{"artifact_id":"L1-518","layer":"L1","title":"X-ray Diffraction Crystal Structure Recovery (analytical core)","domain":"Materials Science","sub_domain":"Powder / single-crystal X-ray diffraction lattice and structure-factor recovery","physics_fingerprint":{"L_DAG":6.8,"title":"X-ray Diffraction Crystal Structure Recovery (analytical core)","domain":"Materials Science","carrier":"x_ray","primitives":["L.xray_source","L.bragg_diffraction","L.structure_factor","L.intensity_calculation","L.profile_function","L.detector_response","int.angular"],"sub_domain":"Powder / single-crystal X-ray diffraction lattice and structure-factor recovery","noise_model":"poisson","problem_class":"nonlinear_inverse","solution_space":"crystal_structure_parameters","difficulty_delta":5,"integration_axis":"angular_spatial","sensing_mechanism":"bragg_diffraction"},"observable_profile":{"metric":"R_factor","regime":"Existence guaranteed within declared Omega bounds. Uniqueness conditional: for known atomic composition + Bravais lattice + sufficient resolution, structure refinement is unique up to centrosymmetric equivalence; phase problem requires Patterson methods (heavy-atom), direct methods (Karle-Hauptman maximum-entropy), or anomalous-scattering for ab-initio. Stability conditional with kappa raw ~ 600 (limited by phase problem and reflection-overlap in powder XRD); kappa_eff ~ 80 with Rietveld refinement under structural constraints. Joint Hadamard well-posedness for the XRD forward established by Rietveld 1969 (foundational), Hill-Howard 1986 (Rietveld profile refinement), Karle-Hauptman 1956 (direct methods, Nobel 1985), McCusker 1999 (Rietveld guidelines), Young 1993 (Rietveld method textbook), Coelho 2018 (TOPAS), Toby-Von Dreele 2013 (GSAS-II).","secondary":"GoF_chi2"},"size_tiers":{"center_spec":{"omega":{"SNR_dB":30,"two_theta_max":120,"two_theta_min":5,"two_theta_step":0.02,"beam_divergence":0.0,"lambda_angstrom":1.5418,"sample_displacement":0.0,"wavelength_dispersion":0.0,"instrumental_broadening":0.05,"monochromator_misalignment":0.0,"background_subtraction_error":0.0,"preferred_orientation_powder":0.0},"input_format":"1d_diffraction_pattern","problem_class":"powder_xrd_rietveld","forward_operator":"powder_xrd_forward","epsilon_fn_center":"0.05_R_factor"},"omega_bounds":{"SNR_dB":[10,50],"two_theta_max":[60,160],"two_theta_min":[1,30],"two_theta_step":[0.001,0.1],"lambda_angstrom":[0.4,2.5],"instrumental_broadening":[0.01,0.5],"preferred_orientation_powder":[0.0,0.5]},"epsilon_bounds":{"R_factor":[0.01,0.3]},"allowed_problem_classes":["powder_xrd_rietveld","single_crystal_structure_solution","powder_indexing","ab_initio_structure_determination"],"allowed_omega_dimensions":["lambda_angstrom","two_theta_min","two_theta_max","two_theta_step","wavelength_dispersion","instrumental_broadening","preferred_orientation_powder","sample_displacement","beam_divergence","monochromator_misalignment","background_subtraction_error","SNR_dB"],"allowed_forward_operators":["powder_xrd_forward","single_crystal_xrd_forward","rietveld_refinement_forward","direct_methods_phase_forward"]},"hardness_fn":{"type":"epsilon_fn","delta":5,"kappa":600,"metric":"R_factor"},"initiator_dataset":[{"name":"primary","weight":1.0,"ipfs_cid":null,"license_hash":null}],"status":"testnet","staked_pwm":0.0,"chain_hash":"0xd3a963f4f3a6f8f1d608a89e37a9410e205b38e2b7b8fbae0f02dd460668155f","chain_tx_hash":"0xb7ec20cef152165728154268692c108ecee957b28dc6a189658eb21ff9e110a2","chain_block":41554142}