{
  "selected_operating_envelope": {
    "geometry": "wide-inlet CAD, unchanged",
    "maximum_commanded_flow_mm3_s": 26.4,
    "viscosity_Pa_s": [
      0.5,
      1.0
    ],
    "pressure_budget_Pa": 6500,
    "worst_computed_pressure_Pa": 6478.59692771179,
    "operating_rule": "Use the unchanged selected CAD within the declared tolerance, feed-tube and meniscus bounds, with commanded flow no greater than the computed 26.4 mm3/s bound. The former 30 mm3/s endpoint is rejected for this combined system envelope. Fixed-pressure pulse dosing is qualified only for the stated nominal de-aired case; changed viscosity requires recalculating pressure or pulse duration."
  },
  "synthetic": true,
  "pressure_envelope_cases": 243,
  "fem_geometry_checks": [
    {
      "case": "minimum_resistance",
      "inlet_radius_mm": 1.26,
      "outlet_radius_mm": 0.51,
      "outlet_land_mm": 1.8999999999999986,
      "fem_pressure_Pa": 2824.5135119318707,
      "reduced_pressure_Pa": 2818.2235310040464,
      "relative_error": 0.002226925416094816
    },
    {
      "case": "nominal",
      "inlet_radius_mm": 1.25,
      "outlet_radius_mm": 0.5,
      "outlet_land_mm": 2.0,
      "fem_pressure_Pa": 3071.309379681716,
      "reduced_pressure_Pa": 3064.5755390976,
      "relative_error": 0.0021924982968709594
    },
    {
      "case": "maximum_resistance",
      "inlet_radius_mm": 1.24,
      "outlet_radius_mm": 0.49,
      "outlet_land_mm": 2.1000000000000014,
      "fem_pressure_Pa": 3345.278757753122,
      "reduced_pressure_Pa": 3338.049964044233,
      "relative_error": 0.002160894272901892
    }
  ],
  "reduced_model_upper_factor": 1.00724305515972,
  "worst_pressure_Pa": 7323.080924347813,
  "safe_flow_mm3_s": 26.4,
  "safe_flow_worst_pressure_Pa": 6478.59692771179,
  "synthetic_observations": 30,
  "dose_cases": [
    {
      "case": "deaired",
      "air_volume_mm3": 0,
      "viscosity_factor": 1,
      "compliance_mm3_Pa": 2.5e-07,
      "steady_flow_mm3_s": 20.0,
      "pulse_mm3": 99.99996278200436,
      "tail_mm3": 0.000767827344920429,
      "stored_at_close_mm3": 0.000767827344920429,
      "remaining_mm3": 0.0,
      "inlet_volume_mm3": 100.00073060934929,
      "tau_on_s": 1.8608997818250052e-06,
      "tau_off_s": 3.8391367246021454e-05,
      "closure_pressure_Pa": 3351.309379681716,
      "balance_residual_mm3": 9.654169824679926e-15,
      "pulse_error_mm3": -3.7217995640048684e-05,
      "pulse_pass": true,
      "tail_pass": true
    },
    {
      "case": "small_air_pocket",
      "air_volume_mm3": 25,
      "viscosity_factor": 1,
      "compliance_mm3_Pa": 0.0002469808166790032,
      "steady_flow_mm3_s": 20.0,
      "pulse_mm3": 99.96323147617017,
      "tail_mm3": 0.7585544988676729,
      "stored_at_close_mm3": 0.7585544988676729,
      "remaining_mm3": 9.524123901827374e-24,
      "inlet_volume_mm3": 100.72178597503783,
      "tau_on_s": 0.0018384261914916743,
      "tau_off_s": 0.037927724943383645,
      "closure_pressure_Pa": 3351.309379681716,
      "balance_residual_mm3": -5.551115132649906e-15,
      "pulse_error_mm3": -0.036768523829834976,
      "pulse_pass": true,
      "tail_pass": true
    },
    {
      "case": "large_air_pocket",
      "air_volume_mm3": 250,
      "viscosity_factor": 1,
      "compliance_mm3_Pa": 0.0024675581667900318,
      "steady_flow_mm3_s": 20.0,
      "pulse_mm3": 99.6326497236624,
      "tail_mm3": 7.5399634371012025,
      "stored_at_close_mm3": 7.578634542572445,
      "remaining_mm3": 0.038671105471242355,
      "inlet_volume_mm3": 107.21128426623484,
      "tau_on_s": 0.018367513816880322,
      "tau_off_s": 0.3789317271286223,
      "closure_pressure_Pa": 3351.309379681716,
      "balance_residual_mm3": -4.85722573273506e-17,
      "pulse_error_mm3": -0.36735027633760353,
      "pulse_pass": true,
      "tail_pass": false
    },
    {
      "case": "high_viscosity_same_setting",
      "air_volume_mm3": 0,
      "viscosity_factor": 1.3333333333333333,
      "compliance_mm3_Pa": 2.5e-07,
      "steady_flow_mm3_s": 15.000000000000002,
      "pulse_mm3": 74.99996278200437,
      "tail_mm3": 0.0007678273449204291,
      "stored_at_close_mm3": 0.0007678273449204291,
      "remaining_mm3": 0.0,
      "inlet_volume_mm3": 75.0007306093493,
      "tau_on_s": 2.481199709100007e-06,
      "tau_off_s": 5.118848966136193e-05,
      "closure_pressure_Pa": 3351.3093796817166,
      "balance_residual_mm3": 9.654061404462677e-15,
      "pulse_error_mm3": -25.000037217995626,
      "pulse_pass": false,
      "tail_pass": true
    }
  ],
  "acceptance": [
    {
      "requirement": "6500 Pa at 30 mm3/s, tolerance + supply + meniscus",
      "outcome": "FAIL",
      "evidence": "Worst 7323.08 Pa; original nominal-only maximum was 6142.62 Pa."
