{
  "protocol": {
    "name": "CVP",
    "version": "1.0.0-proposed",
    "revision": "2026-09-13",
    "spec_sha256": "f62725968356c92930531cd6085db76e216da06e95be53d636b0d2cf3218b148",
    "spec": "https://www.calculatorx.com/developers/cvp/spec/1.0"
  },
  "document_status": "proposed",
  "calculator": {
    "id": "type-a",
    "version": "1.0.0",
    "title": "Type A Uncertainty Calculator",
    "formula_family": "type-a-ua",
    "capability_id": "engineering.uncertainty.type_a",
    "verification_revision": "2026-09-16.o2-o3"
  },
  "profile": "engineering",
  "verified_scope": "Type A u_A = s/√n from a sample (Bessel ddof=1 default, population ddof=0) + O3 mpmath tabulated mean/s/u_A. CSV/JSON/array and sample alias.",
  "deferred_scope": "Not GUM RSS of several uᵢ, not expanded U=k·u_c, not Monte Carlo, and not a standalone SEM product page.",
  "status": "VERIFIED",
  "verification_status": "VERIFIED",
  "production_freshness": "CURRENT",
  "overall_trust": "VERIFIED",
  "runner": {
    "name": "cvp-runner",
    "version": "1.0.0"
  },
  "environment": {
    "runtime": "node",
    "runtime_version": "20.19.2",
    "numeric_model": "IEEE-754 binary64",
    "os": "darwin"
  },
  "suite": {
    "id": "type-a",
    "version": "1.0.0",
    "uri": "https://www.calculatorx.com/evidence/engineering.uncertainty.type_a/1.0.0.json",
    "verification_revision": "2026-09-16.o2-o3"
  },
  "obligation_set": [
    "CVP-PROV-01",
    "CVP-MODEL-01",
    "CVP-SCOPE-01",
    "CVP-UNIT-01",
    "CVP-REF-01",
    "CVP-GOLD-01",
    "CVP-BND-01",
    "CVP-INV-01",
    "CVP-NUM-01",
    "CVP-COV-01",
    "CVP-CONTRACT-01",
    "CVP-DEP-01",
    "CVP-ART-01",
    "CVP-PROD-01",
    "CVP-DIM-01",
    "CVP-PROP-01",
    "CVP-META-01",
    "CVP-IFACE-01"
  ],
  "provenance": {
    "mode": "direct",
    "sources": [
      {
        "label": "JCGM 100:2008 (GUM) — Evaluation of measurement data",
        "kind": "standard",
        "reference": "4.2 Type A evaluation of standard uncertainty",
        "url": "https://www.bipm.org/en/committees/jc/jcgm/publications"
      },
      {
        "label": "JCGM 100:2008 (GUM) — Evaluation of measurement data",
        "kind": "standard",
        "reference": "4.2.3 Experimental standard deviation of the mean",
        "url": "https://www.bipm.org/utils/common/pdf/jcgm/JCGM_100_2008_E.pdf"
      }
    ]
  },
  "reference": {
    "items": [
      {
        "class": "O1",
        "reference_scope": "model",
        "scope": "model",
        "label": "Type A standard uncertainty u_A = s/√n"
      },
      {
        "class": "O3",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Precomputed mpmath high-precision Type A (80 dps) rounded to nearest binary64 — not V8 hypot",
        "engine": {
          "name": "type-a-mpmath-o3",
          "precision_bits": 265,
          "independent_of_iut": true,
          "same_runtime_as_iut": false,
          "library": "mpmath 1.4.1",
          "mpmath_dps": 80,
          "generator_version": "1.0.0",
          "generator_sha256": "4a71448cdb13d2b3e90538b52d9a0dad733b59bcdbc5d97fe8a5a2a951b9b219",
          "table_sha256": "8629cd3cbfd1de1c5f53ac0b6c587c296c4317450809b0d44af2eb2a31712796",
          "seed": "20260916.type-a-o3",
          "source": "https://www.calculatorx.com/developers/cvp/reproduce/type-a-o3-tables.json",
          "public_table": "/developers/cvp/reproduce/type-a-o3-tables.json",
          "public_generator": "/developers/cvp/reproduce/generate-type-a-o3.py"
        }
      },
      {
        "class": "O3",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O3 table vs IUT mean / s / u_A; ≤2 ULP on tabulated vectors only",
        "engine": {
          "name": "type-a-mpmath-o3",
          "precision_bits": 265,
          "independent_of_iut": true,
          "same_runtime_as_iut": false,
          "library": "mpmath 1.4.1",
          "mpmath_dps": 80,
          "generator_version": "1.0.0",
          "generator_sha256": "4a71448cdb13d2b3e90538b52d9a0dad733b59bcdbc5d97fe8a5a2a951b9b219",
          "table_sha256": "8629cd3cbfd1de1c5f53ac0b6c587c296c4317450809b0d44af2eb2a31712796",
          "seed": "20260916.type-a-o3",
          "source": "https://www.calculatorx.com/developers/cvp/reproduce/type-a-o3-tables.json",
          "public_table": "/developers/cvp/reproduce/type-a-o3-tables.json",
          "public_generator": "/developers/cvp/reproduce/generate-type-a-o3.py"
        }
      },
      {
        "class": "O2",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Separate-module Type A oracle — same V8 binary64 as IUT",
        "engine": {
          "name": "type-a-uncertainty-reference",
          "precision_bits": 53,
          "independent_of_iut": true
        }
      },
      {
        "class": "O2",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O2 module backs ≤2 ULP mean / s / u_A comparison vs IUT",
        "engine": {
          "name": "type-a-uncertainty-reference",
          "precision_bits": 53,
          "independent_of_iut": true
        }
      }
    ],
    "notes": "Golden expected values use a separate O2 module (not IUT transcription). O2 shares Node/V8 binary64 with the IUT unless noted otherwise."
