qwen-mm-plugins-edu-agent

Math and Science Tutorials

Turn a math or science problem into a step-by-step Mandarin video tutorial. For an interactive page instead of a video, use the interactive workflow linked below. Teaching components — equations, diagrams, solution steps — are rendered as realistic objects: solid opaque panels (glass-look via borders + layered shadow, NO backdrop-filter, NO translucency), 3D metallic cards, animated SVG constructions, on themed backgrounds with animated gradient orbs and smooth ambient effects. The default theme is "Aurora Scholar" (blue wave texture + indigo/violet/cyan orbs); 4 alternative light themes are available (Elegant Lake Blue, Soft Purple Lightness, Mint Freshness, Warm Yellow Paper Feel) for visual variety across different problem types — see the Background Theme Catalog in design-system.md.

Prerequisites (Environment Preparation — Must-Check Before Starting)

This is a skill-only capability (no MCP server), so its runtime dependencies are NOT auto-installed by uvx. Verify ALL of the following before Step 0 — a missing one silently breaks a later step:

Dependency	Needed for	Install / check
Node.js + npm/npx	scaffold + render (`npx hyperframes`)	`node -v` (≥18)
hyperframes CLI	`init` / `lint` / `validate` / `render`	pulled on demand via `npx hyperframes` (needs npm-registry access at scaffold time; the project then pins a version in `dist/package.json`)
Headless Chromium + OS libs	`npx hyperframes render` (puppeteer) + post-render QA gates (`postcheck.py` / `precheck.py` drive headless Chrome)	the browser itself is auto-downloaded by puppeteer on first `npx hyperframes`; on minimal Linux you must also `apt install libnss3 libatk-bridge2.0-0 libgbm1 libasound2 libxkbcommon0 libgtk-3-0 fonts-noto-cjk` (else Chrome fails to launch, or CJK/formulas render as tofu boxes). Reuse a system Chrome via `export PUPPETEER_EXECUTABLE_PATH=/usr/bin/chromium`.
Python 3 + pip	TTS script	`python3 -m pip --version`
`dashscope` `soundfile` `numpy` `requests`	Step 3 TTS synthesis + assembly	`python3 -m pip install dashscope soundfile numpy requests`
ffmpeg	loudness normalization (`loudnorm`) + frame extraction for self-check	`brew install ffmpeg` / `apt install ffmpeg`
`DASHSCOPE_API_KEY`	Qwen-TTS (`qwen3-tts-flash`)	`export DASHSCOPE_API_KEY="sk-xxx"`, or put `DASHSCOPE_API_KEY=sk-xxx` in `~/.qwen-mm-plugins/config` for GUI-launched setups that don't inherit shell exports. `$EDU_SKILL_ROOT/scripts/generate_voice.py` reads it at runtime — never `cat`/paste the key into the conversation.

Network boundary: npx hyperframes init and the TTS calls need internet. The render itself is air-gapped — that is why fonts / KaTeX / GSAP must be self-hosted into dist/ (see Step 5 Prerequisites). DashScope TTS may rate-limit under high concurrency; if you hit Throttling.RateQuota, lower the thread-pool worker count and add backoff (see step-3).

Before Step 0, resolve EDU_SKILL_ROOT to the absolute directory containing this SKILL.md. All shipped scripts and assets must be addressed through that root; they are not in the user's project. Shell tool calls do not necessarily share state, so set it in every command block that uses it (or substitute the resolved absolute path directly); never rely on an earlier shell invocation:

EDU_SKILL_ROOT="<absolute directory containing qwen-mm-plugins-edu-agent/SKILL.md>"
test -f "$EDU_SKILL_ROOT/scripts/precheck.py" || { echo "invalid EDU_SKILL_ROOT"; exit 1; }

Pipeline Overview

Step	Name	Artifact	Reference
0	Image Input & Problem Extraction	`PROBLEM.md`	step-0-image-input.md
1	Problem Analysis	`ANALYSIS.md`	step-1-problem-analysis.md
2	Teaching Script	`SCRIPT.md`	step-2-teaching-script.md
3	Voice Generation	`narration.wav` + `transcript.json` + `captions.json` (sentence-by-sentence TTS, no Whisper)	step-3-voice-generation.md
4	Storyboard	`STORYBOARD.md`	step-4-storyboard.md
5	Build Components	`compositions/*.html`	step-5-build-components.md
6	Compose & Render	`index.html` + MP4	step-6-compose-render.md

Step 0: Image Input & Problem Extraction

Read references/step-0-image-input.md.

Read all images from the image_assets/ folder using the Read tool (Claude's multimodal vision directly interprets image content). Extract the complete problem text, convert all math expressions to LaTeX, and describe any figures or diagrams. If JSONL metadata is available (subject, sub_subject, question_type, stepwise_explanation), use it as context hints but treat the image as ground truth.

Step 1: Problem Analysis

Read references/step-1-problem-analysis.md.

Parse the input math problem, classify its type, extract knowledge points, and produce a complete solution outline with numbered steps. When PROBLEM.md exists from Step 0, use it as the primary input source.

Step 2: Teaching Script

Read references/step-2-teaching-script.md.

Write the Chinese narration script with scene markers. Apply math symbol pronunciation rules. Target pacing: 3.5-4.0 Chinese characters per second.

Step 3: Voice Generation

Read references/step-3-voice-generation.md. TTS strategy: DashScope Qwen-TTS via the official SDK (dashscope.MultiModalConversation, model qwen3-tts-flash, HTTP — returns a WAV URL) — no self-hosted TTS node, no URL wiring. Speed + accuracy: synthesize every sentence concurrently through a thread pool (wall-clock ≈ the slowest single sentence, not the sum), then measure each returned clip's real duration for exact per-sentence timestamps. No Whisper dependency.

Generate standard Mandarin TTS audio. Each sentence's exact duration is measured from its returned audio clip, producing both narration.wav and transcript.json in one pass with 100% accurate timestamps. No Whisper transcription needed.

Step 4: Storyboard

Read references/step-4-storyboard.md. Read design-system.md for visual tokens.

Design per-scene visual layout, assign component templates from math-components.md, and plan transitions. Check assets/ASSET_CATALOG.md to identify which pre-built visual components can be reused in each scene. Select a background theme from the Background Theme Catalog in design-system.md — set it in the Global Direction block (default: aurora-scholar).

Step 5: Build Components

Read the hyperframes skill — every composition authoring rule applies. Read the gsap skill for animation patterns. Read references/step-5-build-components.md. Read references/math-components.md for component templates. Read assets/ASSET_CATALOG.md for pre-built visual components. For geometry diagrams (Geometric Figures), read references/geometry-construction-guide.md for coordinate computation patterns, angle arc construction, and complete worked examples (triangles, quadrilaterals, circles, rotations, reflections); also read references/golden-example-geometry.md for a complete golden pipeline (PROBLEM → HTML compositions) showing the proven split layout, draw-on animation choreography, and narration-synced note blocks from a top-quality geometry proof video. For circuit schematic diagrams (Circuit Diagrams), read references/circuit-schematic-guide.md for physics rules and SVG symbol templates. For any scene that must ANIMATE A PROCESS with real motion (biological processes/force vectors/waves/titration/motion demonstrations — things that split, move, get pulled, or a quantity that changes across stages), read references/example-process-animation.md — a top-scoring few-shot (Onion Mitosis) with two complete reference scenes and copy-me techniques: staged phase reveal, split-and-move, connectors that track a moving object and shorten (spindle fibers/ropes/vector pulling), live count-up, and a stepped quantity-vs-stage chart (plus the no-360°-spin rule). 🧬 MANDATORY for ANY chromosome/cell division problem (mitosis/meiosis/chromatids/centromeres/spindle fibers/moving to opposite poles): you MUST open and copy references/examples/mitosis-anaphase.scene.html — the spindle fibers must be animated <line>s that TRACK the moving chromatids and SHORTEN (pull them to the poles), with a live chromosome count count-up, and NO 360° spin on chromosomes. This is enforced at render time by scripts/check_chromosome_example.py (a chromosome cell-division scene without the fiber-shorten tween, or with a 360° spin, FAILS precheck).

