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LCFS |B| map from reduced QA controls"}}],"comparison_metrics":{"control_design_heat_flux_mean":0.016063821303104506,"transport_design_heat_flux_mean":0.014338897883061615,"relative_heat_flux_reduction_at_fixed_gradients":0.10737939544369379,"constraints_passed":true,"transport_reduction_gate_passed":true,"long_window_gates_passed":true,"ad_fd_gates_passed":true,"passed":true,"reduced_differentiable_plumbing_passed":true,"full_vmec_nonlinear_differentiable_plumbing_passed":false},"differentiable_plumbing":{"stages":["reduced QA controls","geometry constraints and reduced LCFS visualization","linear ITG feature map","quasilinear mixing-length diagnostic","long-window differentiable nonlinear heat-flux envelope","weighted optimization residuals","scalar, residual, and observable AD-vs-FD gates"],"all_scalar_objective_gates_passed":true,"all_residual_jacobian_gates_passed":true,"all_observable_jacobian_gates_passed":true,"passed":true},"model_equations":{"objective":"||r||^2 with aspect, minimum-iota, operating-iota, QA, QA-compatible helical-shaping, regularization, and optional sqrt(weight * late-window reduced nonlinear heat flux) residuals","nonlinear_envelope":"dE/dt = 2 gamma E - alpha E^2; Q_env = W_i E; fixed-step RK2","gradient_scan":"fixed a/L_T while scanning a/L_n and refitting late-window Q_env means"},"config":{"target_aspect":6.0,"min_iota":0.41,"iota_operating_floor":0.7,"max_mode":1,"aspect_weight":8.0,"iota_floor_weight":160.0,"iota_operating_weight":70.0,"qa_weight":8.0,"target_helical_amplitude":0.16,"helical_shaping_weight":24.0,"regularization":0.002,"nonlinear_weight":8.0,"learning_rate":0.03,"steps":60,"nonlinear_dt":0.2,"nonlinear_steps":2000,"nonlinear_tail_fraction":0.5,"long_window_min_time":300.0,"long_window_max_cv":0.03,"long_window_max_trend":0.02,"long_window_max_half_mean_rel_change":0.02,"fixed_density_gradient":2.2,"fixed_temperature_gradient":6.0,"scan_density_gradients":[0.6,1.0,1.4,1.8,2.2,2.8,3.4,4.0,4.8],"fd_step":0.0001,"surface_ntheta":72,"surface_nzeta":72,"n_field_periods":2},"scope_notes":["The surface and |B| maps are reduced max-mode-1 visualizations, not solved VMEC equilibria.","The nonlinear heat-flux objective is a differentiable envelope used for optimization plumbing.","Production nonlinear claims still require long post-transient replicated SPECTRAX-GK windows."]}