"I simulated the estimated transfer function of my LCD."
Heh. Did you take the inverse of the transfer function of my LCD into account? I was expecting one of Jonathan's trademark image shrinking algorithms, really.
No, you're supposed to correct for your own LCD. I just took the GPU's LUT* and what it's supposed to make the final display like and inverted that.
*On OS X (since 10.3 or so) it's easy to do more than basic gamma→gamma correction. Its calibration assistant in "expert mode" is good enough to turn the final response of anything reasonable into something close to a power curve. There's more to complete calibration, but it's enough for this purpose (and the least you can do to get reasonable colors if the display doesn't fix its own response (like many built-in LCDs)).
Trademark image shrinking: this is effectively infinitely oversampled nearest neighbor. Doesn't need relatively complex caching to prevent having to keep the entire >10 GiB in a 4 GiB address space and 768 MiB physical memory (yes, I actually torrented some 500 m stuff a while ago and used it here), and doesn't look all that bad.
Taking 5 samples isn't all that much work. In fact not enough to get truly accurate response curves. The result depends largely on how your display behaves by itself and what the default correction does.
I'll upload the reason world1.png has a 1 in its name for comparison.