Scaffold the project with npx hyperframes init dist --non-interactive --example blank (the --example blank flag is required — hyperframes ≥0.7.77 rejects a bare --non-interactive). The project root is the current workspace and the scaffold dir MUST be exactly dist/ at that root — never nest it inside another folder (e.g. NOT math-tutorial-output/dist); the renderer and all gates assume ./dist. Build ONE composition per scene listed in STORYBOARD.md — one special ray / one solution step / one concept per scene; NEVER cram several planned scenes into a single composition (that is the #1 cause of under-rendered, blank, or half-empty scenes and of run-to-run instability). Before writing custom HTML for any visual object, check the assets/ directory — it contains 83 pre-built K12 components (motion, optics, circuit, mechanics, fluid, chemistry, wave, indicators, math), including 6 circuit schematic symbols (sch-battery, sch-ammeter, sch-voltmeter, sch-switch, sch-bulb, sch-resistor). If a matching component exists, copy its CSS + HTML + JS hooks verbatim into the composition instead of building from scratch.

EDU_SKILL_ROOT="<absolute directory containing qwen-mm-plugins-edu-agent/SKILL.md>"
python3 "$EDU_SKILL_ROOT/scripts/precheck.py" dist

This script auto-fixes LaTeX escaping, then runs all validation checks. You MUST see ALL CHECKS PASSED in the output before proceeding to Step 6. If any check shows FAIL:

Read the FAIL message — it prints the exact file, line, and fix instruction
Apply the fix to the offending file(s)
Re-run python3 "$EDU_SKILL_ROOT/scripts/precheck.py" dist
Repeat steps 1-3 until the output contains ALL CHECKS PASSED

Do NOT proceed to Step 6 with failing checks. Do NOT skip precheck. Do NOT treat precheck failures as warnings.

The precheck validates all of the following (each is also a standalone script in scripts/):

Asset mirror — GSAP/KaTeX/fonts mirrored into compositions/ (sub-compositions resolve ./ relative to their own directory; without the mirror, GSAP/KaTeX/fonts silently fail → blank scenes)
Composition format — sub-compositions are HTML fragments, not full <!doctype> documents (full docs → blank panels)
No CDN URLs — no cdn.jsdelivr.net or external src/href (render sandbox is air-gapped → all external loads fail silently)
KaTeX CJK — no Chinese inside katex.render() or data-tex (KaTeX fonts lack CJK → tofu)
CJK font on Chinese text (Chinese must use a Chinese font) — any SVG <text>/<tspan> or inline-styled element whose text contains Chinese MUST use a stack including Noto Sans SC (e.g. font-family="Noto Sans SC, Inter, sans-serif"); Inter/sans-serif alone has no CJK glyphs so Chinese renders as NO GLYPH / tofu blocks. Don't mix scripts in one <text> — split Latin (Inter) and Chinese (Noto Sans SC) into separate <tspan>/<text>. Gate: scripts/check_cjk_font.py
KaTeX escaping — LaTeX in JS strings double-escaped (\\\\dfrac, not \\dfrac; JS eats single \\d → "dfrac12" instead of fraction)
Unrendered fractions — no literal "dfrac"/"frac{" leaked into visible HTML text
Caption size — font-size 36–40px (not 64px giant subtitles)
Caption pinned to bottom (subtitles fixed at the bottom of the video) — every caption bar lives ONLY in index.html's root track and is styled position:absolute; bottom:48px; left:50%; transform:translateX(-50%); NEVER use top:, and NEVER put a caption inside a scene composition (it would drift to the top/middle). Gate: scripts/check_caption_position.py
Caption safe zone — every scene reserves the bottom ~180px (content in the top ~900px) so the subtitle never covers content (subtitle occlusion)
Caption overflow — the caption bar is width-bounded (max-width:1600px, never white-space:nowrap), uses width:max-content (so it uses the full width before wrapping instead of shrinking to the ~960px half-frame), and each cue is short (split long sentences into sequential one-line cues); the subtitle never runs off the frame edge (subtitle exceeding boundary). Gate: scripts/check_caption_overflow.py
Caption always on top (subtitles must be at the topmost layer) — the caption bar has an unbeatable z-index (2147483647) so it is ALWAYS above every scene layer/panel and can never be covered (subtitle being occluded); scenes must keep their z-index small (<100). Gate: scripts/check_caption_overflow.py
Scene layout — .scene-content is a centering box that fills the frame (position:absolute;inset:0;display:flex;align-items:center;justify-content:center); filling alone (no flex-center trio) piles a single panel at the TOP with the bottom half empty (layout problem). Gate: scripts/check_scene_layout.py
No oversize/overflow (layout too large) — every element fits within 1920×1080 (content within the 1920×900 safe area with edge margins); no CSS width>1920px / height>1080px, keep scale() ≤ ~1.5; size by container (%/max-width/flex/grid), scale SVG via viewBox. Hero text ≤ ~96px is guidance (decorative watermarks may be larger). Gate: scripts/check_scene_overflow.py
SVG height must be bounded (SVG height must be bounded — prevent the scene from suddenly getting bigger) — never size a content <svg> as width:100%; height:auto with a tall/near-square viewBox: height:auto ties the rendered height to the viewBox aspect ratio, so at full panel width a 1000×760 viewBox becomes ~1050px tall and overflows the ~860px usable height — the scene appears to "suddenly get big" (scene suddenly gets bigger). Bound the height: give the SVG max-height:<usable>px (e.g. max-height:760px), or size it by height inside a bounded flex/grid box with preserveAspectRatio="xMidYMid meet", or choose a viewBox whose aspect ratio matches the available box. Deterministic gate: scripts/check_svg_height_bound.py; the headless-measured scripts/check_scene_fit.py is the runtime backstop.
No overlapping SVG labels (SVG labels must not overlap) — inside a single <svg>, no two <text> labels may collide. Don't stack a fulcrum/center label and its arm/segment labels on one shared line; put the center label above and arm labels below (anchored end/start, pushed outward past the shape edge) with a gap of ≥ ~1 label-height; stagger point labels that share an axis and never let a point label bury an axis tick number (see Rule #28). Gate: scripts/check_svg_label_overlap.py
Node-graph diagrams clean (relationship diagrams/flowcharts) — in a boxes+arrows+in-shape-label diagram: every in-shape label is in the same <g> as its shape (else it slides off → white text disappears), white SVG text only ever sits inside a dark shape, arrow endpoints stop before the box (no arrowhead poking into a box), edge labels stay in the gaps (see Rule #31). Gate: scripts/check_svg_node_graph.py
No CSS-hidden content — no opacity:0 / visibility:hidden in CSS; GSAP handles via autoAlpha:0 in JS
No frosted glass — no backdrop-filter, panels are opaque #ffffff
Scene coverage — one composition per storyboard scene, all wired with data-composition-src and window.__timelines[...]
Root refs — index.html uses data-composition-src (not data-src or src) for all scenes
Geometry verification — every geometry scene (SVG with 3+ labeled points) has a  block; all ASSERT lines verified mathematically (coordinates satisfy parallel/perpendicular/midpoint/intersection/ratio constraints)

Additional requirements NOT checked by precheck (manual verification):

Self-hosted fonts + KaTeX + GSAP copied into dist/ AND mirrored into dist/compositions/
Chinese font NOT subsetted — one full NotoSansSC-Bold.woff2 per weight
KaTeX CSS inlined with local font URLs
No gradient text on KaTeX formulas (use solid color, not background-clip:text)
Grid/lattice figures generated programmatically with deduped edges (not hand-typed coordinates)

Step 6: Compose & Render

Read references/step-6-compose-render.md. Invoke the hyperframes-cli skill for CLI commands.

Assemble root dist/index.html, run lint + validate + inspect, preview, and render. All CLI commands (lint, validate, render) must run from inside dist/.

