{
  "format": "lemonergy/cross-tool-benchmark-evidence@1",
  "benchmarkId": "MW-HPPC-2RC-SOC40-25C",
  "recordedAtUtc": "2026-10-01T15:47:38.477Z",
  "verdict": "pass",
  "source": {
    "vendor": "MathWorks",
    "product": "MATLAB / Simscape Battery",
    "example": "Estimate Battery Model Parameters from HPPC Data",
    "url": "https://www.mathworks.com/help/simscape-battery/ug/estimate-battery-model-parameters-from-hppc-data.html",
    "introduced": "R2025a",
    "evidenceTier": "published-numeric-table",
    "retrievedOn": "2026-08-23",
    "executionMode": "published-parameter-distillation-third-party-tool-not-run",
    "references": [
      {
        "role": "parameter solution and measured pulse observables",
        "url": "https://www.mathworks.com/help/simscape-battery/ug/estimate-battery-model-parameters-from-hppc-data.html"
      },
      {
        "role": "BAK HPPC dataset and cell-characterization context",
        "url": "https://www.mathworks.com/help/simscape-battery/ug/battery-cell-characterization-for-ev.html"
      }
    ]
  },
  "operatingPoint": {
    "cell": "BAK N18650CL-29",
    "capacityAh": 2.84,
    "temperatureC": 25,
    "soc": 0.4,
    "direction": "discharge",
    "sourceCurrentA": -6.1871,
    "lemonergyCurrentPositive": "discharge",
    "lemonergyCurrentA": 6.1871,
    "sourcePulseDurationS": 30
  },
  "distillation": {
    "equation": "V=OCV-I*R0-v1-v2; vk[n]=exp(-dt/tauk)*vk[n-1]+I[n]*Rk*(1-exp(-dt/tauk))",
    "samplePeriodS": 0.1,
    "calibrationCurrentA": 6.1871,
    "holdoutCurrentA": 5,
    "sequence": [
      {
        "mode": "rest",
        "durationS": 10
      },
      {
        "mode": "pulse",
        "durationS": 30
      },
      {
        "mode": "rest",
        "durationS": 70
      },
      {
        "mode": "pulse",
        "durationS": 30
      },
      {
        "mode": "rest",
        "durationS": 70
      }
    ],
    "purpose": "Recover the published R0/R1/tau1 solution with Lemonergy while holding the published slow branch fixed, then score a separately generated current-amplitude holdout.",
    "slowBranchPolicy": "Not tuned in this first run: the public 30 s pulse is shorter than Lemonergy's conservative three-time-constant excitation gate for tau2=20.73 s.",
    "oracleClassification": "synthetic analytical oracle authored from the published parameter row; not a replay of the measured MathWorks HPPC trace",
    "transformations": [
      "Author a uniform 0.1 s grid; this is a benchmark choice, not asserted as the source acquisition sample period.",
      "Normalize the source negative-discharge sign to positive-discharge current.",
      "Prepend a 10 s rest with zero RC polarization.",
      "Use a 30 s constant-current pulse followed by a 70 s rest.",
      "Duplicate the pulse-and-rest pair to exercise repeatability and relaxation memory.",
      "Generate a separate 5 A scale-only synthetic holdout from the same linear 2-RC parameter set.",
      "Hold OCV and all published parameters constant over each authored trace.",
      "Use exact zero-order-hold RC state updates and record voltage at the end of each 0.1 s step.",
      "Represent the cell as a 1s1p Lemonergy pack, so cell and pack current/voltage are numerically identical after the recorded scope normalization."
    ],
    "stateOfChargeMovement": {
      "calibrationApproximateDelta": 0.036309272300469486,
      "holdoutApproximateDelta": 0.029342723004694836,
      "interpretation": "The source row is treated as a local parameter operating point even though the authored two-pulse traces move SOC. OCV and parameters remain frozen by design."
