“It is, therefore, impossible to eliminate them through architectural improvements, dataset enhancements, or fact-checking mechanisms.”
The paper drags in Godel and the Halting Problem to prove that every stage of an LLM carries a non-zero chance of making things up. Any system has a non-zero error rate, so the math is the easy part. The useful line is the one vendors won’t print: no amount of data or fact-checking makes the output trustworthy on its own.