/**
 * Distance from the hub center at which a train should start so its first tile
 * clears its neighbours. Trains fan out 360/slots° apart, so the neighbour gap
 * at distance d is ~2πd/slots; it must exceed a tile's footprint. Offset trains
 * zigzag wider (a perpendicular half-tile seed) and need a bigger ring; linear
 * trains are skinny and stay near the hub. Never smaller than `radius + 20`.
 *
 * Pure geometry — no React — so it lives in the headless core and is shared by
 * the `DominoHub` component (in `double-eighteen-react`) and layout adapters.
 */
export declare function hubTrainStartDistance(slots: number, radius: number, dominoWidth: number, layoutStyle: 'offset' | 'linear'): number;