    }
  },
  "referenceSha256": "1c68e69dac0b4134489c53ae82d03ddf3bba3896be66e8adca8e9f574c4bd280",
  "scientificEvidenceSha256": "103833592267373678bd252ef7730cae25333f96c9489cdb8bb19fe96ec8b8b2",
  "normalization": {
    "upstreamMathWorksCurrentSign": "negative-discharge",
    "oracleCurrentSign": "positive-discharge",
    "lemonergyCurrentSign": "positive-discharge",
    "upstreamMathWorksCurrentScope": "cell",
    "oracleCurrentScope": "cell",
    "lemonergyCurrentScope": "pack",
    "upstreamMathWorksVoltageLocation": "cell-terminal",
    "oracleVoltageLocation": "cell-terminal",
    "lemonergyVoltageLocation": "pack-terminal",
    "topologyScaling": "1s1p-cell-and-pack-numerically-identical",
    "sampleAlignment": "end-of-step",
    "currentHold": "zero-order-hold",
    "samplePeriodS": 0.1,
    "generatedCalibrationSamples": 2100,
    "generatedValidationSamples": 2100,
    "calibrationDatasetChecksum": "23352e756d831d0466e2402aaf98088b1b101073c9d81ab7336f11f8fde72594",
    "validationDatasetChecksum": "efffecc16be44ec009454ca2d4d8e1fc7e9f77fc59684735ea785f6ac624d1c1"
  },
  "environment": {
    "node": "v22.23.2",
    "v8": "12.4.254.21-node.56",
    "platform": "linux",
    "release": "7.0.0-34-generic",
    "arch": "x64",
    "cpuModel": "AMD Ryzen 7 5700U with Radeon Graphics",
    "logicalCpuCount": 4,
    "totalMemoryBytesVisibleToNode": 7784734720
  },
  "runtime": {
    "scope": "dataset materialization, direct forward-model checks, plan construction, governed tuning and fixed-holdout scoring",
    "wallMs": 1831.635097,
    "cpuUserMs": 2307.681,
    "cpuSystemMs": 212.657,
    "rssStartedBytes": 64040960,
    "rssFinishedBytes": 92676096,
    "processMaxRssKiB": 94832
  },
  "comparison": {
    "published": {
      "ocvV": 3.7353,
      "r0Ref": 40.839,
      "rc1R": 2.0343,
      "rc1TauS": 1.1318,
      "rc2R": 12.923,
      "rc2TauS": 20.73,
      "rc1C": 556.35,
      "rc2C": 1604.2,
      "sourceReportedFitPc": 0.000029118
    },
    "lemonergy": {
      "ocvV": 3.7353,
      "r0Ref": 40.841309720795536,
      "rc1R": 2.031905775159659,
      "rc1TauS": 1.1328715909544833,
      "rc1C": 557.5414001987699,
      "rc2R": 12.923,
      "rc2TauS": 20.73,
      "rc2C": 1604.1166911707808,
      "sourceReportedFitPc": null
    },
    "relativeErrorPct": {
      "ocvV": 0,
      "r0Ref": 0.005655674222036224,
      "rc1R": 0.117692810320051,
      "rc1TauS": 0.09468023983772685,
      "rc1C": 0.214145807274177,
      "rc2R": 0,
      "rc2TauS": 0,
      "rc2C": 0.005193169755596369
    },
    "parameterDisposition": {
      "ocvV": "fixed-from-published-operating-point",
      "r0Ref": "fitted-by-lemonergy",
      "rc1R": "fitted-by-lemonergy",
      "rc1TauS": "fitted-by-lemonergy",
      "rc1C": "derived-from-fitted-r1-and-tau1",
      "rc2R": "fixed-at-published-value",
      "rc2TauS": "fixed-at-published-value",
      "rc2C": "derived-from-fixed-r2-and-tau2",
      "sourceReportedFitPc": "recorded-only-source-definition-not-equated-to-rmse"
    },
    "directForwardModelAtPublishedParameters": {
      "calibration": {
        "sampleCount": 2100,
        "rmse": 2.5821992350258483e-13,
        "maxAbs": 4.440892098500626e-13,
        "meanBias": -3.806478941571965e-14,
        "unit": "mV-per-cell"
      },
      "validation": {
        "sampleCount": 2100,
        "rmse": 2.438161272950475e-13,
        "maxAbs": 8.881784197001252e-13,
        "meanBias": 4.842687097888778e-14,
        "unit": "mV-per-cell"
      },
      "work": {
        "calibration": {
          "profileSamples": 2100,
          "nModules": 1,
          "electricalSubstepsPerSample": 1,
          "thermalSubstepsPerElectricalStep": 1,
          "temporalStepsPerSample": 1,
          "integrationStepCount": 2100,
          "thermalNodeUpdateCount": 2100,
          "electricalStepS": 0.1,
          "thermalStepS": 0.1,
          "cthModuleJK": 47,
          "maximumThermalStepS": 0.11897074741245316
        },
        "validation": {
          "profileSamples": 2100,
          "nModules": 1,
          "electricalSubstepsPerSample": 1,
          "thermalSubstepsPerElectricalStep": 1,
          "temporalStepsPerSample": 1,
          "integrationStepCount": 2100,
          "thermalNodeUpdateCount": 2100,
          "electricalStepS": 0.1,
