{
  "capability_id": "math.percent_change",
  "tool_id": "percent-change",
  "engine": "percent-change",
  "calculation_version": "1.1.0",
  "generated_at": "2026-09-16T22:03:43.775Z",
  "engine_build": "2026-09-10",
  "test_count": 8,
  "passed": 8,
  "failed": 0,
  "tests_summary": {
    "golden": {
      "total": 6,
      "passed": 6
    },
    "boundary": {
      "total": 2,
      "passed": 2
    },
    "property": {
      "total": 0,
      "passed": 0
    }
  },
  "engine_tested": true,
  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
    "status": "optional_not_performed",
    "reviewer": null,
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
  },
  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
  },
  "page": "https://www.calculatorx.com/calc/math/percentage-change",
  "api": "https://www.calculatorx.com/api/v1/calc/percent-change",
  "schema_input": "https://www.calculatorx.com/schemas/math.percent_change.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.percent_change.output.json",
  "assumptions": [
    "Interactive evaluation runs locally in the browser. Shared URLs and REST evaluate the same versioned engine (query SSR).",
    "CVP interface evidence is UI (SSR) query-result HTML, REST, and MCP (MCP reuses the calc API handler). That is interface-result consistency, not a live browser session, cache switching, or end-to-end UI test.",
    "Signed-change convention: denominator is |V₁|, so a move from −100 to −50 is a +50% increase. Some definitions use V₁ without absolute value or restrict to positive baselines.",
    "Exactly two fields are inputs. Explicit solve_for selects the output. If all three are supplied without solve_for, they are checked for consistency rather than overwritten.",
    "Solving for V₁ is not always unique. The engine returns both valid initials when they exist."
  ],
  "limitations": [
    "V₁ = 0 → INITIAL_VALUE_ZERO",
    "Invalid reverse solve → NO_REAL_SOLUTION; some cases INFINITELY_MANY"
  ],
  "boundary_conditions": [
    "V₁ = 0 → INITIAL_VALUE_ZERO (percent change undefined)",
    "Fewer than two inputs → MISSING_REQUIRED_INPUT",
    "Invalid solve_for → INVALID_SOLVE_FOR",
    "Positive-initial reverse branch: 1 + P/100 = 0 (P = −100%) is omitted",
    "Negative-initial reverse branch: 1 − P/100 = 0 (P = +100%) is omitted",
    "Solve V₁ may have 0, 1, or 2 solutions",
    "V₂ = 0, P = −100%, solve V₁ → INFINITELY_MANY (any V₁ > 0)",
    "V₂ = 0, P = +100%, solve V₁ → INFINITELY_MANY (any V₁ < 0)",
    "V₂ = 0 and P ≠ ±100%, solve V₁ → NO_REAL_SOLUTION",
    "All three values filled without solve_for and not matching the formula → INCONSISTENT_INPUTS"
  ],
  "sources": [
    {
      "title": "Math is Fun — Percentage Difference vs Percentage Error vs Percentage Change",
      "section": "Percentage change uses |Old| in the denominator",
      "url": "https://www.mathsisfun.com/data/percentage-difference-vs-error.html",
      "supports": "Educational definition % change = (New − Old) / |Old| × 100%, matching CalculatorX’s signed-change convention for a negative baseline.",
      "kind": "reference",
      "accessed": "2026-08-28"
    },
    {
      "title": "Curran-Everett — Explorations in statistics: the analysis of change",
      "section": "Relative change as (final − initial) / initial",
      "url": "https://journals.physiology.org/doi/full/10.1152/advan.00018.2015",
      "supports": "Documents a relative-change definition that divides directly by the initial value rather than |initial|. Negative-baseline percentage change is therefore not a single universal convention.",
      "kind": "reference",
      "accessed": "2026-08-28"
    },
    {
      "title": "CalculatorX signed-change convention",
      "section": "|V₁| denominator, piecewise inverse, and multiple V₁ solutions",
      "supports": "% change = (V₂−V₁)/|V₁|×100% (undefined at V₁ = 0). Inverse: V₂ = V₁(1+P/100) if V₁>0 and V₁(1−P/100) if V₁<0. Solving V₁ publishes both signed branches, INFINITELY_MANY at V₂=0 with P=±100%, and NO_REAL_SOLUTION when no branch is valid.",
      "kind": "definition"
    }
  ],
  "methods": [],
  "fingerprint": "sha256:fcc1ae93840bcc952ec705764db517dec8db909e0f8a2fdfa5b4cad6d54f0572",
  "tests": [
    {
      "id": "up-20",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "oldV": 60,
        "newV": 72
      },
      "expect": 20,
      "expectWarning": null,
      "actual": {
        "solve_for": "p",
        "value": 20,
        "v1": 60,
        "v2": 72,
        "p": 20,
        "percent_change": 20,
        "solution_type": "unique",
        "status": "success",
        "direction": "increase",
        "rounding": {
          "mode": "auto",
          "significant_digits": 10,
          "trailing_zeros": "stripped"
        },
        "calculation_version": "1.1.0",
        "formula": "% change = (V₂ − V₁) / |V₁| × 100%",
        "display": {
          "percent_change": "+20%",
          "value": "+20%"
        },
        "delta": 12,
        "abs_v1": 60,
        "signed_factor": 1.2,
        "multiplier": 1.2,
        "percent_of_initial": 120
      },
      "tol": 1e-9
    },
    {
      "id": "down-25",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "oldV": 3.5,
        "newV": 2.625
      },
      "expect": -25,
      "expectWarning": null,
      "actual": {
        "solve_for": "p",
        "value": -25,
        "v1": 3.5,
        "v2": 2.625,
        "p": -25,
        "percent_change": -25,
        "solution_type": "unique",
        "status": "success",
        "direction": "decrease",
        "rounding": {
          "mode": "auto",
          "significant_digits": 10,
          "trailing_zeros": "stripped"
        },
        "calculation_version": "1.1.0",
        "formula": "% change = (V₂ − V₁) / |V₁| × 100%",
