{
  "schemaVersion": "authored-equation-structural-corpus/v1",
  "version": "2026-10-02-v1",
  "corpusKind": "authored_synthetic_cases",
  "selection": "32 manually authored ordinary mathematical examples across fractions, radicals, scripts, n-ary operators, matrices, alignment, fences, accents, functions, symbols and style; six invalid probes; four extended probes. Not a random or user/OCR corpus.",
  "rubric": "Expected native OMML element names and selected text tokens are prescribed before execution. These are structural checks, not rendered or semantic equality.",
  "cases": [
    {
      "id": "fraction",
      "family": "fraction",
      "latex": "\\frac{a}{b}",
      "expectedOmmlTags": [
        "f"
      ],
      "expectedText": [
        "a",
        "b"
      ],
      "inputClass": "valid"
    },
    {
      "id": "nested-fraction",
      "family": "fraction",
      "latex": "\\frac{1}{1+\\frac{1}{x}}",
      "expectedOmmlTags": [
        "f"
      ],
      "expectedText": [
        "x"
      ],
      "inputClass": "valid"
    },
    {
      "id": "quadratic",
      "family": "fraction",
      "latex": "x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}",
      "expectedOmmlTags": [
        "f",
        "rad",
        "sSup"
      ],
      "expectedText": [
        "b",
        "c"
      ],
      "inputClass": "valid"
    },
    {
      "id": "display-fraction",
      "family": "fraction",
      "latex": "\\dfrac{1}{2}",
      "expectedOmmlTags": [
        "f"
      ],
      "expectedText": [
        "1",
        "2"
      ],
      "inputClass": "valid"
    },
    {
      "id": "square-root",
      "family": "radical",
      "latex": "\\sqrt{x+1}",
      "expectedOmmlTags": [
        "rad"
      ],
      "expectedText": [
        "x"
      ],
      "inputClass": "valid"
    },
    {
      "id": "cube-root",
      "family": "radical",
      "latex": "\\sqrt[3]{x}",
      "expectedOmmlTags": [
        "rad"
      ],
      "expectedText": [
        "3",
        "x"
      ],
      "inputClass": "valid"
    },
    {
      "id": "superscript",
      "family": "scripts",
      "latex": "x^2",
      "expectedOmmlTags": [
        "sSup"
      ],
      "expectedText": [
        "x",
        "2"
      ],
      "inputClass": "valid"
    },
    {
      "id": "subscript",
      "family": "scripts",
      "latex": "a_i",
      "expectedOmmlTags": [
        "sSub"
      ],
      "expectedText": [
        "a",
        "i"
      ],
      "inputClass": "valid"
    },
    {
      "id": "both-scripts",
      "family": "scripts",
      "latex": "x_i^2",
      "expectedOmmlTags": [
        "sSubSup"
      ],
      "expectedText": [
        "x",
        "i",
        "2"
      ],
      "inputClass": "valid"
    },
    {
      "id": "nested-script",
      "family": "scripts",
      "latex": "e^{x^2}",
      "expectedOmmlTags": [
        "sSup"
      ],
      "expectedText": [
        "e",
        "x",
        "2"
      ],
      "inputClass": "valid"
    },
    {
      "id": "sum",
      "family": "nary",
      "latex": "\\sum_{i=1}^{n}a_i",
      "expectedOmmlTags": [
        "nary",
        "sSub"
      ],
      "expectedText": [
        "∑"
      ],
      "inputClass": "valid"
    },
    {
      "id": "product",
      "family": "nary",
      "latex": "\\prod_{k=1}^{n}k",
      "expectedOmmlTags": [
        "nary"
      ],
      "expectedText": [
        "∏"
      ],
      "inputClass": "valid"
    },
    {
      "id": "integral",
      "family": "nary",
      "latex": "\\int_0^1 x^2\\,dx",
      "expectedOmmlTags": [
        "nary",
        "sSup"
      ],
      "expectedText": [
        "∫"
      ],
      "inputClass": "valid"
    },
    {
      "id": "double-integral",
      "family": "nary",
      "latex": "\\iint_D f(x,y)\\,dx\\,dy",
      "expectedOmmlTags": [
        "nary"
      ],
      "expectedText": [
        "∬"
      ],
      "inputClass": "valid"
    },
    {
      "id": "matrix",
      "family": "matrix",
      "latex": "\\begin{matrix}1&2\\\\3&4\\end{matrix}",
      "expectedOmmlTags": [
        "m",
        "mr"
      ],
      "expectedText": [
        "1",
        "2",
        "3",
        "4"
      ],
      "inputClass": "valid"
    },
    {
      "id": "pmatrix",
      "family": "matrix",
      "latex": "\\begin{pmatrix}a&b\\\\c&d\\end{pmatrix}",
      "expectedOmmlTags": [
        "d",
        "m",
        "mr"
      ],
      "expectedText": [
        "a",
        "b",
        "c",
        "d"
      ],
      "inputClass": "valid"
    },
    {
      "id": "bmatrix",
      "family": "matrix",
      "latex": "\\begin{bmatrix}1&0\\\\0&1\\end{bmatrix}",
      "expectedOmmlTags": [
        "d",
        "m"
      ],
      "expectedText": [
        "1",
        "0"
      ],
      "inputClass": "valid"
    },
    {
      "id": "cases",
      "family": "matrix",
      "latex": "f(x)=\\begin{cases}x&x>0\\\\0&x\\le0\\end{cases}",
      "expectedOmmlTags": [
        "m"
      ],
      "expectedText": [
        "x",
        "0"
      ],
      "inputClass": "valid"
    },
    {
      "id": "aligned",
      "family": "aligned",
      "latex": "\\begin{aligned}a&=b\\\\c&=d\\end{aligned}",
