{
  "tool_id": "art-693-isa530-audit-sampling-mus",
  "note": "Golden vectors authored for ISA530-BUILD-1. Worked example provenance: the build spec re-pinned preimage (SLATE-SPEC-REPIN-1) plus independent arithmetic recompute. All amounts synthetic, zero PII. human_sign_off: PENDING.",
  "vectors": [
    {
      "name": "worked-example-mus-sizing",
      "policy_parameters": {
        "method": "monetary_unit_sampling",
        "book_value": 5000000,
        "performance_materiality": 250000,
        "expected_misstatement": 50000,
        "confidence_factor": 3
      },
      "output_payload": {
        "sample_size": 75,
        "sampling_interval": 66667,
        "tolerable_misstatement": 250000,
        "trace": "5000000 * 3 / 200000 = 75; interval = round(5000000 / 75) = 66667",
        "overall": "SAMPLE_COMPUTED"
      },
      "independent_oracle": {
        "source": "ISA530-SAMPLING-BUILD-SPEC.md worked example (SLATE-SPEC-REPIN-1 re-pin, 2026-09-03)",
        "source_digest": "sha256:e79a1004e23351b5bb80cb2ed8ff44892c280da3909e0eca618acbde90fa6712",
        "derivation": "n = ceil(5000000 * 3 / (250000 - 50000)) = 75; interval = round-half-up(5000000 / 75) = 66667; tolerable_misstatement = performance_materiality = 250000. Recomputed independently of the kernel (ISA530-BUILD-1 gate 1): the spec-pinned execution_hash 36492685d0d347c6c3ea669be526ab5325318d3b31ba8516fa3883e1a6a62a1f reproduces from this exact {policy_parameters, output_payload} preimage via _hash.mjs."
      },
      "golden_hash": "36492685d0d347c6c3ea669be526ab5325318d3b31ba8516fa3883e1a6a62a1f"
    },
    {
      "name": "projection-nonzero-misstatement",
      "policy_parameters": {
        "method": "misstatement_projection",
        "sampling_interval": 66667,
        "confidence_factor": 3,
        "sampled_items": [
          {
            "book_amount": 80000,
            "audited_amount": 75000
          },
          {
            "book_amount": 120000,
            "audited_amount": 120000
          },
          {
            "book_amount": 50000,
            "audited_amount": 44000
          }
        ]
      },
      "output_payload": {
        "sampling_interval": 66667,
        "confidence_factor": 3,
        "item_count": 3,
        "usable_item_count": 3,
        "per_item": [
          {
            "seq": 1,
            "book_amount": 80000,
            "audited_amount": 75000,
            "taint_percent": 6.25,
            "projected_amount": 4166.69
          },
          {
            "seq": 2,
            "book_amount": 120000,
            "audited_amount": 120000,
            "taint_percent": 0,
            "projected_amount": 0
          },
          {
            "seq": 3,
            "book_amount": 50000,
            "audited_amount": 44000,
            "taint_percent": 12,
            "projected_amount": 8000.04
          }
        ],
        "projected_misstatement": 12166.73,
        "basic_precision": 200001,
        "basic_precision_note": "basic precision = confidence_factor * sampling_interval, the zero-misstatement reliability allowance added to the projected misstatement before comparison to tolerable misstatement",
        "trace": "3 of 3 sampled item(s) usable; projected misstatement = sum(taint * interval) = 12166.73; basic precision = 3 * 66667 = 200001",
        "overall": "PROJECTED"
      },
      "golden_hash": "5a165cb2ef8102fc291c650e3477c94da6143d8c08f881b4d57e150c6810c709"
    },
    {
      "name": "projection-partial-items-rejected",
      "policy_parameters": {
        "method": "misstatement_projection",
        "sampling_interval": 66667,
        "confidence_factor": 3,
        "sampled_items": [
          {
            "book_amount": 90000,
            "audited_amount": 88000
          },
          {
            "book_amount": -5,
            "audited_amount": 0
          },
          {
            "book_amount": 60000,
            "audited_amount": 60000
          }
        ]
      },
      "output_payload": {
        "sampling_interval": 66667,
        "confidence_factor": 3,
        "item_count": 3,
        "usable_item_count": 2,
        "per_item": [
          {
            "seq": 1,
            "book_amount": 90000,
            "audited_amount": 88000,
            "taint_percent": 2.22,
            "projected_amount": 1481.49
          },
          {
            "seq": 3,
            "book_amount": 60000,
            "audited_amount": 60000,
            "taint_percent": 0,
            "projected_amount": 0
          }
        ],
        "projected_misstatement": 1481.49,
        "basic_precision": 200001,