    },
    {
      "requirement": "Computed conservative operating range",
      "outcome": "PASS",
      "evidence": "Up to 26.4 mm3/s across this bounded input set; maximum 6478.60 Pa."
    },
    {
      "requirement": "Nominal fixed pulse 100 +/- 1 mm3",
      "outcome": "PASS",
      "evidence": "De-aired pulse 99.999963 mm3."
    },
    {
      "requirement": "Shutoff after large air pocket",
      "outcome": "FAIL",
      "evidence": "7.540 mm3 tail in 2 s exceeds 1 mm3."
    },
    {
      "requirement": "Unchanged setting after viscosity increase",
      "outcome": "FAIL",
      "evidence": "75.000 mm3 during pulse."
    }
  ],
  "checks": [
    {
      "id": "resistance_pipe",
      "description": "Constant-radius reduction",
      "expected": "matches 8 mu L/(pi r^4) to 1e-12",
      "observed": 38.19718634205488,
      "passed": true,
      "method": "Independent closed-form benchmark"
    },
    {
      "id": "fem_minimum_resistance",
      "description": "Reduced resistance checked at minimum_resistance",
      "expected": "relative pressure error < 0.01",
      "observed": 0.002226925416094816,
      "passed": true,
      "method": "New axisymmetric P2/P1 Stokes solve at 120x24 mesh"
    },
    {
      "id": "fem_nominal",
      "description": "Reduced resistance checked at nominal",
      "expected": "relative pressure error < 0.01",
      "observed": 0.0021924982968709594,
      "passed": true,
      "method": "New axisymmetric P2/P1 Stokes solve at 120x24 mesh"
    },
    {
      "id": "fem_maximum_resistance",
      "description": "Reduced resistance checked at maximum_resistance",
      "expected": "relative pressure error < 0.01",
      "observed": 0.002160894272901892,
      "passed": true,
      "method": "New axisymmetric P2/P1 Stokes solve at 120x24 mesh"
    },
    {
      "id": "adverse_pressure_detected",
      "description": "Upper range including tolerances, feed and meniscus",
      "expected": "at least one 30 mm3/s case exceeds unchanged 6500 Pa budget",
      "observed": 7323.080924347813,
      "passed": true,
      "method": "Full factorial reduced-order tolerance study; checked FEM correction"
    },
    {
      "id": "guardband",
      "description": "Conservative flow bound from the same model",
      "expected": "pressure <= 6500 Pa for every enumerated case",
      "observed": 6478.59692771179,
      "passed": true,
      "method": "Worst permissible flow rounded down to 0.1 mm3/s; original target retained"
    },
    {
      "id": "creeping_regime",
      "description": "Flow regime over tolerance envelope",
      "expected": "max Re < 0.1",
      "observed": 0.07795344151439773,
      "passed": true,
      "method": "Outlet diameter and mean velocity"
    },
    {
      "id": "synthetic_fit",
      "description": "Recover a declared resistance despite pressure offset/noise",
      "expected": "relative slope error < 1% in both cases",
      "observed": 0.0031243688050183183,
      "passed": true,
      "method": "Least squares with intercept on 3 flows x 5 repeats; seed recorded"
    },
    {
      "id": "obstruction",
      "description": "Detect synthetic added restriction",
      "expected": "fitted resistance increase > 20%",
      "observed": 0.24611992667555804,
      "passed": true,
      "method": "25% resistance challenge compared with clean run"
    },
    {
      "id": "volume_balance",
      "description": "Compliant dosing volume balance",
      "expected": "absolute residual < 1e-10 mm3",
      "observed": 9.654169824679926e-15,
      "passed": true,
      "method": "Closed-form inlet = pulse + tail + stored remainder"
    },
    {
      "id": "zero_compliance",
      "description": "Zero-compliance limiting case",
      "expected": "100 mm3 delivered during pulse and zero tail",
      "observed": 100.0,
      "passed": true,
      "method": "Analytical steady resistance network"
    },
    {
      "id": "adverse_air",
      "description": "Large trapped air affects shutoff",
      "expected": "250 mm3 air case exceeds 1 mm3 tail criterion",
      "observed": 7.5399634371012025,
      "passed": true,
      "method": "Linear isothermal gas-compliance sensitivity; no bubble transport claim"
    },
    {
      "id": "adverse_viscosity",
      "description": "Fixed pulse is not a volume controller",
      "expected": "1 Pa s case misses 100 +/- 1 mm3 target",
      "observed": 74.99996278200437,
      "passed": true,
      "method": "Same regulator setting and pulse length; changed viscosity"
    },
    {
      "id": "input_rejection",
      "description": "Invalid resistance inputs",
      "expected": "3 invalid cases rejected",
      "observed": 3,
      "passed": true,
      "method": "Zero bore, duplicate station and nonfinite viscosity"
    }
  ]
}