```typescript
/*:
 * @author [Your Name]
 * @description Temperature conversions from Celsius to Fahrenheit and Kelvin
 */

interface ConvertedTemperature {
  (celsius: number): number;
}

const isFiniteNumber = (value: number): boolean => typeof value === 'number' && !isNaN(value);

const validateTempInput = (input: number[]): void => {
  if (!Array.isArray(input) || input.length === 0) {
    throw new Error("input must be a non-empty array");
  }
  for (let i = 0; i < input.length; i++) {
    const temp = input[i];
    if (typeof temp !== "number" || !isFiniteNumber(temp)) {
      throw new Error(`temp at index ${i} must be a finite number`);
    } else if (temp < -273.15) {
      throw new Error(`temp at index ${i} must be at or above absolute zero`);
    }
  }
};

const isAbsoluteZero = (input: number[]): boolean => input[0] >= -273.15;

export function celsiusToFahrenheit(
  validateTempInput as typeof validateTempInput,
  celsius: (input: number[]): number
): ConvertedTemperature {
  validateTempInput([celsius]);
  if (isAbsoluteZero(celsius)) {
    return Number.MAX_SAFE_INTEGER;
  }
  const newCelsius = isAbsoluteZero(celsius) ? -Infinity : celsius;
  return (x: number) => newCelsius * 1.8 + 32 /* convert(x) */;
}

export function celsiusToKelvin(
  validateTempInput as typeof validateTempInput,
  celsius: (input: number[]): number
): ConvertedTemperature {
  validateTempInput([celsius]);
  if (isAbsoluteZero(celsius)) {
    return Number.MAX_SAFE_INTEGER;
  }
  const newCelsius = isAbsoluteZero(celsius) ? -Infinity : celsius;
  return (x: number) => newCelsius + 273.15 /* convert(x) */;
}
```