In reality, the market is usually the solution to the tragedy of the commons. In the case of the original, creating a propertization scheme and allowing the market to trade on the property and giving individual owners the responsibility for stewardship gives people incentive to not have their sheep overgraze, and this is better than having a central authority decide how the land should be used, which buts against the knowledge problem, or worse, capture.

The tragedy of the commons is somewhat distinct to regulation of things which directly cause harm (in the extreme example, murder) which we generally don't consider to be part of the 'free market'.

I think you're confusing free markets with artificial markets.

There are many shared resources that are easily exploitable by the free market. A central authority can create artificial markets on that resource to combat the exploitation by the free market, but it's still being heavily regulated which is not a free market characteristic.

One example of this is carbon credits with global warming, another is the Alaskan tradeable fishing quotas. Even following the common example of the Pilgrims, it was the enforcement of property regulations that solved the free-market exploitation of the land.

I think most free marketers would lump (certain) fishing quotas and property rights under "free markets", artificial though they may be.

SOX and NOX markets as well. Carbon markets (as they exist), not so much, but mostly because of completely insane equivalencies baked in, and weird credit schemes.

Not in any sense of the word free market is an enforced artificial market "free".

In fact, free market socialists see property rights on any productive property as skewing markets to favor the owners, which leads to wealth disparity and disproportionate ownership, making it not a free market. We see that today with free-market capitalism and the top 1%, which is why we have social welfare programs in place to redistribute wealth.

Free in free market usually refers to free will, and has little to do with disparity or disproportionality. You can choose to define free market however you wish but I think it's worth noting that you're out of line with how most people use language. Your point that property ownership is enforced is taken, but usually that's within the scope of "free" markets.

Precisely - disproportionate wealth skewing causing market shifts that favor the wealthy.