  },
  "controls": {
    "CVP-PROV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Sources present on evidence"
    },
    "CVP-MODEL-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Type A u_A = s/√n; Bessel default; O3 tabulated mean/s/u_A"
    },
    "CVP-SCOPE-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Single-sample Type A. Not GUM combination. O3 tabulated vectors only."
    },
    "CVP-UNIT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Homogeneous implied unit on the observations. No implicit conversion."
    },
    "CVP-REF-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "O1 model + O2 expected_values + O2 numerical_behavior + O3 tabulated Type A"
    },
    "CVP-GOLD-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "1/1 legacy golden; 6/6 oracle-backed numeric"
    },
    "CVP-BND-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "3/3 CVP boundary · 3/3 legacy Evidence boundary"
    },
    "CVP-INV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "3 Evidence illegal-input + 4/4 oracle-backed error-code (exact_error_match, not ULP)"
    },
    "CVP-NUM-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "max_error_observed_ulp=1; policy declared a priori"
    },
    "CVP-COV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "7/7 partitions (bessel, population, csv, json, sample-alias, constant, invalid-domain)"
    },
    "CVP-CONTRACT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "4/4 CVP contract"
    },
    "CVP-DEP-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "engine type-a; Node binary64"
    },
    "CVP-ART-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "release_integrity.status=verified · digests: artifact_evidence_sha256=Evidence core (Trust freshness) · cvp_evidence_digest=artifacts.evidence_digest (fingerprint v2) · evidence_bundle_sha256=legacy Evidence JSON bytes · evidence_catalog_digest=attested_catalog_sha256 · production_sha256=bound production report · see artifacts.digest_registry"
    },
    "CVP-PROD-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "this calculator CURRENT · bound snapshot pass @ 2026-09-16T23:18:54.751Z · live site-wide report stale @ 2026-09-16T23:18:57.131Z (4 other capabilities) · local checks pass · attestation_id=bf3fe5ab59e4bbc9e50f340c6c537d3cf046a9b32473980b03131666eea4e751 · This calculator CURRENT · This calculator is not affected · Bound attestation PASS @ 2026-09-16T23:18:54.751Z · Live production status STALE (4 capabilities; 160 remain CURRENT) @ 2026-09-16T23:18:57.131Z · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.0.0 · report output-const=pass · evidence-sha256=pass · semantic-contract=pass · capability-html-public-origin-agree=pass · cvp-manifest-public-origin-agree=pass · cvp-latest-alias-agrees=pass · cvp-immutable-manifest-fetch=pass · cvp-immutable-manifest-sha256=pass · cvp-latest-alias-matches-immutable=pass · cvp-reproduce-manifest-agree=pass · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=58fe84b53a8948a8ed33bf1d0f10c2dc305d423b0415cb204b41bee40e09d0f5 · verified_at=2026-09-16T03:55:31.761Z · evidence_attested_at=2026-09-16T03:55:31.761Z · last_confirmed_current_at=2026-09-16T23:18:54.751Z · rendered_at=2026-09-16T23:18:57.170Z · binds=cvp_core_sha256",
      "check_result": "PASS",
      "production_state": "CURRENT",
      "binding_current": true
    },
    "CVP-DIM-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "Type A standard uncertainty of the mean"
    },
    "CVP-PROP-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "2/2 property · enumerated fixed assertions (not generated; no seed)"
    },
    "CVP-META-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "2/2 metamorphic"
    },
    "CVP-ROUND-01": {
      "result": "SKIP",
      "applicability": "not_applicable",
      "notes": "No inverse / round-trip vectors in pack — control not in obligation set"
    },
    "CVP-XCAL-01": {
      "result": "SKIP",
      "applicability": "not_applicable",
      "notes": "No related calculator in the same formula family / no related-identity peers declared — control not in obligation set"
    },
    "CVP-IFACE-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only."
