I'm calling the combination of balloon, parachute and capsule "the stack". Here's a diagram of how GAGA-1 will fly:
cord which has a strength of 120 daN (decanewtons). That corresponds to roughly 120x the force of gravity on a 1kg mass. As the capsule has a mass of roughly 1kg there's plenty of safety margin (unless things get really hairy in the jet stream).
4m of cord attach the top of the parachute (where is has an X for that purpose) to the balloon. The balloon is 4m above the parachute so that when the balloon bursts the remnants fall well clear of the parachute and don't get tangled. Note that the parachute is open at all times, when ascending it's pulled taut by the lift from the balloon; once the balloon is gone the parachute simply opens slowing the descent.
double bowline with a stopper.
On the capsule there are cords that pass through the polystyrene itself (I pierced it with a long metal skewer and threaded the cord through). Here's a shot of the capsule hanging by its four cords. On the top are the two GPS antennas, the GSM backup antenna for the recovery computer, and the small black tube is the external temperature sensor sticking through.
antenna that will transmit telemetry to the ground (there's a cardboard cover protecting it which will be removed before flight).
Here's the underside showing the cord threaded through.
And here's the top where the cords come through both the capsule and its cover.