🔎 MANDATORY after rendering — visual overlap self-check loop (after rendering, extract frames for self-check; if overlap is seen, must change coordinates and re-render until there is no overlap): precheck.py now includes check_render_overlap.py, a headless render-truth gate that measures REAL bounding boxes and FAILs when a <text> is painted under/over a box it doesn't belong to (text covered by/overlapping a box — e.g. 取食→取, 捕食→捕; static coordinate gates miss this because scaling + CJK glyph width + SVG paint order make a "clear on paper" label collide in the render). That gate must pass. In addition, you MUST look at the pixels: for every scene with boxes/connectors/labels/charts, extract a settled frame (ffmpeg -ss <scene_midpoint> -i output.mp4 -frames:v 1 /tmp/ov.png), open it with the Read tool, and check by eye for Text covered/clipped by a box, boxes and lines overlapping, boxes misaligned, as well as direction/orientation/semantic errors(figure drawn reversed/wrong orientation: the flame of a burning wooden stick must be inside the bottle, not outside the bottle mouth; inclined plane orientation; arrow vector direction; instrument insertion end; pouring spout orientation; battery polarity/current direction; whether the chart truly reflects the stated trend). If you see ANY overlap/misalignment/wrong-orientation, edit the offending coordinates (move labels into the gap with clearance / shorten connectors / align boxes / draw highlight rings inside the box / flip the reversed figure), re-render, and look again — repeat until every frame is visually clean and physically correct. Never claim "visually verified" without having actually extracted and read the frames. Full loop in references/step-6-compose-render.md → "Post-Render Visual Overlap Self-Check".

🚫 MANDATORY after rendering — line/curve render-truth gate (line/curve missing-drawing detection): run python3 "$EDU_SKILL_ROOT/scripts/postcheck.py" dist and loop until it prints ALL POST-RENDER CHECKS PASSED. Its check_curves_rendered.py is renderer-agnostic: it renders a KNOWN-GOOD reference of each scene (GSAP + fonts injected by absolute path), then checks that every solid line/curve that scene should draw is actually painted in output.mp4. This catches the most deceptive render bug — a graph that shows its dots/axes/labels but drops the connecting curves ("has points, no lines") because JS-generated path d never ran (typically a hand-rolled renderer that stripped GSAP without re-injecting it by absolute file://). Pre-render gates cannot catch this — the composition is correct; only the rendered pixels reveal the loss. Prevention: render with npx hyperframes render; do NOT hand-roll a CDP/puppeteer renderer — and if you must, re-inject GSAP/KaTeX/fonts via absolute file:// paths (as you already do for bg-texture), never strip ./gsap/gsap.min.js and leave it. Full section in references/step-6-compose-render.md → "Post-Render Line/Curve Render-Truth Gate".

🌊 MANDATORY after rendering — smooth-curve render-truth gate (curves must not be approximated by polylines; if you see a polyline you must change the code and re-render until it passes): the same postcheck.py now also runs check_smooth_curve_render.py. It loads each continuous-curve scene (parabola/hyperbola/sine/exponential/inverse-proportional decay …), seeks the animation to its settled state, then walks the ACTUAL rendered curve geometry (getPointAtLength) and FAILs when a curve is drawn as a handful of straight chords — a jagged zig-zag with sharp kinks and long dead-straight runs between them (<path d="M488,585 L500,540 L530,480 …"> this kind of "curve" pieced together from ~7 straight segments). This is a visual/render-truth check: it sees the rendered shape, so it also catches curves whose d is generated by JS (which the static pre-render check_smooth_curve.py cannot see). When it FAILs, you MUST rewrite that curve's code and re-render, looping until it passes — do NOT ship a jagged curve. Fix: build the path d with the Catmull-Rom smoothPath() helper (sparse control points → cubic Béziers), OR emit a densely-sampled point list (~1 pt per ≤10 px, ~120+ pts across a wide axis). Genuinely piecewise-linear graphs (y=|x|, piecewise functions, line charts, uniform-speed distance-time) are exempt. See references/step-5-build-components.md → "Smooth curves (smooth curves)".

Before rendering, confirm that python3 "$EDU_SKILL_ROOT/scripts/precheck.py" dist was already run in Step 5 and printed ALL CHECKS PASSED. If you skipped it or are unsure, run it now — it takes seconds. Do NOT render with failing prechecks.

npx hyperframes lint and npx hyperframes validate pass with zero errors (run from dist/). Video rendered to MP4 via npx hyperframes render inside dist/. The output .mp4 file must exist inside dist/ and be reported to the user. Preview-only is NOT sufficient — rendering is mandatory. After rendering: check_render_overlap.py passes AND you have extracted+viewed a frame from every box/connector/label/chart scene and confirmed no clipped/covered text, no line-into-box, no misaligned boxes — fixing coordinates and re-rendering until clean. AND python3 "$EDU_SKILL_ROOT/scripts/postcheck.py" dist prints ALL POST-RENDER CHECKS PASSED (every line/curve the scene should draw is actually painted in output.mp4 — no line/curve is missing).

Design System

Read design-system.md before writing ANY HTML. It defines the "Aurora Scholar" light-themed visual identity. Use its exact color tokens, font specs, and component styles. Do not invent colors.

Problem Type Reference

Problem Type	Typical Duration	Scenes	Key Components
Single equation	30-60s	4-5	Problem Card + 2-3 Formula Panels + Conclusion
Multi-step algebra	60-120s	6-8	Problem Card + Analysis + Steps + Summary
Geometry proof	90-150s	7-10	Problem Card + Geometry Canvas + Proof Steps
Word problem	60-90s	5-7	Problem Card + Modeling + Solve + Verify