    },
    "CVP-ORACLE-01": {
      "result": "PASS",
      "applicability": "higher_assurance",
      "notes": "O3 8/8 tabulated vectors vs IUT · O2: mean / sample s / u_A = s/√n vs separate-module identities (≤2 ULP). Not GUM combination, not SEM product page, not Monte Carlo. ≤2 ULP vs O3 applies only to the published tabulated Type A vectors (Bessel, population, scale, constant, two-point, n=5, centered, default ddof). It is not a whole-domain sample-statistics guarantee."
    },
    "CVP-EXP-01": {
      "result": "SKIP",
      "applicability": "optional",
      "notes": "named expert review not performed"
    }
  },
  "tests": {
    "golden": {
      "passed": 6,
      "total": 6,
      "failed": 0,
      "case_ids": [
        "g-123",
        "g-csv",
        "g-json",
        "g-ddof0",
        "g-const",
        "g-sample"
      ]
    },
    "boundary": {
      "passed": 3,
      "total": 3,
      "failed": 0,
      "case_ids": [
        "boundary-type-a-n1",
        "boundary-type-a-missing",
        "boundary-type-a-ddof"
      ]
    },
    "invalid": {
      "passed": 7,
      "total": 7,
      "failed": 0,
      "case_ids": [
        "boundary-type-a-n1",
        "boundary-type-a-missing",
        "boundary-type-a-ddof",
        "inv-n1",
        "inv-missing",
        "inv-ddof",
        "inv-empty"
      ],
      "comparison": "exact_error_match",
      "records": [
        {
          "id": "inv-n1",
          "comparison": "exact_error_match",
          "expected": {
            "code": "VALUE_OUT_OF_RANGE"
          },
          "actual": {
            "code": "VALUE_OUT_OF_RANGE"
          },
          "match": true
        },
        {
          "id": "inv-missing",
          "comparison": "exact_error_match",
          "expected": {
            "code": "MISSING_REQUIRED_INPUT"
          },
          "actual": {
            "code": "MISSING_REQUIRED_INPUT"
          },
          "match": true
        },
        {
          "id": "inv-ddof",
          "comparison": "exact_error_match",
          "expected": {
            "code": "INVALID_INPUT"
          },
          "actual": {
            "code": "INVALID_INPUT"
          },
          "match": true
        },
        {
          "id": "inv-empty",
          "comparison": "exact_error_match",
          "expected": {
            "code": "MISSING_REQUIRED_INPUT"
          },
          "actual": {
            "code": "MISSING_REQUIRED_INPUT"
          },
          "match": true
        }
      ]
    },
    "property": {
      "passed": 2,
      "total": 2,
      "failed": 0,
      "case_ids": [
        "prop-ua",
        "prop-csv"
      ],
      "kind": "fixed",
      "claim_scope": "Enumerated identities: 1,2,3 → mean=2, s=1, u_A=1/√3; CSV equals array. Not generated property tests.",
      "definition_ids": [
        "ua-s-over-sqrt-n",
        "csv-equals-array"
      ]
    },
    "round_trip": {
      "passed": 0,
      "total": 0,
      "failed": 0,
      "case_ids": []
    },
    "metamorphic": {
      "passed": 2,
      "total": 2,
      "failed": 0,
      "case_ids": [
        "meta-scale",
        "meta-shift"
      ],
      "definition_ids": [
        "homogeneous-scale",
        "location-invariance"
      ]
    },
    "contract": {
      "passed": 4,
      "total": 4,
      "failed": 0
    },
    "cross_interface": {
      "passed": 4,
      "total": 4,
      "failed": 0,
      "case_ids": [
        "iface-array",
        "iface-csv",
        "iface-json",
        "iface-invalid-n1"
      ]
    },
    "o3": {
      "passed": 8,
      "total": 8,
      "failed": 0,
      "case_ids": [
        "o3-123",
        "o3-ddof0",
        "o3-scale",
        "o3-const",
        "o3-two",
        "o3-five",
        "o3-neg",
        "o3-default-ddof"
      ],
      "generator_id": "type-a-mpmath-o3",
      "seed": "20260916.type-a-o3",
      "table_sha256": "8629cd3cbfd1de1c5f53ac0b6c587c296c4317450809b0d44af2eb2a31712796",
      "max_error_ulp": 1,
      "reproduce": "python3 generate-type-a-o3.py",
      "table_url": "/developers/cvp/reproduce/type-a-o3-tables.json",
      "generator_url": "/developers/cvp/reproduce/generate-type-a-o3.py",
      "claim_scope": "O2: mean / sample s / u_A = s/√n vs separate-module identities (≤2 ULP). Not GUM combination, not SEM product page, not Monte Carlo. ≤2 ULP vs O3 applies only to the published tabulated Type A vectors (Bessel, population, scale, constant, two-point, n=5, centered, default ddof). It is not a whole-domain sample-statistics guarantee.",
      "reproduce_url": "https://www.calculatorx.com/evidence/engineering.uncertainty.type_a/reproduce"
    }
  },
  "coverage": {
    "partitions": [
      {
        "id": "bessel",
        "description": "Bessel ddof=1 array",
        "exercised": true,
        "case_count": 14
      },
      {
        "id": "population",
        "description": "Population ddof=0",
        "exercised": true,
        "case_count": 2
      },
      {
        "id": "csv",
        "description": "Comma/space separated string",
