This ignores the first part of my response - if I, as a legitimate user, might get caught up in one of these trees, either by mistakenly approving a bot, or approving a user who approves a bot, and I risk losing my account if this happens, what is my incentive to approve anyone?

Additionally, let’s assume I’m a really dumb bot creator, and I keep all of my bots in the same tree. I don’t bother to maintain a few legitimate accounts, and I don’t bother to have random users approve some of the bots. If my entire tree gets nuked, it’s still only a few weeks until I’m back at full force.

With a very slightly smarter bot creator, you also won’t have a nice tree:

As a new user looking for an approver, how do I know I’m not requesting (or otherwise getting) approved by a bot? To appear legitimate, they would be incentivized to approve legitimate users, in addition to bots.

A reasonably intelligent bot creator would have several accounts they directly control and use legitimately (this keeps their foot in the door), would mix reaching out to random users for approval with having bots approve bots, and would approve legitimate users in addition to bots. The tree ends up as much more of a tangled graph.

This ignores the first part of my response - if I, as a legitimate user, might get caught up in one of these trees, either by mistakenly approving a bot, or approving a user who approves a bot, and I risk losing my account if this happens, what is my incentive to approve anyone?

Additionally, let’s assume I’m a really dumb bot creator, and I keep all of my bots in the same tree. I don’t bother to maintain a few legitimate accounts, and I don’t bother to have random users approve some of the bots. If my entire tree gets nuked, it’s still only a few weeks until I’m back at full force.

With a very slightly smarter bot creator, you also won’t have a nice tree:

As a new user looking for an approver, how do I know I’m not requesting (or otherwise getting) approved by a bot? To appear legitimate, they would be incentivized to approve legitimate users, in addition to bots.

A reasonably intelligent bot creator would have several accounts they directly control and use legitimately (this keeps their foot in the door), would mix reaching out to random users for approval with having bots approve bots, and would approve legitimate users in addition to bots. The tree ends up as much more of a tangled graph.

I think this would be too limiting for humans, and not effective for bots.

As a human, unless you know the person in real life, what’s the incentive to approve them, if there’s a chance you could be banned for their bad behavior?

As a bot creator, you can still achieve exponential growth - every time you create a new bot, you have a new approver, so you go from 1 -> 2 -> 4 -> 8. Even if, on average, you had to wait a week between approvals, in 25 weeks (less that half a year), you could have over 33 million accounts. Even if you play it safe, and don’t generate/approve the maximal accounts every week, you’d still have hundreds of thousands to millions in a matter of weeks.

In a scientific context, a hypothesis is a guess, based on current knowledge, including existing laws and theories. It explicitly leaves room to be wrong, and is intended to be tested to determine correctness (to be a valid hypothesis, it must be testable). The results of testing the hypothesis (i.e. running an experiment) may support or disprove existing laws/theories.

A theorem is something that is/can be proven from axioms (accepted/known truths). These are pretty well relegated to math and similar disciplines (e.g. computer science), that aren’t dealing with “reality,” so much as “ideas.” In the real world, a perfect right triangle can’t exist, so there’s no way to look at the representation of a triangle and prove anything about the lengths of its sides and their relations to each other, and certainly no way to extract truth that applies to all other right triangles. But in the conceptual world of math, it’s trivial to describe a perfect right triangle, and prove from simple axioms that the length of the hypotenuse is equal to the square root of the sum of the squares of the remaining two sides (the Pythagorean Theorem).

Note that while theorems are generally accepted as truth, they are still sometimes disproved - errors in proofs are possible, and even axioms can be found to be false, shaking up any theorems that were built from them.

A law describes what happens, a theory explains why. The law of gravity says that if you drop an item, it will fall to the ground. The theory of relativity explains that the “fall” occurs due to the curvature of space time.