Non-Negotiable Rules

Caption text from original script (captions must use the original script text). Video captions/subtitles MUST use text from captions.json (which contains the original narration script text with timestamps measured from TTS output). The timestamps are 100% accurate because they are measured from each sentence's actual TTS audio duration during sentence-by-sentence synthesis. The OpenCC t2s conversion is no longer needed — transcript text comes directly from the original script.
KaTeX for layout-dependent math; plain HTML/Chinese for simple symbols (use KaTeX for complex formulas, HTML or Chinese for simple symbols). Use KaTeX only when the expression needs math layout features (fractions, roots, summations, matrices). For simple comparisons and standalone symbols (≤, ≥, °, ×), prefer HTML entities or Chinese text directly — e.g., write <span>OP' ≤ 1</span> not katex.render("OP' \\leq 1", ...) — this avoids the fragile JS backslash-escaping pipeline entirely (see Rule #25). Never display raw LaTeX source code. When you DO use KaTeX in JS strings, ALWAYS double-escape LaTeX backslashes — write "\\\\dfrac{1}{2}" not "\\dfrac{1}{2}". The \\d escape is silent: JS turns \\d → d, so \\dfrac becomes dfrac and KaTeX renders italic text "dfrac12" instead of a fraction. This is the single most common rendering bug. After building all compositions, run python3 "$EDU_SKILL_ROOT/scripts/check_katex_escaping.py" dist and fix every reported line BEFORE proceeding to Step 6.
Chinese pacing. Narration at 3.5-4.0 characters/second. Leave 0.5-1.0s pauses between steps.
Three layers per scene. Background treatment (wave texture + aurora mesh orbs) + content layer + accent elements. No flat single-layer scenes. See design-system.md "Background Treatment" for the exact CSS pattern and aurora palette guide.
Solid opaque panels — frosted glass is FORBIDDEN (frosted glass is forbidden; avoid occlusion completely). All content panels use the solid panel style from design-system.md — OPAQUE background:#ffffff (or white alpha ≥ 0.92), depth from borders + layered box-shadow + inset top highlight. NEVER use backdrop-filter / -webkit-backdrop-filter, and NEVER a see-through translucent panel background — a blurred/see-through panel washes out and OCCLUDES the problem text / diagram / formulas behind it (this is a hard defect). Enforced by scripts/check_no_glass.py (in precheck.py): render is blocked if any glass/translucent panel is found.
SVG geometry. Geometric figures use SVG path drawing animation, never static images.
Deterministic. No Math.random(), Date.now(), or async timeline construction.
Delegate. Use the hyperframes skill for composition rules, hyperframes-cli for CLI commands. TTS uses DashScope Qwen-TTS via the official SDK (dashscope.MultiModalConversation, model qwen3-tts-flash, HTTP) — no self-hosted node, no URL wiring; needs DASHSCOPE_API_KEY. Synthesize sentences concurrently (thread pool) for speed, and take per-sentence timestamps from each returned clip's measured duration (see step-3-voice-generation.md). This skill defines the math-and-science tutorial domain logic only.
Dark text on light backgrounds (dark text on light backgrounds). This is a light-theme design system. All text — KaTeX equations, SVG labels, Chinese body text, HTML table cells — MUST use dark colors (#0f172a or darker). Every composition MUST include the full "Mandatory Global Color Reset" block from design-system.md: root selector with color: #0f172a, .katex, .katex * { color: #0f172a; }, .katex-mathml { display: none !important; }, and table, th, td { color: #0f172a; }. Never use #fff, #f8fafc, #e8ecf4, or any light color for text on the light background.
Pre-built assets first. Before writing custom HTML/CSS for any visual object (car, train, candle, battery, lens, etc.), check assets/ASSET_CATALOG.md. If a matching component exists, copy its CSS and HTML verbatim. If NO match exists, follow the "Quality Fallback Template" in ASSET_CATALOG.md — every custom object must have ≥3 gradient layers, inset shadows, ground shadow, glow halo, and no CSS @keyframes. Compare against the candle component for quality level.
No emoji. Never use emoji characters (🔧⚙️🔵🔴🟢⭕📐✅❌⚡💡 etc.) anywhere in visible text — titles, labels, captions, formula notes, phase titles, badge text, or any string rendered in the video. Headless Chromium has no emoji font installed; all emoji render as □ (tofu boxes) in the final video. Use plain Chinese text or SVG/CSS shapes instead.
Math symbols: simple via HTML entities, complex via KaTeX — NO Chinese inside KaTeX (use HTML entities for simple symbols, KaTeX for complex formulas; KaTeX must not contain Chinese). Common math comparison and operator symbols are safe as HTML entities in Noto Sans SC / Inter: ≤ (≤), ≥ (≥), ≠ (≠), ° (°), × (×), ÷ (÷), ± (±), ² (²), ³ (³) — use these directly in HTML text instead of KaTeX when no layout structure is needed (see Rule #25). Greek letters (α, β, γ, δ, ε, θ, λ, μ, π, φ, ω) are safe as Unicode characters in HTML text — Inter-Variable.woff2 contains all Greek glyphs (Noto Sans SC does NOT). The font-family stack "Noto Sans SC", Inter, sans-serif will fall back to Inter for Greek. NEVER write the English word ("alpha", "beta", "theta") — always use the Unicode character (α, β, θ). Do NOT insert other specialized Unicode math symbols (∠, △, ⊥, ∥, √, ∞, ₁, ₂, etc.) directly into HTML text — use KaTeX for these in formulas, or Chinese equivalents in non-formula context ("角ABC" not "∠ABC", "三角形" not "△"). For inline subscripts/superscripts in labels, use HTML <sub>/<sup> tags (e.g., F<sub>1</sub> not F₁). The only safe non-ASCII characters in plain text are standard CJK Unified Ideographs (U+4E00–U+9FFF), common CJK punctuation, the HTML-entity math symbols listed above, and Greek letters (U+0370–U+03FF). CRITICAL: Never put Chinese text inside KaTeX \text{...} or any KaTeX command. KaTeX's math fonts (KaTeX_Main, KaTeX_Math, etc.) do NOT contain CJK glyphs — any Chinese character inside \text{} renders as □ tofu boxes. When a formula needs to be mixed with Chinese text, break it into separate HTML elements:
```

<span id="eq" data-tex="n \text{ 还是 } V"></span>


<span>判断操作对 </span><span id="eq-n" data-tex="n"></span><span> 或 </span><span id="eq-v" data-tex="V"></span><span> 的影响</span>
```
KaTeX CSS must be inlined, fonts self-hosted (the CSS for captions and formulas must be inlined, fonts offline). The HyperFrames compiler processes CDN <link rel="stylesheet"> tags by extracting ONLY @font-face rules and discarding all other CSS. This silently breaks KaTeX layout (fractions, subscripts, spacing render as flat plain text). Never use <link rel="stylesheet" href="...katex.min.css">. Instead: copy the shipped assets/katex/katex.min.css into dist/katex/, rewrite its font URLs to the local self-hosted path (url(./katex/fonts/), and paste the full CSS as <style id="katex-inline-css"> in every composition and in index.html. Load katex.min.js from the local dist/katex/ copy, not a CDN. See step-5 for the exact procedure.
Circuit schematic physics accuracy (circuit schematic physics accuracy). When drawing circuit schematic diagrams (circuit diagrams) in SVG: (a) battery symbol — long line = positive terminal (+), short line = negative terminal (-), never reverse the labels; (b) current direction — conventional current flows from battery + terminal through external circuit to - terminal, all arrows must form a consistent closed loop; (c) ammeter — must be wired in series, current enters + terminal; (d) voltmeter — must be wired in parallel with dashed branch wires (stroke-dasharray), + terminal toward higher potential; (e) wire segmentation (wire segmentation) — wires must STOP at component terminals, never draw a continuous wire that passes through components (components are NOT decorative overlays on wires); (f) switch must break the circuit (switch must break the circuit) — incoming wire ends at switch pivot, outgoing wire starts at contact terminal, switch orientation must match wire direction (vertical wire → vertical switch), no zero-length line segments; (g) layout distribution (layout distribution) — distribute series components across multiple sides of the rectangular loop, do NOT stack all components on one side; an empty side of the loop may be JUST a wire (wire) — never add/duplicate a component only to "fill" or "balance" a side; (h) no duplicate wires — each wire gap between components is drawn exactly once; (h2) component inventory correctness (component inventory correctness) — each real component appears exactly once — the set of components must match the problem's actual circuit; single-instance instruments (rheostat/sliding rheostat, ammeter, voltmeter, switch, power supply) must each appear EXACTLY ONCE — never invent or duplicate a component (drawing two 变阻器 in series is a physics error). Only true multiples in the problem (e.g. 