{
  "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": "lcm",
    "version": "1.0.3",
    "title": "LCM Calculator",
    "formula_family": "lcm",
    "capability_id": "math.lcm",
    "verification_revision": "2026-09-16.sources-no-wolfram"
  },
  "profile": "core",
  "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": "exact_integer",
    "os": "darwin"
  },
  "suite": {
    "id": "lcm",
    "version": "1.0.3",
    "uri": "https://www.calculatorx.com/evidence/math.lcm/1.0.3.json",
    "verification_revision": "2026-09-16.sources-no-wolfram"
  },
  "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-PROP-01",
    "CVP-META-01",
    "CVP-XCAL-01",
    "CVP-IFACE-01"
  ],
  "provenance": {
    "mode": "direct",
    "sources": [
      {
        "label": "Encyclopedia of Mathematics — Least common multiple",
        "kind": "other",
        "reference": "Definition; pairwise fold; relation to GCD",
        "url": "https://encyclopediaofmath.org/wiki/Least_common_multiple"
      },
      {
        "label": "Python math.lcm — zero convention",
        "kind": "other",
        "reference": "If any argument is zero, LCM = 0",
        "url": "https://docs.python.org/3/library/math.html#math.lcm"
      },
      {
        "label": "CalculatorX integer convention",
        "kind": "other",
        "reference": "Absolute value; 48-digit BigInt domain; divide-first identity"
      }
    ]
  },
  "reference": {
    "items": [
      {
        "class": "O1",
        "reference_scope": "model",
        "scope": "model",
        "label": "Least common multiple (pairwise fold)"
      },
      {
        "class": "O2",
        "reference_scope": "expected_values",
        "scope": "expected_values",
        "label": "Separate-module lcm oracle — independent BigInt pairwise |a/GCF×b| dual-checked against prime-power LCM when factorable (own Euclidean GCD; same runtime as IUT; not IUT transcription)",
        "engine": {
          "name": "lcm-reference",
          "independent_of_iut": true,
          "same_runtime_as_iut": true,
          "runtime": "node",
          "numeric_model": "exact_integer",
          "representation": "exact_integer",
          "criterion": "actual exact decimal string === independent oracle exact decimal string",
          "algorithms": [
            "pairwise-gcf-identity",
            "prime-power"
          ],
          "arithmetic": "BigInt",
          "comparison": "exact_equality"
        }
      },
      {
        "class": "O2",
        "reference_scope": "numerical_behavior",
        "scope": "numerical_behavior",
        "label": "Same O2 module backs exact decimal-string identity vs IUT — exact_equality, ULP not applicable",
        "engine": {
          "name": "lcm-reference",
          "independent_of_iut": true,
          "same_runtime_as_iut": true,
          "runtime": "node",
          "numeric_model": "exact_integer",
          "representation": "exact_integer",
          "criterion": "actual exact decimal string === independent oracle exact decimal string",
          "algorithms": [
            "pairwise-gcf-identity",
            "prime-power"
          ],
          "arithmetic": "BigInt",
          "comparison": "exact_equality"
        }
      }
    ],
    "notes": "Golden expected values use a separate O2 module (not IUT transcription). O2 dual-checks pairwise |a/GCF×b| against prime-power LCM when fully factorable. same_runtime_as_iut. Numeric model is exact_integer (ECMAScript BigInt arithmetic, exact_equality). Node is a runtime dependency, not IEEE-754 binary64."
