{ "schema_version": 2, "experiment": "comp-050", "contract_sha256": "01072ab3ec9960657ee001f36a7ee1573f69135ede6d28023e96e88d392d6602", "verdict": "METHOD_MAP_DERIVED", "method_statuses": { "conditional_capacity_algebra": "DERIVED", "concentration_only_nonidentifiability": "DEMONSTRATED", "measurement_structural_audit": "COMPLETED", "product_prerequisite_failure_sensitivity": "PASSED", "biological_regime": "NOT_EVALUATED" }, "definitions": { "ledger_basis": "amounts integrated over one declared window", "response_surface_denominator": "mean_total_local_urate_influx", "local_gross_removal_fraction": "R_UOX / (I_systemic + I_other)", "systemic_attributed_fraction": "R_UOX,systemic / I_systemic; requires source-resolved fate", "global_minimality_claim": false }, "equations": { "integrated_local_mass_balance": "U_T - U_0 = I_systemic + I_other - R_UOX - R_reabsorption - R_outflow - R_unattributed", "conditional_occupancy": "occupancy = (C/Km) / (1 + C/Km)", "active_capacity_time_area": "A_time = integral(Vmax_active(t) dt) / (Vmax_initial * T)", "integrated_conditional_capacity": "R_capacity = Vmax_initial * T * occupancy * A_time", "conditional_capacity_boundary": "Vmax_initial/J_total_mean = q / (occupancy * A_time)", "qualified_product_observations": { "total_uox_removal": "R_UOX = (delta_product_inventory + recovered_product_outflow + recovered_product_sampling + quantified_product_degradation_or_scavenging - non_UOX_product_formation) / (validated_stoichiometric_yield * validated_matrix_recovery)", "systemic_origin_uox_removal": "R_UOX,systemic = the same corrected product-fate equation applied to source-resolved tracer or equivalent systemic-origin product observations" } }, "product_observation_contract": { "status": "ideal_assumption_only_not_empirically_evaluated", "required_prerequisites": [ "analyte_identity_and_uox_product_specificity", "validated_stoichiometric_conversion", "initial_background_and_non_uox_formation_quantified", "time_resolved_matrix_recovery", "product_inventory_outflow_sampling_degradation_and_scavenging_fate", "no_uox_or_inactive_uox_no_urate_and_matrix_controls", "prespecified_recovery_mass_balance_and_interference_acceptance", "source_resolved_product_fate_for_systemic_attribution" ], "empirically_evaluated": false }, "checks": { "required_capacity_decreases_as_substrate_to_km_increases": true, "required_capacity_decreases_as_active_time_area_increases": true, "required_capacity_increases_as_gross_removal_target_increases": true, "constant_volume_declared": true, "all_concentration_derivatives_equal_zero": true, "uox_attributed_fluxes_are_not_identical": true, "terminal_urate_alone_does_not_identify_local_uox_removal": true, "qualified_product_conditionally_identifies_local_uox_removal": true, "qualified_product_does_not_close_local_ledger": true, "calibrated_capacity_combination_identifies_active_capacity": true, "source_and_boundary_combination_closes_declared_ledger": true, "source_resolved_product_fate_identifies_systemic_origin_uox_removal": true, "product_failure_blocks_local_uox_attribution_in_every_combination": true, "product_failure_blocks_systemic_origin_uox_attribution": true, "product_failure_prevents_declared_ledger_closure": true, "integrated_capacity_equals_influx_boundary_present": true }, "response_surface": { "row_count": 120, "minimum_required_capacity_multiple_exact": "101/400", "minimum_required_capacity_multiple_decimal": "0.2525", "maximum_required_capacity_multiple_exact": "1010", "maximum_required_capacity_multiple_decimal": "1010", "scope": "conditional dimensionless capacity map; not a solved dynamic mass balance or biological target" }, "same_concentration_counterexample": { "scenario_count": 3, "minimum_uox_attributed_flux_exact": "1/10", "minimum_uox_attributed_flux_decimal": "0.1", "maximum_uox_attributed_flux_exact": "9/10", "maximum_uox_attributed_flux_decimal": "0.9", "interpretation": "under the declared constant-volume rate law, the same concentration trajectory does not identify UOX removal flux" }, "measurement_structural_audit": { "unknowns": [ "initial_urate_inventory", "terminal_urate_inventory", "systemic_urate_influx", "other_urate_influx", "uox_urate_removal", "reabsorption_loss", "outflow_loss", "unattributed_residual_loss", "systemic_origin_uox_removal", "integrated_active_capacity" ], "governing_equations": [ { "name": "integrated_local_urate_mass_balance", "coefficients": { "initial_urate_inventory": "-1", "terminal_urate_inventory": "1", "systemic_urate_influx": "-1", "other_urate_influx": "-1", "uox_urate_removal": "1", "reabsorption_loss": "1", "outflow_loss": "1", "unattributed_residual_loss": "1" } } ], "ideal_product_observation": [ { "order": 1, "measurement_combination": "terminal_urate_amount_only", "product_observation_mode": "ideal_product_observation", "direct_observations": [ "terminal_urate_inventory" ], "conditional_observations_included": [], "equations": [ "governing:integrated_local_urate_mass_balance", "direct_observation:terminal_urate_inventory" ], "coefficient_matrix": [ [ "-1", "1", "-1", "-1", "1", "1", "1", "1", "0", "0" ], [ "0", "1", "0", "0", "0", "0", "0", "0", "0", "0" ] ], "unknown_order": [ "initial_urate_inventory", "terminal_urate_inventory", "systemic_urate_influx", "other_urate_influx", "uox_urate_removal", "reabsorption_loss", "outflow_loss", "unattributed_residual_loss", "systemic_origin_uox_removal", "integrated_active_capacity" ], "matrix_rank": 2, "targets": [ { "target": "local_uox_removal", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 3 ] }, { "target": "inventory_change", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 3 ] }, { "target": "total_local_influx", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 3 ] }, { "target": "systemic_origin_uox_removal", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 3 ] }, { "target": "integrated_active_capacity", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 3 ] }, { "target": "local_ledger_closed", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 3, 2, 3, 3, 3, 3, 3, 3 ] } ] }, { "order": 2, "measurement_combination": "inventory_plus_qualified_product_equivalent", "product_observation_mode": "ideal_product_observation", "direct_observations": [ "initial_urate_inventory", "terminal_urate_inventory" ], "conditional_observations_included": [ "uox_urate_removal" ], "equations": [ "governing:integrated_local_urate_mass_balance", "direct_observation:initial_urate_inventory", "direct_observation:terminal_urate_inventory", "conditional_product_observation:uox_urate_removal" ], "coefficient_matrix": [ [ "-1", "1", "-1", "-1", "1", "1", "1", "1", "0", "0" ], [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "0", "0", "0", "1", "0", "0", "0", "0", "0" ] ], "unknown_order": [ "initial_urate_inventory", "terminal_urate_inventory", "systemic_urate_influx", "other_urate_influx", "uox_urate_removal", "reabsorption_loss", "outflow_loss", "unattributed_residual_loss", "systemic_origin_uox_removal", "integrated_active_capacity" ], "matrix_rank": 4, "targets": [ { "target": "local_uox_removal", "status": "STRUCTURALLY_IDENTIFIABLE_UNDER_IDEAL_OBSERVATION", "augmented_ranks": [ 4 ] }, { "target": "inventory_change", "status": "STRUCTURALLY_IDENTIFIABLE_UNDER_IDEAL_OBSERVATION", "augmented_ranks": [ 4 ] }, { "target": "total_local_influx", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 5 ] }, { "target": "systemic_origin_uox_removal", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 5 ] }, { "target": "integrated_active_capacity", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 5 ] }, { "target": "local_ledger_closed", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 4, 4, 5, 5, 4, 5, 5, 5 ] } ] }, { "order": 3, "measurement_combination": "add_calibrated_reaction_site_capacity", "product_observation_mode": "ideal_product_observation", "direct_observations": [ "initial_urate_inventory", "terminal_urate_inventory", "integrated_active_capacity" ], "conditional_observations_included": [ "uox_urate_removal" ], "equations": [ "governing:integrated_local_urate_mass_balance", "direct_observation:initial_urate_inventory", "direct_observation:terminal_urate_inventory", "direct_observation:integrated_active_capacity", "conditional_product_observation:uox_urate_removal" ], "coefficient_matrix": [ [ "-1", "1", "-1", "-1", "1", "1", "1", "1", "0", "0" ], [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "0", "0", "0", "0", "1" ], [ "0", "0", "0", "0", "1", "0", "0", "0", "0", "0" ] ], "unknown_order": [ "initial_urate_inventory", "terminal_urate_inventory", "systemic_urate_influx", "other_urate_influx", "uox_urate_removal", "reabsorption_loss", "outflow_loss", "unattributed_residual_loss", "systemic_origin_uox_removal", "integrated_active_capacity" ], "matrix_rank": 5, "targets": [ { "target": "local_uox_removal", "status": "STRUCTURALLY_IDENTIFIABLE_UNDER_IDEAL_OBSERVATION", "augmented_ranks": [ 5 ] }, { "target": "inventory_change", "status": "STRUCTURALLY_IDENTIFIABLE_UNDER_IDEAL_OBSERVATION", "augmented_ranks": [ 5 ] }, { "target": "total_local_influx", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 6 ] }, { "target": "systemic_origin_uox_removal", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 6 ] }, { "target": "integrated_active_capacity", "status": "STRUCTURALLY_IDENTIFIABLE_UNDER_IDEAL_OBSERVATION", "augmented_ranks": [ 5 ] }, { "target": "local_ledger_closed", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 5, 5, 6, 6, 5, 6, 6, 6 ] } ] }, { "order": 4, "measurement_combination": "add_source_and_boundary_fate", "product_observation_mode": "ideal_product_observation", "direct_observations": [ "initial_urate_inventory", "terminal_urate_inventory", "systemic_urate_influx", "other_urate_influx", "reabsorption_loss", "outflow_loss", "integrated_active_capacity" ], "conditional_observations_included": [ "uox_urate_removal", "systemic_origin_uox_removal" ], "equations": [ "governing:integrated_local_urate_mass_balance", "direct_observation:initial_urate_inventory", "direct_observation:terminal_urate_inventory", "direct_observation:systemic_urate_influx", "direct_observation:other_urate_influx", "direct_observation:reabsorption_loss", "direct_observation:outflow_loss", "direct_observation:integrated_active_capacity", "conditional_product_observation:uox_urate_removal", "conditional_product_observation:systemic_origin_uox_removal" ], "coefficient_matrix": [ [ "-1", "1", "-1", "-1", "1", "1", "1", "1", "0", "0" ], [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "0", "1", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "0", "0", "1", "0", "0", "0", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "1", "0", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "0", "1", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "0", "0", "0", "0", "1" ], [ "0", "0", "0", "0", "1", "0", "0", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "0", "0", "0", "1", "0" ] ], "unknown_order": [ "initial_urate_inventory", "terminal_urate_inventory", "systemic_urate_influx", "other_urate_influx", "uox_urate_removal", "reabsorption_loss", "outflow_loss", "unattributed_residual_loss", "systemic_origin_uox_removal", "integrated_active_capacity" ], "matrix_rank": 10, "targets": [ { "target": "local_uox_removal", "status": "STRUCTURALLY_IDENTIFIABLE_UNDER_IDEAL_OBSERVATION", "augmented_ranks": [ 10 ] }, { "target": "inventory_change", "status": "STRUCTURALLY_IDENTIFIABLE_UNDER_IDEAL_OBSERVATION", "augmented_ranks": [ 10 ] }, { "target": "total_local_influx", "status": "STRUCTURALLY_IDENTIFIABLE_UNDER_IDEAL_OBSERVATION", "augmented_ranks": [ 10 ] }, { "target": "systemic_origin_uox_removal", "status": "STRUCTURALLY_IDENTIFIABLE_UNDER_IDEAL_OBSERVATION", "augmented_ranks": [ 10 ] }, { "target": "integrated_active_capacity", "status": "STRUCTURALLY_IDENTIFIABLE_UNDER_IDEAL_OBSERVATION", "augmented_ranks": [ 10 ] }, { "target": "local_ledger_closed", "status": "STRUCTURALLY_IDENTIFIABLE_UNDER_IDEAL_OBSERVATION", "augmented_ranks": [ 10, 10, 10, 10, 10, 10, 10, 10 ] } ] } ], "product_prerequisites_failed": [ { "order": 