{
 "about": {
  "method": "one-intermediate-dilution",
  "recordedOn": "2026-10-10",
  "script": "pipeline/lab-calculators/intermediate_reference.py",
  "scriptSha256": "7af26f5de3dbf462ff809a6ef7953a7011328cf26e71adaa224cdd29844000e1",
  "source": "docs/design/intermediate-dilution-increment.md (constraints and the selection rule); every case self-constructed",
  "tolerances": {
   "feasibility": "exact agreement (feasible, or refused with no plan)",
   "direct plans": "within 1e-9 relative",
   "selection": "the engine's final transfer is no larger than the grid plan's and at most one grid step smaller; its stock draw within one grid step of the grid plan's; the engine's plan itself satisfies every constraint within 1e-9 relative",
   "hand case": "exact in rational arithmetic; the engine within 1e-9 relative"
  }
 },
 "oracle": {
  "name": "Python fractions and decimal",
  "version": "3.11.15"
 },
 "count": 13,
 "recordedOn": "2026-10-10",
 "cases": [
  {
   "name": "hand-10mM-to-1uM",
   "about": "The design record's hand case: 10 mM to 1 uM in 1 mL, 2 to 1000 uL transfers, 20 uL stock, 100 uL intermediate vessel, DMSO stock, carrier-free diluents, 0.1 % limit: 2 + 38 uL, then 2 + 998 uL",
   "gridStepMicrolitres": 0.1,
   "source": {
    "stockConcentration": 0.01,
    "finalConcentration": 1e-06,
    "finalVolume": 0.001,
    "concentrationUnit": "mol/L"
   },
   "constraints": {
    "v": 1,
    "solvent": "DMSO",
    "minimumTransfer": 2e-06,
    "maximumTransfer": 0.001,
    "stockAvailable": 2e-05,
    "intermediateCapacity": 0.0001,
    "extraVolume": 0.0,
    "stockSolventFraction": 1.0,
    "intermediateDiluentSolventFraction": 0.0,
    "finalDiluentSolventFraction": 0.0,
    "maximumFinalSolventFraction": 0.001
   },
   "directStockMicrolitres": 0.1,
   "feasible": true,
   "kind": "one-intermediate",
   "gridPlanMicrolitres": {
    "stock": 2.0,
    "intermediateDiluent": 38.0,
    "intermediateVolume": 40.0,
    "transfer": 2.0,
    "finalDiluent": 998.0,
    "remaining": 38.0
   },
   "gridPlanCarrier": 0.0001,
   "gridPlanIntermediateConcentration": 0.0005
  },
  {
   "name": "extra-intermediate-volume",
   "about": "The hand case with 50 uL kept back in the intermediate: the stock draw rises to 2.6 uL",
   "gridStepMicrolitres": 0.1,
   "source": {
    "stockConcentration": 0.01,
    "finalConcentration": 1e-06,
    "finalVolume": 0.001,
    "concentrationUnit": "mol/L"
   },
   "constraints": {
    "v": 1,
    "solvent": "DMSO",
    "minimumTransfer": 2e-06,
    "maximumTransfer": 0.001,
    "stockAvailable": 2e-05,
    "intermediateCapacity": 0.0001,
    "extraVolume": 5e-05,
    "stockSolventFraction": 1.0,
    "intermediateDiluentSolventFraction": 0.0,
    "finalDiluentSolventFraction": 0.0,
    "maximumFinalSolventFraction": 0.001
   },
   "directStockMicrolitres": 0.1,
   "feasible": true,
   "kind": "one-intermediate",
   "gridPlanMicrolitres": {
    "stock": 2.6,
    "intermediateDiluent": 49.4,
    "intermediateVolume": 52.0,
    "transfer": 2.0,
    "finalDiluent": 998.0,
    "remaining": 50.0
   },
   "gridPlanCarrier": 0.0001,
   "gridPlanIntermediateConcentration": 0.0005
  },
  {
   "name": "carrier-in-both-diluents",
   "about": "The hand case with 10 % carrier in the intermediate diluent and 0.02 % in the final diluent, limit 100 %",
   "gridStepMicrolitres": 0.1,
   "source": {
    "stockConcentration": 0.01,
    "finalConcentration": 1e-06,
