Semantic state is the source of truth; transforms are its presentation. Keep one writer for each position, orientation, velocity, phase, and event channel.

Name the observable motion, SI units, coordinate frame, stable actor identity, initial state, phase/event state, and duration contract: finite with a terminal pose plus velocity/hand-off rule, periodic with a wrap rule, or open-ended with a stop/reset policy. Assign one writer to every animated channel; clips, procedural roots, instance storage, camera rigs, and external solvers may own different channels only through an explicit layering order.

When another simulation supplies or reacts to motion, declare:

Keep frame-critical state on its owning device; schedule diagnostic readback asynchronously outside state advance and presentation.

Complete when: every animated channel has exactly one writer, one frame and unit convention, one stable identity, and a defined initial state plus finite, periodic, or open-ended duration contract; every cross-system boundary closes every applicable declaration above.

Choose by state dependence first, then actor count:

Object3D

dt

Use for repeated identical topology. Use for varied topology with compatible material state. Use storage and compute only when the measured CPU traversal/upload crossover is passed.

The canonical path initializes from with and verifies .

Complete when: each motion branch has one time model and one representation, and each GPU route states the measured workload threshold that justifies it.

Sample analytic motion directly from authoritative elapsed seconds. Advance recurrent state by a fixed step, retain immutable previous/current states, and move every complete unprocessed step into separate debt state so before presenting with . Define raw-delta clamping, maximum substeps, debt handling, pause/resume, and replay behavior once for the whole motion owner. A debt drop or scheduled catch-up and a discontinuity reset are separate decisions. Coupled state advances on its simulation owner's cadence, not the render callback's cadence.

For perceptual follow, declare the target as a continuous function integrated over the interval, a timestamped zero-order hold, or timestamped interpolated samples. Apply changes at their timestamps; presentation cadence never changes the underlying target signal.

Use stored seeds, counters, and one-shot event flags. A direct seek reconstructs the same phase and event state as replay to that time. either updates at the fixed step or uses for seeking; it does not sample an independent clock.

Complete when: analytic and recurrent clocks cannot diverge after a stall, the interpolation pair brackets presentation time with a bounded accumulator, debt and reset decisions are independently observable, and identical initial state plus every applicable seed, fixed step, event schedule, and target signal reproduce the same matched-time state at every tested presentation cadence.

Name source and destination frames for every position, direction, velocity, and quaternion. Normalize axes, handle parallel and antiparallel vector alignment, canonicalize quaternion signs before interpolation, state multiplication order, and normalize accumulated rotations.

Preserve world pose during reparenting with . Decompose to TRS only when the residual passes; retain an affine matrix or wrapper when non-uniform ancestry creates shear. Released children inherit moving-frame velocity, including for a rotating parent. Docking error is decomposed in the current docking frame, not a stale world frame.

Complete when: every transform has a declared frame chain and quaternion order, reparenting preserves the world matrix within tolerance, zero/antiparallel inputs stay finite, and moving-frame release includes all transport terms.

Publish immutable previous/current pose generations with stable actor identity; derive render pose, motion vectors, bounds, shadows, and temporal consumers from that same pair. A cut, teleport, spawn/despawn, reparent, topology or deformation change, LOD/quality change, storage-slot reuse, or identity change starts a new validity epoch and resets the affected history instead of deriving an extreme velocity.

Reset phase timestamps, accumulator and debt records, seed counters, event flags, finite terminal locks, and previous/current buffers together only for a semantic motion reset. A camera cut or other temporal-only reset clears the affected presentation history without restarting semantic motion. Disposal releases storage, compute resources, readback staging, listeners, timers, and the renderer loop owned by the system.

Complete when: every discontinuity selects preserve, migrate, or reset for each history consumer; temporal-only resets preserve semantic state; semantic resets restore the declared initial state atomically; no old identity can observe a reused slot; disposal leaves no live owner, listener, buffer, or animation loop.

For each selected branch, run only its applicable checks. Analytic motion compares direct seek with replay at 30, 60, 120, and 240 Hz presentation. Recurrent motion holds one fixed-step schedule across those presentation rates and passes step-halving. Perceptual follow consumes one timestamped or analytically integrated target signal and compares shared wall-time checkpoints. Finite motion reaches its exact terminal pose and declared velocity or hand-off; only a terminal lock requires zero residual velocity. Periodic and open-ended motion verify their declared wrap or stop/reset transition.

Where selected, also check quaternion norm and sign continuity, world-matrix equality across reparenting, stable instance identity, and reset behavior for every discontinuity. GPU motion records dispatches, hot bytes, p50/p95 time, and zero frame-critical readbacks. Node post proves one presentation/output owner.

Complete when: every selected branch passes its cadence, ownership, frame, reset, lifecycle, and visible-failure checks, with thresholds and target hardware recorded where performance claims are made.

Use for camera motion and handoffs, when pooled effects are the deliverable, and the relevant water or terrain skill for environment state. Use when the request spans motion plus rendering, geometry, materials, shadows, post, or another simulation.