两个灯泡 L₁/L₂, 两个电阻 R₁/R₂) may repeat. check_circuit_inventory.py gates this; (h3) circuit loop MUST be closed / 电源两端必须都接线 (回路闭合) — the main series loop is a single closed path: trace it from the 电源 + terminal through every component back to the 电源 - terminal — every gap must have a wire, and the power source's BOTH terminals must each connect to a wire. No unwired component terminal, no dangling wire stub (悬空导线端点 — a wire end that lands in empty space instead of on a component terminal or another wire at a corner). In physical wiring diagrams whose wire coordinates live in a JS array (var wires=[["w1",x1,y1,x2,y2],…]), it is easy to forget the segment that closes the left side back up to the source — do not. check_circuit_closed.py gates this; (i) physical wiring diagram layout (实物连接图布局) — "连接电表" and "连接主回路" operation scenes must use a rectangular loop layout (NOT a flat horizontal line) with ammeter IN the series loop (on the bottom return wire) and voltmeter on a visually separate dashed parallel branch; wire routing stays compact (≤100px margin beyond components); use Circuit Wiring Operation (C12) template from math-components.md, NOT Chemistry Operation Flow (C9); see circuit-schematic-guide.md Section 12; (j) voltmeter connection wires must not protrude (电压表连接导线禁止突出) — the sch-voltmeter template has NO built-in wire stubs; terminal endpoints are at the circle edge (±30 from center, not ±50); all dashed connection wires must be drawn as separate <line> elements from the main circuit T-junction point to the voltmeter circle edge — wires must start at the junction and end at the circle edge, never extending past either point; (k) voltmeter branch junctions must have dots and clean routing (电压表分支点必须有圆点且路由干净) — every T-junction where a voltmeter dashed wire meets the main circuit wire must have a filled junction dot (<circle r="4-5">); the dashed wire endpoint coordinates must be exactly ON the main wire (no offset); position the voltmeter so its terminals align with junction points to allow straight dashed lines; if L-shaped routing is unavoidable, use a single <path> with stroke-linejoin="round" — NEVER two separate <line> elements (they create gaps/protrusions at corners). Use sch-* templates from assets/ASSET_CATALOG.md and read references/circuit-schematic-guide.md for the full pre-flight checklist.
Caption formulas use KaTeX inline rendering (字幕公式必须用KaTeX渲染). Video captions must display proper math notation — never show spoken-form Chinese like "G M m除以R的平方". When assembling caption <div> elements in index.html, replace all spoken-form math expressions from captions.json with <span class="cm">LaTeX code</span> elements. The root index.html must load KaTeX JS and include a script that renders all .cm spans with katex.render() in inline mode. Use \tfrac for fractions (compact, fits single-line captions). KaTeX angle pitfall: for degrees use ^\circ, for arcminutes use a plain ASCII ' (prime), for arcseconds use ''. NEVER use \' or \" in KaTeX math — these are text-mode accent commands that cause the entire formula to render as red error text. See step-6 for the full template, common replacements table, KaTeX pitfalls, and examples.
Self-hosted offline fonts — Chinese MUST NOT be tofu (中文字体必须离线内嵌). The font files are shipped with this skill under assets/fonts/ and MUST be copied into dist/assets/fonts/ (see step-5 Prerequisites). Every sub-composition file AND the root index.html MUST embed them via an inline @font-face <style> block (the exact block is in step-6 for the root and assets/k12-scholar-font-template.css for compositions). Do NOT use a Google Fonts / CDN <link> and do NOT rely on the compiler's built-in embedding or system fonts (PingFang SC): the render sandbox is air-gapped, so a CDN font that fails to load makes ALL Chinese render as garbled boxes (乱码). Use a CJK-first stack everywhere — font-family: "Noto Sans SC", Inter, sans-serif — and never Inter, sans-serif alone. This applies no matter HOW font-family is set — SVG <text> attr, inline style=, AND CSS class rules. The #1 miss is a small label/eyebrow/badge class (e.g. .block-number{font-family:Inter,sans-serif}) that the design intends for a Latin number like "01" but the model fills with Chinese (对称性/题目所给) → those 3–4 characters render as 豆腐块 while the rest of the card is fine. Any class that could ever hold Chinese must include "Noto Sans SC". Enforced by scripts/check_cjk_font.py (now also scans class-based font-family, not just SVG/inline).
No CDN/external URLs at render time (渲染时禁止任何CDN/外部URL). Every <script src>, <link href>, and CSS url() in compositions and index.html MUST use local relative paths. The AP render sandbox is air-gapped with no internet access — CDN URLs that load successfully on a local machine will silently fail on AP, breaking GSAP timelines (no animations), KaTeX rendering (raw LaTeX in captions), and font loading (tofu boxes). Specifically: (a) GSAP — load from ./gsap/gsap.min.js (shipped in assets/gsap/, copied to dist/gsap/ AND dist/compositions/gsap/ in step-5); (b) KaTeX JS — load from ./katex/katex.min.js; (c) KaTeX CSS — inline as <style>, fonts from ./katex/fonts/; (d) body fonts — inline @font-face from ./assets/fonts/. Never use cdn.jsdelivr.net, cdnjs.cloudflare.com, unpkg.com, or any other external host in a src or href attribute. CRITICAL: sub-compositions in dist/compositions/ resolve ./ relative to their own directory — the assets MUST be mirrored into dist/compositions/ (gsap/, katex/, assets/) or all ./ paths silently 404 and GSAP/KaTeX/fonts fail to load (blank scenes, no animations, tofu). Enforced by scripts/check_asset_mirror.py in precheck.py.
Defensive rendering — no CSS-hidden content (防御性渲染 — CSS禁止隐藏内容). The #1 cause of blank videos is CSS opacity: 0 on .scene-content or content elements, combined with a JS error that prevents GSAP from revealing them. Rules: (a) Never set opacity: 0, visibility: hidden, or display: none on any content element in CSS — GSAP handles the initial hidden state dynamically via autoAlpha: 0 in fromTo(); (b) Wrap the entire GSAP timeline construction in a try-catch block — if any tween fails, the timeline still registers and content stays visible; (c) Each katex.render() call must have its own try-catch — one bad LaTeX string must not crash the entire composition; (d) Always pass throwOnError: false to katex.render(). See step-5 "Defensive Script Pattern" for the complete code template.
Reproducibility — stable structure every run (稳定复现 — 结构固定). The same problem must yield the same well-formed video every time; the biggest source of run-to-run quality swing is the BUILD step deviating from the plan. Rules: (a) Fixed output path — scaffold and render in exactly ./dist at the workspace root; never nest it (math-tutorial-output/dist etc.) — the renderer and gates assume ./dist. (b) One composition per storyboard scene — build exactly the scenes listed in STORYBOARD.md, one concept/ray/step per scene; never merge several planned scenes into one file, never skip a planned scene. index.html must wire ≥ the planned scene count. (c) Every scene self-contained & complete — each composition draws its full content (e.g. an optics scene MUST include the horizontal principal axis through O with 2F/F/O/F′/2F′ marked) and registers window.__timelines[...]. (d) Determinism — no Math.random() / Date.now() / async timeline construction (see rule #7). (e) These are enforced deterministically by $EDU_SKILL_ROOT/scripts/check_scene_coverage.py and $EDU_SKILL_ROOT/scripts/check_no_hidden_content.py inside $EDU_SKILL_ROOT/scripts/precheck.py — precheck.py dist must print ALL CHECKS PASSED before rendering.
Root MUST reference scenes via data-composition-src (根合成引用名固定 — 否则全白). In dist/index.html, every scene clip MUST use the EXACT attribute data-composition-src="compositions/scene-X.html" — never data-src, src, or a missing src. HyperFrames only loads/compiles an external scene when it sees data-composition-src; any other name means no scene loads and the whole video renders white (only the caption bar shows). Also: each clip's data-composition-id must match that scene's registered window.__timelines["<id>"], and scenes are laid out directly inside the root composition div (do NOT wrap them in an extra data-composition-id="mt-root" container). Enforced by scripts/check_root_compositions.py in precheck.py.
几何图形坐标必须数学精确 (Geometry SVG coordinates must be mathematically exact). When drawing geometric figures in SVG (Geometry Canvas scenes), all vertex coordinates MUST be computed from the problem's mathematical constraints (perpendicularity, parallelism, similarity ratios, length ratios, etc.) — never placed by visual estimation. Mandatory steps: (a) solve the problem's equations to get exact proportional relationships between all segments before writing any SVG; (b) choose a base unit in the SVG viewBox, then compute every point's coordinates from the ratios; (c) verify perpendicularity — if two lines are perpendicular, compute the dot product of their direction vectors and confirm it equals 0; (d) verify length ratios — compute Euclidean distances and confirm they match the problem's given ratios; (e) write a  block above the SVG with a POINTS: line declaring all coordinates and ASSERT lines for every problem constraint (parallel, perpendicular, midpoint, on_line, on_segment, intersection, ratio, collinear) — the pre-render gate scripts/check_geometry_verification.py dist mathematically verifies every assertion against the declared coordinates and exits 0; (f) right angle marks (直角符号) must be drawn as small L-shaped squares (not V-shapes or arcs), with edges computed from the actual line direction unit vectors — see step-5-build-components.md "Geometry Coordinate Accuracy" for the verification block format, assertion types, and construction algorithms.