    "finalVolume": 0.001,
    "concentrationUnit": "mol/L"
   },
   "constraints": {
    "v": 1,
    "solvent": "DMSO",
    "minimumTransfer": 2e-06,
    "maximumTransfer": 0.001,
    "stockAvailable": 2e-05,
    "intermediateCapacity": 0.0001,
    "extraVolume": 0.0,
    "stockSolventFraction": 1.0,
    "intermediateDiluentSolventFraction": 0.1,
    "finalDiluentSolventFraction": 0.0002,
    "maximumFinalSolventFraction": 1.0
   },
   "directStockMicrolitres": 0.1,
   "feasible": true,
   "kind": "one-intermediate",
   "gridPlanMicrolitres": {
    "stock": 2.0,
    "intermediateDiluent": 38.0,
    "intermediateVolume": 40.0,
    "transfer": 2.0,
    "finalDiluent": 998.0,
    "remaining": 38.0
   },
   "gridPlanCarrier": 0.0004896,
   "gridPlanIntermediateConcentration": 0.0005
  },
  {
   "name": "larger-minimum-3uL",
   "about": "The hand case with a 3 uL minimum transfer and a 300 uL vessel",
   "gridStepMicrolitres": 0.1,
   "source": {
    "stockConcentration": 0.01,
    "finalConcentration": 1e-06,
    "finalVolume": 0.001,
    "concentrationUnit": "mol/L"
   },
   "constraints": {
    "v": 1,
    "solvent": "DMSO",
    "minimumTransfer": 3e-06,
    "maximumTransfer": 0.001,
    "stockAvailable": 2e-05,
    "intermediateCapacity": 0.0003,
    "extraVolume": 0.0,
    "stockSolventFraction": 1.0,
    "intermediateDiluentSolventFraction": 0.0,
    "finalDiluentSolventFraction": 0.0,
    "maximumFinalSolventFraction": 0.001
   },
   "directStockMicrolitres": 0.1,
   "feasible": true,
   "kind": "one-intermediate",
   "gridPlanMicrolitres": {
    "stock": 3.0,
    "intermediateDiluent": 87.0,
    "intermediateVolume": 90.0,
    "transfer": 3.0,
    "finalDiluent": 997.0,
    "remaining": 87.0
   },
   "gridPlanCarrier": 0.0001,
   "gridPlanIntermediateConcentration": 0.0003333333333333333
  },
  {
   "name": "direct-preferred",
   "about": "10 mM to 100 uM in 1 mL: a 10 uL direct addition is in range and within a 1 % carrier limit, so no intermediate",
   "gridStepMicrolitres": 0.1,
   "source": {
    "stockConcentration": 0.01,
    "finalConcentration": 0.0001,
    "finalVolume": 0.001,
    "concentrationUnit": "mol/L"
   },
   "constraints": {
    "v": 1,
    "solvent": "DMSO",
    "minimumTransfer": 2e-06,
    "maximumTransfer": 0.001,
    "stockAvailable": 2e-05,
    "intermediateCapacity": 0.0001,
    "extraVolume": 0.0,
    "stockSolventFraction": 1.0,
    "intermediateDiluentSolventFraction": 0.0,
    "finalDiluentSolventFraction": 0.0,
    "maximumFinalSolventFraction": 0.01
   },
   "directStockMicrolitres": 10.0,
   "feasible": true,
   "kind": "direct",
   "gridPlanMicrolitres": {
    "stock": 10.0,
    "transfer": 10.0,
    "finalDiluent": 990.0
   },
   "gridPlanCarrier": 0.01
  },
  {
   "name": "small-volumes-with-reserve",
   "about": "10 mM to 2 mM in 20 uL with 2 to 12 uL transfers, 10 uL stock, 20 uL vessel, 2 uL reserve: the 4 uL direct addition would leave 16 uL of diluent, above the maximum",
   "gridStepMicrolitres": 0.05,
   "source": {
    "stockConcentration": 0.01,
    "finalConcentration": 0.002,
    "finalVolume": 2e-05,
    "concentrationUnit": "mol/L"
   },
   "constraints": {
    "v": 1,
    "solvent": "DMSO",
    "minimumTransfer": 2e-06,
    "maximumTransfer": 1.2e-05,
    "stockAvailable": 1e-05,
    "intermediateCapacity": 2e-05,
    "extraVolume": 2e-06,
    "stockSolventFraction": 1.0,
    "intermediateDiluentSolventFraction": 0.0,