        "basic_precision_note": "basic precision = confidence_factor * sampling_interval, the zero-misstatement reliability allowance added to the projected misstatement before comparison to tolerable misstatement",
        "trace": "2 of 3 sampled item(s) usable; projected misstatement = sum(taint * interval) = 1481.49; basic precision = 3 * 66667 = 200001",
        "overall": "PROJECTED",
        "warnings": [
          "sampled_items[1]: book_amount must be a positive number and audited_amount a non-negative number"
        ]
      },
      "golden_hash": "b0a6f6d4441f021d80a3b36961492561fea87da320e25e129e4c36781d528361"
    },
    {
      "name": "benford-screen-consistent",
      "policy_parameters": {
        "method": "benford_screen",
        "amounts": [
          10000,
          10138.1,
          10276.2,
          10414.3,
          10552.4,
          10690.5,
          10828.6,
          10959,
          11097.1,
          11235.2,
          11373.3,
          11511.4,
          11649.5,
          11787.6,
          11918,
          12056.1,
          12194.2,
          12332.3,
          12470.4,
          12608.5,
          12746.6,
          12877,
          13015.1,
          13153.2,
          13291.3,
          13429.4,
          13567.5,
          13705.6,
          13836,
          13974.1,
          14112.2,
          14250.3,
          14388.4,
          14526.5,
          14664.6,
          14795,
          14933.1,
          15071.2,
          15209.3,
          15347.4,
          15485.5,
          15623.6,
          15754,
          15892.1,
          16030.2,
          16168.3,
          16306.4,
          16444.5,
          16582.6,
          16713,
          16851.1,
          16989.2,
          17127.3,
          17265.4,
          17403.5,
          17541.6,
          17672,
          17810.1,
          17948.2,
          18086.3,
          20000,
          20138.1,
          20276.2,
          20414.3,
          20552.4,
          20690.5,
          20828.6,
          20959,
          21097.1,
          21235.2,
          21373.3,
          21511.4,
          21649.5,
          21787.6,
          21918,
          22056.1,
          22194.2,
          22332.3,
          22470.4,
          22608.5,
          22746.6,
          22877,
          23015.1,
          23153.2,
          23291.3,
          23429.4,
          23567.5,
          23705.6,
          23836,
          23974.1,
          24112.2,
          24250.3,
          24388.4,
          24526.5,
          24664.6,
          30000,
          30138.1,
          30276.2,
          30414.3,
          30552.4,
          30690.5,
          30828.6,
          30959,
          31097.1,
          31235.2,
          31373.3,
          31511.4,
          31649.5,
          31787.6,
          31918,
          32056.1,
          32194.2,
          32332.3,
          32470.4,
          32608.5,
          32746.6,
          32877,
          33015.1,
          33153.2,
          33291.3,
          40000,
          40138.1,
          40276.2,
          40414.3,
          40552.4,
          40690.5,
          40828.6,
          40959,
          41097.1,
          41235.2,
          41373.3,
          41511.4,
          41649.5,
          41787.6,
          41918,
          42056.1,
          42194.2,
          42332.3,
          42470.4,
          50000,
          50138.1,
          50276.2,
          50414.3,
          50552.4,
          50690.5,
          50828.6,
          50959,
          51097.1,
          51235.2,
          51373.3,
          51511.4,
          51649.5,
          51787.6,
          51918,
          52056.1,
          60000,
          60138.1,
          60276.2,
          60414.3,
          60552.4,
          60690.5,
          60828.6,
          60959,
          61097.1,
          61235.2,
          61373.3,
          61511.4,
          61649.5,
          70000,
          70138.1,
          70276.2,
          70414.3,
          70552.4,
          70690.5,
          70828.6,
          70959,
          71097.1,
          71235.2,
          71373.3,
          71511.4,
          80000,
          80138.1,
          80276.2,
          80414.3,
          80552.4,
          80690.5,
          80828.6,
          80959,
          81097.1,
          81235.2,
          90000,
          90138.1,
          90276.2,
          90414.3,
          90552.4,
          90690.5,
          90828.6,
          90959,
          91097.1,
          91235.2
        ]
      },
      "output_payload": {
        "item_count": 200,
        "usable_count": 200,
        "first_digit_counts": {
          "1": 60,
          "2": 35,
