Fraction & Percent Toolkit mechanism

Model scope

The empty honest_label is a concern: the catalog entry should either provide the missing formulas and validation behavior or honestly limit its claim to fraction reduction and percent change. The current specification is not sufficient for implementation verification.

• The specification only defines fraction reduction and percent change, but claims mixed-to-improper conversion, improper-to-mixed conversion, LCD addition, percent-of, markup, discount, and ratio splitting without providing formulas for them.
• The reduction expression "a/gcd:b/gcd" is ambiguous unless gcd is explicitly defined as gcd(|a|,|b|), with the result interpreted as (a/g):(b/g).
• Percent change requires the original value to be nonzero; this domain constraint is missing.
• No formula is provided for decimal conversion or conversion from a decimal result to a percent result.
• No rules are given for sign normalization, denominator positivity, mixed-number validity, LCD selection, or rounding.

Units and conventions

• Fractions, ratios, and percentage calculations are dimensionless unless an instrument field explicitly supplies physical units.
• Percent inputs are interpreted as numeric percentage points: 15 means 15%, and calculations convert it to 0.15 when multiplying a quantity.
• Percent change uses old as the baseline: (new-old)/old × 100, with old != 0.
• Markup and discount percentages are applied multiplicatively: price × (1 + rate) and price × (1 - rate).
• Ratio splitting assumes the total is divided according to nonnegative ratio parts and that the ratio-part sum is nonzero.
• Decimal outputs shown as repeating values are mathematical representations; the required display precision is unspecified.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "operation": "simplify_fraction",
    "numerator": 84,
    "denominator": 126
  },
  "expected_outputs": {
    "simplified_fraction": "2/3",
    "decimal": "0.666666...",
    "percent": "66.666666...%"
  },
  "working": "gcd(84,126)=42. Reduce numerator: 84/42=2. Reduce denominator: 126/42=3. Therefore 84/126=2/3. Decimal: 2 ÷ 3 = 0.666666.... Percent: (2 ÷ 3) × 100 = 66.666666...%."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

A zero old-value percent-change input produces an undefined division by zero. The instrument must reject it or explicitly return undefined; any finite numeric result would be incorrect.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche2/batch10-output.jsonl
• BOUNDARY_HAZARD_CATALOG.json