        "display": {
          "percent_change": "-25%",
          "value": "-25%"
        },
        "delta": -0.875,
        "abs_v1": 3.5,
        "signed_factor": 0.75,
        "multiplier": 0.75,
        "percent_of_initial": 75
      },
      "tol": 1e-9
    },
    {
      "id": "neg-to-pos",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "oldV": -25,
        "newV": 25
      },
      "expect": 200,
      "expectWarning": null,
      "actual": {
        "solve_for": "p",
        "value": 200,
        "v1": -25,
        "v2": 25,
        "p": 200,
        "percent_change": 200,
        "solution_type": "unique",
        "status": "success",
        "direction": "increase",
        "rounding": {
          "mode": "auto",
          "significant_digits": 10,
          "trailing_zeros": "stripped"
        },
        "calculation_version": "1.1.0",
        "formula": "% change = (V₂ − V₁) / |V₁| × 100%",
        "display": {
          "percent_change": "+200%",
          "value": "+200%"
        },
        "delta": 50,
        "abs_v1": 25,
        "signed_factor": -1,
        "multiplier": -1,
        "percent_of_initial": -100
      },
      "tol": 1e-9
    },
    {
      "id": "solve-final-neg",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "v1": -25,
        "p": 200,
        "solve_for": "v2"
      },
      "expect": 25,
      "expectWarning": null,
      "actual": {
        "solve_for": "v2",
        "value": 25,
        "v1": -25,
        "v2": 25,
        "p": 200,
        "percent_change": 200,
        "solution_type": "unique",
        "status": "success",
        "direction": "increase",
        "rounding": {
          "mode": "auto",
          "significant_digits": 10,
          "trailing_zeros": "stripped"
        },
        "calculation_version": "1.1.0",
        "formula": "V₂ = V₁ + (P/100)·|V₁|",
        "display": {
          "percent_change": "+200%",
          "value": "25"
        },
        "delta": 50,
        "abs_v1": 25,
        "signed_factor": -1,
        "multiplier": -1,
        "percent_of_initial": -100,
        "formula_branch": "V₂ = V₁(1 − P/100)"
      },
      "tol": 1e-9
    },
    {
      "id": "two-initials",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "v2": 25,
        "p": 200,
        "solve_for": "v1"
      },
      "expect": {
        "status": "multiple_solutions",
        "solution_type": "two"
      },
      "expectWarning": null,
      "actual": {
        "solve_for": "v1",
        "value": 8.333333333333334,
        "v1": null,
        "v2": 25,
        "p": 200,
        "percent_change": 200,
        "solutions": [
          8.333333333333334,
          -25
        ],
        "candidates": [
          8.333333333333334,
          -25
        ],
        "solution_type": "two",
        "status": "multiple_solutions",
        "direction": "increase",
        "rounding": {
          "mode": "auto",
          "significant_digits": 10,
          "trailing_zeros": "stripped"
        },
        "calculation_version": "1.1.0",
        "formula": "V₁ = V₂/(1±P/100) with signed |V₁| branches",
        "display": {
          "percent_change": "+200%",
          "value": "8.333333333 or -25"
        },
        "delta": null,
        "abs_v1": null,
        "signed_factor": null,
        "multiplier": null,
        "percent_of_initial": null,
        "branches": [
          {
            "v1": 8.333333333333334,
            "branch": "positive",
            "formula": "V₁ = V₂ / (1 + P/100)"
          },
          {
            "v1": -25,
            "branch": "negative",
            "formula": "V₁ = V₂ / (1 − P/100)"
          }
        ]
      },
      "tol": null
    },
    {
      "id": "zero-initial",
      "ok": true,
      "kind": "boundary",
      "inputs": {
        "v1": 0,
        "v2": 10
      },
      "expectError": "INITIAL_VALUE_ZERO",
      "code": "INITIAL_VALUE_ZERO",
      "error": "Initial value cannot be 0 (percent change is undefined)."
    },
    {
      "id": "infinite-neg-100",
      "ok": true,
      "kind": "golden",
      "inputs": {
        "v2": 0,
        "p": -100,
        "solve_for": "v1"
      },
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        "value": null,
        "v1": null,
        "v2": 0,
        "p": -100,
        "percent_change": -100,
        "status": "infinite",
        "code": "INFINITELY_MANY",
        "solution_type": "infinite",
        "constraint": "V₁ > 0",
        "rounding": {
          "mode": "auto",
          "significant_digits": 10,
          "trailing_zeros": "stripped"
        },
        "calculation_version": "1.1.0",
        "formula": "V₂ = V₁ + (P/100)·|V₁|",
        "display": {
          "percent_change": "-100%",
          "value": "any V₁ > 0"
        },
        "message": "Any positive initial value satisfies a −100% change to final 0, because V₂ = V₁ − |V₁| = 0 when V₁ > 0. V₁ = 0 remains undefined."
      },
      "tol": null
    },
    {
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      "ok": true,
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        "p": -100,
        "solve_for": "v1"
      },
      "expectError": "NO_REAL_SOLUTION",
      "code": "NO_REAL_SOLUTION",
      "error": "No valid initial value for this final value and percent change."
    }
  ],
  "tier": "engine_tested",
  "verification": {
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      "passed": 8,
      "total": 8,
      "golden": 6,
      "boundary": 2,
      "property": 0
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    "contract_checks": {
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  "evidence_core_generated_at": "2026-09-10T22:48:17.762Z",
  "rendered_at": "2026-09-16T22:03:43.775Z",
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