t27f R4b.1: beat graph -- the reel's three scenes crossfaded at the beat clock's cuts, on whole frames #10603

Sub-issue of epic #10560 (content factory), R4b part 1. It builds on R4a (#10596, PR #10598).

R4a's beat clock says when each of a reel's three beats (open, main, close) is on screen. Nothing yet turns those cuts into video.

How the reference tools do it:

• Remotion's TransitionSeries takes per-sequence frame counts and overlapping transitions.
• ffmpeg's xfade takes an offset in seconds and starts reading the incoming stream at that offset.

Cuts given in milliseconds also do not sit on frames. A crossfade that starts between two frames shifts by up to one frame, and two cuts rounded independently could take a frame from a scene that has exactly MIN_SCENE_FRAMES.

Boundary

• In: specs/t27f/lesson_reel.t27 and its seal.
  • Each cut gets a crossfade start frame.
  • main gains LR_MODE=4, which prints the beat graph: three scene videos (inputs 0, 1, 2: open, main, close) crossfaded at the clock's cuts and trimmed to the reel's 15 s.
• Out:
  • Drawing the scenes (R3, t27f factory R3: a renderer per scene archetype and the still anomaly gate (SSIM) #10571 / PR t27f: scene renderers for the 12 archetypes and the still anomaly gate (R3) #10592).
  • Laying mode 3's captions and address over the beat video (R4c).
  • Rendering every lesson.

User Scenarios

• A frame renderer that has the three scene clips runs one ffmpeg command with the mode 4 graph. It gets a 450-frame reel whose picture changes when the goal starts being spoken and when the address appears.
• A reviewer reads the crossfade start frames for any lesson and voice, without rendering.

Requirements

• R1. The crossfade for cut c starts at frame floor((c - 250) * BASE_FPS / 1000) and lasts TRANSITION_FRAMES.
• R2. On every voice of R4a's grid where the clock gives every beat a scene, every beat is alone for at least MIN_SCENE_FRAMES whole frames once both cuts are on frames.
• R3. The xfade offset printed for a start frame f is beat_frame_ms(f). It selects frame f and no earlier one: beat_frame_ms(f) * BASE_FPS lies in ((f - 1) * 1000, f * 1000].
• R4. Mode 4 refuses a voice that does not fit, exactly as mode 3 does.
• R5. Measured on the Railway lab with ffmpeg: the graph run on three solid-colour 15 s inputs gives 450 frames. The frame just before each crossfade is still the outgoing colour, and the frame just after it is the incoming colour.

Success Criteria

• t27c test-report specs/t27f/lesson_reel.t27 passes on the lab with 0 vacuous tests.
• Seal saved and verified; the ledger row is unchanged; max_not_pass is unchanged.
• The PR records the ffmpeg measurement: frame count, and the pixel colour at the frames around each cut.

Requirements

• FR-001: The crossfade for cut c MUST start at frame floor((c - 250) * BASE_FPS / 1000) and MUST last TRANSITION_FRAMES.
• FR-002: On every voice of R4a's grid where the clock gives every beat a scene, every beat MUST be alone for at least MIN_SCENE_FRAMES whole frames once both cuts are on frames.
• FR-003: The xfade offset printed for a start frame f MUST be beat_frame_ms(f). It MUST select frame f and no earlier one: beat_frame_ms(f) * BASE_FPS MUST lie in ((f - 1) * 1000, f * 1000].
• FR-004: Mode 4 MUST refuse a voice that does not fit, exactly as mode 3 does.
• FR-005: Measured on the Railway lab with ffmpeg, the graph run on three solid-colour 15 s inputs MUST give 450 frames. The frame just before each crossfade MUST still be the outgoing colour, and the frame just after it MUST be the incoming colour.