  },
  "controls": {
    "CVP-PROV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "Sources present on evidence"
    },
    "CVP-MODEL-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "LCM(a,b)=|a/GCF(a,b)×b|; exact_integer / BigInt / exact_equality"
    },
    "CVP-SCOPE-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "≥2 integers; any zero → 0"
    },
    "CVP-UNIT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "dimensionless integer"
    },
    "CVP-REF-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "O1 model + O2 expected_values/numerical_behavior (|a/GCF×b| dual-checked against prime-power when factorable; exact_equality; same_runtime_as_iut)"
    },
    "CVP-GOLD-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "6/6 legacy golden; 6/6 oracle-backed numeric"
    },
    "CVP-BND-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "7/7 CVP boundary · 7/7 legacy Evidence boundary"
    },
    "CVP-INV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "3 invalid-domain cases"
    },
    "CVP-NUM-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "exact_integer · BigInt · exact_equality (actual exact decimal string === independent oracle exact decimal string); mismatches=0; ULP not applicable"
    },
    "CVP-COV-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "8/8 declared partitions (lcm, zero, negative, beyond-safe-integer, multi-input-fold, method-unavailable, xcal, invalid-domain) · 6 legacy golden / 7 CVP boundary unique cases · 3 Evidence invalid-input (may overlap boundary)"
    },
    "CVP-CONTRACT-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "3/3 CVP contract"
    },
    "CVP-DEP-01": {
      "result": "PASS",
      "applicability": "required",
      "notes": "engine lcm; exact_integer BigInt (IUT/O2). Node is a runtime dependency, not the numeric model"
    },
    "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 @ 2026-09-16T06:43:50.908Z · live site-wide report stale @ 2026-09-16T06:44:02.844Z (8 other capabilities) · local checks pass · attestation_id=9864b02dd59e627629179439ae27934aea8c6fd24193702e66c56019c5e3e050 · This calculator CURRENT · This calculator is not affected · Bound attestation PASS @ 2026-09-16T06:43:50.908Z · Live production status STALE (8 capabilities; 156 remain CURRENT) @ 2026-09-16T06:44:02.844Z · Public schema 1.0.3 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓ · schema_const=1.0.3 · 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 · calculator-html-cvp-projection=pass · evidence-html-cvp-projection=pass · attested_evidence_sha256=31e075dd2788e7c13520557df716a4e118f4844aca3908f8b06acf4a41fad0cc · verified_at=2026-09-16T06:43:10.491Z · evidence_attested_at=2026-09-16T06:43:10.491Z · last_confirmed_current_at=2026-09-16T06:43:50.908Z · rendered_at=2026-09-16T06:44:02.894Z · binds=cvp_core_sha256",
      "check_result": "PASS",
      "production_state": "CURRENT",
      "binding_current": true
    },
    "CVP-DIM-01": {
      "result": "SKIP",
      "applicability": "not_applicable",
      "notes": "Unitless core calculator — no physical dimension algebra"
    },
    "CVP-PROP-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "3/3 property"
    },
    "CVP-META-01": {
      "result": "PASS",
      "applicability": "applicable",
      "notes": "1/1 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": "PASS",
      "applicability": "applicable",
      "notes": "5/5 cross-calculator · xcal-gcf-8-12 PASS vs math.gcf; xcal-gcf-18-27 PASS vs math.gcf; xcal-gcf-coprime PASS vs math.gcf; xcal-gcf-neg PASS vs math.gcf; xcal-gcf-bigint-unsafe PASS vs math.gcf; xcal-gcf-all-zero-na N/A (GCF(a,b)·LCM(a,b)=|ab| is claimed for nonzero integers. GCF(0,0) is undefined, so the identity is not evaluated on the all-zero set.); xcal-fractions-na N/A (Fractions is listed as a related tool because LCD/GCF appear in reduction. It does not encode GCF(a,b)·LCM(a,b)=|ab| as a peer identity on this calculator.); xcal-factorial-na N/A (Factorial is listed as a related integer tool. It does not encode GCF(a,b)·LCM(a,b)=|ab|.); xcal-division-na N/A (Division is listed as a related tool. It does not encode GCF(a,b)·LCM(a,b)=|ab|.)"
    },
    "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."
