The outline has to land on a band edge, or the figure dissolves

The one arithmetic rule the authored looks are built on, and nothing checks it for you. A band edge sits at every multiple of 1 / palette_steps, and the figure’s outline sits at color_center + color_span. Put the second exactly on the first and the silhouette reads crisp — the seam at the outline is a band boundary, so it is a hard edge. Miss it and the outline falls inside a band, which draws the figure in the same flat colour as the ring just outside it and the silhouette dissolves into the ring family around it.

It is not a subtle difference. Measured over four spans on the maple: at 5 and at 8 interior bands the leaf is simply gone.

[params]
palette_steps = "16"
color_span    = "0.1875"                            # 3/16
color_center  = "mod(0.875 + beat_index / 16, 1)"   # 14/16, stepping by 1/16

Every number is a multiple of 1/16, which is why presets/shape_maple.toml looks the way it does: 14/16 + 3/16 lands on an edge, and so does every step of the travel. A figure with two interior bands does the same at 14/16 + 2/16.

Two consequences, and they are what you act on:

• color_span must not be bound at all on a figure whose edge has to stay crisp. Any value between two multiples of 1 / palette_steps walks the outline off its edge, and there is no increment small enough to read as a change while still landing on one.
• color_center moves in whole band steps — beat_index / 16 at palette_steps = 16, not time * 0.15. A continuous drift blunts the figure in every frame between two steps. Stepping keeps the alignment exact at all times, which is why the shipped authored looks travel on beat_index rather than on time.

gamma is the safe interior binding, and the reason is the useful part. At the outline the coordinate is exactly 1, and 1^g = 1 for any g, so gamma provably cannot move the outline off its band edge — it only redistributes the bands inside the figure. That reason is also the test for a binding you think of next: it is safe exactly when it leaves the coordinate at the outline equal to 1, and scale and pan_* qualify because they move the figure in the frame rather than the coordinate on it.

The rule is the same under both coord_mode values, because the outline is at coordinate 1 under both. What changes with the mode is what the interior bands are, not where the outline sits.