角度弧线必须用叉积确定扫描方向 (Angle arcs must use cross-product to determine sweep direction). When marking a non-right angle at vertex V with arms pointing to adjacent vertices P1 and P2 in SVG, the arc MUST sweep through the interior of the angle being marked. The sweep direction is determined by the cross product of the two arm vectors — never by visual estimation or guesswork. Algorithm:

// 1. Direction vectors from vertex V to each arm endpoint
dx1 = P1.x - V.x;  dy1 = P1.y - V.y;
dx2 = P2.x - V.x;  dy2 = P2.y - V.y;

// 2. Cross product (in SVG screen coordinates, y-down)
cross = dx1 * dy2 - dy1 * dx2;

// 3. Arc start/end points on each arm at radius distance
angle1 = Math.atan2(dy1, dx1);
angle2 = Math.atan2(dy2, dx2);
startX = V.x + R * Math.cos(angle1);
startY = V.y + R * Math.sin(angle1);
endX   = V.x + R * Math.cos(angle2);
endY   = V.y + R * Math.sin(angle2);

// 4. Sweep flag: cross > 0 → interior is CW → sweep=1
//                cross < 0 → interior is CCW → sweep=0
sweepFlag = cross > 0 ? 1 : 0;

// 5. SVG path (large-arc-flag = 0 for angles < 180°)
d = `M ${startX},${startY} A ${R},${R} 0 0,${sweepFlag} ${endX},${endY}`;

Worked example — rhombus with ∠A = 60°, ∠B = 120°:

// Vertices: A(200,400) B(400,180) C(600,400) D(400,620), R=30

// ∠A = 60° — arms AB and AD
dx1=200, dy1=-220; dx2=200, dy2=220;
cross = 200*220 - (-220)*200 = 88000 > 0 → sweep=1
// Arc sweeps CW through interior (rightward between AB and AD) ✅

// ∠B = 120° — arms BA and BC
dx1=-200, dy1=220; dx2=200, dy2=220;
cross = (-200)*220 - 220*200 = -88000 < 0 → sweep=0
// Arc sweeps CCW through interior (downward between BA and BC) ✅

Common mistakes: (a) Hardcoding sweep-flag=1 or sweep-flag=0 without computing cross product — causes arcs to appear on the exterior (reflex) side of the angle; (b) Drawing the arc between the wrong pair of arms (e.g., marking ∠ABC but using arms BA and BD); (c) Using a right-angle L-shaped mark for non-90° angles; (d) Forgetting that SVG y-axis points down, which reverses the visual rotation direction. Always verify: visually, the arc must curve TOWARD the interior of the polygon, not away from it.

坐标分隔符只用逗号，禁止分号 (Coordinate separators: comma only, never semicolon). When writing coordinate pairs, point notation, or ordered tuples in KaTeX (e.g., vertex coordinates, intersection points), use only a comma as the separator between components — never a semicolon, and never both. Add a KaTeX thin space \, after the comma for readability. JS string escaping pitfall: in a JavaScript string passed to katex.render(), write \\, (double backslash) so KaTeX receives \,. Writing \; in a JS string does NOT produce a KaTeX thick space — JS treats the unknown escape \; as a literal semicolon character ;, so KaTeX renders a visible ,; (comma followed by semicolon). This is a confirmed rendering bug. Correct examples:
```
// In JS strings (double-escaped for JS → KaTeX):
katex.render("(1,\\, b-1)", el);          // ✅ renders (1, b−1)
katex.render("(x_0,\\, y_0)", el);        // ✅ renders (x₀, y₀)

// WRONG:
katex.render("(1,\; b-1)", el);           // ❌ renders (1,; b−1) — JS turns \; into literal ;
katex.render("(1,\\; b-1)", el);          // ❌ renders (1, b−1) with excessive space

// In HTML (e.g., <span class="cm"> for caption KaTeX):
<span class="cm">(1,\, b-1)</span>        // ✅
<span class="cm">(1,\; b-1)</span>        // ❌ overly wide space, inconsistent
```
General rule: coordinates are (a,\, b) in LaTeX, (a,\\, b) in JS strings. No semicolons anywhere in coordinate notation — this is Chinese math convention (中国数学用逗号分隔坐标，不用分号).
Sub-composition files must be HTML fragments, NOT full documents (子合成文件必须是HTML片段，不能是完整HTML文档). Every file in dist/compositions/*.html must be an HTML fragment — a root <div data-composition-id="..."> with inline <style> and <script> blocks. NEVER wrap sub-compositions in <!doctype html>, <html>, <head>, or <body> tags. HyperFrames loads sub-compositions by injecting their content into the parent document; a full HTML document wrapper prevents the renderer from properly executing GSAP scripts inside the sub-composition, causing all content elements to remain invisible (blank white panels with only background texture showing — audio and captions play normally, making the bug deceptive). Only the root index.html is a full HTML document. Enforced by scripts/check_composition_format.py in precheck.py.

简单符号优先用中文或HTML实体，避免不必要的KaTeX (Prefer Chinese/HTML entities over KaTeX for simple math symbols). KaTeX rendering in JS strings requires double-escaped backslashes (\\leq not \leq); a single-backslash error is silent — JS eats \l→l, \a→a, \c→c, producing garbled text like "OP'leq1" or "angleMPNleq90^circ" instead of proper symbols. To avoid this fragile pipeline, prefer plain HTML or Chinese text whenever the expression does NOT need math layout features (fractions, roots, matrices, complex sub/superscripts). Decision table:

Expression type	Display goal	Method	Code
Simple comparison	OP' ≤ 1	HTML entity	`<span>OP' ≤ 1</span>` or `OP' ≤ 1`
Angle expression	角MPN ≤ 90°	Chinese + entity	`<span>角MPN ≤ 90°</span>`
Degree symbol	90°	HTML entity	`90°` or `90°`
Multiplication	3 × 4	HTML entity	`3 × 4`
Simple inequality	x ≥ 5	HTML entity	`<span>x ≥ 5</span>`
Fraction layout	½	KaTeX	`katex.render("\\\\frac{1}{2}", ...)`
Complex formula	quadratic	KaTeX	`katex.render("\\\\frac{-b\\\\pm\\\\sqrt{b^2-4ac}}{2a}", ...)`
Root expression	√(a²+b²)	KaTeX	`katex.render("\\\\sqrt{a^2+b^2}", ...)`
Subscript variable	x₁, y₂	HTML `<sub>`	`x<sub>1</sub>`, `y<sub>2</sub>`
Greek letter	α, β, θ	Unicode char	`<span>α</span>` — NEVER write "alpha"
Safe HTML entities: `≤` (`≤`), `≥` (`≥`), `≠` (`≠`), `°` (`°`), `×` (`×`), `÷` (`÷`), `±` (`±`), `²` (`²`), `³` (`³`).
Safe Unicode Greek letters (in Inter font): α, β, γ, δ, ε, θ, λ, μ, π, φ, ω — use directly, never write English names.
Chinese replacements for geometric symbols: "角" (∠), "三角形" (△), "垂直于" (⊥), "平行于" (∥).
Rule of thumb: if the expression is a simple comparison, a standalone symbol, or a Chinese-friendly geometric term, use HTML/Chinese. If it has fractions, roots, summations, or nested structure, use KaTeX.

