# Insert a diagram into a manuscript in one frame and let the body text step down to make room

Manual DaVinci Resolve / Fusion construction guide generated from the recipe. It is not a tested .drp.
The accompanying Remotion project (recipe.json) is the executable definition; the numbers below are copied from it.
Neither construction establishes source fidelity: this is an original vector approximation of an inspected editing moment.

## Source and clock
Reference: OpenAI's "Introducing Prism, a free workspace for scientists to write and collaborate on research" (xnInEsaaj9c), published 2026-01-27.
Source interval [3330, 3450) on the 60/1 fps master: 120 frames, 2.000000 s. Local frame 0 = source frame 3330.
Create a 1920x1080 progressive timeline at 60/1 fps and a Fusion composition exactly 120 frames long. Keep integer frames; do not round the frame rate.
Background field: #7fb4e6. Export silent H.264 yuv420p to match the intended playback container.

## Observation
A magnified view of a typeset paper page fills most of the frame, with a dark assistant panel visible at the left edge. Equations occupy the upper third and a numbered list of results begins below them. Nothing moves for about 44 frames. On f44-46 a commutative diagram (labelled nodes joined by arrows) appears between the last equation and the list, and the list steps down by the diagram's height in the same instant. The page then holds still.

## Mechanism
An insert as a hard state change: new content appears in place with no animation, and everything below reflows downward by exactly its height on the same frame.

## Phases (local frames)
- 0: Page holds: equations above, results list below
- 44: Diagram appears; list steps down 260px
- 47: Hold on the new layout

## Layer inventory (absolute 1920x1080 top-left pixels, back to front)
- panel [rect] at (0, 0) size 230x1080 fill #111111
- panel-text [text] at (10, 420) text "it an emergent conformal / ts three continuous / conformal group SL(2,R) / air of this symmetry group." 13px weight 400 #cfcfcf
- panel-icons [text] at (150, 640) text "↺  ⊡  ⌄" 16px weight 400 #bbbbbb
- page [group] at (230, 0) size 1560x1080 fill #ffffff
  - eq1 [text] at (530, 40) text "ds² = −(Δ/Σ)[dt − a(1 − x²)dφ]² + (1 − x²)/Σ [(r² + a²)dφ − a dt]² + (Σ/Δ)dr² + Σ/(1 − x²) dx²," 22px weight 400 #222
  - eq1l [text] at (1670, 40) text "(1a)" 20px weight 400 #222
  - eq2 [text] at (790, 80) text "Δ(r) = r² − 2Mr + a²,      Σ(r, x) = r² + a²x²," 22px weight 400 #222
  - eq2l [text] at (1670, 80) text "(1b)" 20px weight 400 #222
  - para [text] at (530, 130) size 1160x0 text "where a = J/M is the specific angular momentum of the black hole. Massless spin-s perturbations of the Kerr black hole are described by two scalar fields that obey the same decoupled equation. For vacuum perturbations this is the master equation with the operator" 17px weight 400 #333
  - eq3 [text] at (590, 230) text "T = [ (r² + a²)² / Δ  −  a²(1 − x²) ] ∂t²  +  (4Mar/Δ) ∂t∂φ  +  [ a²/Δ − 1/(1 − x²) ] ∂φ² /      − 2s [ M(r² − a²)/Δ − (r + iax) ] ∂t  −  2s [ a(r − M)/Δ + ix/(1 − x²) ] ∂φ /      − Δ^(−s) ∂r (Δ^(s+1) ∂r)  −  ∂x ((1 − x²) ∂x)  +  s²x²/(1 − x²)  −  s  ." 22px weight 400 #222
  - eq3l [text] at (1670, 300) text "(2)" 20px weight 400 #222
  - para2 [text] at (530, 372) text "When s = 0, this equation reduces to the simple wave equation for a massless scalar field ψ ≡ Ψ⁽⁰⁾," 17px weight 400 #333
  - eq4 [text] at (1030, 404) text "∇²ψ(t, r, x, φ) = 0." 22px weight 400 #222
  - eq4l [text] at (1670, 404) text "(3)" 20px weight 400 #222
  - figure [group] at (790, 450) size 640x250 visible [44, 120)
    - f-E [text] at (830, 450) text "E" 22px weight 400 #111
    - f-AB [text] at (1040, 520) text "A × B" 22px weight 400 #111
    - f-B [text] at (1350, 520) text "B" 22px weight 400 #111
    - f-A [text] at (1040, 660) text "A" 22px weight 400 #111
    - f-C [text] at (1350, 660) text "C" 22px weight 400 #111
    - f-l1 [line] at (790, 450) stroke #111 1.5px
    - f-l2 [line] at (790, 450) stroke #111 1.5px
    - f-l3 [line] at (790, 450) stroke #111 1.5px
    - f-l4 [line] at (790, 450) stroke #111 1.5px
    - f-l5 [line] at (790, 450) stroke #111 1.5px
    - f-l6 [line] at (790, 450) stroke #111 1.5px
    - f-l7 [line] at (790, 450) stroke #111 1.5px
    - f-lab [text] at (1190, 506) text "π₂" 15px weight 400 #111
    - f-lab2 [text] at (1022, 590) text "π₁" 15px weight 400 #111
    - f-lab3 [text] at (1372, 590) text "g" 15px weight 400 #111
    - f-lab4 [text] at (1200, 676) text "f" 15px weight 400 #111
  - body [text] at (530, 460) text "This paper presents four new results: / 1. Sec. II shows that perturbations of a Kerr black hole exhibit an emergent conformal symmetry in the stationary /    and axisymmetric limit. More precisely, in that regime, the space of solutions to Eq. (2) admits three continuous /    symmetries that map solutions to solutions, and that together generate the global conformal group SL(2, R). / 2. Sec. III shows that each of the three SL(2, R) generators is associated with an infinite family of exact solutions /    that diagonalize it. These solutions are not separable in the usual coordinates, but each symmetry generator is /    associated with a different coordinate system in which the solutions that diagonalize it become R-separable." 17px weight 400 #333
      keyframes y: f43=460, f44=720
- pointer [cursor] at (236, 130)

