A picture that changes

The four primitives are canvas props (docs/canvas.md, "Explanation primitives"). find "how an input changes an output" and find --id mechanism:estimate print each one's uses outside maths, with an example beat. Start from the explanation treatment (new DIR --treatment explanation). examples/settling is a worked example: three beats, both shapes.

The grammar

• Intuition before symbols. Show the picture change, then name it. A formula, if you show one at all, comes after the viewer has seen what it describes.
• One idea changes at a time. Everything else holds still. If two things move, the viewer has to choose which one to watch.
• A colour means one thing for the whole film. In settling, the accent is "the wobble": the band in the first beat and the curve in the second.
• Keep the same object in the same place. Two beats that show one plot should use one box, so the second reads as the first, changed. An estimate with gather and one without get different default boxes.
• Hold after a change. Give the viewer time to see what it did. Use hold, or tail for a breath after the line. The beat's lines ask for this; it is not dead air.
• Cue each move to the word that names it. Use say on draw, sweep, show, gather, fill, stack, flow and marks, and after for "just after that word". Land something meaningful in the first 1–3 s: cue the first move to the opening word, not to a word halfway through the line.

Precise graph, or a metaphor?

• Use a graph when the shape is the point and you can state the formula, such as 1/√n, a saturating response or an M/M/1 queue. Say what the formula assumes in the narration. The picture shows a shape, not data, and carries no tick numbers.
• Use an estimate for chance and spread. It is always a simulation, labelled Simulated. More samples shrink random error, assuming independent, fairly drawn samples; they do not remove bias. Show bias when the scope matters (a poll's sampling error, but not who was asked; reviews, but not who writes them).
• A field is a qualitative picture. Its kinds are textbook shapes, not models fitted to a crowd, a market or traffic. Say so if the subject sounds measurable.
• Never present invented numbers as evidence. Real figures go in chart blocks, with a source. A primitive explains how something behaves; it does not report how much.

Motion

• Rate functions adapted from Manim (MIT; packages/engine/src/scene/native/THIRD_PARTY.md) are available on any key: thereAndBack to point or nudge and return, wiggle to draw the eye, runningStart for anticipation, overshoot to settle, smooth, and lingering. Use them where the character fits, not everywhere.
• Boards. place makes any primitive a panel of a board, so the camera can hold close on each and then pull back to the whole (docs/canvas.md, "Worlds").

Voice

The explanation treatment sets Charon with the style "warm, curious, measured". This is a provisional choice made from the voice's published description, not from listening. Iapetus and Schedar are the alternatives to audition. Direct the voice by generic traits, never by naming or imitating a real presenter.

Review

Draft, then read a motion sheet at phone size: qa DIR, or clearframe_look with phone in the studio. Check that each move lands on its word, labels stay clear of dots and curves, and nothing important is too small at 360 px. critique scores explanation films low on held frames and a locked plot. Weigh each warning against the grammar above, and record deliberate holds; don't add motion to raise the score.