        "exercised": true,
        "case_count": 2
      },
      {
        "id": "json",
        "description": "JSON array string",
        "exercised": true,
        "case_count": 1
      },
      {
        "id": "sample-alias",
        "description": "sample[] alias for values",
        "exercised": true,
        "case_count": 1
      },
      {
        "id": "constant",
        "description": "Zero-variance sample",
        "exercised": true,
        "case_count": 2
      },
      {
        "id": "invalid-domain",
        "description": "Invalid inputs",
        "exercised": true,
        "case_count": 7
      }
    ]
  },
  "numerical": {
    "representation": "IEEE-754 binary64",
    "claim_scope": "O2: mean / sample s / u_A = s/√n vs separate-module identities (≤2 ULP). Not GUM combination, not SEM product page, not Monte Carlo. ≤2 ULP vs O3 applies only to the published tabulated Type A vectors (Bessel, population, scale, constant, two-point, n=5, centered, default ddof). It is not a whole-domain sample-statistics guarantee.",
    "tolerance": {
      "type": "ulp",
      "value": 2,
      "rationale": "Independent Type A identities vs IUT on same V8 binary64. ≤2 ULP declared a priori.",
      "declared_before_evaluation": true
    },
    "max_error_observed": 1,
    "records": [
      {
        "id": "g-123",
        "reference": {
          "mean": 2,
          "std": 1,
          "u_A": 0.5773502691896258,
          "n": 3,
          "ddof": 1,
          "values": [
            1,
            2,
            3
          ]
        },
        "actual": {
          "mean": 2,
          "std": 1,
          "u_A": 0.5773502691896258,
          "n": 3,
          "ddof": 1,
          "values": [
            1,
            2,
            3
          ]
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "u_A": {
            "ok": true,
            "error_ulp": 0
          },
          "mean": {
            "ok": true,
            "error_ulp": 0
          },
          "std": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "golden"
      },
      {
        "id": "g-csv",
        "reference": {
          "mean": 2,
          "std": 1,
          "u_A": 0.5773502691896258,
          "n": 3,
          "ddof": 1,
          "values": [
            1,
            2,
            3
          ]
        },
        "actual": {
          "mean": 2,
          "std": 1,
          "u_A": 0.5773502691896258,
          "n": 3,
          "ddof": 1,
          "values": [
            1,
            2,
            3
          ]
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "u_A": {
            "ok": true,
            "error_ulp": 0
          },
          "mean": {
            "ok": true,
            "error_ulp": 0
          },
          "std": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "golden"
      },
      {
        "id": "g-json",
        "reference": {
          "mean": 2,
          "std": 1,
          "u_A": 0.5773502691896258,
          "n": 3,
          "ddof": 1,
          "values": [
            1,
            2,
            3
          ]
        },
        "actual": {
          "mean": 2,
          "std": 1,
          "u_A": 0.5773502691896258,
          "n": 3,
          "ddof": 1,
          "values": [
            1,
            2,
            3
          ]
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "u_A": {
            "ok": true,
            "error_ulp": 0
          },
          "mean": {
            "ok": true,
            "error_ulp": 0
          },
          "std": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "golden"
      },
      {
        "id": "g-ddof0",
        "reference": {
          "mean": 2,
          "std": 0.816496580927726,
          "u_A": 0.47140452079103173,
          "n": 3,
          "ddof": 0,
          "values": [
            1,
            2,
            3
          ]
        },
        "actual": {
          "mean": 2,
          "std": 0.816496580927726,
          "u_A": 0.47140452079103173,
          "n": 3,
          "ddof": 0,
          "values": [
            1,
            2,
            3
          ]
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "u_A": {
            "ok": true,
            "error_ulp": 0
          },
          "mean": {
            "ok": true,
            "error_ulp": 0
          },
          "std": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "golden"
      },
      {
        "id": "g-const",
        "reference": {
          "mean": 5,
          "std": 0,
          "u_A": 0,
          "n": 3,
          "ddof": 1,
          "values": [
            5,
            5,
            5
          ]
        },
        "actual": {
          "mean": 5,
          "std": 0,
          "u_A": 0,
          "n": 3,
          "ddof": 1,
          "values": [
            5,
            5,
            5
          ]
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "u_A": {
            "ok": true,
            "error_ulp": 0
          },
          "mean": {
            "ok": true,