SVG coordinate-axis arrows must use orient="auto" + a right-pointing triangle (Axis arrows: always use a single right-pointing marker with orient="auto"). When drawing coordinate axes in SVG, define ONE arrowhead marker with its polygon pointing in the +x direction of the marker's local coordinate system, and set orient="auto". This same marker works for ALL axis directions (x-axis, y-axis, or any angle) because orient="auto" rotates the marker to match the stroke direction at the endpoint. NEVER define a separate "upward" marker with a polygon pre-rotated to point up — orient="auto" will rotate it an additional -90°, making the arrowhead point LEFT instead of UP. Correct pattern:
```
<defs>
  
  <marker id="axis-arrow" markerWidth="10" markerHeight="7" refX="10" refY="3.5" orient="auto">
    <polygon points="0 0, 10 3.5, 0 7" fill="#0f172a"/>
  </marker>
</defs>

<line x1="50" y1="400" x2="570" y2="400" marker-end="url(#axis-arrow)"/>

<line x1="300" y1="470" x2="300" y2="30" marker-end="url(#axis-arrow)"/>
```
Common mistake (y-axis arrow points LEFT):
```

<marker id="arrowU" orient="auto"><polygon points="0 10, 3.5 0, 7 10"/></marker>
```
Why: orient="auto" aligns the marker's local +x axis with the line's tangent direction. For a line from (300,470) to (300,30), the tangent is (0,−1) = upward, so the local +x rotates −90°. A right-pointing triangle (+x direction) correctly becomes upward. An already-upward triangle (−y direction) gets rotated to point left.
Force arrows/coordinate axes must never have a glow filter (NEVER apply a glow/blur filter to an axis-aligned <line>). A perfectly horizontal or vertical <line> — every force arrow (gravity G↓ / normal force N↑ / friction f / tension), coordinate axis, horizontal light ray, or wire — has a degenerate bounding box (zero height when horizontal, zero width when vertical). SVG filters default to filterUnits="objectBoundingBox" with a region of -10%…120% of the bbox, so a zero dimension makes the filter region zero-area → the line AND its marker-end arrowhead render completely invisible. The <text> label carries no filter, so it still shows — producing the deceptive symptom "In a force diagram there are only force labels (G/N/v), no force arrow lines." This bug hides on slanted rays (a diagonal line has a nonzero-area bbox and survives), so it only surfaces on vertical/horizontal force arrows. Fix: give force arrows a solid stroke (width 4–6) + marker-end and NO filter — a force arrow reads perfectly without a glow. If a glow on straight strokes is truly needed, make the filter absolute so it ignores the bbox: <filter id="fGlow" filterUnits="userSpaceOnUse" x="0" y="0" width="<viewBoxW>" height="<viewBoxH>">…</filter>. Glow filters remain safe on circles/particles/ions/text (non-degenerate bbox). Enforced by scripts/check_svg_filter_bbox.py in precheck.py.
SVG labels must not overlap each other (SVG <text> labels must NOT overlap each other). SVG <text> is positioned by hand (absolute x/y in viewBox units), so labels crammed around a shared point or along a short line collide and the text mashes together (text overlap). The classic failure is a pulley/lever diagram that places the fulcrum label 支点 O and the two arm labels 动力臂 r / 阻力臂 r on the SAME horizontal diameter through the circle center — three centered labels in ~90px of room overlap into "effort arm fulcrum O resistance arm r". This class of overlap is invisible to the other layout gates (check_scene_overflow.py ignores SVG user coordinates; check_scene_layout.py only checks the DOM wrapper). Rules: (a) never stack multiple labels on a shared point or a short segment — give each label its own side with a clear gap of ≥ ~1 label-height (≥ the label's font-size in viewBox units) between neighbouring boxes; (b) for a center/fulcrum + two arm labels, put the center label ABOVE the line and the arm labels BELOW it (or vice-versa) so their vertical bands don't collide; (c) anchor arm/segment labels text-anchor="end" (left side) / "start" (right side) and push them outward past the shape edge rather than toward the crowded center; (d) offset a label perpendicular to the line/arm it names, not along it; (e) when two point labels sit on the same axis (e.g. A(-3,0) and E(-5,0)), stagger their y or shorten to bare letters so their boxes clear. Do NOT let a point label sit on top of an axis tick number — move the tick or drop the redundant one. Enforced by scripts/check_svg_label_overlap.py in precheck.py (conservative: flags only substantial 2-D overlap, accounts for <g transform="translate"> and GSAP-repositioned elements).
Force/vector arrows must be correct (SVG force/vector arrows — fixed-size head, full-length line). Hand-rolled SVG arrows (<line marker-end>) fail in three severe ways at once, as seen in a trampoline force scene (giant sideways arrowheads with no shaft): (a) arrow too big — a <marker> with no markerUnits defaults to markerUnits="strokeWidth", so the arrowhead is multiplied by the (thick, 6–8) force stroke → a ~72–96px triangle. Fix: <marker markerUnits="userSpaceOnUse" markerWidth="14" markerHeight="14" refX=… refY=… orient="auto"> sized in absolute px. (b) wrong direction + (c) the line was not drawn — drawing the <line> collapsed to a point (x1==x2 && y1==y2) and growing it via GSAP attr:{y2}: a zero-length line has no shaft, and orient="auto" on it is undefined so the head points sideways; if the attr tween doesn't seek at render, the shaft never appears. Fix: draw the line at its full, correct length (so orient is right and the shaft always exists) and reveal it with stroke-dashoffset draw-on — never animate a marker line's length from zero. BEST: reuse the prebuilt CSS force-arrow component (assets/components/mechanics/force-arrow.html) — fixed head, rotate for direction, --arrow-length for magnitude. Enforced by scripts/check_svg_arrow.py in precheck.py.
Graphic labels must not sit on top of the graphic (SVG labels must NOT overlap the drawing — text must not cover lines or points). A point/vertex/curve letter (A/B/O/F/M…) must never sit ON a line, axis, symmetry line, curve, or vertex dot — it must be offset OUTWARD, away from the figure, by ~18–24 units. Classic failure: a point M on the symmetry axis gets its label placed straddling that axis's x, so the dashed axis line runs straight through the "M". Rules: (a) place a small dot at the point and the letter ~20u beside it, on the side away from the shape centre (never at the exact point coordinate); (b) a point on the x-axis → label ~22u below/above the axis, not on it; the origin O → offset into a quadrant (x−14, y+20); (c) a label near a vertical/symmetry line → anchor end and push left (or start/right) so the stroke clears the glyphs; (d) a curve label sits in the empty area beside the curve. Nudging a label a little to clear the figure is expected and encouraged. This is distinct from label-vs-label overlap (Rule #28) — here the collision is label-vs-geometry. Enforced by scripts/check_svg_label_on_figure.py in precheck.py.
Relationship-diagram/flowchart nodes must be grouped, arrows must not press on boxes, and white text inside shapes must be visible (SVG node-and-connector diagrams). When a scene draws a food chain / feedback loop / flow diagram from SVG boxes + arrows + in-shape labels, three failures ruin it (seen in an ecological-balance case: white 负反馈 invisible, arrows poking into the box). Rules: (a) a label inside a shape MUST be in the SAME <g> as that shape — <g><circle/><text/></g>, never independent siblings; otherwise a GSAP scale/pulse/back.out overshoot or svgOrigin residue moves the shape but not the text, so the label slides off the shape onto the panel and disappears (the "white text not displayed" bug). Animate/position the group, not the shape alone. (b) white SVG <text> is allowed ONLY inside a dark shape that contains it (white-on-light is invisible; #ffffff text is otherwise forbidden — see Rule on light-theme colors), and it must be grouped with that shape per (a); size the shape so the text fits with margin. (c) arrow/connector endpoints stop ≥ ~10u before the target box edge (account for markerWidth) — never end a marker-end line/path inside or flush against a <rect> node, or the arrowhead hides under / pokes into the box. (d) edge labels ("feeding"/"predation") go in the gap between boxes with clearance, not against a box; space boxes so connector + label + clearances fit. Enforced by scripts/check_svg_node_graph.py in precheck.py.
SVG height must be bounded, never let width:100%;height:auto blow up the scene (SVG height must be bounded — never let width drive an unbounded height). A content <svg> styled width:100%; height:auto sizes its width to the panel (~1380px in a full-width panel) and then, because height:auto, sets its height from the viewBox aspect ratio — a near-square viewBox like 0 0 1000 760 becomes ~1050px tall, far past the ~860px usable height (1080 − top padding − 180px caption safe zone). The SVG overflows the frame and the scene looks like it "suddenly got bigger" (the scene suddenly gets bigger) than the earlier text scenes. This is invisible to the literal-px overflow gate (there is no px > frame). Rules: (a) never write width:100%; height:auto on a content SVG with a tall/near-square viewBox (and equally never width:100%; aspect-ratio:1 — a CSS aspect-ratio drives the height from the width just the same); (b) bound the height — either add max-height:<usable>px (e.g. max-height:760px) so the SVG letterboxes, or size it by height (height:100% inside a bounded flex/grid box) and let preserveAspectRatio="xMidYMid meet" shrink the width to fit; (c) alternatively choose a viewBox aspect ratio that matches the available box (wide/landscape, ratio ≲ 0.5) so width:100% keeps the height under ~820px. The origin of the "the rendered scene behind suddenly gets bigger" bug was exactly a graph-verification (graph) scene with #svg{width:100%;height:auto} on a 1000×760 viewBox. Enforced deterministically by scripts/check_svg_height_bound.py (browserless) and measured at runtime by scripts/check_scene_fit.py, both in precheck.py.
Never tween x/y/rotation/scale on an SVG element with a positioning transform attribute (never GSAP-tween a transform prop on a transform-positioned SVG element — otherwise the object flies off the screen). An SVG element placed with a hard-coded transform attribute, e.g. <g transform="translate(390,364) rotate(-30)"> (a block on an incline, a rotated arrow, a positioned symbol), must NOT be the target of a GSAP tween that animates a transform shorthand (x, y, rotation, rotationX/Y/Z, scale, scaleX/Y, xPercent, yPercent, skewX/Y). GSAP parses the element's existing transform into its own model, then the tween overwrites it — e.g. fromTo("g[transform]", {y:10}, {y:0}) drives translateY from its real 364 down to 0, so the element jumps ~364px off its position and flies out of frame (the object flies off the screen). The classic failure is a broad selector like g[transform] or a bare g/rect selector that happens to hit a positioned group. Rules: (a) on a transform-positioned SVG element, animate ONLY opacity/autoAlpha (never x/y/rotation/scale); (b) to also slide/scale it, NEST — keep the positioning transform on a static outer <g transform=...> and put the fade/slide tween on an inner <g> (or wrapper); (c) if you truly must animate its transform, use attr:{transform:'translate(...) rotate(...)'} with the full transform written out at both ends, never a bare x/y shorthand; (d) never target positioned groups with a broad g[transform] / bare-tag selector. Animating x/y/scale on elements without a transform attribute (plain circles, HTML panels positioned by CSS) is fine. (e) When doing scale/rotation scaling/rotation on an SVG element, never use a px-unit transformOrigin（such as transformOrigin:"470px 270px"）——on SVG it converts using the element's bounding-box local coordinates, and for a <g> whose child-element coordinates are far from the SVG origin, scaling comes with a huge translation that flings/misplaces the element (even if that <g> has no transform attribute and is positioned purely by absolute child-element coordinates, it will still fly — this is exactly the real incident where "the rheostat-shortening animation flung the entire R₁ off the screen"). Instead use GSAP's SVG-specific svgOrigin:"x y"(user coordinate system, such as svgOrigin:"470 270"), or nest the element inside <g transform="translate(...)"> then scale the inner layer.transformOrigin Using percentages (e.g. "50% 50%") is safe on SVG. Enforced by scripts/check_svg_transform_anim.py in precheck.py.

