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analysis exams
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‎.claude/commands/mathml-general-exam.md‎

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@@ -96,10 +96,12 @@ Use this entity mapping:
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- Relations: ≤ (≤), ≥ (≥), ≠ (≠), ≈ (≈), ≡ (≡), ⟂ (⊥), ∥ (∥)
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- Calculus: ∂ (∂), ∫ (∫), ∮ (∮), ∑ (∑), ∏ (∏), ∇ (∇), √ (√)
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- Logic: ∀ (∀), ∃ (∃), ¬ (¬), ∧ (∧), ∨ (∨)
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- Number sets: ℝ (ℝ), ℂ (ℂ), ℕ (ℕ), ℤ (ℤ), ℚ (ℚ)
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- Greek letters: α (α), β (β), γ (γ), δ (δ), ε (ε), η (η), θ (θ), λ (λ), μ (μ), ν (ν), π (π), σ (σ), τ (τ), φ (φ), ω (ω), Γ (Γ), Δ (Δ), Θ (Θ), Λ (Λ), Σ (Σ), Φ (Φ), Ω (Ω)
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- Number sets: ℝ (ℝ), ℂ (ℂ), ℕ (ℕ), ℤ (ℤ), ℚ (ℚ), **𝔻 (𝔻)**, 𝔸 (𝔸), 𝔹 (𝔹), 𝔼 (𝔼), 𝔽 (𝔽), 𝔾 (𝔾), ℍ (ℍ), 𝕀 (𝕀), 𝕁 (𝕁), 𝕂 (𝕂), 𝕃 (𝕃), 𝕄 (𝕄), 𝕆 (𝕆), ℙ (ℙ), 𝕊 (𝕊), 𝕋 (𝕋), 𝕌 (𝕌), 𝕍 (𝕍), 𝕎 (𝕎), 𝕏 (𝕏), 𝕐 (𝕐)
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- Greek letters: α (α), β (β), γ (γ), δ (δ), ε (ε), η (η), θ (θ), λ (λ), μ (μ), ν (ν), π (π), σ (σ), τ (τ), φ (φ), ψ (ψ), χ (χ), ω (ω), Γ (Γ), Δ (Δ), Θ (Θ), Λ (Λ), Σ (Σ), Φ (Φ), Ψ (Ψ), Ω (Ω)
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- Other: ∞ (∞), × (×), ⋅ (⋅), ± (±), ∠ (∠), ⊕ (⊕), ⊗ (⊗)
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**CRITICAL**: Blackboard bold letters (especially **𝔻**) frequently appear in exams and MUST be converted to HTML entities. This is a common source of accessibility violations.
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### Step 6: Handle Images (Diagrams, Figures)
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**IMPORTANT**: Many exams contain diagrams (commutative diagrams, geometric figures, knot diagrams, etc.) that are extracted by Mathpix.
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@@ -221,36 +223,131 @@ After saving the HTML file, you MUST update the link in `graduate/general_exams.
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- Clearly labeling the PDF as "for printing" to indicate its purpose
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- Using ARIA labels to communicate that PDFs may have accessibility limitations
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### Step 10: Final Review - Read Both Files
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After completing all processing steps, you MUST read both the original PDF and the generated HTML file to provide a final quality assessment:
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### Step 10: COMPREHENSIVE LEGAL COMPLIANCE AUDIT
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**⚠️ CRITICAL**: This step is MANDATORY as accessibility violations expose the website to ADA lawsuits. All items must pass.
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After completing all processing steps, you MUST:
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1. Read both the original PDF and the generated HTML file
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2. Perform a thorough WCAG 2.1 Level AA compliance audit
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3. Fix any violations immediately before declaring the file production-ready
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```bash
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# Read both files
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Read <PATH_TO_PDF>
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Read <PATH_TO_HTML>
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```
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**Review and report on:**
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1. **Content Accuracy**: Verify that all mathematical expressions, problems, and text from the PDF are correctly represented in the HTML
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2. **MathML Quality**: Confirm that math expressions render correctly as MathML (not SVG or Unicode)
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3. **Accessibility**: Check that all accessibility features are present and correct:
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- Proper title and H1 heading
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- **H2 headings for EVERY problem** (e.g., "Problem 1", "Problem 2", etc.)
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- Breadcrumb and back button navigation
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- ARIA labels on math elements
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- Semantic HTML structure
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4. **Formatting and Spacing**: Ensure the HTML preserves the PDF's visual structure:
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- Proper vertical spacing between main problems
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- Problem structure is clear and readable
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5. **Completeness**: Verify nothing was lost or corrupted during conversion
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- Count problems in PDF and verify matching H2 headings in HTML
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**Provide a concise summary stating:**
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- ✓ What looks correct
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- ⚠️ Any issues found (and fix them if possible)
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- Overall assessment: "Ready for production" or "Needs fixes"
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This final human-in-the-loop check ensures quality before the files go live.
