{"artifact_id":"L1-435","layer":"L1","title":"4D-Var Data Assimilation","domain":"Control Theory","sub_domain":"Variational data assimilation","physics_fingerprint":{"L_DAG":4.5,"title":"4D-Var Data Assimilation","domain":"Control Theory","carrier":"N/A","primitives":["D.space","S.adjoint.gradient_4dvar","O.cost_function.4dvar"],"sub_domain":"Variational data assimilation","noise_model":"gaussian","problem_class":"nonlinear_inverse","solution_space":"initial_condition_vector","difficulty_delta":5,"integration_axis":"assimilation_window","sensing_mechanism":"variational_state_estimation"},"observable_profile":{"metric":"analysis_RMSE_vs_background","regime":"Existence of the recovered initial_condition_vector 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 ~= 10000.0); model_error_within_window dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.","secondary":"cost_function_reduction"},"size_tiers":{"center_spec":{"omega":{"window_hours":6,"N_observations":5000,"state_dimension_n":10000,"observation_density":1.0},"input_format":"measurement_only","problem_class":"nonlinear_inverse","forward_operator":"variational_state_estimation","epsilon_fn_center":"0.5 analysis_RMSE_vs_background"},"omega_bounds":{"window_hours":[1,24],"N_observations":[100,10000000],"state_dimension_n":[100,1000000],"observation_density":[0.1,10.0]},"epsilon_bounds":{"analysis_RMSE_vs_background":[0.1,1.0]},"allowed_problem_classes":["nonlinear_inverse"],"allowed_omega_dimensions":["state_dimension_n","N_observations","window_hours","observation_density"],"allowed_forward_operators":["variational_state_estimation"]},"hardness_fn":{"type":"epsilon_fn","delta":5,"kappa":1000000.0,"metric":"analysis_RMSE_vs_background"},"initiator_dataset":[{"name":"primary","weight":1.0,"ipfs_cid":null,"license_hash":null}],"status":"testnet","staked_pwm":0.0,"chain_hash":"0x9641f2631b1a13749ead5c81801872e13fe277403e72819087cd6bde2c95aba7","chain_tx_hash":"0xa9c24989164e6d9a5bbb4ff8b516e1a5b4e444b0a32ad763440d8352438b5d91","chain_block":41555258}