feat: manim scenes render

[TanKhoiTV]

Linked issue

Closes #28

What this PR does

Adds the source code for Manim video generation, as well as the complete demo video with narration.

Checklist

Code

• All acceptance criteria on the linked issue are checked off
• No numpy.linalg, scipy.linalg, or sympy solver calls in implementation code
• All file paths use pathlib.Path, no hardcoded OS separators
• No commented-out code committed
• No debugging print() statements left in

Tests

• At least 5 test cases per new function
• Edge cases covered (singular matrix, zero input, identity, etc.)
• All tests pass without errors

Notebooks (if applicable)

• All cells run top-to-bottom without errors
• Output cells are visible — outputs not cleared before committing

Report (SM only — sprint-end export PRs)

• report.tex exported from Prism and committed to report/
• report.pdf compiled and committed to report/
• No placeholder text remaining in exported sections

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ℹ️ Review info

⚙️ Run configuration

Configuration used: Organization UI

Review profile: CHILL

Plan: Pro

Run ID: 3e2c9e40-bff6-46c9-b753-a23473395c7f

📥 Commits

Reviewing files that changed from the base of the PR and between 13a34b1 and 373e859.

⛔ Files ignored due to path filters (9)

• part2/manim/demo_video.mp4 is excluded by !**/*.mp4
• part2/manim/img/Surprised_Pikachu.jpg is excluded by !**/*.jpg
• part2/manim/img/base.png is excluded by !**/*.png
• part2/manim/img/gthj_bonk.jpg is excluded by !**/*.jpg
• part2/manim/img/k-1.png is excluded by !**/*.png
• part2/manim/img/k-10.png is excluded by !**/*.png
• part2/manim/img/k-50.png is excluded by !**/*.png
• part2/manim/svg/noun-gear-21438.svg is excluded by !**/*.svg
• part2/manim/svg/noun-key-8371021.svg is excluded by !**/*.svg

📒 Files selected for processing (21)

• .flake8
• .github/workflows/ci.yml
• main.py
• part2/manim-prod-assets/assets_attribution_list.md
• part2/manim-prod-assets/narration_script.md
• part2/manim-prod-assets/svd-animation-refs.md
• part2/manim-prod-assets/svd-animation-rules.md
• part2/manim/inputs.txt
• part2/manim/main.py
• part2/manim/manim.cfg
• part2/manim/manim_scene.py
• part2/manim/manim_v2.py
• part2/manim/scene_app.py
• part2/manim/scene_compare.py
• part2/manim/scene_intro.py
• part2/manim/scene_svd.py
• part2/manim/svg/noun-gear-21438.svg:Zone.Identifier
• part2/manim/svg/noun-key-8371021.svg:Zone.Identifier
• part2/manim/theme.py
• part2/narration_script.md
• part2/theme.py

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