            "error_ulp": 0
          },
          "std": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "golden"
      },
      {
        "id": "g-sample",
        "reference": {
          "mean": 2,
          "std": 1,
          "u_A": 0.5773502691896258,
          "n": 3,
          "ddof": 1,
          "values": [
            1,
            2,
            3
          ]
        },
        "actual": {
          "mean": 2,
          "std": 1,
          "u_A": 0.5773502691896258,
          "n": 3,
          "ddof": 1,
          "values": [
            1,
            2,
            3
          ]
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "u_A": {
            "ok": true,
            "error_ulp": 0
          },
          "mean": {
            "ok": true,
            "error_ulp": 0
          },
          "std": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "golden"
      },
      {
        "id": "meta-scale",
        "reference": 10,
        "actual": 10,
        "error_ulp": 0,
        "threshold_ulp": 2,
        "suite": "metamorphic",
        "hops": {
          "base": {
            "reference": {
              "mean": 2,
              "std": 1,
              "u_A": 0.5773502691896258,
              "n": 3,
              "ddof": 1,
              "values": [
                1,
                2,
                3
              ]
            },
            "actual": {
              "mean": 2,
              "std": 1,
              "u_A": 0.5773502691896258,
              "n": 3,
              "ddof": 1,
              "values": [
                1,
                2,
                3
              ]
            },
            "error_ulp": 0
          },
          "follow": {
            "reference": {
              "mean": 20,
              "std": 10,
              "u_A": 5.773502691896258,
              "n": 3,
              "ddof": 1,
              "values": [
                10,
                20,
                30
              ]
            },
            "actual": {
              "mean": 20,
              "std": 10,
              "u_A": 5.773502691896258,
              "n": 3,
              "ddof": 1,
              "values": [
                10,
                20,
                30
              ]
            },
            "error_ulp": 0
          },
          "relation": {
            "reference": 10,
            "actual": 10,
            "error_ulp": 0
          }
        }
      },
      {
        "id": "meta-shift",
        "reference": 1,
        "actual": 1,
        "error_ulp": 0,
        "threshold_ulp": 2,
        "suite": "metamorphic",
        "hops": {
          "base": {
            "reference": {
              "mean": 2,
              "std": 1,
              "u_A": 0.5773502691896258,
              "n": 3,
              "ddof": 1,
              "values": [
                1,
                2,
                3
              ]
            },
            "actual": {
              "mean": 2,
              "std": 1,
              "u_A": 0.5773502691896258,
              "n": 3,
              "ddof": 1,
              "values": [
                1,
                2,
                3
              ]
            },
            "error_ulp": 0
          },
          "follow": {
            "reference": {
              "mean": 102,
              "std": 1,
              "u_A": 0.5773502691896258,
              "n": 3,
              "ddof": 1,
              "values": [
                101,
                102,
                103
              ]
            },
            "actual": {
              "mean": 102,
              "std": 1,
              "u_A": 0.5773502691896258,
              "n": 3,
              "ddof": 1,
              "values": [
                101,
                102,
                103
              ]
            },
            "error_ulp": 0
          },
          "relation": {
            "reference": 1,
            "actual": 1,
            "error_ulp": 0
          }
        }
      },
      {
        "id": "o3-123",
        "reference": {
          "oracle_layer": "analytic",
          "mean": 2,
          "std": 1,
          "u_A": 0.5773502691896257
        },
        "actual": {
          "mean": 2,
          "std": 1,
          "u_A": 0.5773502691896258,
          "n": 3,
          "ddof": 1,
          "values": [
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          ]
        },
        "error_ulp": 1,
        "threshold_ulp": 2,
        "fields": {
          "u_A": {
            "ok": true,
            "error_ulp": 1
          },
          "mean": {
            "ok": true,
            "error_ulp": 0
          },
          "std": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      },
      {
        "id": "o3-ddof0",
        "reference": {
          "oracle_layer": "analytic",
          "mean": 2,
          "std": 0.816496580927726,
          "u_A": 0.4714045207910317
        },
        "actual": {
          "mean": 2,
          "std": 0.816496580927726,
          "u_A": 0.47140452079103173,