          "thermalStepS": 0.1,
          "cthModuleJK": 47,
          "maximumThermalStepS": 0.11897074741245316
        }
      }
    },
    "authoredTraceSummary": {
      "calibration": {
        "amplitudeA": 6.1871,
        "sampleCount": 2100,
        "durationS": 210,
        "firstPulseEndVoltageV": 3.4088909912841134,
        "minimumVoltageV": 3.408399659588967,
        "approximateEndSocUnderFrozenParameterOracle": 0.36369072769953015,
        "deltaFromSourceMeasuredMinimumMv": 8.299659588967057
      },
      "derivedHoldout": {
        "amplitudeA": 5,
        "sampleCount": 2100,
        "durationS": 210,
        "firstPulseEndVoltageV": 3.471518091904214,
        "minimumVoltageV": 3.47112103052235,
        "approximateEndSocUnderFrozenParameterOracle": 0.3706572769953052,
        "deltaFromSourceMeasuredMinimumMv": 71.02103052234997
      }
    },
    "uncomparedSourceObservables": [
      {
        "name": "measured minimum voltage",
        "sourceValue": 3.4001,
        "unit": "V",
        "status": "not-compared-source-trace-not-imported-authored-protocol-differs"
      },
      {
        "name": "measured voltage trace",
        "sourceValue": null,
        "unit": "V",
        "status": "not-imported"
      },
      {
        "name": "FitPc",
        "sourceValue": 0.000029118,
        "unit": "source-defined-not-assumed",
        "status": "recorded-only-not-equated-to-rmse"
      }
    ],
    "calibrationVoltage": {
      "sampleCount": 2100,
      "rmse": 0.001040870671302867,
      "maxAbs": 0.012598767732630023,
      "meanBias": 0.00014938142149795958,
      "unit": "mV-per-cell"
    },
    "validationVoltage": {
      "sampleCount": 2100,
      "rmse": 0.0008411619913894695,
      "maxAbs": 0.01018148060749624,
      "meanBias": 0.00012072006409666986,
      "unit": "mV-per-cell"
    }
  },
  "gates": {
    "overallRule": "all benchmark checks must pass",
    "checks": [
      {
        "id": "direct-forward-calibration-voltage-rmse",
        "status": "pass",
        "observed": 2.5821992350258483e-13,
        "limit": 0.000001,
        "direction": "less-than-or-equal",
        "unit": "mV-per-cell",
        "detail": "Lemonergy forward simulation at the exact published parameter values must reproduce the separate synthetic analytical oracle.",
        "origin": "Lemonergy benchmark contract; not a MathWorks tolerance",
        "contractRevision": "1.1.0",
        "frozenAtUtc": "2026-08-23T04:00:00.000Z"
      },
      {
        "id": "direct-forward-calibration-voltage-max-absolute",
        "status": "pass",
        "observed": 4.440892098500626e-13,
        "limit": 0.000001,
        "direction": "less-than-or-equal",
        "unit": "mV-per-cell",
        "detail": "Lemonergy forward simulation at the exact published parameter values must preserve sign, units and end-step time alignment.",
        "origin": "Lemonergy benchmark contract; not a MathWorks tolerance",
        "contractRevision": "1.1.0",
        "frozenAtUtc": "2026-08-23T04:00:00.000Z"
      },
      {
        "id": "direct-forward-validation-voltage-rmse",
        "status": "pass",
        "observed": 2.438161272950475e-13,
        "limit": 0.000001,
        "direction": "less-than-or-equal",
        "unit": "mV-per-cell",
        "detail": "Lemonergy forward simulation at the exact published parameter values must reproduce the separate synthetic analytical oracle.",
        "origin": "Lemonergy benchmark contract; not a MathWorks tolerance",
        "contractRevision": "1.1.0",
        "frozenAtUtc": "2026-08-23T04:00:00.000Z"
      },
      {
        "id": "direct-forward-validation-voltage-max-absolute",
        "status": "pass",
        "observed": 8.881784197001252e-13,
        "limit": 0.000001,
        "direction": "less-than-or-equal",
        "unit": "mV-per-cell",
        "detail": "Lemonergy forward simulation at the exact published parameter values must preserve sign, units and end-step time alignment.",
        "origin": "Lemonergy benchmark contract; not a MathWorks tolerance",
        "contractRevision": "1.1.0",
        "frozenAtUtc": "2026-08-23T04:00:00.000Z"
      },
      {
        "id": "lemonergy-caller-policy",
        "status": "pass",
        "observed": "accepted",
