{"artifact_id":"L1-499","layer":"L1","title":"Shape Optimization","domain":"Optimization","sub_domain":"Boundary shape","physics_fingerprint":{"L_DAG":3.0,"title":"Shape Optimization","domain":"Optimization","carrier":"N/A","primitives":["S.shape.derivative","O.iter","O.gradient.descent"],"sub_domain":"Boundary shape","noise_model":"deterministic","problem_class":"nonlinear_inverse","solution_space":"2D_boundary_curve","difficulty_delta":3,"integration_axis":"boundary_surface","sensing_mechanism":"shape_sensitivity_analysis"},"observable_profile":{"metric":"objective_reduction_ratio","regime":"Existence of the recovered 2D_boundary_curve 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 ~= 100); mesh_quality_degradation dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Deterministic sets the irreducible data-fidelity floor.","secondary":"constraint_violation"},"size_tiers":{"center_spec":{"omega":{"step_size_dt":0.1,"N_control_pts":50,"regularization_alpha":0.01},"input_format":"measurement_only","problem_class":"nonlinear_inverse","forward_operator":"shape_sensitivity_analysis","epsilon_fn_center":"0.30 objective_reduction_ratio"},"omega_bounds":{"step_size_dt":[0.01,1.0],"N_control_pts":[10,200],"regularization_alpha":[0.001,0.1]},"epsilon_bounds":{"objective_reduction_ratio":[0.1,0.6]},"allowed_problem_classes":["nonlinear_inverse"],"allowed_omega_dimensions":["N_control_pts","regularization_alpha","step_size_dt"],"allowed_forward_operators":["shape_sensitivity_analysis"]},"hardness_fn":{"type":"epsilon_fn","delta":3,"kappa":5000,"metric":"objective_reduction_ratio"},"initiator_dataset":[{"name":"primary","weight":1.0,"ipfs_cid":null,"license_hash":null}],"status":"testnet","staked_pwm":0.0,"chain_hash":"0xdc96f40d3e84826813b0ddb0c1843e6922da9104742e19ffb27457113e3af136","chain_tx_hash":"0xd945e1c325827dfc3d0806d148f0b1ef9e34bcf195e2811b702c7eea212b49bc","chain_block":41555318}