    },
    "CVP-ORACLE-01": {
      "result": "SKIP",
      "applicability": "higher_assurance",
      "notes": "O2 present; O3 not required this wave"
    },
    "CVP-EXP-01": {
      "result": "SKIP",
      "applicability": "optional",
      "notes": "named expert review not performed"
    }
  },
  "tests": {
    "golden": {
      "passed": 6,
      "total": 6,
      "failed": 0,
      "case_ids": [
        "g-pair",
        "g-zero",
        "g-all-zero",
        "g-neg",
        "g-triple",
        "g-bigint"
      ]
    },
    "boundary": {
      "passed": 7,
      "total": 7,
      "failed": 0,
      "case_ids": [
        "boundary-one-number",
        "boundary-missing",
        "boundary-non-integer",
        "boundary-alias-numsInput",
        "boundary-all-zero",
        "boundary-bigint-unsafe",
        "boundary-negatives"
      ]
    },
    "invalid": {
      "passed": 3,
      "total": 3,
      "failed": 0,
      "case_ids": [
        "boundary-one-number",
        "boundary-missing",
        "boundary-non-integer"
      ]
    },
    "property": {
      "passed": 3,
      "total": 3,
      "failed": 0,
      "case_ids": [
        "prop-self",
        "prop-multiple",
        "prop-commute"
      ],
      "definition_ids": [
        "lcm-self",
        "lcm-is-multiple",
        "commutative"
      ]
    },
    "round_trip": {
      "passed": 0,
      "total": 0,
      "failed": 0,
      "case_ids": []
    },
    "metamorphic": {
      "passed": 1,
      "total": 1,
      "failed": 0,
      "case_ids": [
        "meta-scale"
      ],
      "definition_ids": [
        "scale-both"
      ]
    },
    "contract": {
      "passed": 3,
      "total": 3,
      "failed": 0
    },
    "cross_interface": {
      "passed": 1,
      "total": 1,
      "failed": 0,
      "case_ids": [
        "iface-pair"
      ]
    },
    "cross_calculator": {
      "passed": 5,
      "total": 5,
      "failed": 0,
      "case_ids": [
        "xcal-gcf-8-12",
        "xcal-gcf-18-27",
        "xcal-gcf-coprime",
        "xcal-gcf-neg",
        "xcal-gcf-bigint-unsafe"
      ]
    }
  },
  "coverage": {
    "partitions": [
      {
        "id": "lcm",
        "description": "LCM compute",
        "exercised": true,
        "case_count": 27
      },
      {
        "id": "zero",
        "description": "Zero in the input set",
        "exercised": true,
        "case_count": 4
      },
      {
        "id": "negative",
        "description": "Negative inputs (absolute-value convention)",
        "exercised": true,
        "case_count": 3
      },
      {
        "id": "beyond-safe-integer",
        "description": "Magnitude beyond Number.MAX_SAFE_INTEGER",
        "exercised": true,
        "case_count": 4
      },
      {
        "id": "multi-input-fold",
        "description": "Fold of three or more inputs",
        "exercised": true,
        "case_count": 2
      },
      {
        "id": "method-unavailable",
        "description": "Listing/prime/factor cross-check not available",
        "exercised": true,
        "case_count": 4
      },
      {
        "id": "xcal",
        "description": "Cross-calculator vs GCF: GCF(a,b)·LCM(a,b)=|ab| for nonzero integers",
        "exercised": true,
        "case_count": 5
      },
      {
        "id": "invalid-domain",
        "description": "Invalid inputs",
        "exercised": true,
        "case_count": 3
      }
    ]
  },
  "numerical": {
    "profile": "exact_integer",
    "representation": "exact_integer",
    "arithmetic": "BigInt",
    "comparison": "exact_equality",
    "criterion": "actual exact decimal string === independent oracle exact decimal string",
    "exact_policy": true,
    "ulp_applicable": false,
    "tolerance": {
      "type": "exact",
      "value": 0,
      "declared_before_evaluation": true,
      "rationale": "LCM is an exact integer. Acceptance is exact decimal-string identity vs an O2 module that dual-checks pairwise |a/GCF×b| (own Euclidean GCD) against prime-power LCM when fully factorable. Comparison is exact_equality; ULP is not applicable. Node/V8 is a runtime dependency, not the numeric model. Declared a priori."
