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    "Interactive evaluation runs locally in the browser. Shared URLs and REST evaluate the same versioned engine (query SSR).",
    "Denominators (whole, old, average of A and B, P) must be nonzero where required.",
    "Percent change uses |old| in the denominator (signed increase/decrease). Typically used with a nonzero baseline; old = 0 is undefined.",
    "Percentage difference is defined for A ≥ 0, B ≥ 0, and A+B ≠ 0."
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    "Reject nonzero values that round to zero and overflow (including published delta/average); rescale on NUMERIC_RANGE.",
    "Change uses |old|; difference needs nonnegative a,b and nonzero sum. Near zero baseline is ill-conditioned; shortest round-trip display is not significant-figure tracking.",
    "At most512 characters per scalar; active fields only and aliases must agree."
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  "boundary_conditions": [
    "Division by zero → DIVISION_BY_ZERO",
    "Percentage difference with A < 0 or B < 0 → VALUE_MUST_BE_NON_NEGATIVE",
    "Unknown mode → INVALID_MODE",
    "Nonzero input/output rounding to zero or overflow (including delta/average) → NUMERIC_RANGE; rescale",
    "Matching active aliases only; decimal tokens at most512 characters; explicit zero canonicalizes to +0"
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    {
      "title": "BIPM — The International System of Units (SI), 9th edition",
      "section": "Units accepted for use with the SI — percent (symbol %), 1% = 0.01",
      "url": "https://www.bipm.org/en/publications/si-brochure",
      "supports": "Defines percent as the number 0.01 (one part in one hundred). The core relation P% of X = X × P/100 follows from that definition.",
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      "title": "NIST Special Publication 811 — Guide for the Use of the International System of Units (SI)",
      "section": "Writing values of quantities — the percent",
      "url": "https://www.nist.gov/pml/special-publication-811",
      "supports": "NIST usage of percent as 0.01 with the SI. Does not prescribe percent-change vs percent-difference conventions.",
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      "accessed": "2026-08-28"
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    {
      "title": "CalculatorX percentage conventions",
      "section": "Six phrase modes, |old| percent change, non-negative percentage difference",
      "supports": "Percent change Δ% = 100×(new−old)/|old| (undefined at old = 0). Percentage difference Δ% = 100×|A−B|/((A+B)/2) on A ≥ 0, B ≥ 0, A+B ≠ 0. Increase/decrease is X×(1±P/100).",
      "kind": "definition"
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    {
      "title": "NIST — SI Unit Rules and Style Conventions",
      "section": "Percent and fractions",
      "url": "https://physics.nist.gov/cuu/Units/checklist.html",
      "supports": "The symbol % represents the number 0.01. Thus p% = p/100 and a part of p% of base b equals b×p/100; inverse percentage equations are algebraic rearrangements. CalculatorX’s negative-baseline signed-change convention is separately specified, not attributed to NIST. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.",
      "kind": "reference",
      "publisher": "National Institute of Standards and Technology"
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