math-atlas-problem

name	math-atlas-problem
description	Optimize or create a math problem page in Math Atlas. Covers research, formula verification, visualization rewrite, problem data accuracy, and browser testing. Use when asked to optimize, fix, or create a /problems/<slug> page.

Math Atlas Problem Optimization

End-to-end workflow for creating or optimizing an interactive math problem page with verified formulas, accurate history, and a high-quality Canvas visualization.

When to use

• User asks to optimize/fix/create a problem page at /problems/<slug>
• User reports incorrect formulas, bad visualization, or missing references
• User wants to add a new mathematical problem to the atlas

Workflow

Phase 1 — Audit

1. Navigate to the page in the browser and take a full-page screenshot
2. Read the problem data in src/lib/problems.ts (find by slug)
3. Read the formula entry in the coreFormulas record (same file, search slug)
4. Read the draw function in src/components/viz/classic-viz.tsx
5. Note issues: vague descriptions, missing authors, weak references, flat visualization

Phase 2 — Research

Spawn a research agent to gather verified data. See references/research-checklist.md for what to collect:

• Precise formal statement with LaTeX
• Related theorems / equivalent formulations (2-3 formulas total)
• Verified historical timeline with exact paper citations
• Key contributors beyond the obvious names
• DOI links for all papers when possible

Phase 3 — Update problem data

Edit src/lib/problems.ts. See references/data-schema.md for field-by-field guidance:

• longDescription: mention the key mathematical mechanism, not just intuition
• authors: include all major contributors (provers, generalisers)
• papers: 3 well-chosen references with DOI URLs, not encyclopedia links
• timeline: 4-6 events covering origin → proof → generalization → applications
• year: use the publication year of the definitive proof
• connections: add related theorem names

Phase 4 — Update formulas

Replace the single coreFormula(...) call with a multi-formula array (2-3 entries):

1. Theorem — the main formal statement
2. Key mechanism — the underlying theorem that makes it work (e.g. index theorem, Lefschetz number)
3. Classification / structure — the structural quantity that governs the result

Each entry: { label, latex, description }. Keep descriptions under 120 chars.

Phase 5 — Rewrite visualization

Replace the draw function in classic-viz.tsx. See references/viz-patterns.md for conventions:

• Use 3D projection when the theorem concerns spheres/manifolds
• Show the mathematical objects (vector fields, mappings, deformations), not abstract decoration
• Add pointer interactivity (mouse controls a parameter)
• Use depth-sorting, alpha-fading, arrowheads for vectors
• Mark key features (fixed points, singularities) with blue glow + label
• Style: dark bg (#050505), white strokes, blue (#60a5fa) for highlights

Phase 6 — Verify

1. Reload the page in the browser, take screenshot
2. Check formulas render correctly (no KaTeX errors)
3. Check visualization animates and responds to mouse
4. Run npx next build to confirm no type/compile errors
5. Verify all DOI/arXiv links are syntactically correct

File map

What	Where
Problem data	src/lib/problems.ts — rawProblems array
Formula data	src/lib/problems.ts — coreFormulas record
Visualization	src/components/viz/classic-viz.tsx — draw* function
Viz exports	src/components/viz/classic-viz.tsx — bottom of file
Viz registry	src/components/viz/viz-loader.tsx + src/components/ui/problem-card.tsx
Page template	src/app/problems/[slug]/page.tsx

References

• references/research-checklist.md — what to verify during research
• references/data-schema.md — field-by-field guide for problems.ts
• references/viz-patterns.md — Canvas visualization conventions and patterns