolute_growth_mixing_length": 0.0012789800961953367,
          "quasilinear_flux_lapillonne_2011": 0.0012789800961953367,
          "quasilinear_flux_linear_weight": 1.3494569364616906,
          "quasilinear_flux_mixing_length": 0.0012789800961953367,
          "quasilinear_flux_shape_aware_power_law": 1.3890427523064424
        },
        "relative_fraction": -0.05,
        "sem": 0.18257469699392806
      },
      {
        "coefficient_value": 0.12662450813837142,
        "label": "0",
        "mean": 11.009004455010071,
        "metrics": {
          "growth": 0.00032901121102689,
          "quasilinear_flux_absolute_growth_mixing_length": 0.0024377204608587795,
          "quasilinear_flux_lapillonne_2011": 0.0024377204608587795,
          "quasilinear_flux_linear_weight": 1.3607083812623606,
          "quasilinear_flux_mixing_length": 0.0024377204608587795,
          "quasilinear_flux_shape_aware_power_law": 1.4004462693129638
        },
        "relative_fraction": 0.0,
        "sem": 0.16644554696572134
      },
      {
        "coefficient_value": 0.13295573354529,
        "label": "p0p05",
        "mean": 10.843325046699418,
        "metrics": {
          "growth": 0.00023956061999930113,
          "quasilinear_flux_absolute_growth_mixing_length": 0.0017126669550800555,
          "quasilinear_flux_lapillonne_2011": 0.0017126669550800555,
          "quasilinear_flux_linear_weight": 1.4069019921062087,
          "quasilinear_flux_mixing_length": 0.0017126669550800555,
          "quasilinear_flux_shape_aware_power_law": 1.4472463664978035
        },
        "relative_fraction": 0.05,
        "sem": 0.20685460756513127
      },
      {
        "coefficient_value": 0.13928695895220858,
        "label": "p0p1",
        "mean": 9.644776290257335,
        "metrics": {
          "growth": 0.00031847627532501137,
          "quasilinear_flux_absolute_growth_mixing_length": 0.0023711488686465002,
          "quasilinear_flux_lapillonne_2011": 0.0023711488686465002,
          "quasilinear_flux_linear_weight": 1.428521259669323,
          "quasilinear_flux_mixing_length": 0.0023711488686465002,
          "quasilinear_flux_shape_aware_power_law": 1.4691398756474823
        },
        "relative_fraction": 0.1,
        "sem": 0.17743799108381675
      },
      {
        "coefficient_value": 0.14561818435912713,
        "label": "p0p15",
        "mean": 10.908443750936266,
        "metrics": {
          "growth": 0.0004998710619642414,
          "quasilinear_flux_absolute_growth_mixing_length": 0.0024149178395888294,
          "quasilinear_flux_lapillonne_2011": 0.0024149178395888294,
          "quasilinear_flux_linear_weight": 1.513101337818716,
          "quasilinear_flux_mixing_length": 0.0024149178395888294,
          "quasilinear_flux_shape_aware_power_law": 1.554736998620037
        },
        "relative_fraction": 0.15,
        "sem": 0.17145893734310266
      },
      {
        "coefficient_value": 0.1519494097660457,
        "label": "p0p2",
        "mean": 9.254512809515218,
        "metrics": {
          "growth": 0.0007155590250868938,
          "quasilinear_flux_absolute_growth_mixing_length": 0.005489956618270852,
          "quasilinear_flux_lapillonne_2011": 0.005489956618270852,
          "quasilinear_flux_linear_weight": 1.5898524623916634,
          "quasilinear_flux_mixing_length": 0.005489956618270852,
          "quasilinear_flux_shape_aware_power_law": 1.6323386651547653
        },
        "relative_fraction": 0.2,
        "sem": 0.4138402902814722
      },
      {
        "coefficient_value": 0.15828063517296428,
        "label": "p0p25",
        "mean": 10.0771448854589,
        "metrics": {
          "growth": 0.00021877935534762473,
          "quasilinear_flux_absolute_growth_mixing_length": 0.0005954131491888503,
          "quasilinear_flux_lapillonne_2011": 0.0005954131491888503,
          "quasilinear_flux_linear_weight": 1.7133875650420602,
          "quasilinear_flux_mixing_length": 0.0005954131491888503,
          "quasilinear_flux_shape_aware_power_law": 1.7571114975502058
        },
        "relative_fraction": 0.25,
        "sem": 0.24372929254990924
      },
      {
        "coefficient_value": 0.16461186057988286,
        "label": "p0p3",
        "mean": 9.648222098749015,
        "metrics": {
          "growth": 0.0007038494218809832,