          "3": 25,
          "4": 19,
          "5": 16,
          "6": 13,
          "7": 12,
          "8": 10,
          "9": 10
        },
        "chi_square_statistic": 0.120379,
        "critical_value": 15.507,
        "deviation_flag": false,
        "trace": "200 of 200 amount(s) usable; chi-square = 0.120379 vs 15.507 (8 degrees of freedom, 5% level); observed first digits are CONSISTENT with the Benford distribution",
        "overall": "SCREENED_CONSISTENT"
      },
      "golden_hash": "aca77063d24e2a0d49477fc3851abd6b80ef654e652dbb2f88066177d4e8e1fe"
    },
    {
      "name": "benford-screen-deviates",
      "policy_parameters": {
        "method": "benford_screen",
        "amounts": [
          10000,
          10138.1,
          10276.2,
          10414.3,
          10552.4,
          10690.5,
          10828.6,
          10959,
          11097.1,
          11235.2,
          11373.3,
          11511.4,
          11649.5,
          20000,
          20138.1,
          20276.2,
          20414.3,
          20552.4,
          20690.5,
          20828.6,
          20959,
          21097.1,
          21235.2,
          21373.3,
          21511.4,
          21649.5,
          30000,
          30138.1,
          30276.2,
          30414.3,
          30552.4,
          30690.5,
          30828.6,
          30959,
          31097.1,
          31235.2,
          31373.3,
          31511.4,
          31649.5,
          40000,
          40138.1,
          40276.2,
          40414.3,
          40552.4,
          40690.5,
          40828.6,
          40959,
          41097.1,
          41235.2,
          41373.3,
          41511.4,
          41649.5,
          50000,
          50138.1,
          50276.2,
          50414.3,
          50552.4,
          50690.5,
          50828.6,
          50959,
          51097.1,
          51235.2,
          51373.3,
          51511.4,
          51649.5,
          60000,
          60138.1,
          60276.2,
          60414.3,
          60552.4,
          60690.5,
          60828.6,
          60959,
          61097.1,
          61235.2,
          61373.3,
          61511.4,
          61649.5,
          70000,
          70138.1,
          70276.2,
          70414.3,
          70552.4,
          70690.5,
          70828.6,
          70959,
          71097.1,
          71235.2,
          71373.3,
          71511.4,
          71649.5,
          80000,
          80138.1,
          80276.2,
          80414.3,
          80552.4,
          80690.5,
          80828.6,
          80959,
          81097.1,
          81235.2,
          81373.3,
          81511.4,
          81649.5,
          90000,
          90138.1,
          90276.2,
          90414.3,
          90552.4,
          90690.5,
          90828.6,
          90959,
          91097.1,
          91235.2,
          91373.3,
          91511.4,
          91649.5
        ]
      },
      "output_payload": {
        "item_count": 117,
        "usable_count": 117,
        "first_digit_counts": {
          "1": 13,
          "2": 13,
          "3": 13,
          "4": 13,
          "5": 13,
          "6": 13,
          "7": 13,
          "8": 13,
          "9": 13
        },
        "chi_square_statistic": 46.9987,
        "critical_value": 15.507,
        "deviation_flag": true,
        "trace": "117 of 117 amount(s) usable; chi-square = 46.9987 vs 15.507 (8 degrees of freedom, 5% level); observed first digits DEVIATE from the Benford distribution",
        "overall": "SCREENED_DEVIATES"
      },
      "golden_hash": "cbc1e27514610349595fb66925bf825769eccd018b7a23b0572b97f86f17a621"
    },
    {
      "name": "benford-screen-small-sample",
      "policy_parameters": {
        "method": "benford_screen",
        "amounts": [
          10000,
          10138.1,
          10276.2,
          10414.3,
          20000,
          20138.1,
          30000,
          30138.1,
          40000,
          50000,
          60000,
          70000,
          80000,
          90000
        ]
      },
      "output_payload": {
        "item_count": 14,
        "usable_count": 14,
        "first_digit_counts": {
          "1": 4,
          "2": 2,
          "3": 2,
          "4": 1,
          "5": 1,
          "6": 1,
          "7": 1,
          "8": 1,
          "9": 1
        },
        "chi_square_statistic": 0.601062,
        "critical_value": 15.507,
        "deviation_flag": false,
        "trace": "14 of 14 amount(s) usable; chi-square = 0.601062 vs 15.507 (8 degrees of freedom, 5% level); observed first digits are CONSISTENT with the Benford distribution; small sample: fewer than 110 usable amounts leave every expected cell below 5, weakening the screen",