    },
    "exact_mismatches": 0,
    "records": [
      {
        "id": "g-pair",
        "reference": {
          "values": [
            8,
            12
          ],
          "value": 24,
          "exact": "24",
          "count": 2,
          "max_digits": 48
        },
        "actual": {
          "values": [
            8,
            12
          ],
          "value": 24,
          "exact": "24",
          "count": 2,
          "formula": "LCM(a,b,c,…) = LCM(LCM(a,b),c,…)",
          "binary_formula": "LCM(a,b)=|a/GCF(a,b)×b|",
          "zero_formula": "If any input is 0, LCM = 0",
          "methods": {
            "listing": {
              "available": true,
              "result": 24,
              "matches": true
            },
            "prime": {
              "available": true,
              "result": 24,
              "matches": true
            },
            "gcf": {
              "available": true,
              "result": 24,
              "matches": true
            },
            "agree": true,
            "independent_count": 3
          },
          "work": {
            "listing": [
              "--- Listing multiples ---",
              "8: 8, 16, [24]",
              "12: 12, [24]",
              "First common multiple: 24"
            ],
            "primes": [
              "--- Prime factorization ---",
              "8 = 2 × 2 × 2 = 2^3",
              "12 = 2 × 2 × 3 = 2^2 × 3",
              "Highest powers: 2^3 × 3 = 24"
            ],
            "gcf": [
              "--- GCF method ---",
              "GCF(8, 12) = 4",
              "LCM = (8 / 4) × 12 = 24"
            ]
          },
          "max_digits": 48
        },
        "criterion": "actual exact decimal string === independent oracle exact decimal string",
        "match": true,
        "digits": 2,
        "reference_sha256": "c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db",
        "actual_sha256": "c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db",
        "suite": "golden"
      },
      {
        "id": "g-zero",
        "reference": {
          "values": [
            8,
            0
          ],
          "value": 0,
          "exact": "0",
          "count": 2,
          "max_digits": 48
        },
        "actual": {
          "values": [
            8,
            0
          ],
          "value": 0,
          "exact": "0",
          "count": 2,
          "formula": "LCM(a,b,c,…) = LCM(LCM(a,b),c,…)",
          "binary_formula": "LCM(a,b)=|a/GCF(a,b)×b|",
          "zero_formula": "If any input is 0, LCM = 0",
          "methods": {
            "listing": {
              "available": false,
              "result": null
            },
            "prime": {
              "available": false,
              "result": null
            },
            "gcf": {
              "available": true,
              "result": 0,
              "matches": true
            },
            "agree": true,
            "independent_count": 1
          },
          "work": {
            "listing": [],
            "primes": [],
            "gcf": [
              "--- GCF method ---",
              "If any input is 0, LCM = 0",
              "LCM(8, 0) = 0"
            ]
          },
          "max_digits": 48
        },
        "criterion": "actual exact decimal string === independent oracle exact decimal string",
        "match": true,
        "digits": 1,
        "reference_sha256": "5feceb66ffc86f38d952786c6d696c79c2dbc239dd4e91b46729d73a27fb57e9",
        "actual_sha256": "5feceb66ffc86f38d952786c6d696c79c2dbc239dd4e91b46729d73a27fb57e9",
        "suite": "golden"
      },
      {
        "id": "g-all-zero",
        "reference": {
          "values": [
            0,
            0
          ],
          "value": 0,
          "exact": "0",
          "count": 2,
          "max_digits": 48
        },
        "actual": {
          "values": [
            0,
            0
          ],
          "value": 0,
          "exact": "0",
          "count": 2,
          "formula": "LCM(a,b,c,…) = LCM(LCM(a,b),c,…)",
          "binary_formula": "LCM(a,b)=|a/GCF(a,b)×b|",
          "zero_formula": "If any input is 0, LCM = 0",
          "methods": {
            "listing": {
              "available": false,
              "result": null
            },
            "prime": {
              "available": false,
              "result": null
            },
            "gcf": {
              "available": true,
