As I mentioned in the note you referenced, ID can report false negatives (i.e., it can fail to detect CSI when in fact it is present), not false positives (i.e., it never reports CSI where none is present).

For example, if we received a transmission from outer space such as "Hello earthlings, this is a message from Alpha Centauri", we could definitely conclude that it was the product of an intelligence (but not the veracity of the statement, nor its source). This is because it exhibits:

• Contingency - there is nothing in the physics of the transmission that causes it to contain the message it contains
• Specification - the message obeys grammatical rules and expresses a cogent idea that has a real-life referent
• Complexity - there is (barely) enough information to rule out spontaneous chance occurrence

If instead we received the signal "d643b18c0fad2024202e03328a163a950d6341d4324f4b46a77dbd6a8ffa3d37", which is the SHA-256 hash of the above sentence (calculate it yourself here, we would be receiving a signal that could only be the product of an intelligence, but since SHA-256 is a cryptographic "trap-door" function (which means that it is "computationally infeasible" to determine the source text from the hash), ID methods would not be able to determine that it was CSI (false negative). However, at a later time the intelligence could produce the source text so that an ID theory researcher could verify after the fact that it was indeed the author.

So, to answer your question, the data sent would have to be recognizable by the researcher applying ID theory principles. If the signal is being generated by an intelligence that wishes to announce its presence, that intelligence would take pains to ensure that it is as easily readable as possible. In the movie "Contact", the aliens transmitted the primes from 2 to 101. Prime numbers would be universally understood and easy to format into a simple transmission, and there is no known natural process that generates prime numbers (unlike Fibonacci numbers, for example).

Earthlings (the US specifically) sent two objects into space, known as the Voyager Golden Records. The ID theory principles I outlined above were utilized in the creation of these records (although the scientists would not admit it). They are intended to be obvious examples of CSI that contains information about our planet and its inhabitants.

Another example is the signal beamed into space known as the Arecibo message.