/**
 * Promise-based mutex for serializing async storage operations.
 *
 * Operations are queued and executed in FIFO order. The lock is released
 * automatically whether the operation succeeds or throws.
 *
 * Limitations:
 * - In-process only. This lock does not coordinate across browser tabs,
 *   web workers, or extension background scripts that share the same
 *   localStorage origin. Cross-context isolation requires the Web Locks API
 *   or equivalent, which is not in scope here.
 * - Not reentrant. Calling run() from within a run() callback on the same
 *   AsyncMutex instance will deadlock: the inner call appends to the chain
 *   that the outer call is already holding. Always acquire the lock at the
 *   outermost call site and do not re-enter it from private helpers.
 */
export declare class AsyncMutex {
    private chain;
    /**
     * Runs fn exclusively under the lock.
     *
     * All concurrent callers are serialized in FIFO order. The lock is released
     * even if fn throws or rejects, so subsequent waiters always proceed.
     *
     * @param fn - Async function to run under the lock
     * @returns A promise that settles with the same value or error as fn()
     */
    run<T>(fn: () => Promise<T>): Promise<T>;
}