feat(skills): add manim-video skill for mathematical and technical animations

Production pipeline for creating 3Blue1Brown-style animated videos
using Manim Community Edition. The agent handles the full workflow:
creative planning, Python code generation, rendering, scene stitching,
audio muxing, and iterative refinement.

Modes: concept explainers, equation derivations, algorithm
visualizations, data stories, architecture diagrams, paper explainers,
3D visualizations.

9 reference files, setup verification script, README.
All API references verified against ManimCommunity/manim source.

skills/creative/manim-video/references/mobjects.md

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+# Mobjects Reference
+
+Everything visible on screen is a Mobject. They have position, color, opacity, and can be animated.
+
+## Text
+
+```python
+title = Text("Hello World", font_size=48, color=BLUE)
+eq = MathTex(r"E = mc^2", font_size=40)
+
+# Multi-part (for selective coloring)
+eq = MathTex(r"a^2", r"+", r"b^2", r"=", r"c^2")
+eq[0].set_color(RED)
+eq[4].set_color(BLUE)
+
+# Mixed text and math
+t = Tex(r"The area is $\pi r^2$", font_size=36)
+
+# Styled markup
+t = MarkupText('<span foreground="#58C4DD">Blue</span> text', font_size=30)
+```
+
+**Always use raw strings (`r""`) for any string with backslashes.**
+
+## Shapes
+
+```python
+circle = Circle(radius=1, color=BLUE, fill_opacity=0.5)
+square = Square(side_length=2, color=RED)
+rect = Rectangle(width=4, height=2, color=GREEN)
+dot = Dot(point=ORIGIN, radius=0.08, color=YELLOW)
+line = Line(LEFT * 2, RIGHT * 2, color=WHITE)
+arrow = Arrow(LEFT, RIGHT, color=ORANGE)
+rrect = RoundedRectangle(corner_radius=0.3, width=4, height=2)
+brace = Brace(rect, DOWN, color=YELLOW)
+```
+
+## Positioning
+
+```python
+mob.move_to(ORIGIN)                        # center
+mob.move_to(UP * 2 + RIGHT)               # relative
+label.next_to(circle, DOWN, buff=0.3)     # next to another
+title.to_edge(UP, buff=0.5)               # screen edge (buff >= 0.5!)
+mob.to_corner(UL, buff=0.5)               # corner
+```
+
+## VGroup vs Group
+
+**VGroup** is for collections of shapes (VMobjects only — Circle, Square, Arrow, Line, MathTex):
+```python
+shapes = VGroup(circle, square, arrow)
+shapes.arrange(DOWN, buff=0.5)
+shapes.set_color(BLUE)
+```
+
+**Group** is for mixed collections (Text + shapes, or any Mobject types):
+```python
+# Text objects are Mobjects, not VMobjects — use Group when mixing
+labeled_shape = Group(circle, Text("Label").next_to(circle, DOWN))
+labeled_shape.move_to(ORIGIN)
+
+# FadeOut everything on screen (may contain mixed types)
+self.play(FadeOut(Group(*self.mobjects)))
+```
+
+**Rule: if your group contains any `Text()` objects, use `Group`, not `VGroup`.** VGroup will raise a TypeError on Manim CE v0.20+. MathTex and Tex are VMobjects and work with VGroup.
+
+Both support `arrange()`, `arrange_in_grid()`, `set_opacity()`, `shift()`, `scale()`, `move_to()`.
+
+## Styling
+
+```python
+mob.set_color(BLUE)
+mob.set_fill(RED, opacity=0.5)
+mob.set_stroke(WHITE, width=2)
+mob.set_opacity(0.4)
+mob.set_z_index(1)                         # layering
+```
+
+## Specialized Mobjects
+
+```python
+nl = NumberLine(x_range=[-3, 3, 1], length=8, include_numbers=True)
+table = Table([["A", "B"], ["C", "D"]], row_labels=[Text("R1"), Text("R2")])
+code = Code("example.py", tab_width=4, font_size=20, language="python")
+highlight = SurroundingRectangle(target, color=YELLOW, buff=0.2)
+bg = BackgroundRectangle(equation, fill_opacity=0.7, buff=0.2)
+```
+
+## Custom Mobjects
+
+```python
+class NetworkNode(Group):
+    def __init__(self, label_text, color=BLUE, **kwargs):
+        super().__init__(**kwargs)
+        self.circle = Circle(radius=0.4, color=color, fill_opacity=0.3)
+        self.label = Text(label_text, font_size=20).move_to(self.circle)
+        self.add(self.circle, self.label)
+```
+
+## Constants
+
+Directions: `UP, DOWN, LEFT, RIGHT, ORIGIN, UL, UR, DL, DR`
+Colors: `RED, BLUE, GREEN, YELLOW, WHITE, GRAY, ORANGE, PINK, PURPLE, TEAL, GOLD`
+Frame: `config.frame_width = 14.222, config.frame_height = 8.0`