{"artifact_id":"L1-461","layer":"L1","title":"Hydraulic Fracture Propagation Modeling","domain":"Petroleum Engineering","sub_domain":"Well stimulation","physics_fingerprint":{"L_DAG":4.0,"title":"Hydraulic Fracture Propagation Modeling","domain":"Petroleum Engineering","carrier":"acoustic","primitives":["N.pointwise","S.pressure_decline.analysis","O.microseismic.inversion"],"sub_domain":"Well stimulation","noise_model":"microseismic_gaussian","problem_class":"nonlinear_inverse","solution_space":"fracture_geometry_vector","difficulty_delta":5,"integration_axis":"fracture_surface","sensing_mechanism":"fracture_geometry_inversion"},"observable_profile":{"metric":"fracture_half_length_RMSE_m","regime":"Existence of the recovered fracture_geometry_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 ~= 500); stress_shadow_complexity dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Microseismic gaussian sets the irreducible data-fidelity floor.","secondary":"pressure_match_RMSE_psi"},"size_tiers":{"center_spec":{"omega":{"stage_spacing_ft":200,"Young_modulus_GPa":30,"fluid_viscosity_cP":50,"injection_rate_bbl_min":15},"input_format":"measurement_only","problem_class":"nonlinear_inverse","forward_operator":"fracture_geometry_inversion","epsilon_fn_center":"30 fracture_half_length_RMSE_m"},"omega_bounds":{"stage_spacing_ft":[50,500],"Young_modulus_GPa":[5,80],"fluid_viscosity_cP":[5,5000],"injection_rate_bbl_min":[2,50]},"epsilon_bounds":{"fracture_half_length_RMSE_m":[5,200]},"allowed_problem_classes":["nonlinear_inverse"],"allowed_omega_dimensions":["Young_modulus_GPa","fluid_viscosity_cP","injection_rate_bbl_min","stage_spacing_ft"],"allowed_forward_operators":["fracture_geometry_inversion"]},"hardness_fn":{"type":"epsilon_fn","delta":5,"kappa":10000.0,"metric":"fracture_half_length_RMSE_m"},"initiator_dataset":[{"name":"primary","weight":1.0,"ipfs_cid":null,"license_hash":null}],"status":"testnet","staked_pwm":0.0,"chain_hash":"0xf11d527efd059c6ee9e552f27b84d4d426762705d8a099c84e865ca7d60990a0","chain_tx_hash":"0x03496d371ad73925d841e6ca6858681f36cb1ac3ede4aec81e437f78a55ad215","chain_block":41555279}