    "finalDiluentSolventFraction": 0.0,
    "maximumFinalSolventFraction": 1.0
   },
   "directStockMicrolitres": 4.0,
   "feasible": true,
   "kind": "one-intermediate",
   "gridPlanMicrolitres": {
    "stock": 5.0,
    "intermediateDiluent": 5.0,
    "intermediateVolume": 10.0,
    "transfer": 8.0,
    "finalDiluent": 12.0,
    "remaining": 2.0
   },
   "gridPlanCarrier": 0.2,
   "gridPlanIntermediateConcentration": 0.005
  },
  {
   "name": "small-volumes-mixed-carrier",
   "about": "10 mM to 1.5 mM in 20 uL, carriers 0.2 / 0.4 / 0.1 and a 0.2 limit",
   "gridStepMicrolitres": 0.05,
   "source": {
    "stockConcentration": 0.01,
    "finalConcentration": 0.0015,
    "finalVolume": 2e-05,
    "concentrationUnit": "mol/L"
   },
   "constraints": {
    "v": 1,
    "solvent": "DMSO",
    "minimumTransfer": 2e-06,
    "maximumTransfer": 1.2e-05,
    "stockAvailable": 1e-05,
    "intermediateCapacity": 2e-05,
    "extraVolume": 2e-06,
    "stockSolventFraction": 0.2,
    "intermediateDiluentSolventFraction": 0.4,
    "finalDiluentSolventFraction": 0.1,
    "maximumFinalSolventFraction": 0.2
   },
   "directStockMicrolitres": 3.0,
   "feasible": true,
   "kind": "one-intermediate",
   "gridPlanMicrolitres": {
    "stock": 3.75,
    "intermediateDiluent": 6.25,
    "intermediateVolume": 10.0,
    "transfer": 8.0,
    "finalDiluent": 12.0,
    "remaining": 2.0
   },
   "gridPlanCarrier": 0.19,
   "gridPlanIntermediateConcentration": 0.00375
  },
  {
   "name": "all-final-volume-transfer",
   "about": "A transfer equal to the final volume (no final diluent) when no smaller transfer leaves an in-range diluent",
   "gridStepMicrolitres": 0.05,
   "source": {
    "stockConcentration": 0.01,
    "finalConcentration": 0.001,
    "finalVolume": 4e-06,
    "concentrationUnit": "mol/L"
   },
   "constraints": {
    "v": 1,
    "solvent": "DMSO",
    "minimumTransfer": 3e-06,
    "maximumTransfer": 6e-05,
    "stockAvailable": 1e-05,
    "intermediateCapacity": 6e-05,
    "extraVolume": 0.0,
    "stockSolventFraction": 1.0,
    "intermediateDiluentSolventFraction": 0.0,
    "finalDiluentSolventFraction": 0.0,
    "maximumFinalSolventFraction": 1.0
   },
   "directStockMicrolitres": 0.4,
   "feasible": true,
   "kind": "one-intermediate",
   "gridPlanMicrolitres": {
    "stock": 3.0,
    "intermediateDiluent": 27.0,
    "intermediateVolume": 30.0,
    "transfer": 4.0,
    "finalDiluent": 0.0,
    "remaining": 26.0
   },
   "gridPlanCarrier": 0.1,
   "gridPlanIntermediateConcentration": 0.001
  },
  {
   "name": "refused-carrier-limit",
   "about": "The hand case with a 0.009 % carrier limit: with carrier-free diluents the stock alone carries Fs x Cf / Cs = 0.01 %",
   "gridStepMicrolitres": 0.5,
   "source": {
    "stockConcentration": 0.01,
    "finalConcentration": 1e-06,
    "finalVolume": 0.001,
    "concentrationUnit": "mol/L"
   },
   "constraints": {
    "v": 1,
    "solvent": "DMSO",
    "minimumTransfer": 2e-06,
    "maximumTransfer": 0.001,
    "stockAvailable": 2e-05,
    "intermediateCapacity": 0.0001,
    "extraVolume": 0.0,
    "stockSolventFraction": 1.0,
    "intermediateDiluentSolventFraction": 0.0,
    "finalDiluentSolventFraction": 0.0,
    "maximumFinalSolventFraction": 9e-05
   },
   "directStockMicrolitres": 0.1,
   "feasible": false,
   "certificate": "With carrier-free diluents every plan carries Fs * q / Vfinal = 1e-4 > 9e-5 of carrier into the final volume."
