The Trashcan of Time

A thought experiment in time travel:

The lid of the time-door drops a payload atop it one second into the past. The receiver is directly beneath, such that any payload in the receiver blocks the trapdoor and it cannot open.

If the lid is not open, the box is empty, so the lids opens.

If the lid is open, the box is blocked, so the lid cannot open.

What does an observer see?

Assume the timeline splits at the moment of the experiment, so that one experimenter places the payload on the trapdoor, but two experimenters in two parallel continua see two different results. What does each one see?

For sake of simplicity, and to prevent facile or facetious answers, let us imagine the time-door to be a trashcan lid one foot square, the receiver is a box one foot on a side, and the payload a cube that snugly fits within it. The time-door is placed atop the box like a trashcan lid. There is no leftover room for some intruding fly or whatnot to enter the experiment or meddle with the result.

The experiment takes place on the moon, so we need not concern ourselves with details like air pressure or air displacement or the bampf noise when the cube vanishes in one point in time and appears in a prior.

Also for the sake of simplicity, we assume the experimenter is armed with the dread and dreaded oblivion pistol, which he uses on any time cops or paradox police, historical revisionists, killjoys, or Gallifreyans who show up to stop him, to remove such intruders retroactively before they exist.