Spring animation API for Unity UI

Spring<T>(Func<T> target, Value<double>? period = null, Value<double>? dampingRatio = null, SpringSpace<T> space = null) creates a spring in a stable scope. Defaults are period 1 second and damping ratio 1.

Core spaces support float, double and double[]. Unity spaces support Vector2, Vector3, Vector4, Color, Rect, Quaternion and Pose. Supply SpringSpace<T>(pack,unpack) for another type. Its public Pack and Unpack delegates translate to numeric lanes; lane count must stay constant and values must be finite.

Member	Behavior
spring.Value getter	Read current output reactively; a disposed spring throws.
spring.Value setter	Jump immediately and clear velocity, retaining the existing target.
spring.Control(position,velocity,impulse)	Change internal motion; omitted controls remain unchanged. Output publishes on a later clock update. Impulse adds to velocity.
spring.Dispose()	Release target observation and clock updates. Idempotent.
Step(deltaTime)	Advance the shared clock and enter manual mode.

Targets, period and damping are tracked. Period must be finite and positive; damping finite and non-negative. Use a Source<double> or explicit Value<double> getter for reactive parameters. Control inputs are read when the method is called.

The Unity host advances unscaled frame time. Springs use an analytic damped solver at fixed 1/120 second substeps and unregister from the clock when settled. Independent clock tasks continue after failures, followed by an aggregate error.

Color clamps RGBA; Rect packs min/max; quaternion/pose rotations normalize and canonicalize input quaternion sign. Rotation uses component-based motion. SpringSpaces.Float, .Double, .Array and UnitySpringSpaces expose built-in mappings.

Step durations must be finite and non-negative. The first explicit step switches the runtime session to manual time, so continue stepping springs, delayed branch exits and polled properties.