Also the energies, specifically of the more penetrating gamma rays (very energetic photons). And the more dangerous stuff has shorter half-lives, so it wouldn'

Also the energies, specifically of the more penetrating gamma rays (very energetic photons). And the more dangerous stuff has shorter half-lives, so it wouldn't take all that long to get the full picture. WRT to nuclear weapons, we can determine what the fissionables were, where they were mined, and some details of design all from sniffing the air downwind.