{
  "schemaVersion": 1,
  "title": "公式识别器：根号覆盖范围的成对实测",
  "observedDate": "2026-10-20",
  "dateTimeZone": "Asia/Shanghai",
  "canonicalPath": "/ocr/formulaocr.html",
  "fragment": "formula-radical-scope-proof",
  "input": {
    "asset": "/assets/formula-radical-scope-input.png",
    "bytes": 34976,
    "sha256": "2a4b62b97ead5b9d10411a4255e211d0d0edf00c1a2369e477ec04ffcf2df0ec",
    "width": 1600,
    "height": 680,
    "origin": "self-authored SVG drawing rendered to PNG; not a product output",
    "referenceExpressions": [
      {
        "label": "A",
        "referenceLatex": "f(x)=\\sqrt{x+1}",
        "rootScope": "x+1"
      },
      {
        "label": "B",
        "referenceLatex": "g(x)=\\sqrt{x}+1",
        "rootScope": "x",
        "outsideRoot": "+1"
      }
    ],
    "radicalBars": "A 的根号横线覆盖 x+1；B 的根号横线仅覆盖 x，+1 留在根号外。"
  },
  "productObservation": {
    "modelVisibleInUI": "doc2x",
    "readOnlyVersionObserved": 0,
    "modelHeaderIncludedInPublicScreenshot": false,
    "counts": {
      "fileSelections": 1,
      "startParseClicks": 1,
      "successfulImageResults": 1,
      "paragraphs": 2,
      "extraModelClicks": 0,
      "scanEnhancementClicks": 0,
      "editClicks": 0,
      "saveClicks": 0,
      "wholeLatexCopyClicks": 1,
      "wholeCopiedBodyReceived": 0,
      "paragraphTextareaReads": 2,
      "additionalProductTasks": 0
    },
    "paragraphs": [
      {
        "label": "A",
        "text": "(A) \\( f\\left( x\\right)  = \\sqrt{x + 1} \\)",
        "download": "/assets/formula-radical-scope-paragraph-a.txt",
        "source": "untouched readonly paragraph textarea value, saved separately as UTF-8 TXT",
        "trailingNewlineAdded": false,
        "productFileExport": false,
        "rootScopeMatchesSource": true,
        "rootContains": "x+1",
        "outsideRoot": null
      },
      {
        "label": "B",
        "text": "(B) \\( g\\left( x\\right)  = \\sqrt{x} + 1 \\)",
        "download": "/assets/formula-radical-scope-paragraph-b.txt",
        "source": "untouched readonly paragraph textarea value, saved separately as UTF-8 TXT",
        "trailingNewlineAdded": false,
        "productFileExport": false,
        "rootScopeMatchesSource": true,
        "rootContains": "x",
        "outsideRoot": "+1"
      }
    ],
    "result": "本次两段识别值的根号范围均与自编原图一致；这是一张图片的一次观察，不代表其他图片的准确率。",
    "wholeLatexCopy": {
      "clicks": 1,
      "uiToastObserved": "已复制全部解析结果",
      "wholeCopiedBodyReceived": false,
      "wholeClipboardSuccessConfirmed": false,
      "publicWholeCopyFile": null,
      "limitation": "没有取得整图复制正文。本样例的两个 TXT 来自分别读取的只读段落原值，不是整图剪贴板内容，也不是产品原生文件导出。"
    },
    "billingLimit": "当前界面说明每张图片消耗一页解析额度；本证据不宣称本次免费，也不推断余额扣减因果。"
  },
  "publicScreenshot": {
    "asset": "/assets/formula-radical-scope-result.jpg",
    "shows": "cropped original input and parsed result panels",
    "excludes": "property panel and model header",
    "derivative": "Byte-preserved root-reviewed JPEG crop, with no content edits or re-encoding."
  },
  "checks": [
    {
      "label": "A",
      "reference": "f(x)=\\sqrt{x+1}",
      "check": "\\sqrt{...} 的花括号包含 x + 1，原图横线也覆盖 x+1。",
      "result": "matches"
    },
    {
      "label": "B",
      "reference": "g(x)=\\sqrt{x}+1",
      "check": "\\sqrt{...} 的花括号只包含 x，+ 1 位于结束花括号之后。",
      "result": "matches"
    }
  ],
  "keywordEvidence": {
    "observedQuery": "公式识别器",
    "observedWindow": {
      "start": "2026-10-11",
      "end": "2026-10-17"
    },
    "observedImpressions": 25,
    "observedClicks": 0,
    "scope": "Bing Search Performance disclosed Web keyword row",
    "editorialQueries": [
      "根号公式图片转LaTeX怎么核对",
      "根号里面和外面的加号怎么区分",
      "公式识别根号范围不对怎么办",
      "sqrt{x+1}和sqrt{x}+1有什么区别"
    ],
    "editorialQueriesMeasured": false,
    "limitation": "25 次展示和 0 次点击只是该窗口已披露搜索词的观察；长尾词未量化，不代表搜索量、实时排名或本次发布效果。"
  },
  "limits": [
    "仅提交一张自编 PNG 一次，观察两个未改写的只读段落值；没有额外模型、扫描增强、编辑或保存。",
    "公开截图只证明原图与解析结果面板的可见内容，不能用于证明裁切之外的模型标题。",
    "没有确认整图复制成功；没有将失败的空 TEX 文件作为下载资产。",
    "错误范围的修正步骤属于使用建议；本轮没有制造识别错误，也没有执行编辑修正。"
  ]
}