Connections are semantic objects, not decoration. Warm gold or camel hairline at rest; secondary enamel light only when active; anchored into visible studs or constellation nodes; curved by gravity, never arbitrary Bézier flourish; star glints only at meaningful crossings; motion only when the relationship is active or newly relevant.
Connection motion runs 3–6s and communicates a change, transfer, or active relation — never all lines at once; a Field at rest may breathe locally but lines stay quiet. Reduced motion resolves instantly to the same visible state. Route behind labels and object faces; no more than two equally bright paths may cross at an unmarked point — use a tiny dark knockout for depth ordering, a star glint only when the crossing itself has meaning. Favor fewer legible relationships over a complete but noisy graph.