code: final long transform(
          int cycle,
          int yearOfCycle,
          EastAsianMonth month,
          int dayOfMonth
      ) {
          if (!this.isValid(cycle, yearOfCycle, month, dayOfMonth)) {
              throw new IllegalArgumentException("Invalid date.");
          }
  
          return this.firstDayOfMonth(cycle, yearOfCycle, month) + dayOfMonth - 1;
      }
docs: result in utc-days