/**
 * Return the overlapping span of two date intervals, or null when they do not overlap.
 *
 * - Uses `Temporal.PlainDate.compare` for comparison.
 * - Adjacent intervals (e.g. `aEnd === bStart`) share one instant and DO overlap.
 * - Returns `null` if either interval is invalid (`start > end`).
 * - Returns `null` on invalid input (wrong type, malformed strings).
 * - Accepts GMT calendar-annotated PlainDate strings — E5 (issue #78). Since the result is a
 *   date *value*, all four arguments must carry the *same* calendar tag (or all be bare ISO);
 *   a mismatch returns `null` (E5 decision of record D4). The output's tag is re-derived from
 *   the intersection span, never copied from an input.
 *
 * @param aStart ISO 8601 date string for the first interval start, optionally calendar-annotated
 * @param aEnd ISO 8601 date string for the first interval end, optionally calendar-annotated
 * @param bStart ISO 8601 date string for the second interval start, optionally calendar-annotated
 * @param bEnd ISO 8601 date string for the second interval end, optionally calendar-annotated
 * @returns `{ start, end }` with the overlapping span, or null on invalid input / no overlap / mismatched calendars
 *
 * @example intervalIntersectionDate("2024-01-01", "2024-06-30", "2024-04-01", "2024-12-31") // { start: "2024-04-01", end: "2024-06-30" }
 * @example intervalIntersectionDate("2024-01-01", "2024-06-30", "2024-06-30", "2024-12-31") // { start: "2024-06-30", end: "2024-06-30" }
 * @example intervalIntersectionDate("2024-01-01", "2024-06-30", "2024-07-01", "2024-12-31") // null
 * @example intervalIntersectionDate("2024-01-01", "2024-06-30", "2024-02-01", "2024-03-01") // { start: "2024-02-01", end: "2024-03-01" }
 * @example intervalIntersectionDate("invalid", "2024-06-30", "2024-04-01", "2024-12-31") // null
 */
export declare function intervalIntersectionDate(aStart: string, aEnd: string, bStart: string, bEnd: string): {
    start: string;
    end: string;
} | null;