          "n": 3,
          "ddof": 0,
          "values": [
            1,
            2,
            3
          ]
        },
        "error_ulp": 1,
        "threshold_ulp": 2,
        "fields": {
          "u_A": {
            "ok": true,
            "error_ulp": 1
          },
          "mean": {
            "ok": true,
            "error_ulp": 0
          },
          "std": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      },
      {
        "id": "o3-scale",
        "reference": {
          "oracle_layer": "analytic",
          "mean": 20,
          "std": 10,
          "u_A": 5.773502691896257
        },
        "actual": {
          "mean": 20,
          "std": 10,
          "u_A": 5.773502691896258,
          "n": 3,
          "ddof": 1,
          "values": [
            10,
            20,
            30
          ]
        },
        "error_ulp": 1,
        "threshold_ulp": 2,
        "fields": {
          "u_A": {
            "ok": true,
            "error_ulp": 1
          },
          "mean": {
            "ok": true,
            "error_ulp": 0
          },
          "std": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      },
      {
        "id": "o3-const",
        "reference": {
          "oracle_layer": "analytic",
          "mean": 5,
          "std": 0,
          "u_A": 0
        },
        "actual": {
          "mean": 5,
          "std": 0,
          "u_A": 0,
          "n": 3,
          "ddof": 1,
          "values": [
            5,
            5,
            5
          ]
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "u_A": {
            "ok": true,
            "error_ulp": 0
          },
          "mean": {
            "ok": true,
            "error_ulp": 0
          },
          "std": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      },
      {
        "id": "o3-two",
        "reference": {
          "oracle_layer": "analytic",
          "mean": 5,
          "std": 2.8284271247461903,
          "u_A": 2
        },
        "actual": {
          "mean": 5,
          "std": 2.8284271247461903,
          "u_A": 2,
          "n": 2,
          "ddof": 1,
          "values": [
            3,
            7
          ]
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "u_A": {
            "ok": true,
            "error_ulp": 0
          },
          "mean": {
            "ok": true,
            "error_ulp": 0
          },
          "std": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      },
      {
        "id": "o3-five",
        "reference": {
          "oracle_layer": "analytic",
          "mean": 3,
          "std": 1.5811388300841898,
          "u_A": 0.7071067811865476
        },
        "actual": {
          "mean": 3,
          "std": 1.5811388300841898,
          "u_A": 0.7071067811865476,
          "n": 5,
          "ddof": 1,
          "values": [
            1,
            2,
            3,
            4,
            5
          ]
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "u_A": {
            "ok": true,
            "error_ulp": 0
          },
          "mean": {
            "ok": true,
            "error_ulp": 0
          },
          "std": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      },
      {
        "id": "o3-neg",
        "reference": {
          "oracle_layer": "analytic",
          "mean": 0,
          "std": 1.5811388300841898,
          "u_A": 0.7071067811865476
        },
        "actual": {
          "mean": 0,
          "std": 1.5811388300841898,
          "u_A": 0.7071067811865476,
          "n": 5,
          "ddof": 1,
          "values": [
            -2,
            -1,
            0,
            1,
            2
          ]
        },
        "error_ulp": 0,
        "threshold_ulp": 2,
        "fields": {
          "u_A": {
            "ok": true,
            "error_ulp": 0
          },
          "mean": {
            "ok": true,
            "error_ulp": 0
          },
          "std": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      },
      {
        "id": "o3-default-ddof",
        "reference": {
          "oracle_layer": "analytic",
          "mean": 2,
          "std": 1,
          "u_A": 0.5773502691896257
        },
        "actual": {
          "mean": 2,
          "std": 1,
          "u_A": 0.5773502691896258,
          "n": 3,
          "ddof": 1,
          "values": [
            1,
            2,
            3
          ]
        },
        "error_ulp": 1,
        "threshold_ulp": 2,
        "fields": {
          "u_A": {
            "ok": true,
            "error_ulp": 1
          },
          "mean": {
            "ok": true,
            "error_ulp": 0
          },
          "std": {
            "ok": true,
            "error_ulp": 0
          }
        },
        "suite": "o3"
      }
    ]
  },
  "interfaces": {
    "compared": [
      "ui-ssr",
      "rest",
      "mcp"
    ],
    "result": "PASS",
    "notes": "UI (SSR) · REST · MCP equivalent (MCP uses calc API handler). ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only."