          "quasilinear_flux_absolute_growth_mixing_length": 0.003183561668149664,
          "quasilinear_flux_lapillonne_2011": 0.003183561668149664,
          "quasilinear_flux_linear_weight": 1.7563785070534466,
          "quasilinear_flux_mixing_length": 0.003183561668149664,
          "quasilinear_flux_shape_aware_power_law": 1.800498220044598
        },
        "relative_fraction": 0.3,
        "sem": 0.20161203831546382
      },
      {
        "coefficient_value": 0.17094308598680144,
        "label": "p0p35",
        "mean": 8.586609942714288,
        "metrics": {
          "growth": 0.0034347937199041326,
          "quasilinear_flux_absolute_growth_mixing_length": 0.012697307067833804,
          "quasilinear_flux_lapillonne_2011": 0.012697307067833804,
          "quasilinear_flux_linear_weight": 1.827868612948163,
          "quasilinear_flux_mixing_length": 0.012697307067833804,
          "quasilinear_flux_shape_aware_power_law": 1.8726096272707742
        },
        "relative_fraction": 0.35,
        "sem": 0.17884367077336255
      },
      {
        "coefficient_value": 0.17727431139372,
        "label": "p0p4",
        "mean": 7.106718769073449,
        "metrics": {
          "growth": 0.0047690101274776445,
          "quasilinear_flux_absolute_growth_mixing_length": 0.022637717468361795,
          "quasilinear_flux_lapillonne_2011": 0.022637717468361795,
          "quasilinear_flux_linear_weight": 1.7974227149853979,
          "quasilinear_flux_mixing_length": 0.022637717468361795,
          "quasilinear_flux_shape_aware_power_law": 1.8419045990364096
        },
        "relative_fraction": 0.4,
        "sem": 0.14279109245892385
      }
    ],
    "nonlinear_points_semantics": "RBC(1,1) landscape points that passed the long-window convergence/window gates; these are diagnostics, not admitted optimized-QA candidates."
  },
  "landscape_json": "docs/_static/vmec_boundary_transport_landscape_rbc11_full.json",
  "literature_context": [
    {
      "source": "VMEC-JAX discrete-adjoint documentation",
      "topic": "smooth_QA_constraints",
      "url": "https://vmec-jax.readthedocs.io/en/latest/discrete_adjoint.html"
    },
    {
      "source": "Direct microstability optimization of stellarator devices",
      "topic": "linear_quasilinear_microstability_optimization",
      "url": "https://doi.org/10.1103/PhysRevE.110.035201"
    },
    {
      "source": "Optimization of nonlinear turbulence in stellarators",
      "topic": "noisy_nonlinear_heat_flux_optimization",
      "url": "https://doi.org/10.1017/S0022377824000369"
    }
  ],
  "optimizer_recommendations": [
    {
      "method": "vmec_jax_exact_discrete_adjoint_least_squares",
      "reason": "Start from the same simple-seed max-mode-5 path as VMEC-JAX QA_optimization.py, solve the aspect, iota, and QS residuals, then append one SPECTRAX-GK transport residual.",
      "stage": "strict_qa_baseline",
      "status": "preferred_for_smooth_aspect_iota_qs_constraints"
    },
    {
      "method": "constraint_aware_adjoint_trust_or_lbfgs_with_weight_continuation",
      "reason": "The current scalar-trust rows move the internal objective but remain just below the strict iota gate. Use transport-weight continuation, active iota/aspect filters, and multistarts from simple-seed QA solves; use the RBC(1,1) landscape only to diagnose conditioning and metric noise.",
      "stage": "linear_and_quasilinear_transport",
      "status": "next_deterministic_campaign"
    },
    {
      "method": "spsa_common_random_numbers_then_cma_es_or_bo_for_low_dimensional_projected_controls",
      "reason": "Long-window Q has seed/timestep variability and cannot be promoted from reduced-window gradients. Use two-sided noisy objectives with common random numbers, then promote only matched t=1500 replicated audits.",
      "stage": "long_window_nonlinear_heat_flux",
      "status": "preferred_noisy_outer_loop"
    },
    {
      "method": "screening_and_model_development_only",
      "reason": "On the converged RBC(1,1) landscape, simple linear/QL metrics are not reliable absolute nonlinear-Q predictors; promote correlation/screening only when held-out gates pass.",
      "stage": "quasilinear_claims",
      "status": "absolute_flux_promotion_blocked"
    }
  ],
  "panel_json": "docs/_static/vmec_jax_qa_full_sweep_panel.json",
  "schema_version": 1
}