      "expectedOmmlTags": [
        "eqArr"
      ],
      "expectedText": [
        "a",
        "b",
        "c",
        "d"
      ],
      "inputClass": "valid"
    },
    {
      "id": "parentheses",
      "family": "fences",
      "latex": "\\left(\\frac{a}{b}\\right)",
      "expectedOmmlTags": [
        "d",
        "f"
      ],
      "expectedText": [
        "a",
        "b"
      ],
      "inputClass": "valid"
    },
    {
      "id": "brackets",
      "family": "fences",
      "latex": "\\left[x\\right]",
      "expectedOmmlTags": [
        "d"
      ],
      "expectedText": [
        "x"
      ],
      "inputClass": "valid"
    },
    {
      "id": "absolute",
      "family": "fences",
      "latex": "\\left|x\\right|",
      "expectedOmmlTags": [
        "d"
      ],
      "expectedText": [
        "x"
      ],
      "inputClass": "valid"
    },
    {
      "id": "binomial",
      "family": "fences",
      "latex": "\\binom{n}{k}",
      "expectedOmmlTags": [
        "d",
        "f"
      ],
      "expectedText": [
        "n",
        "k"
      ],
      "inputClass": "valid"
    },
    {
      "id": "hat",
      "family": "accent",
      "latex": "\\hat{x}",
      "expectedOmmlTags": [
        "acc"
      ],
      "expectedText": [
        "x"
      ],
      "inputClass": "valid"
    },
    {
      "id": "vector",
      "family": "accent",
      "latex": "\\vec{v}",
      "expectedOmmlTags": [
        "acc"
      ],
      "expectedText": [
        "v"
      ],
      "inputClass": "valid"
    },
    {
      "id": "overline",
      "family": "accent",
      "latex": "\\overline{AB}",
      "expectedOmmlTags": [
        "bar"
      ],
      "expectedText": [
        "A",
        "B"
      ],
      "inputClass": "valid"
    },
    {
      "id": "underbrace",
      "family": "accent",
      "latex": "\\underbrace{a+b}_{n}",
      "expectedOmmlTags": [
        "groupChr"
      ],
      "expectedText": [
        "a",
        "b"
      ],
      "inputClass": "valid"
    },
    {
      "id": "trig",
      "family": "function",
      "latex": "\\sin^2\\theta+\\cos^2\\theta=1",
      "expectedOmmlTags": [
        "func"
      ],
      "expectedText": [
        "sin",
        "cos"
      ],
      "inputClass": "valid"
    },
    {
      "id": "log",
      "family": "function",
      "latex": "\\log_2 8",
      "expectedOmmlTags": [
        "func",
        "sSub"
      ],
      "expectedText": [
        "log",
        "2",
        "8"
      ],
      "inputClass": "valid"
    },
    {
      "id": "limit",
      "family": "function",
      "latex": "\\lim_{x\\to0}\\frac{\\sin x}{x}=1",
      "expectedOmmlTags": [
        "func",
        "limLow",
        "f"
      ],
      "expectedText": [
        "lim",
        "sin"
      ],
      "inputClass": "valid"
    },
    {
      "id": "greek",
      "family": "symbols",
      "latex": "\\alpha+\\beta=\\gamma",
      "expectedOmmlTags": [],
      "expectedText": [
        "α",
        "β",
        "γ"
      ],
      "inputClass": "valid"
    },
    {
      "id": "blackboard",
      "family": "style",
      "latex": "\\mathbb{R}",
      "expectedOmmlTags": [],
      "expectedText": [
        "R"
      ],
      "inputClass": "valid"
    },
    {
      "id": "unclosed-fraction",
      "family": "invalid",
      "latex": "\\frac{a}{",
      "expectedOmmlTags": [],
      "expectedText": [],
      "inputClass": "invalid"
    },
    {
      "id": "unknown-command",
      "family": "invalid",
      "latex": "\\definitelyunknown{x}",
      "expectedOmmlTags": [],
      "expectedText": [],
      "inputClass": "invalid"
    },
    {
      "id": "empty",
      "family": "invalid",
      "latex": "",
      "expectedOmmlTags": [],
      "expectedText": [],
      "inputClass": "invalid"
    },
    {
      "id": "spaces",
      "family": "invalid",
      "latex": "   ",
      "expectedOmmlTags": [],
      "expectedText": [],
      "inputClass": "invalid"
    },
    {
      "id": "unclosed-matrix",
      "family": "invalid",
      "latex": "\\begin{matrix}1&2",
      "expectedOmmlTags": [],
      "expectedText": [],
      "inputClass": "invalid"
    },
    {
      "id": "extra-brace",
      "family": "invalid",
      "latex": "x}",
      "expectedOmmlTags": [],
      "expectedText": [],
      "inputClass": "invalid"
    },
    {
      "id": "cancellation",
      "family": "decoration",
      "latex": "\\cancel{x}",
      "expectedOmmlTags": [
        "borderBox"
      ],
      "expectedText": [
        "x"
      ],
      "inputClass": "extended"
    },
    {
      "id": "color",
      "family": "style",
      "latex": "\\color{red}{x}",
      "expectedOmmlTags": [],
      "expectedText": [
        "x"
      ],
      "inputClass": "extended"
    },
    {
      "id": "custom-macro",
      "family": "macro",
      "latex": "\\newcommand{\\foo}{x}\\foo",
      "expectedOmmlTags": [],
      "expectedText": [
        "x"
      ],
      "inputClass": "extended"
    },
    {
      "id": "spacing",
      "family": "spacing",
      "latex": "a\\qquad b",
      "expectedOmmlTags": [],
      "expectedText": [
        "a",
        "b"
      ],
      "inputClass": "extended"
    }
  ]
}