  },
  "artifacts": {
    "evidence_bundle_sha256": "d721f65867e04918ae1e65db569e949ca8af3c7255a7405e2a82cae8f53f49dd",
    "evidence_digest": "091eb0d8d4cd8cc5cb0303e1528a1532abc5dc950bc604d40da65095b24fe896",
    "production_sha256": "58fe84b53a8948a8ed33bf1d0f10c2dc305d423b0415cb204b41bee40e09d0f5",
    "attested_catalog_sha256": "006a786d7fd29244ed7da1c582af2a6072358ff25a2e07cbc8909b3ae65fb0af",
    "production_checks": [
      {
        "id": "engineering.uncertainty.type_a:output-const",
        "status": "pass",
        "detail": "output const 1.0.0 vs capability 1.0.0",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T03:55:31.761Z"
      },
      {
        "id": "engineering.uncertainty.type_a:evidence-sha256",
        "status": "pass",
        "detail": "7094386abc48",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T03:55:31.761Z"
      },
      {
        "id": "engineering.uncertainty.type_a:semantic-contract",
        "status": "pass",
        "detail": "7/7",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T03:55:31.761Z"
      },
      {
        "id": "engineering.uncertainty.type_a:capability-html-public-origin-agree",
        "status": "pass",
        "detail": "public 1.0.0 vs origin 1.0.0",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T03:55:31.761Z"
      },
      {
        "id": "engineering.uncertainty.type_a:cvp-manifest-public-origin-agree",
        "status": "pass",
        "detail": "engineering.uncertainty.type_a/1.0.0/2026-09-16.o2-o3/engineering/091eb0d8d4cd",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T03:55:31.761Z",
        "projection_compared": false
      },
      {
        "id": "engineering.uncertainty.type_a:cvp-latest-alias-agrees",
        "status": "pass",
        "detail": "engineering.uncertainty.type_a/1.0.0/2026-09-16.o2-o3/engineering/091eb0d8d4cd",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T03:55:31.761Z",
        "projection_compared": false
      },
      {
        "id": "engineering.uncertainty.type_a:cvp-immutable-manifest-fetch",
        "status": "pass",
        "detail": "public=200 origin=200",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T03:55:31.761Z"
      },
      {
        "id": "engineering.uncertainty.type_a:cvp-immutable-manifest-sha256",
        "status": "pass",
        "detail": "091eb0d8d4cd",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T03:55:31.761Z"
      },
      {
        "id": "engineering.uncertainty.type_a:cvp-latest-alias-matches-immutable",
        "status": "pass",
        "detail": "engineering.uncertainty.type_a/1.0.0/2026-09-16.o2-o3/engineering/091eb0d8d4cd",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T03:55:31.761Z",
        "projection_compared": false
      },
      {
        "id": "engineering.uncertainty.type_a:cvp-reproduce-manifest-agree",
        "status": "pass",
        "detail": "2026-09-16.o2-o3 · 8629cd3cbfd1",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T03:55:31.761Z"
      },
      {
        "id": "engineering.uncertainty.type_a:calculator-html-cvp-projection",
        "status": "pass",
        "detail": "matches Trust display",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T03:55:31.761Z"
      },
      {
        "id": "engineering.uncertainty.type_a:evidence-html-cvp-projection",
        "status": "pass",
        "detail": "matches Trust display",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T03:55:31.761Z"
      }
    ],
    "digest_registry": {
      "digest_algorithm": "sha256",
      "canonicalization": "json-sorted-keys-utf8",
      "entries": [
        {
          "name": "cvp_core_sha256",
          "field": "artifacts.cvp_core_sha256",
          "digest_scope": "cvp_verification_fingerprint_v2",
          "value": "091eb0d8d4cd8cc5cb0303e1528a1532abc5dc950bc604d40da65095b24fe896",
          "note": "Immutable verification core; excludes attestation/live-status and Evidence contract counts"
        },
        {
          "name": "cvp_evidence_digest",
          "field": "artifacts.evidence_digest",
          "digest_scope": "cvp_verification_fingerprint_v2",
          "value": "091eb0d8d4cd8cc5cb0303e1528a1532abc5dc950bc604d40da65095b24fe896",
          "note": "Alias of cvp_core_sha256 (historical field name)"
        },
