WAI Extension: Volumetric / 4D Splats

Mirrored from the canonical text at commit 117bad22 (2026-10-01).

Status: Draft. Phase 5 of the cargo roadmap (the frontier). A scene that is volumetric and moves: ship a Gaussian cloud as per-Gaussian keyframed tracks, the sink interpolates the cloud at any frame and renders it with the EWA pipeline. Conformance is frame-state-equivalence. Reference impl: the splat4d feature of wai-rs; corpus: volumetric-conformance/; live sink: wai.transaction.science/volumetric. Keywords MUST, MUST NOT, SHOULD, MAY are RFC 2119/8174.

1. Scope and model

A wai.splat.4d object is a temporal Gaussian splat: the static splat (wai.splat.spz) is a single anisotropic-Gaussian cloud; this extension gives each Gaussian a keyframed track — position, scale, rotation, color, opacity over time — and the sink reconstructs the cloud at any frame by interpolating the tracks in the wai.det.fixed64 floor. It is lever 3 (instructions-at-the-sink) for volumetric capture: the wire carries the trajectories, the sink reconstructs the frame.

In scope: the container, the per-Gaussian keyframe model, the deterministic reconstruct contract, the frame-state-equivalence conformance criterion, and the receipt profile.

Out of scope: a transport; the render (EWA splatting, depth sort, alpha blend — the sink’s, exactly as the static splat’s rasterization is); a codec for the cloud bytes (a real capture is authored by an upstream 3DGS/4DGS pipeline; this extension carries and verifies its trajectories, it does not fit Gaussians to video).

Relationship to the core spec: mirrors haptics / spatial audio. The reconstruct runs in the wai.det.fixed64 floor; media takes the informational value "volumetric"; wai.splat.4d is authoritative.

2. Container (W4DS)

"W4DS" | u16 n_sections | section table (u8 kind, u32 off, u32 len) | sections

2.1 Contract

{ "frame_rate": 30, "n_frames": 13, "n_gaussians": 2,
  "numeric": "wai.det.fixed64" }

2.2 Gaussian tracks

n_gaussians u32, then per Gaussian: n_keys u16, then n × ( frame u64 | pos[3] | scale[3] | rot[4] | color[3] | opacity ), the 14 attributes as i64 Fx in that field order. Each track MUST be ascending by frame. color and opacity are in [0, 1]; rot is a quaternion (x, y, z, w).

3. Reconstruct contract

For each Gaussian, at frame f: each of the 14 attributes is the Fx linear interpolation of the track’s keyframes at f; before the first / after the last key the endpoint holds. The canonical reconstruction of a frame is n_gaussians u32 | per-Gaussian 14×i64 in the field order above. The floor stays trig-free — rotations interpolate component-wise (nlerp without renormalization, deterministic); the sink normalizes the quaternion for rendering, which is presentation.

4. Conformance — frame-state-equivalence

Given the same wai.splat.4d, a conforming sink MUST reconstruct the identical Gaussian set at every frame, hence the identical BLAKE3 — on every machine, no tolerance parameter.

frame_hash = BLAKE3("wai:splat4d-frame\x01" || frame_le || canonical frame bytes)
clip_hash  = BLAKE3("wai:splat4d-clip\x01"  || contract_bytes || tracks)

frame_hash is the temporal counterpart of the static splat’s content hash; clip_hash is the frame-independent identity.

5. Fidelity and size (honest)

A splat approximates a captured scene, so wai.splat.4d is tiered Lossy like wai.splat.spz — even though the per-frame reconstruction from the tracks is frame-state-exact. Volumetric is heavy: a real cloud is megabytes per frame. The win here is the same as the static splat — content-addressing, dedup, one signed envelope, and a verifiable per-frame state — not payload reduction. We state that plainly rather than imply a compression claim the format does not make.

6. Receipt (JWP profile)

clip_hash is the identity; the group’s objects are per-frame reconstruction blocks (frame_hash per frame), Merkle-bound; one Ed25519 signature over clip_hash + root + work (= n_frames × n_gaussians) + carried joules_micro; parent_receipt_hash chains — the worlds / audio / haptics receipt shape reused. The figure’s acquisition class rides beside it as an optional signed label (energy-measurement §2.8): absent, the receipt keeps its legacy bytes and the figure is unlabelled; present, it is inside the signature. The reference meter labels every figure it measures OnChipCounter, with its declared uncertainty.

Appendix

Frame-state-equivalence is sample-equivalence with the haptic sample replaced by a whole Gaussian cloud, and the static splat extended to time. The same fixed-point floor that makes a world replay, a mix sum, an actuator buzz, a feed converge, and a body pose now makes a volumetric frame reconstruct — one floor, six cargo classes, one verification. The representation is heavy and approximate; the reconstruction of it is exact and auditable, and that is the honest thing the standard adds.