        "overall": "SCREENED_CONSISTENT"
      },
      "golden_hash": "abb04c54454a336ef0d6883e710b148bd6e9bca991fb70b9dd224ca306b19e3b"
    },
    {
      "name": "sizing-fail-closed-em-not-below-pm",
      "policy_parameters": {
        "method": "monetary_unit_sampling",
        "book_value": 5000000,
        "performance_materiality": 250000,
        "expected_misstatement": 300000,
        "confidence_factor": 3
      },
      "output_payload": {
        "sample_size": null,
        "sampling_interval": null,
        "tolerable_misstatement": 250000,
        "trace": "sizing refused: expected_misstatement 300000 is not below performance_materiality 250000, so the denominator performance_materiality - expected_misstatement is not positive",
        "overall": "INPUT_REJECTED",
        "warnings": [
          "expected_misstatement: expected_misstatement >= performance_materiality leaves no positive sizing denominator (fail closed)"
        ]
      },
      "golden_hash": "550a9b6e4542eda1790b5a1e2589b4248f0e36b3a85343240c1a9235db19dc0c"
    },
    {
      "name": "sizing-negative-book-value",
      "policy_parameters": {
        "method": "monetary_unit_sampling",
        "book_value": -5,
        "performance_materiality": 250000,
        "expected_misstatement": 50000,
        "confidence_factor": 3
      },
      "output_payload": {
        "sample_size": null,
        "sampling_interval": null,
        "tolerable_misstatement": 250000,
        "trace": "sizing refused: book_value absent or not a positive finite number",
        "overall": "INPUT_REJECTED",
        "warnings": [
          "book_value: absent or not a positive finite number"
        ]
      },
      "golden_hash": "b3dd61c8266377aa0d9497c509af5f05f2faa4471635cccb98fd963a6f3ecfd1"
    },
    {
      "name": "projection-all-items-rejected",
      "policy_parameters": {
        "method": "misstatement_projection",
        "sampling_interval": 66667,
        "confidence_factor": 3,
        "sampled_items": [
          {
            "book_amount": -1,
            "audited_amount": 0
          },
          {
            "book_amount": 0,
            "audited_amount": 5
          }
        ]
      },
      "output_payload": {
        "sampling_interval": 66667,
        "confidence_factor": 3,
        "item_count": 2,
        "usable_item_count": 0,
        "per_item": [],
        "projected_misstatement": null,
        "basic_precision": 200001,
        "basic_precision_note": "basic precision = confidence_factor * sampling_interval, the zero-misstatement reliability allowance",
        "trace": "projection refused: every sampled item was rejected (book_amount must be positive, audited_amount non-negative); nothing to project",
        "overall": "INPUT_REJECTED",
        "warnings": [
          "sampled_items[0]: book_amount must be a positive number and audited_amount a non-negative number",
          "sampled_items[1]: book_amount must be a positive number and audited_amount a non-negative number"
        ]
      },
      "golden_hash": "14bcba1ceb874c58b8e1b49bdab879bb4a09b109c9f943666f8f0ec245709b90"
    },
    {
      "name": "benford-empty-amounts",
      "policy_parameters": {
        "method": "benford_screen",
        "amounts": []
      },
      "output_payload": {
        "item_count": 0,
        "usable_count": 0,
        "first_digit_counts": null,
        "chi_square_statistic": null,
        "critical_value": 15.507,
        "deviation_flag": null,
        "trace": "screen refused: amounts absent, not an array, or empty",
        "overall": "INPUT_REJECTED",
        "warnings": [
          "amounts: absent, not an array, or empty"
        ]
      },
      "golden_hash": "62525b6a97b570ca22607b6008c30d71420578d2054a3bf85781be5aba13db1a"
    },
    {
      "name": "method-not-recognized",
      "policy_parameters": {
        "method": "attribute_sampling",
        "book_value": 5000000,
        "performance_materiality": 250000,
        "expected_misstatement": 50000,
        "confidence_factor": 3
      },
      "output_payload": {
        "sample_size": null,
        "sampling_interval": null,
        "tolerable_misstatement": null,
        "trace": "method absent or not one of monetary_unit_sampling, misstatement_projection, benford_screen; nothing to compute",
        "overall": "INPUT_REJECTED",
        "warnings": [
          "method: absent or not one of monetary_unit_sampling, misstatement_projection, benford_screen"
        ]
      },
      "golden_hash": "9606d0423f00148451fc101e55acfd0bda7732315d0dc4f4f925334694ed4aae"
    }
  ]
}