        {
          "name": "artifact_evidence_sha256",
          "field": "release_integrity.digests.evidence_core_sha256",
          "digest_scope": "evidence_artifact_core",
          "value": "7094386abc48072e8840f84fd8fb69f94e6d4d7252934e46cd5a0491b759037d",
          "note": "Published Evidence JSON core — Trust freshness / production bind subject"
        },
        {
          "name": "evidence_catalog_digest",
          "field": "artifacts.attested_catalog_sha256",
          "digest_scope": "capability_catalog",
          "value": "006a786d7fd29244ed7da1c582af2a6072358ff25a2e07cbc8909b3ae65fb0af",
          "note": "Capability catalog integrity; site-wide, not per-suite fingerprint"
        }
      ]
    },
    "cvp_core_sha256": "091eb0d8d4cd8cc5cb0303e1528a1532abc5dc950bc604d40da65095b24fe896"
  },
  "dependencies": [
    {
      "name": "type-a-engine",
      "version": "1.0.0"
    },
    {
      "name": "type-a-reference-oracle",
      "version": "1.0.0"
    },
    {
      "name": "type-a-mpmath-o3-table",
      "version": "type-a-mpmath-o3"
    },
    {
      "name": "node",
      "version": "20.19.2"
    }
  ],
  "attestation": {
    "status": "CURRENT",
    "href": "/.well-known/calculatorx-production-attestation.json",
    "id": "bf3fe5ab59e4bbc9e50f340c6c537d3cf046a9b32473980b03131666eea4e751",
    "attested_at": "2026-09-16T03:55:31.761Z",
    "last_confirmed_current_at": "2026-09-16T23:18:54.751Z",
    "site_attestation_current": false,
    "capability_attestation_current": true,
    "bound_snapshot_status": "pass",
    "live_report_status": "stale",
    "bound_attested_at": "2026-09-16T23:18:54.751Z",
    "live_updated_at": "2026-09-16T23:18:57.131Z",
    "bound_snapshot": {
      "status": "pass",
      "attested_at": "2026-09-16T23:18:54.751Z",
      "site_stale_count": 4
    },
    "live_site_status": {
      "href": "/.well-known/calculatorx-production-attestation.json"
    },
    "bound_snapshot_site_stale_count": 4,
    "site_stale_capability_count": 4,
    "evidence_attested_at": "2026-09-16T03:55:31.761Z"
  },
  "domain_review": {
    "status": "ABSENT",
    "spec_version": "1.0.0",
    "external_third_party": false,
    "note": "Named expert review not performed"
  },
  "timestamps": {
    "verified_at": "2026-09-16T03:55:31.761Z",
    "generated_at": "2026-09-16T03:55:31.761Z",
    "rendered_at": "2026-09-16T23:18:57.170Z",
    "notes": "verified_at/generated_at mark the first publication of this cvp_core_sha256 (artifacts.evidence_digest alias) for suite verification. evidence_attested_at/attested_at is the first production bind of that core digest. last_confirmed_current_at is the latest site-wide report that still confirms CURRENT. rendered_at is this JSON serialization and is not part of cvp_core_sha256 / evidence_digest. Production attestation binds cvp_core_sha256 (binds evidence_digest). Causal order: verified_at ≤ evidence_attested_at ≤ last_confirmed_current_at. attestation.bound_snapshot.site_stale_count is the site-wide stale capability count at Manifest bind time — not a live value. Fetch attestation.live_site_status.href for the current site report."
  },
  "links": {
    "legacy_evidence": "https://www.calculatorx.com/evidence/engineering.uncertainty.type_a/1.0.0.json",
    "evidence_page": "https://www.calculatorx.com/evidence/engineering.uncertainty.type_a/1.0.0",
    "calculator": "https://www.calculatorx.com/calc/engineering/type-a-uncertainty",
    "schema": "https://www.calculatorx.com/developers/cvp/schema/cvp-evidence-1.0.json",
    "protocol": "https://www.calculatorx.com/developers/cvp/spec/1.0",
    "manifest": "https://www.calculatorx.com/evidence/engineering.uncertainty.type_a/1.0.0.cvp.json",
    "manifest_immutable": "https://www.calculatorx.com/evidence/engineering.uncertainty.type_a/1.0.0/2026-09-16.o2-o3.cvp.json",
    "reproduce": "https://www.calculatorx.com/evidence/engineering.uncertainty.type_a/reproduce",
    "o3_table": "https://www.calculatorx.com/developers/cvp/reproduce/type-a-o3-tables.json",
    "o3_generator": "https://www.calculatorx.com/developers/cvp/reproduce/generate-type-a-o3.py",
    "manifest_core": "https://www.calculatorx.com/evidence/engineering.uncertainty.type_a/1.0.0/2026-09-16.o2-o3.091eb0d8d4cd.cvp.json"
  }
}