The ABSOLUTE MINIMUM is a fully-redundant source of gas sufficient for (1) some problem solving, and (2) an ascent.
Ideally, that redundant source of gas can be taken with you in the event you need to ditch or remove your KIT (which is possible.)
Also, consider that if you have a medical problem underwater, you're probably dead (e.g. heart attack). However, if you have one underwater, you're probably dead anyway, with or without a buddy.
A buddy can kill you just as he can save you (or vice-versa.)
A person in full-blown panic is going to be able to overpower you irrespective of your size differences. Witness the little old ladies that have been known to lift CARS off someone in a panic situation. Will YOUR mask and reg stay in place in the face of such an onslaught of strength? No, they will not.
The choice to dive solo .vs. with a buddy is a serious one. While there are many who preach that buddy diving is the ONLY way to dive, and you'll die if you dive solo, the truth is nowhere near that simple.
Most of those who are opposed to solo diving consider the "spare brain" to be the best defense against an accident. However, since human brains are fallible, and in fact fail to act correctly in an amazing percentage of situations, it can be argued that you are adding significantly to the risk of a dive by using one.
For a new diver, diving solo in a depth that exceeds that from which you can COMFORTABLY make a free, no-gas ascent, and in ANY condition where entanglement is a reasonably-likely risk, is, IMHO, foolish.
Beyond that point you wll have the knowledge and skills, along with the tools, to determine what you need to take with you if you choose to dive solo.
I dive both solo and with buddies, and am an advocate of neither system. It is a choice.
