Affine Studio Cinema And NLE Specification

Affine Studio Cinema & Non-Linear Editing (NLE) Specification (AFFINE-SPEC-STUDIO-026)

Status: LIVE & SEALED · Surface: /language-game/studio.html & AffineIDE.app (apps/AffineIDE/Sources/AffineIDE/AffineStudioTimelineEngine.swift) · Prover: AffineIDE --prove-studio

Standard non-linear editing suites (Adobe Premiere, DaVinci Resolve, Final Cut) fail two mathematical invariants in feature-length cinema:

1. Drop-Frame Floating-Point Audio/Video Desync: Irrational or non-terminating decimal rates ($29.97 / 23.976\text{ fps}$) drift across a 2-hour timeline ($172,800\text{ frames}$), separating spoken phoneme visemes from their acoustic sample buffers.
2. Non-Reproducible GPU Color & Compositing: IEEE-754 trilinear 3D LUT hardware interpolators produce divergent pixel digests between Apple Metal, NVIDIA CUDA, and CPU software renderers.

Affine Studio (AFFINE-SPEC-STUDIO-026) closes the loop between the Director's Console (H_start -> H_end), the Iliad Book 1 Zero-Float OpenUSD Stage (Study 51), the 64-Vertex Franklin Avatar & Kelly-Lochbaum 24-Bit WAV Voice Engine, and the 6-Deliverable Multi-Format Download Center in pure Swift 6.4 with zero floating-point types.

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1. Master 705,600,000 Hz Flicks Clock & OTIO / FCPXML Interchange (StudioFlickTime)

Every timeline event in Affine Studio is anchored to a single Int64 flick counter at $705,600,000\text{ ticks/second}$—the exact least common multiple (LCM) of all standard cinema frame rates ($24, 25, 30, 48, 50, 60, 90, 100, 120\text{ fps}$) and digital audio sample rates ($8000, 16000, 22050, 24000, 32000, 44100, 48000, 88200, 96000, 192000\text{ Hz}$):

Rate / Event	Exact Integer Flicks	Remainder
$1\text{ frame @ }24\text{ fps}$	$29,400,000\text{ flicks}$	$0$
$1\text{ frame @ }30\text{ fps}$	$23,520,000\text{ flicks}$	$0$
$1\text{ frame @ }60\text{ fps}$	$11,760,000\text{ flicks}$	$0$
$1\text{ audio sample @ }44.1\text{ kHz}$	$16,000\text{ flicks}$	$0$
$1\text{ audio sample @ }48\text{ kHz}$	$14,700\text{ flicks}$	$0$
2-Hour Feature Film ($172,800\text{ frames @ }24\text{ fps}$)	$5,080,320,000,000\text{ flicks}$	$0$ (345,600,000 samples @ $48\text{ kHz}$)

• OpenTimelineIO (.otio) & Final Cut XML (.fcpxml v1.10): AffineFeatureProject.exportOpenTimelineIOJSON() and exportFCPXML() emit strictly integer RationalTime.1 ({"rate": 24, "value": N}) and rational frame strings ("864/24s"). Any wire containing a floating-point rate (29.97) is refused at the ingress membrane (HTTP_400_REFUSED_FLOAT_TIMECODE).

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2. Automated 120-Page Master Script $\leftrightarrow$ OpenUSD Beat Compiler (AffineScriptCompiler)

AffineScriptCompiler ingests the canonical Fountain (.fountain) screenplay ("ILIAD & FRANKLIN: THE INVARIANT SHORE") and compiles each scene heading, character cue, and stage bracket into a deterministic NarrativeManifoldBeat:

• Manifold Trajectory: H_start -> H_end (e.g., 144 -> 233 -> 377 -> 610 -> 987), rational Gravity (981/100), and rational Intent (19/20, 21/20, 24/25, 1/1).
• Exact Rational Camera Rig (ExactRationalRotation3D): Cayley transform $R = (I - S)(I + S)^{-1} \in \text{SO}(3, \mathbb{Q})$ verified against the LAW-FRAMING [100, 900]³ bounding cage (delta = 0 on all beats; synthetic control arm y = 950 triggers CURE delta = 50).
• Synchronized K-G7 Viseme & Voice Schedule: Each dialogue line binds directly to one of the 12 canonical K-G7 phoneme keys (S:OO>REST, S:AH>TH, S:AW>NASAL, S:EE>DNTLS), fundamental pitch $F_0 \in [60, 400]\text{ Hz}$, breath permille, and hnr permille.

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3. 16-Bit Rational Alpha Compositor & Tetrahedral 3D LUT Court (AffineGOPCompositor)

To eliminate GPU float variance during color grading and multi-layer compositing:

• 16-Bit Per-Channel Rational Alpha Over (RGBA64Pixel): $$C_{\text{out}} = \left\lfloor \frac{\alpha \cdot C_{\text{fg}} + (65535 - \alpha) \cdot C_{\text{bg}}}{65535} \right\rfloor$$
• Tetrahedral Integer 3D LUT Interpolation: Partitions each $9 \times 9 \times 9$ color lattice cell into 6 canonical tetrahedra ($T_1 \dots T_6$) by ordinal comparison of $(d_r, d_g, d_b) \in [0, 65535]^3$, evaluating three cinema print looks identically across all 9 cells:
  1. Kodak 2383 Print · Warm Gold
  2. IMAX 15/70 · Silver Bleach Bypass
  3. Iliad Shore · Achaean Night Cyan-Amber

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4. 3D OpenUSD Quadrance Room Acoustics & Multi-Bus Stem Mixer (AffineSpatialAcousticsCourt)

Every character dialogue stem is spatialized directly from the 3D integer millimeter coordinates of the OpenUSD stage:

• 3D Rational Quadrance ($Q = \Delta x^2 + \Delta y^2 + \Delta z^2$): Computes direct path quadrance and first-order image-source wall reflection quadrance without sqrt() or Float32 buffers.
• Binaural Interaural Time Difference (ITD): Computes exact integer sample delay ($\pm 32\text{ samples @ }48\text{ kHz}$) between left and right ear channels.
• ITU-R BS.1770 Integer Ceiling Limiter: Clamps the master 24-bit signed integer bus strictly within $\pm 8,388,607$ (AudioFormat = 1 uncompressed PCM WAV).

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5. Multi-Format Download Center & 4-Gate C2PA Merkle Release Seal (StudioReleaseSeal)

Both /language-game/studio.html and AffineIDE.app package and verify all 6 deliverables:

1. 📷 Still PNG Ordinal (512×512) with Merkle frame digest
2. 🎬 HEVC / HLS Stream (.m3u8) carrying #EXT-X-AFFINE-CLOCK:705600000 and #EXT-X-AFFINE-SHA256 per reel
3. 🎵 24-Bit 48 kHz Integer PCM WAV (AudioFormat = 1)
4. 📦 .affine Archival Bundle (.otio, .fcpxml, and SHA256SUMS)
5. 📜 C2PA Content Credentials Manifest (c2pa_manifest.json) with the 9-cell Merkle Mountain Range (MMR) root
6. 📖 120-Page Master Script (master_script_120p.fountain)

One-Command Verification

apps/AffineIDE/.build/out/Products/Release/AffineIDE --prove-studio