Golden Examples (Few-Shot References)

Before building compositions for a new problem, read the matching golden example to see the complete pipeline (PROBLEM → ANALYSIS → SCRIPT → STORYBOARD → HTML compositions → index.html) executed at top quality. These are condensed from real high-scoring videos — no binary files, just the essential pipeline artifacts and representative composition code.

Example	Problem Type	When to Read
references/golden-example-geometry.md	Geometry proof (rotation, equilateral triangle, perpendicular bisector)	Any geometry proof problem — shows coordinate computation, GEOMETRY VERIFICATION blocks, split layout (SVG + note blocks), progressive draw-on animations synced to narration, proof-step overlay patterns
references/golden-example-interactive-transform.md	Interactive HTML explorer (interactive webpage, not a video)	When the user asks for an interactive page / interactive interface / lets the user drag and experience (sliders/controls that update a graph AND the equation live), instead of an MP4. Ships a complete offline `index.html` (Canvas graph + KaTeX live equation + dropdown/sliders/checkboxes/reset, Aurora theme) plus the 6 rules to reproduce it exactly. Skip the Step 0–6 video pipeline for this.

⚙️ Two output modalities. Most requests → a narrated MP4 via the Step 0–6 pipeline (use the geometry / process-animation examples above). But when the user explicitly wants an interactive web page (drag parameters, real-time linkage, not a video), switch to the interactive golden example above — same Aurora look & offline assets, but the deliverable is a self-contained index.html opened by double-click, not a rendered video.

KaTeX must render [synchronously] when the composition loads, and be scoped by id/data-composition-id scope selection; a id selector without an #合成id is forbidden, and deferring rendering with setTimeout is forbidden (render KaTeX synchronously at load, scoped correctly; never a #composition-id selector without a matching id, never defer with setTimeout). Two confirmed classes of "formula blank" pitfalls (blank screen; options/steps/formulas not visible):(1) Missing root id(deterministic, most common) — the root div is <div data-composition-id="mt-x">（data-composition-id is a data attribute, not a DOM id), but the render loop uses document.querySelectorAll("#mt-x [data-tex]")；#mt-x matches 0 → no rendering → all formulas blank.Fix: add to the root div both id="mt-x"(keeping data-composition-id), or use [data-composition-id="mt-x"] / document.currentScript.closest("[data-composition-id]") as an id-agnostic scope. Intercepted by scripts/check_composition_root_id.py (the q067 arc-length formula showing only "=" is due to this; after adding id the re-render is fixed).(2) Must render synchronously; never defer — the HyperFrames renderer, which seeks the GSAP timeline todeterministically capture frames，does not guarantee execution of setTimeout/requestAnimationFrame and other asynchronous callbacks; therefore KaTeX must render synchronously when the composition's inline <script> loads(at this point index.html has already <head> synchronously loaded katex, globally available),do notwrap katex.render in setTimeout/polling, and do not rely on onload/scripts appended at the end (those appended after the root </div> of <script> are discarded at injection time and do not execute at all). Prefer static data-tex attributes + a synchronous querySelectorAll render loop (see step-5 Rule 4).Known unresolved edge cases: in some scenarios, when opened in hyperframes validate/standalone the formulas are fine, but in the final MP4 they are still blank (that scenario's imperative KaTeX was not preserved by frame capture, e.g. q062's annotation box) — when encountered, always verify against therendered MP4 , and rewrite that scene's markup if necessary.

References Index

File	When to Read
design-system.md	Before writing any HTML
references/golden-example-geometry.md	Few-shot example — geometry proof pipeline (PROBLEM → HTML compositions)
references/golden-example-interactive-transform.md	Few-shot example — interactive HTML explorer (interactive webpage, not a video): live graph + live equation via sliders, offline self-contained; full reference index.html + 6 reproduce-rules
references/example-process-animation.md	Few-shot example — process/motion animation (biological process/forces/waves/demonstration): split-and-move, connectors that shorten & pull (spindle fibers/ropes/vectors), live count-up, stepped chart; 2 complete reference scenes
references/step-0-image-input.md	Step 0 — when input is image_assets/
references/math-components.md	When building scene compositions (Step 5)
references/step-1-problem-analysis.md	Step 1
references/step-2-teaching-script.md	Step 2
references/step-3-voice-generation.md	Step 3
references/step-4-storyboard.md	Step 4
references/step-5-build-components.md	Step 5
assets/ASSET_CATALOG.md	Must-read before generating visual objects, index of 83 preset components
references/circuit-schematic-guide.md	Circuit schematic (circuit diagram) drawing specification — battery polarity, current direction, meter connections
references/geometry-construction-guide.md	Geometric figure construction — coordinate calculation mode, angle arcs, triangle/quadrilateral/circle/rotation/reflection examples
references/step-6-compose-render.md	Step 6