              "result": 0,
              "matches": true
            },
            "agree": true,
            "independent_count": 1
          },
          "work": {
            "listing": [],
            "primes": [],
            "gcf": [
              "--- GCF method ---",
              "If any input is 0, LCM = 0",
              "LCM(0, 0) = 0"
            ]
          },
          "max_digits": 48
        },
        "criterion": "actual exact decimal string === independent oracle exact decimal string",
        "match": true,
        "digits": 1,
        "reference_sha256": "5feceb66ffc86f38d952786c6d696c79c2dbc239dd4e91b46729d73a27fb57e9",
        "actual_sha256": "5feceb66ffc86f38d952786c6d696c79c2dbc239dd4e91b46729d73a27fb57e9",
        "suite": "golden"
      },
      {
        "id": "g-neg",
        "reference": {
          "values": [
            -8,
            12
          ],
          "value": 24,
          "exact": "24",
          "count": 2,
          "max_digits": 48
        },
        "actual": {
          "values": [
            -8,
            12
          ],
          "value": 24,
          "exact": "24",
          "count": 2,
          "formula": "LCM(a,b,c,…) = LCM(LCM(a,b),c,…)",
          "binary_formula": "LCM(a,b)=|a/GCF(a,b)×b|",
          "zero_formula": "If any input is 0, LCM = 0",
          "methods": {
            "listing": {
              "available": true,
              "result": 24,
              "matches": true
            },
            "prime": {
              "available": true,
              "result": 24,
              "matches": true
            },
            "gcf": {
              "available": true,
              "result": 24,
              "matches": true
            },
            "agree": true,
            "independent_count": 3
          },
          "work": {
            "listing": [
              "--- Listing multiples ---",
              "8: 8, 16, [24]",
              "12: 12, [24]",
              "First common multiple: 24"
            ],
            "primes": [
              "--- Prime factorization ---",
              "8 = 2 × 2 × 2 = 2^3",
              "12 = 2 × 2 × 3 = 2^2 × 3",
              "Highest powers: 2^3 × 3 = 24"
            ],
            "gcf": [
              "--- GCF method ---",
              "GCF(8, 12) = 4",
              "LCM = (8 / 4) × 12 = 24"
            ]
          },
          "max_digits": 48
        },
        "criterion": "actual exact decimal string === independent oracle exact decimal string",
        "match": true,
        "digits": 2,
        "reference_sha256": "c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db",
        "actual_sha256": "c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db",
        "suite": "golden"
      },
      {
        "id": "g-triple",
        "reference": {
          "values": [
            8,
            12,
            20
          ],
          "value": 120,
          "exact": "120",
          "count": 3,
          "max_digits": 48
        },
        "actual": {
          "values": [
            8,
            12,
            20
          ],
          "value": 120,
          "exact": "120",
          "count": 3,
          "formula": "LCM(a,b,c,…) = LCM(LCM(a,b),c,…)",
          "binary_formula": "LCM(a,b)=|a/GCF(a,b)×b|",
          "zero_formula": "If any input is 0, LCM = 0",
          "methods": {
            "listing": {
              "available": true,
              "result": 120,
              "matches": true
            },
            "prime": {
              "available": true,
              "result": 120,
              "matches": true
            },
            "gcf": {
              "available": true,
              "result": 120,
              "matches": true
            },
            "agree": true,
            "independent_count": 3
          },
          "work": {
            "listing": [
              "--- Listing multiples ---",
              "8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, [120]",
              "12: 12, 24, 36, 48, 60, 72, 84, 96, 108, [120]",
              "20: 20, 40, 60, 80, 100, [120]",
              "First common multiple: 120"
            ],
            "primes": [
              "--- Prime factorization ---",
              "8 = 2 × 2 × 2 = 2^3",
              "12 = 2 × 2 × 3 = 2^2 × 3",
              "20 = 2 × 2 × 5 = 2^2 × 5",
              "Highest powers: 2^3 × 3 × 5 = 120"
            ],
            "gcf": [