1, "measurement_combination": "terminal_urate_amount_only", "product_observation_mode": "product_prerequisites_failed", "direct_observations": [ "terminal_urate_inventory" ], "conditional_observations_included": [], "equations": [ "governing:integrated_local_urate_mass_balance", "direct_observation:terminal_urate_inventory" ], "coefficient_matrix": [ [ "-1", "1", "-1", "-1", "1", "1", "1", "1", "0", "0" ], [ "0", "1", "0", "0", "0", "0", "0", "0", "0", "0" ] ], "unknown_order": [ "initial_urate_inventory", "terminal_urate_inventory", "systemic_urate_influx", "other_urate_influx", "uox_urate_removal", "reabsorption_loss", "outflow_loss", "unattributed_residual_loss", "systemic_origin_uox_removal", "integrated_active_capacity" ], "matrix_rank": 2, "targets": [ { "target": "local_uox_removal", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 3 ] }, { "target": "inventory_change", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 3 ] }, { "target": "total_local_influx", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 3 ] }, { "target": "systemic_origin_uox_removal", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 3 ] }, { "target": "integrated_active_capacity", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 3 ] }, { "target": "local_ledger_closed", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 3, 2, 3, 3, 3, 3, 3, 3 ] } ] }, { "order": 2, "measurement_combination": "inventory_plus_qualified_product_equivalent", "product_observation_mode": "product_prerequisites_failed", "direct_observations": [ "initial_urate_inventory", "terminal_urate_inventory" ], "conditional_observations_included": [], "equations": [ "governing:integrated_local_urate_mass_balance", "direct_observation:initial_urate_inventory", "direct_observation:terminal_urate_inventory" ], "coefficient_matrix": [ [ "-1", "1", "-1", "-1", "1", "1", "1", "1", "0", "0" ], [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "1", "0", "0", "0", "0", "0", "0", "0", "0" ] ], "unknown_order": [ "initial_urate_inventory", "terminal_urate_inventory", "systemic_urate_influx", "other_urate_influx", "uox_urate_removal", "reabsorption_loss", "outflow_loss", "unattributed_residual_loss", "systemic_origin_uox_removal", "integrated_active_capacity" ], "matrix_rank": 3, "targets": [ { "target": "local_uox_removal", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 4 ] }, { "target": "inventory_change", "status": "STRUCTURALLY_IDENTIFIABLE_WITHOUT_PRODUCT_OBSERVATION", "augmented_ranks": [ 3 ] }, { "target": "total_local_influx", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 4 ] }, { "target": "systemic_origin_uox_removal", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 4 ] }, { "target": "integrated_active_capacity", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 4 ] }, { "target": "local_ledger_closed", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 3, 3, 4, 4, 4, 4, 4, 4 ] } ] }, { "order": 3, "measurement_combination": "add_calibrated_reaction_site_capacity", "product_observation_mode": "product_prerequisites_failed", "direct_observations": [ "initial_urate_inventory", "terminal_urate_inventory", "integrated_active_capacity" ], "conditional_observations_included": [], "equations": [ "governing:integrated_local_urate_mass_balance", "direct_observation:initial_urate_inventory", "direct_observation:terminal_urate_inventory", "direct_observation:integrated_active_capacity" ], "coefficient_matrix": [ [ "-1", "1", "-1", "-1", "1", "1", "1", "1", "0", "0" ], [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "0", "0", "0", "0", "1" ] ], "unknown_order": [ "initial_urate_inventory", "terminal_urate_inventory", "systemic_urate_influx", "other_urate_influx", "uox_urate_removal", "reabsorption_loss", "outflow_loss", "unattributed_residual_loss", "systemic_origin_uox_removal", "integrated_active_capacity" ], "matrix_rank": 4, "targets": [ { "target": "local_uox_removal", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 5 ] }, { "target": "inventory_change", "status": "STRUCTURALLY_IDENTIFIABLE_WITHOUT_PRODUCT_OBSERVATION", "augmented_ranks": [ 