  },
  {
   "name": "refused-small-vessel",
   "about": "The hand case with a 10 uL intermediate vessel",
   "gridStepMicrolitres": 0.1,
   "source": {
    "stockConcentration": 0.01,
    "finalConcentration": 1e-06,
    "finalVolume": 0.001,
    "concentrationUnit": "mol/L"
   },
   "constraints": {
    "v": 1,
    "solvent": "DMSO",
    "minimumTransfer": 2e-06,
    "maximumTransfer": 0.001,
    "stockAvailable": 2e-05,
    "intermediateCapacity": 1e-05,
    "extraVolume": 0.0,
    "stockSolventFraction": 1.0,
    "intermediateDiluentSolventFraction": 0.0,
    "finalDiluentSolventFraction": 0.0,
    "maximumFinalSolventFraction": 0.001
   },
   "directStockMicrolitres": 0.1,
   "feasible": false,
   "certificate": "A direct addition (0.1 uL) is below the minimum, and any intermediate needs V = x t / q >= min * min / q = 40 uL > 10 uL."
  },
  {
   "name": "refused-final-diluent-split",
   "about": "The hand case with a 100 uL maximum single transfer: about 998 uL of final diluent would need splitting",
   "gridStepMicrolitres": 0.5,
   "source": {
    "stockConcentration": 0.01,
    "finalConcentration": 1e-06,
    "finalVolume": 0.001,
    "concentrationUnit": "mol/L"
   },
   "constraints": {
    "v": 1,
    "solvent": "DMSO",
    "minimumTransfer": 2e-06,
    "maximumTransfer": 0.0001,
    "stockAvailable": 2e-05,
    "intermediateCapacity": 0.0001,
    "extraVolume": 0.0,
    "stockSolventFraction": 1.0,
    "intermediateDiluentSolventFraction": 0.0,
    "finalDiluentSolventFraction": 0.0,
    "maximumFinalSolventFraction": 0.001
   },
   "directStockMicrolitres": 0.1,
   "feasible": false,
   "certificate": "Any final transfer t <= 100 uL leaves Vfinal - t >= 900 uL of final diluent, above the 100 uL maximum and not zero."
  },
  {
   "name": "refused-insufficient-stock",
   "about": "Only 0.09 uL of stock for a 0.1 uL stock equivalent",
   "gridStepMicrolitres": 0.5,
   "source": {
    "stockConcentration": 0.01,
    "finalConcentration": 1e-06,
    "finalVolume": 0.001,
    "concentrationUnit": "mol/L"
   },
   "constraints": {
    "v": 1,
    "solvent": "DMSO",
    "minimumTransfer": 2e-06,
    "maximumTransfer": 0.001,
    "stockAvailable": 9e-08,
    "intermediateCapacity": 0.0001,
    "extraVolume": 0.0,
    "stockSolventFraction": 1.0,
    "intermediateDiluentSolventFraction": 0.0,
    "finalDiluentSolventFraction": 0.0,
    "maximumFinalSolventFraction": 0.001
   },
   "directStockMicrolitres": 0.1,
   "feasible": false,
   "certificate": "Every plan draws at least q = 0.1 uL of stock; 0.09 uL is available."
  },
  {
   "name": "refused-reserve-exceeds-vessel",
   "about": "A 101 uL reserve in a 100 uL vessel",
   "gridStepMicrolitres": 0.5,
   "source": {
    "stockConcentration": 0.01,
    "finalConcentration": 1e-06,
    "finalVolume": 0.001,
    "concentrationUnit": "mol/L"
   },
   "constraints": {
    "v": 1,
    "solvent": "DMSO",
    "minimumTransfer": 2e-06,
    "maximumTransfer": 0.001,
    "stockAvailable": 2e-05,
    "intermediateCapacity": 0.0001,
    "extraVolume": 0.000101,
    "stockSolventFraction": 1.0,
    "intermediateDiluentSolventFraction": 0.0,
    "finalDiluentSolventFraction": 0.0,
    "maximumFinalSolventFraction": 0.001
   },
   "directStockMicrolitres": 0.1,
   "feasible": false,
   "certificate": "The direct addition is below the minimum, and the intermediate must hold more than its 101 uL reserve, above its 100 uL capacity."
  }
 ]
}