              "--- GCF method ---",
              "Fold pairwise: LCM(LCM(…), next)",
              "GCF(8, 12) = 4",
              "LCM(8, 12) = (8 / 4) × 12 = 24",
              "GCF(24, 20) = 4",
              "LCM(24, 20) = (24 / 4) × 20 = 120"
            ]
          },
          "max_digits": 48
        },
        "criterion": "actual exact decimal string === independent oracle exact decimal string",
        "match": true,
        "digits": 3,
        "reference_sha256": "2abaca4911e68fa9bfbf3482ee797fd5b9045b841fdff7253557c5fe15de6477",
        "actual_sha256": "2abaca4911e68fa9bfbf3482ee797fd5b9045b841fdff7253557c5fe15de6477",
        "suite": "golden"
      },
      {
        "id": "g-bigint",
        "reference": {
          "values": [
            "9007199254740993",
            3
          ],
          "value": "9007199254740993",
          "exact": "9007199254740993",
          "count": 2,
          "max_digits": 48
        },
        "actual": {
          "values": [
            "9007199254740993",
            3
          ],
          "value": "9007199254740993",
          "exact": "9007199254740993",
          "count": 2,
          "formula": "LCM(a,b,c,…) = LCM(LCM(a,b),c,…)",
          "binary_formula": "LCM(a,b)=|a/GCF(a,b)×b|",
          "zero_formula": "If any input is 0, LCM = 0",
          "methods": {
            "listing": {
              "available": false,
              "result": null
            },
            "prime": {
              "available": false,
              "result": null
            },
            "gcf": {
              "available": true,
              "result": "9007199254740993",
              "matches": true
            },
            "agree": true,
            "independent_count": 1
          },
          "work": {
            "listing": [],
            "primes": [],
            "gcf": [
              "--- GCF method ---",
              "GCF(9007199254740993, 3) = 3",
              "LCM = (9007199254740993 / 3) × 3 = 9007199254740993"
            ]
          },
          "max_digits": 48
        },
        "criterion": "actual exact decimal string === independent oracle exact decimal string",
        "match": true,
        "digits": 16,
        "reference_sha256": "a1c367c29158357e62a3ff5d3e800fb7698a22396439dbc0a9d4929322afd35d",
        "actual_sha256": "a1c367c29158357e62a3ff5d3e800fb7698a22396439dbc0a9d4929322afd35d",
        "suite": "golden"
      },
      {
        "id": "meta-scale",
        "reference": {
          "exact": "2"
        },
        "actual": {
          "exact": "2"
        },
        "criterion": "actual exact decimal string === independent oracle exact decimal string",
        "match": true,
        "digits": 1,
        "reference_sha256": "d4735e3a265e16eee03f59718b9b5d03019c07d8b6c51f90da3a666eec13ab35",
        "actual_sha256": "d4735e3a265e16eee03f59718b9b5d03019c07d8b6c51f90da3a666eec13ab35",
        "suite": "metamorphic",
        "hops": {
          "base": {
            "reference": {
              "values": [
                8,
                12
              ],
              "value": 24,
              "exact": "24",
              "count": 2,
              "max_digits": 48
            },
            "actual": {
              "values": [
                8,
                12
              ],
              "value": 24,
              "exact": "24",
              "count": 2,
              "formula": "LCM(a,b,c,…) = LCM(LCM(a,b),c,…)",
              "binary_formula": "LCM(a,b)=|a/GCF(a,b)×b|",
              "zero_formula": "If any input is 0, LCM = 0",
              "methods": {
                "listing": {
                  "available": true,
                  "result": 24,
                  "matches": true
                },
                "prime": {
                  "available": true,
                  "result": 24,
                  "matches": true
                },
                "gcf": {
                  "available": true,
                  "result": 24,
                  "matches": true
                },
                "agree": true,
                "independent_count": 3
              },
              "work": {
                "listing": [
                  "--- Listing multiples ---",
                  "8: 8, 16, [24]",
                  "12: 12, [24]",
                  "First common multiple: 24"
                ],
                "primes": [
                  "--- Prime factorization ---",
                  "8 = 2 × 2 × 2 = 2^3",
