```ts
export function foldMachine(machine: Record<string, unknown>): Record<string, unknown> {
  // Helper to validate that all elements in an array are non-empty strings and unique
  const validateStrings = (arr: any[], name: string): arr is string[] => {
    if (!Array.isArray(arr) || arr.length === 0) throw new Error(`${name} must be a non-empty list`);
    const seen = new Set<string>();
    for (const item of arr) {
      if (typeof item !== 'string' || item.trim() === '') throw new Error(`${name} must contain only non-empty strings`);
      if (seen.has(item)) throw new Error(`${name} contains duplicates`);
      seen.add(item);
    }
    return true;
  };

  // Validate alphabet and states
  const alphabet = machine.alphabet as string[];
  const states = machine.states as string[];
  validateStrings(alphabet, 'alphabet');
  validateStrings(states, 'states');

  // Validate start state
  if (typeof machine.start !== 'string' || !states.includes(machine.start)) {
    throw new Error('start must be a valid state name');
  }

  // Validate accepting states
  const accepting = Array.isArray(machine.accepting) ? machine.accepting : [];
  for (const acc of accepting) {
    if (typeof acc !== 'string' || !states.includes(acc)) {
      throw new Error('accepting states must be valid state names');
    }
  }

  // Validate moves
  const moves = machine.moves as [string, string, string][];
  if (!Array.isArray(moves) || moves.length === 0) throw new Error('moves must be a non-empty list');
  const moveMap = new Map<string, Map<string, string>>();
  for (const [state, symbol, next] of moves) {
    if (!states.includes(state) || !alphabet.includes(symbol) || !states.includes(next)) {
      throw new Error('moves must reference valid states and symbols');
    }
    if (!moveMap.has(state)) moveMap.set(state, new Map());
    const stateMoves = moveMap.get(state)!;
    if (stateMoves.has(symbol)) throw new Error('each state-symbol pair must have exactly one move');
    stateMoves.set(symbol, next);
  }

  // Reachable states from start
  const reachableStates = new Set<string>();
  const exploreReachable = (current: string) => {
    if (!reachableStates.has(current)) {
      reachableStates.add(current);
      for (const symbol of alphabet) {
        const next = moveMap.get(current)?.get(symbol);
        if (next) exploreReachable(next);
      }
    }
  };
  exploreReachable(machine.start);

  // Filter out unreachable states
  const reachableMoves = moves.filter(([state, ,]) => reachableStates.has(state));

  // Merge indistinguishable states
  const groupMap = new Map<string, number>();
  let currentGroup = 0;
  const exploreGroups = (current: string) => {
    if (!groupMap.has(current)) {
      groupMap.set(current, currentGroup);
      for (const symbol of alphabet) {
        const next = moveMap.get(current)?.get(symbol);
        if (next && reachableStates.has(next)) exploreGroups(next);
      }
    }
  };
  exploreGroups(machine.start);

  // Build the result
  const size = new Set(groupMap.values()).size;
  const acceptingGroups = Array.from(new Set(accepting.map(state => groupMap.get(state)!))).sort((a, b) => a - b);
  const movesByGroup: [number, string, number][] = [];
  for (const move of reachableMoves)