        "limit": "accepted",
        "direction": "equal",
        "detail": "All governed tuning and fixed-holdout caller-policy checks must pass.",
        "origin": "Lemonergy benchmark contract; not a MathWorks tolerance",
        "contractRevision": "1.1.0",
        "frozenAtUtc": "2026-08-23T04:00:00.000Z"
      },
      {
        "id": "published-r0-relative-error",
        "status": "pass",
        "observed": 0.005655674222036224,
        "limit": 5,
        "direction": "less-than-or-equal",
        "unit": "percent",
        "detail": "Fitted R0 must satisfy the predeclared internal recovery gate against the rounded published value.",
        "origin": "Lemonergy benchmark contract; not a MathWorks tolerance",
        "contractRevision": "1.1.0",
        "frozenAtUtc": "2026-08-23T04:00:00.000Z"
      },
      {
        "id": "published-r1-relative-error",
        "status": "pass",
        "observed": 0.117692810320051,
        "limit": 10,
        "direction": "less-than-or-equal",
        "unit": "percent",
        "detail": "Fitted R1 must satisfy the predeclared internal recovery gate against the rounded published value.",
        "origin": "Lemonergy benchmark contract; not a MathWorks tolerance",
        "contractRevision": "1.1.0",
        "frozenAtUtc": "2026-08-23T04:00:00.000Z"
      },
      {
        "id": "published-tau1-relative-error",
        "status": "pass",
        "observed": 0.09468023983772685,
        "limit": 10,
        "direction": "less-than-or-equal",
        "unit": "percent",
        "detail": "Fitted tau1 must satisfy the predeclared internal recovery gate against the rounded published value.",
        "origin": "Lemonergy benchmark contract; not a MathWorks tolerance",
        "contractRevision": "1.1.0",
        "frozenAtUtc": "2026-08-23T04:00:00.000Z"
      }
    ],
    "acceptance": {
      "maxVoltageRmseMvPerCell": 2,
      "maxVoltageMaxAbsMvPerCell": 5,
      "maxTemperatureRmseC": null,
      "maxTemperatureMaxAbsC": null,
      "minValidationDatasets": 1,
      "minIncludedSamplesPerDataset": 100,
      "requiredModes": [
        "pulse",
        "rest"
      ],
      "requireNoHoldoutRegression": true,
      "requireNoFittedParameterAtBound": true
    },
    "parameterRelativeErrorPct": {
      "r0Ref": 5,
      "rc1R": 10,
      "rc1TauS": 10
    }
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  "execution": {
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    "adoptedParamsChecksum": "21b0eb473358d38d54161b2368300efa649e5fbdbdd7fd5970c41b2571a55f57",
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      "r0EaJ": 0,
      "r0SocRise": 1,
      "rc1R": 2.746305,
      "rc1TauS": 1.5845199999999997,
      "rc2R": 12.923,
      "rc2TauS": 20.73,
      "hystV": 0,
      "coulombEff": 1,
      "cpCellJkgK": 1000,
      "entropyVK": 0,
      "kCondWK": 4,
      "hCoolWK": 6,
      "uaAmbWK": 2,
      "mdotKgS": 0.05,
      "cpCoolJkgK": 3600,
      "coolantInC": 25,
      "currentImbalance": 1.08,
      "calA": 0.09,
      "calEaJ": 48000,
      "calSocK": 1.2,
      "cycA": 0.55,
      "cycEaJ": 32000,
      "cycCrateK": 0.3,
      "resGrowthK": 2.5,
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      "maxDtS": 0.1
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    "stages": [
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        "id": "ohmic",
        "status": "completed",
        "kind": "group",
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        "fit": [
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        "optimizer": {
          "terminationReason": "max-evaluations",
          "iterations": 12,
          "proposalEvaluations": 27,
          "uniqueEvaluations": 22,
          "simulatedEvaluations": 22,
          "cacheHitProposals": 5,
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          "temporalIntegrationSteps": 46200,
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          "pivotOrder": [
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      "validation": {
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    "authoredTraceSummary": {
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    },
    "uncomparedSourceObservables": [
      {
        "name": "measured minimum voltage",