                  "12 = 2 × 2 × 3 = 2^2 × 3",
                  "Highest powers: 2^3 × 3 = 24"
                ],
                "gcf": [
                  "--- GCF method ---",
                  "GCF(8, 12) = 4",
                  "LCM = (8 / 4) × 12 = 24"
                ]
              },
              "max_digits": 48
            },
            "error_ulp": null
          },
          "follow": {
            "reference": {
              "values": [
                16,
                24
              ],
              "value": 48,
              "exact": "48",
              "count": 2,
              "max_digits": 48
            },
            "actual": {
              "values": [
                16,
                24
              ],
              "value": 48,
              "exact": "48",
              "count": 2,
              "formula": "LCM(a,b,c,…) = LCM(LCM(a,b),c,…)",
              "binary_formula": "LCM(a,b)=|a/GCF(a,b)×b|",
              "zero_formula": "If any input is 0, LCM = 0",
              "methods": {
                "listing": {
                  "available": true,
                  "result": 48,
                  "matches": true
                },
                "prime": {
                  "available": true,
                  "result": 48,
                  "matches": true
                },
                "gcf": {
                  "available": true,
                  "result": 48,
                  "matches": true
                },
                "agree": true,
                "independent_count": 3
              },
              "work": {
                "listing": [
                  "--- Listing multiples ---",
                  "16: 16, 32, [48]",
                  "24: 24, [48]",
                  "First common multiple: 48"
                ],
                "primes": [
                  "--- Prime factorization ---",
                  "16 = 2 × 2 × 2 × 2 = 2^4",
                  "24 = 2 × 2 × 2 × 3 = 2^3 × 3",
                  "Highest powers: 2^4 × 3 = 48"
                ],
                "gcf": [
                  "--- GCF method ---",
                  "GCF(16, 24) = 8",
                  "LCM = (16 / 8) × 24 = 48"
                ]
              },
              "max_digits": 48
            },
            "error_ulp": null
          },
          "relation": {
            "reference": {
              "exact": "2"
            },
            "actual": {
              "exact": "2"
            },
            "error_ulp": null
          }
        }
      }
    ]
  },
  "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."
  },
  "artifacts": {
    "evidence_bundle_sha256": "6dd1f69b5c7d289c45e002748408e40fec87c0f9ed84c7e64be433d4033bf4d4",
    "evidence_digest": "243e5df785916922d451ec831a8b81172dbde317d96fcd59206c30563574920a",
    "production_sha256": "31e075dd2788e7c13520557df716a4e118f4844aca3908f8b06acf4a41fad0cc",
    "attested_catalog_sha256": "f89399c8dda78af9b2d784bf34d77b786cf749392d54e5e00bd3707c3fcdd13e",
    "production_checks": [
      {
        "id": "math.lcm:output-const",
        "status": "pass",
        "detail": "output const 1.0.3 vs capability 1.0.3",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T06:43:10.491Z"
      },
      {
        "id": "math.lcm:evidence-sha256",
        "status": "pass",
        "detail": "7b50edb47d98",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T06:43:10.491Z"
      },
      {
        "id": "math.lcm:semantic-contract",
        "status": "pass",
        "detail": "20/20",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T06:43:10.491Z"
      },
      {
        "id": "math.lcm:capability-html-public-origin-agree",
        "status": "pass",
        "detail": "public 1.0.3 vs origin 1.0.3",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T06:43:10.491Z"
      },
      {
        "id": "math.lcm:cvp-manifest-public-origin-agree",
        "status": "pass",
        "detail": "math.lcm/1.0.3/2026-09-16.sources-no-wolfram/core/243e5df78591",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T06:43:10.491Z",
        "projection_compared": false
      },
      {
        "id": "math.lcm:cvp-latest-alias-agrees",
        "status": "pass",
        "detail": "math.lcm/1.0.3/2026-09-16.sources-no-wolfram/core/243e5df78591",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T06:43:10.491Z",
        "projection_compared": false
      },
      {
        "id": "math.lcm:cvp-immutable-manifest-fetch",
