Koinos was launched with fair mining on ethereum. Meaning anyone who wanted to obtain $KOIN was able to do so by running a PoW miner powered by Ethereum. This was how ERC-20 KOIN was originally distributed. You can find the now deprecated miner in the archived github repo here:
The full history of the ERC-20 $KOIN token can be found here:
While ERC-20 mining was underway, the test net was also under development. During this time an anon user created the Uniswap $KOIN contract and public trading began.
Koinos Group has outright stated that they did not create the trading pair, nor did they ever provide liquidity to the contract. They have however confirmed that they mined and purchased (but never sold) tokens from Uniswap.
ERC-20 $KOIN token holders who held their ERC-20 $KOIN during the snapshot on October 31, were eligible for a 1:1 main net $KOIN tokens.
Those who claimed the main net tokens could run a Koinos mining node. Effectively there are about 30+ nodes producing blocks on Koinos. You can see these nodes producing blocks on https://koinosblocks.com/.
Koinos nodes are permissionless, anyone may run a consensus node to verify the state of the chain without any $KOIN tokens. Running a Koinos mining node is also permissionless, but you need $KOIN and $VHP to produce blocks and generate new $KOIN tokens.