## Construction steps
1. Timeline 1920x1080 at 60 fps; Fusion composition 120 frames. Local 0 = master frame 3330.
2. Page: white 1560x1080 plate from x=230 with a black 230px assistant strip at the left carrying a few 13px mono lines; equations are 22px mono, prose 17px with 24px leading.
3. Figure group (five labelled nodes, seven 1.5px arrows, four small labels) at (790,450) in canvas space, 640x250; make it visible from frame 44 with no fade.
4. Body list: Text+ block at y=460; keyframe its Y with a hold key, 460 on frame 43 and 720 on frame 44, so it steps down by the figure height in one frame.
5. Easy mistake: easing the step or fading the figure. The source is a hard reflow: both changes land on the same frame with no in-between.
6. Keep the pointer static at the panel edge; nothing else on the page moves.

## Content variants
Default copy:
- eqLabel1: (1a)
- eqLabel2: (1b)
- eqLabel3: (2)
- eqLabel4: (3)
- body: This paper presents four new results: / 1. Sec. II shows that perturbations of a Kerr black hole exhibit an emergent conformal symmetry in the stationary /    and axisymmetric limit. More precisely, in that regime, the space of solutions to Eq. (2) admits three continuous /    symmetries that map solutions to solutions, and that together generate the global conformal group SL(2, R). / 2. Sec. III shows that each of the three SL(2, R) generators is associated with an infinite family of exact solutions /    that diagonalize it. These solutions are not separable in the usual coordinates, but each symmetry generator is /    associated with a different coordinate system in which the solutions that diagonalize it become R-separable.
- panelLines: it an emergent conformal / ts three continuous / conformal group SL(2,R) / air of this symmetry group.
- nodeA: A
- nodeB: B
- nodeC: C
- nodeE: E
- nodeAB: A × B
Adaptation changes:
- body: This paper establishes three results: / 1. Sec. II proves that the reduced equations inherit a hidden scaling symmetry in the slowly rotating regime. /    In that limit, the space of solutions admits a one-parameter family of dilatations that preserve the boundary /    conditions and therefore act on the physical spectrum. / 2. Sec. III constructs the eigenfunctions of the dilatation generator and shows they are complete on the /    exterior region. The construction relies on a coordinate system in which the generator becomes a pure /    translation, so separability is restored.
- nodeA: X
- nodeB: Y
- nodeC: Z
- nodeE: P
- nodeAB: X × Y

## Limits
Easing names map to Fusion spline shapes: linear = linear, in/out/inOut = ease curves on the same frames, hold = step, spring/overshoot = slight overshoot past the target before settling.
Text reveal frames give the first and last unit; distribute characters/words evenly between them. Cursor click rings last 14 frames.
Vector illustration is an approximation of layout and motion, not the product UI or recovered production assets.