        "status": "pass",
        "detail": "public=200 origin=200",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T06:43:10.491Z"
      },
      {
        "id": "math.lcm:cvp-immutable-manifest-sha256",
        "status": "pass",
        "detail": "243e5df78591",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T06:43:10.491Z"
      },
      {
        "id": "math.lcm:cvp-latest-alias-matches-immutable",
        "status": "pass",
        "detail": "math.lcm/1.0.3/2026-09-16.sources-no-wolfram/core/243e5df78591",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T06:43:10.491Z",
        "projection_compared": false
      },
      {
        "id": "math.lcm:calculator-html-cvp-projection",
        "status": "pass",
        "detail": "matches Trust display",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T06:43:10.491Z"
      },
      {
        "id": "math.lcm:evidence-html-cvp-projection",
        "status": "pass",
        "detail": "matches Trust display",
        "scope": "last_attestation_snapshot",
        "current": true,
        "attestation_binding_current": true,
        "attested_at": "2026-09-16T06:43:10.491Z"
      }
    ],
    "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": "243e5df785916922d451ec831a8b81172dbde317d96fcd59206c30563574920a",
          "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": "243e5df785916922d451ec831a8b81172dbde317d96fcd59206c30563574920a",
          "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": "7b50edb47d98b007d36e4b83a73a2c05fcad714bb6a79303c600193beba90cfb",
          "note": "Published Evidence JSON core — Trust freshness / production bind subject"
        },
        {
          "name": "evidence_catalog_digest",
          "field": "artifacts.attested_catalog_sha256",
          "digest_scope": "capability_catalog",
          "value": "f89399c8dda78af9b2d784bf34d77b786cf749392d54e5e00bd3707c3fcdd13e",
          "note": "Capability catalog integrity; site-wide, not per-suite fingerprint"
        }
      ]
    },
    "cvp_core_sha256": "243e5df785916922d451ec831a8b81172dbde317d96fcd59206c30563574920a"
  },
  "dependencies": [
    {
      "name": "lcm-engine",
      "version": "1.0.3"
    },
    {
      "name": "lcm-reference-oracle",
      "version": "1.0.0"
    },
    {
      "name": "math.gcf",
      "version": "1.0.2",
      "role": "cross_calculator_peer",
      "capability_id": "math.gcf",
      "evidence_digest": "2f7e2bf9bb702cfa4f9b98f0152ecb1bf66ce98e73314f943591a5526bf48453",
      "evidence": "https://www.calculatorx.com/evidence/math.gcf/1.0.2.cvp.json"
    },
    {
      "name": "node",
      "version": "20.19.2"
    }
  ],
  "attestation": {
    "status": "CURRENT",
    "href": "/.well-known/calculatorx-production-attestation.json",
    "id": "9864b02dd59e627629179439ae27934aea8c6fd24193702e66c56019c5e3e050",
    "attested_at": "2026-09-16T06:43:10.491Z",
    "last_confirmed_current_at": "2026-09-16T06:43:50.908Z",
    "site_attestation_current": false,
    "capability_attestation_current": true,
    "bound_snapshot_status": "pass",
    "live_report_status": "stale",
    "bound_attested_at": "2026-09-16T06:43:50.908Z",
    "live_updated_at": "2026-09-16T06:44:02.844Z",
    "bound_snapshot": {
      "status": "pass",
      "attested_at": "2026-09-16T06:43:50.908Z",
      "site_stale_count": 8
    },
    "live_site_status": {
      "href": "/.well-known/calculatorx-production-attestation.json"
    },
    "bound_snapshot_site_stale_count": 8,
    "site_stale_capability_count": 8,
    "evidence_attested_at": "2026-09-16T06:43:10.491Z"
  },
  "domain_review": {
    "status": "ABSENT",
    "spec_version": "1.0.3",
    "external_third_party": false,
    "note": "Named expert review not performed"
  },
  "timestamps": {
    "verified_at": "2026-09-16T06:43:10.491Z",
    "generated_at": "2026-09-16T06:43:10.491Z",
    "rendered_at": "2026-09-16T06:44:02.894Z",
    "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/math.lcm/1.0.3.json",
    "evidence_page": "https://www.calculatorx.com/evidence/math.lcm/1.0.3",
    "calculator": "https://www.calculatorx.com/calc/math/lcm",
    "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/math.lcm/1.0.3.cvp.json",
    "manifest_immutable": "https://www.calculatorx.com/evidence/math.lcm/1.0.3/2026-09-16.sources-no-wolfram.cvp.json",
    "manifest_core": "https://www.calculatorx.com/evidence/math.lcm/1.0.3/2026-09-16.sources-no-wolfram.243e5df78591.cvp.json"
  }
}