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## WCAG 2.1 Level AA Compliance Checklist
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### 1. Document Structure (WCAG 1.3.1, 2.4.1)
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- [ ] Valid HTML5 DOCTYPE present
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- [ ] `lang="en"` attribute on `<html>` element
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- [ ] UTF-8 character encoding declared
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- [ ] Viewport meta tag for mobile accessibility
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### 2. Page Title (WCAG 2.4.2)
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- [ ] Descriptive `<title>` tag present (e.g., "Analysis General Exam August 2017 - UVA Mathematics")
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- [ ] Title accurately describes page content
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### 3. Semantic Heading Hierarchy (WCAG 1.3.1, 2.4.6) **[CRITICAL]**
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- [ ] Exactly ONE H1 heading (exam title)
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- [ ] H2 heading for EVERY problem (e.g., `<h2 class="unnumbered" id="problem-1">Problem 1</h2>`)
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- [ ] No skipped heading levels (H1 → H2, never H1 → H3)
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- [ ] Each heading has unique `id` attribute
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- [ ] Count problems in PDF = count of H2 headings in HTML
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### 4. Landmark Elements (WCAG 1.3.1, 2.4.1)
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- [ ] Breadcrumb `<nav>` with `aria-label="Breadcrumb"`
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- [ ] Page navigation `<nav>` with `aria-label="Page navigation"`
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- [ ] Main content wrapped in `<main>` element
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- [ ] Proper opening/closing tags for all landmarks
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### 5. Navigation Accessibility (WCAG 2.4.4, 2.4.8, 4.1.2)
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- [ ] Breadcrumb uses ordered list (`<ol>`)
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- [ ] Breadcrumb separators have `aria-hidden="true"`
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- [ ] Current page marked with `aria-current="page"`
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- [ ] Back button is semantic `<a>` element with descriptive text
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- [ ] All links have clear, descriptive text
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### 6. MathML Accessibility (WCAG 1.3.1, 1.4.5, 4.1.2) **[CRITICAL]**
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**Audit ALL math elements - check a representative sample:**
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- [ ] All have `role="math"`
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- [ ] All have `aria-label` with LaTeX source
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- [ ] All have `xmlns="http://www.w3.org/1998/Math/MathML"`
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- [ ] All use `<semantics>` wrapper
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- [ ] All have `<annotation encoding="application/x-tex">`
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### 7. Unicode Character Verification **[LAWSUIT RISK - CRITICAL]**
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**NO Unicode mathematical characters allowed. All MUST be HTML entities.**
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Run these verification commands:
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```bash
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# Check for Unicode mathematical operators (U+2200-U+22FF)
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grep -P '[\x{2200}-\x{22FF}]' <PATH_TO_HTML>
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# Check for Unicode mathematical alphanumeric symbols (U+1D400-U+1D7FF)
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# This includes blackboard bold: 𝔸 𝔹 ℂ 𝔻 𝔼 𝔽 𝔾 ℍ 𝕀 𝕁 𝕂 𝕃 𝕄 ℕ 𝕆 ℙ ℚ ℝ 𝕊 𝕋 𝕌 𝕍 𝕎 𝕏 𝕐 ℤ
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grep -P '[\x{1D400}-\x{1D7FF}]' <PATH_TO_HTML>
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# Check for common Greek letters
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grep -P '[α-ωΑ-Ω]' <PATH_TO_HTML>
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```
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**If ANY Unicode characters are found, FIX IMMEDIATELY:**
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- **Most common violation**: 𝔻 (U+1D53B) → Must be `&Dopf;`
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- ℝ → `&Ropf;`, ℂ → `&Copf;`, ℕ → `&Nopf;`, ℤ → `&Zopf;`, ℚ → `&Qopf;`
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- → → `&rarr;`, ≥ → `&ge;`, ≤ → `&le;`, ∈ → `&isin;`, ∞ → `&infin;`
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- α → `&alpha;`, β → `&beta;`, π → `&pi;`, φ → `&phi;`, ψ → `&psi;`, χ → `&chi;`
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**Manual inspection required for:**
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- [ ] Check `<mi>` elements inside `<math>` tags for raw Unicode
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- [ ] Verify blackboard bold letters (𝔻, ℝ, ℂ, ℕ, ℤ, ℚ) use entities
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- [ ] Verify Greek letters use entities
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- [ ] Verify mathematical operators use entities
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### 8. Color Contrast (WCAG 1.4.3)
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- [ ] Body text has minimum 4.5:1 contrast ratio (7:1 for AA)
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- [ ] Link colors have sufficient contrast
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- [ ] Navigation elements have sufficient contrast
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### 9. Keyboard Accessibility (WCAG 2.1.1, 2.4.3, 2.4.7)
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- [ ] All interactive elements keyboard accessible
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- [ ] Logical tab order (breadcrumb → back → main content)
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- [ ] No keyboard traps
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### 10. Mobile/Responsive (WCAG 1.4.4, 1.4.10)
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- [ ] Responsive meta viewport tag present
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- [ ] Flexible layout (no fixed widths)
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- [ ] Mobile-specific CSS (@media queries)
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### 11. Content Quality (WCAG 3.1.1, 3.1.2)
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- [ ] Language declared: `lang="en"`
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- [ ] All content is in declared language
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## Legal Compliance Summary
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After completing the audit, provide:
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**✅ PASS / ❌ FAIL Summary:**
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- Document Structure: [PASS/FAIL]
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- Page Title: [PASS/FAIL]
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- Heading Hierarchy: [PASS/FAIL]
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- Landmark Elements: [PASS/FAIL]
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- Navigation: [PASS/FAIL]
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- MathML: [PASS/FAIL]
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- **Unicode Verification: [PASS/FAIL]** ← CRITICAL
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- Color Contrast: [PASS/FAIL]
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- Keyboard: [PASS/FAIL]
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- Mobile: [PASS/FAIL]
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- Content: [PASS/FAIL]
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**Final Verdict:**
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- ✅ **PRODUCTION READY** - All WCAG 2.1 Level AA requirements met. Lawsuit risk: MINIMAL.
