From the introduction "[...]Because signers prove computational work,
rather than proving secret knowledge as
is typical for digital signatures, we refer to them as miners. To
achieve stable consensus on the
blockchain history, economic incentives are provided where miners are
rewarded with fees and
subsidies in the form of coins that are valuable only if the miners
form a shared valid history,
incentivising them to behave honestly.[...]"

This isn't applicable in case of sidechains: anybody with sufficient hashpower will be able to unlock a locked coin on the parent chain by producing an SPV proof.

"Only if the miners form a shared valid history" isn't a requirement here, as miner will get bitcoins which aren't in any way connect to sidechain he have wrecked. Thus there is no incentive to behave honestly.

Thus sidechains, in principle, reward their miners

with the same Bitcoin will use in the future: only transaction fees.
Since some people claim that won't be enough

Whether it is enough depends on a variety of factors, including existence of other chains miner can mine.

You cannot assume that it is the same situation as with a simple single-chain model.

E.g. imagine 1000 BTC were moved to a sidechain. Miners can keep mining bitcoins as usual, and in parallel work on an SPV proof to claim these 1000 BTC. (I assume that merged-mining is allowed.)

In this case the amount of fees which miners could collect by honest mining on the sidechain is irrelevant, as long as it is smaller than 1000 BTC.

This is quite different from attacks which can be performed on vanilla Bitcoin (see below), so I don't think you can say that the security model is the same.

Also says "Given our assumption that p > q, the probability drops

exponentially as the number of blocks the
attacker has to catch up with increases."

Yes, but that doesn't apply to reorganizations which attacker might cause intentionally.

Hence I think it was disingenuous to include these two very different treats into one section:

it sounds like you claim that attacker-induced reorganizations are unlikely, while it isn't the case.

So the longer the contest period is, the harder it is to succeed with
a fraudulent transfer.

Yes, but "harder" isn't same as "unlikely".

Another problem with this section is that it only mentions reorganizations.

But a fraudulent transfer can happen without a reorganization, as an attacker can produce an SPV proof which is totally fake. So this is not similar to double-spending, attacker doesn't need to own coins to perform an attack.

I hope this clarifies our assumptions.

Yep, thanks. It looks like you assume that sidechain security will be similar to Bitcoin security in the long term.

Now quite the assumptions I've been looking for, but OK...

I'm sorry for the harsh tone, but I just find it hilarious that people who explained that proof-of-stake is not going to work because an attacker might collect everybody's past signing keys to rewrite the whole history

(I'm referring to this: https://download.wpsoftware.net/bitcoin/pos.pdf )

didn't bother to mention that miners can collude to wreck a sidechain and get an awesome reward, basically for free.

something something the mote in thy brother's eye something something