t27f: beat_clock.t27 -- the three beats cut on the voice (R4a of #10560) #10596

Sub-issue of epic #10560 (content factory), R4a: the first part of R4. R7 (#10584) gave every lesson reel three beats: open, main and close. Nothing yet says when each beat is on screen. A cut at fixed thirds of the 15 s reel would land in the middle of a spoken phrase. Editing tools cut on speech: Descript cuts a scene per sentence, CapCut's auto-cut uses pauses, and Remotion's TransitionSeries needs explicit frame counts per sequence.

Boundary

• In: a new module specs/t27f/beat_clock.t27, its seal and its ledger row.
• It decides, for any millisecond or frame of a lesson reel, which beat is on screen and the crossfade weight of each beat. It uses lesson_reel.t27's own voice timing (phrase_start, cta_from) and reel.t27's transition and minimum-scene constants.
• Out: drawing the beats (R3, t27f factory R3: a renderer per scene archetype and the still anomaly gate (SSIM) #10571), and wiring the clock into lesson_reel's ffmpeg graph (R4b). No change to existing specs.

User Scenarios

• A viewer sees the picture change when the goal starts being spoken and when the address appears, not mid-word.
• A lesson with a very short title still shows its open beat long enough to read.
• The frame renderer asks the clock for frame f and gets the beat and the blend, so a reel needs no hand-made edit list.

Requirements

• R1. Cut 0 (open to main) is at the goal phrase's start. It moves later only when the open beat would otherwise be on screen alone for less than the minimum scene length.
• R2. Cut 1 (main to close) is where the address takes over, cta_from.
• R3. Each cut is a crossfade of TRANSITION_FRAMES at BASE_FPS, centred on the cut. At every millisecond the three beats' weights sum to 1000 permille.
• R4. Each beat is on screen alone for at least MIN_SCENE_FRAMES. This holds for every lesson in both languages, across a grid of phrase lengths that the voice rule accepts.
• R5. A negative control shows that a fixed-thirds cut lands inside a spoken phrase for the measured lesson-1 lengths.

Success Criteria

• t27c test-report specs/t27f/beat_clock.t27 passes on the Railway lab with 0 vacuous tests.
• Seal saved and verified; one ledger row; max_not_pass unchanged.
• The PR is based on master and does not depend on the open loop PRs.

Requirements

• FR-001: The clock MUST place Cut 0 (open to main) at the goal phrase's start, and MUST move it later only when the open beat would otherwise be on screen alone for less than the minimum scene length.
• FR-002: The clock MUST place Cut 1 (main to close) at cta_from where the address takes over.
• FR-003: Each cut MUST be a crossfade of TRANSITION_FRAMES at BASE_FPS, centred on the cut, and at every millisecond the three beats' weights MUST sum to 1000 permille.
• FR-004: Each beat MUST be on screen alone for at least MIN_SCENE_FRAMES, and this MUST hold for every lesson in both languages across a grid of phrase lengths that the voice rule accepts.
• FR-005: A negative control MUST demonstrate that a fixed-thirds cut lands inside a spoken phrase for the measured lesson-1 lengths.