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- ❌ **NOT PRODUCTION READY** - Fix violations immediately before deployment.
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**If ANY items fail: FIX THEM IMMEDIATELY. Do not proceed until all items pass.**
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This comprehensive audit ensures legal compliance and protects the university from ADA lawsuits.
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## Important Notes
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- **CONCURRENT EXECUTION**: This command uses unique PDF_ID-based filenames in `/tmp/`, so multiple instances can run simultaneously without conflicts
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- Verify proper heading hierarchy (use grep or check a sample)
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- The final HTML should be fully accessible with screen readers
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## Success Criteria
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The output HTML must have:
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✓ Actual MathML elements (<math>, <mrow>, <mi>, <mo>, etc.)
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✓ NO Unicode characters - all replaced with HTML/MathML entities
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✓ Proper heading hierarchy (H1 for title, H2 for EVERY problem)
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✓ **H2 heading for each problem** (e.g., `<h2 class="unnumbered" id="problem-1">Problem 1</h2>`)
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✓ ARIA attributes on all math elements (role="math", aria-label)
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✓ lang="en" attribute on <html> element
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✓ Descriptive page title derived from H1 content (e.g., "TITLE - UVA Mathematics")
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✓ Breadcrumb navigation with aria-label="Breadcrumb" at top
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✓ Back button navigation with aria-label="Page navigation" below breadcrumb
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✓ Main content wrapped in <main> landmark element
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## Success Criteria - WCAG 2.1 Level AA Compliance
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The output HTML must meet ALL of these criteria to be production-ready:
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### Technical Requirements
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✓ Actual MathML elements (`<math>`, `<mrow>`, `<mi>`, `<mo>`, etc.)
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✓ **NO Unicode characters** - all replaced with HTML/MathML entities (especially **𝔻 → &Dopf;**)
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✓ Proper heading hierarchy (ONE H1, H2 for EVERY problem, no skipped levels)
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✓ H2 heading for each problem (e.g., `<h2 class="unnumbered" id="problem-1">Problem 1</h2>`)
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✓ ARIA attributes on all math elements (`role="math"`, `aria-label` with LaTeX)
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✓ `lang="en"` attribute on `<html>` element
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✓ Descriptive page title (e.g., "Analysis General Exam August 2017 - UVA Mathematics")
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✓ Breadcrumb navigation with `aria-label="Breadcrumb"`
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✓ Back button navigation with `aria-label="Page navigation"`
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✓ Main content wrapped in `<main>` landmark element
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✓ Valid, well-formed HTML5 document with proper semantic structure
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✓ Proper vertical spacing between main problems
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✓ HTML file saved next to the PDF with .html extension
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✓ Link in graduate/general_exams.md updated with HTML as primary, PDF as secondary with aria-label
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✓ Both PDF and HTML reviewed side-by-side with final quality assessment provided
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✓ Link in `graduate/general_exams.md` updated (HTML primary, PDF secondary with aria-label)
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### Legal Compliance Requirements
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✓ **WCAG 2.1 Level AA compliant** - All 11 checklist items pass
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✓ **Unicode verification passed** - No raw Unicode mathematical characters
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✓ **Screen reader compatible** - All math properly labeled with ARIA
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✓ **Keyboard accessible** - Logical tab order, no traps
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✓ **Mobile responsive** - Viewport meta tag, flexible layout
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✓ **Color contrast compliant** - Minimum 4.5:1 ratio for text
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✓ **Semantic structure** - Proper landmarks, headings, lists
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✓ **ADA Title II & III compliant** - Ready for public deployment
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✓ **Section 508 compliant** - Federal accessibility standards met
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### Final Review Completed
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✓ Both PDF and HTML reviewed side-by-side
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✓ Comprehensive WCAG 2.1 Level AA audit performed
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✓ All violations fixed immediately
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✓ Legal compliance summary provided
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✓ **Lawsuit risk: MINIMAL** - File is legally defensible
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**If any criterion fails, the file is NOT production-ready and must be fixed immediately.**

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