Exactly. We have the same information showing he hasn't. Therefore, there is no evidence either way. I'm not making any assumptions, but simply evaluating the question on its own merits.

Quite the contrary. I have no idea whether he has or hasn't. Frankly, I don't care. It's an interesting question either way.

We know that folks at the highest levels of the sport have considered the issue. Whether they do a thorough test and publish results is more likely a function of whether tubeless continues to improve, making the question moot, or whether we still see people racing with tubes for several years.

I'm not quite sure why the notion that someone might investigate a very small difference sticks in your craw so much. You're free to ignore the issue. No one expects you to do the research. The history of science is full of experiments that test for the presence of (presumably) small differences and subsequent tests to evaluate the significance of those differences.

You have a great day.

Yes but the effects are within epsilon of zero.

The added rubber would increase rolling resistance just like moving from thin latex tubes to thicker butyl rubber.

With about 1% of the wheel circumference covered and not 1/3 of the tire carcass width I'd expect far less than 1% impact on rolling resistance.

With a 3-7W difference between a pair of latex and butyl tubes at 20 MPH 1% would be 0.015W to 0.035W from one patch on one wheel.

The effect of weight on climbing is proportional to the total. Divide into 70,000 grams as an average 5'9" 2 pound per inch climber on a UCI minimum weight bike.

A Rema patch kit including plastic box and metal tube of vulcanizing fluid weighs 16g for five patches or 3g each. 3g / 70000 = 0.0043% slower up hill. Grinding away at 250W that would cost you 0.011W.

Double the climbing effect on acceleration.