        "sourceValue": 3.4001,
        "unit": "V",
        "status": "not-compared-source-trace-not-imported-authored-protocol-differs"
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      {
        "name": "measured voltage trace",
        "sourceValue": null,
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        "status": "not-imported"
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      {
        "name": "FitPc",
        "sourceValue": 0.000029118,
        "unit": "source-defined-not-assumed",
        "status": "recorded-only-not-equated-to-rmse"
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    "calibrationVoltage": {
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    "validationVoltage": {
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    "work": {
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      "sensitivityProbeEvaluations": 9,
      "optimizerProposalEvaluations": 171,
      "rejectedOptimizerProposals": 0,
      "optimizerCacheHits": 5,
      "temporalIntegrationSteps": 375900,
      "moduleWeightedIntegrationSteps": 375900,
      "limits": {
        "candidateEvaluations": 180,
        "temporalIntegrationSteps": 3000000,
        "moduleWeightedIntegrationSteps": 3000000
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      "countersResetBetweenStages": false
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    "scientificEvidenceSha256": "103833592267373678bd252ef7730cae25333f96c9489cdb8bb19fe96ec8b8b2"
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  "classification": {
    "caseCompletion": "partial-one-of-multiple-soc-and-temperature-operating-points",
    "publishedParameterAndSyntheticOracleConsistency": "passed",
    "sourceMeasuredWaveformComparison": "not-run-source-trace-not-imported",
    "independentPhysicalValidation": "not-established",
    "matlabExecutionInRunner": "not-run-published-parameter-table-imported",
    "gtSuiteComparison": "not-run-no-authorized-model-or-trace",
    "slowRcFit": "not-run-source-pulse-fails-lemonergy-excitation-gate",
    "optimizerConvergence": "not-claimed-all-stages-used-their-evaluation-budgets"
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  "limitations": [
    "This is a synthetic analytical-oracle distillation from MathWorks' published parameter row, not execution of MATLAB and not replay of the measured MathWorks HPPC waveform.",
    "The derived holdout amplitude is generated from the same published linear 2-RC parameter set; it is not a second measured experiment or statistically independent physical validation.",
    "The source reports a 3.4001 V measured minimum for this row; CT-01 records but does not compare that observable because it does not import the measured trace and authors a different two-pulse protocol.",
    "Passing establishes published-parameter forward-model and governed tuning consistency for one disclosed operating point. It does not establish broad MATLAB parity, GT-SUITE parity, or independent physical validation of the cell model.",
    "The source parameter values are rounded and published without confidence intervals; numerical differences below the source precision must not be presented as physical certainty."
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        "sample": 2003,
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        "sample": 2004,
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        "sample": 2005,
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        "sample": 2006,
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        "sample": 2007,
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      {
        "sample": 2008,
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        "sample": 2009,
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        "sample": 2010,
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        "sample": 2011,
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        "sample": 2016,
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        "sample": 2019,
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      {
        "sample": 2020,
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        "sample": 2022,
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