4 ] }, { "target": "total_local_influx", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 5 ] }, { "target": "systemic_origin_uox_removal", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 5 ] }, { "target": "integrated_active_capacity", "status": "STRUCTURALLY_IDENTIFIABLE_WITHOUT_PRODUCT_OBSERVATION", "augmented_ranks": [ 4 ] }, { "target": "local_ledger_closed", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 4, 4, 5, 5, 5, 5, 5, 5 ] } ] }, { "order": 4, "measurement_combination": "add_source_and_boundary_fate", "product_observation_mode": "product_prerequisites_failed", "direct_observations": [ "initial_urate_inventory", "terminal_urate_inventory", "systemic_urate_influx", "other_urate_influx", "reabsorption_loss", "outflow_loss", "integrated_active_capacity" ], "conditional_observations_included": [], "equations": [ "governing:integrated_local_urate_mass_balance", "direct_observation:initial_urate_inventory", "direct_observation:terminal_urate_inventory", "direct_observation:systemic_urate_influx", "direct_observation:other_urate_influx", "direct_observation:reabsorption_loss", "direct_observation:outflow_loss", "direct_observation:integrated_active_capacity" ], "coefficient_matrix": [ [ "-1", "1", "-1", "-1", "1", "1", "1", "1", "0", "0" ], [ "1", "0", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "1", "0", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "0", "1", "0", "0", "0", "0", "0", "0", "0" ], [ "0", "0", "0", "1", "0", "0", "0", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "1", "0", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "0", "1", "0", "0", "0" ], [ "0", "0", "0", "0", "0", "0", "0", "0", "0", "1" ] ], "unknown_order": [ "initial_urate_inventory", "terminal_urate_inventory", "systemic_urate_influx", "other_urate_influx", "uox_urate_removal", "reabsorption_loss", "outflow_loss", "unattributed_residual_loss", "systemic_origin_uox_removal", "integrated_active_capacity" ], "matrix_rank": 8, "targets": [ { "target": "local_uox_removal", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 9 ] }, { "target": "inventory_change", "status": "STRUCTURALLY_IDENTIFIABLE_WITHOUT_PRODUCT_OBSERVATION", "augmented_ranks": [ 8 ] }, { "target": "total_local_influx", "status": "STRUCTURALLY_IDENTIFIABLE_WITHOUT_PRODUCT_OBSERVATION", "augmented_ranks": [ 8 ] }, { "target": "systemic_origin_uox_removal", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 9 ] }, { "target": "integrated_active_capacity", "status": "STRUCTURALLY_IDENTIFIABLE_WITHOUT_PRODUCT_OBSERVATION", "augmented_ranks": [ 8 ] }, { "target": "local_ledger_closed", "status": "NOT_IDENTIFIABLE", "augmented_ranks": [ 8, 8, 8, 8, 9, 8, 8, 9 ] } ] } ], "scope": "exact structural identifiability under ideal noiseless observation equations; not practical identifiability or assay validation" }, "interpretation": "The conditional capacity identity, concentration-only negative counterexample, and exact structural-identifiability audit passed their preregistered method checks. Positive identifiability is conditional on the named ideal observations; the biological regime and assay performance were not evaluated.", "limitations": [ "The response surface holds C/Km fixed and does not solve a dynamic concentration trajectory.", "No human supply, reabsorption, outflow, oxygen, residence, active-UOX, dose, or serum-urate parameter is estimated.", "The qualified product and source-resolved observations are ideal assumptions, not validated assays.", "Structural identifiability under noiseless equations does not establish practical identifiability, precision, recovery, or a usable biological regime.", "The cumulative measurement combinations are not claimed to be globally minimal.", "A practical local ledger requires a prespecified acceptance bound for unattributed residual loss.", "Peroxide generation, scavenging, tissue exposure, and safety remain assigned to validation section 1.36.", "A measured dynamic compartmental model remains blocked until exact-configuration and boundary-fate data exist." ] }