{"artifact_id":"L1-432","layer":"L1","title":"Optimal Control (LQR)","domain":"Control Theory","sub_domain":"Linear quadratic control","physics_fingerprint":{"L_DAG":2.5,"title":"Optimal Control (LQR)","domain":"Control Theory","carrier":"N/A","primitives":["E.eigensolve","S.lqr.gain_computation","O.lyapunov.closed_loop"],"sub_domain":"Linear quadratic control","noise_model":"deterministic","problem_class":"parameter_estimation","solution_space":"control_gain_matrix","difficulty_delta":3,"integration_axis":"time_horizon","sensing_mechanism":"full_state_feedback_lqr"},"observable_profile":{"metric":"closed_loop_performance_index","regime":"Existence of the recovered control_gain_matrix is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 20); model_uncertainty_A_B dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Deterministic sets the irreducible data-fidelity floor.","secondary":"stability_margin_dB"},"size_tiers":{"center_spec":{"omega":{"Q_R_ratio":1.0,"n_inputs_m":1,"system_order_n":4,"spectral_radius_A":0.9},"input_format":"measurement_only","problem_class":"parameter_estimation","forward_operator":"full_state_feedback_lqr","epsilon_fn_center":"1.05 closed_loop_performance_index"},"omega_bounds":{"Q_R_ratio":[0.01,100],"n_inputs_m":[1,10],"system_order_n":[1,50],"spectral_radius_A":[0.0,0.999]},"epsilon_bounds":{"closed_loop_performance_index":[0.9,2.0]},"allowed_problem_classes":["parameter_estimation"],"allowed_omega_dimensions":["system_order_n","Q_R_ratio","spectral_radius_A","n_inputs_m"],"allowed_forward_operators":["full_state_feedback_lqr"]},"hardness_fn":{"type":"epsilon_fn","delta":3,"kappa":500,"metric":"closed_loop_performance_index"},"initiator_dataset":[{"name":"primary","weight":1.0,"ipfs_cid":null,"license_hash":null}],"status":"testnet","staked_pwm":0.0,"chain_hash":"0xec453bc6b303c57f8ed7c38e68dc69f7f37ac381200764f902b1645782b13e78","chain_tx_hash":"0x2a18c6e029f0d084e0113108cf9d25d0b316b60d89c51e8a94c126a64707b504","chain_block":41555257}