Let's settle this: does bourbon actually get better after the bottle's been open a few weeks?

It's real, and there's actual chemistry behind it. When you open a bottle, oxygen interacts with the volatile compounds in the whiskey. Some of the harsher, more volatile ethanol notes dissipate, and certain flavor compounds (esters, aldehydes) can evolve. It's essentially a very slow, gentle oxidation process. The effect is more noticeable with higher-proof bourbons because they have more volatile compounds to begin with. Your ECBP observation is consistent with what most people report. The sweet spot seems to be 2-4 weeks open with the bottle at least half full. Once you get below 1/3 full, the increased air exposure can start to flatten the flavors.

I did exactly the test you described with a bottle of Wild Turkey Rare Breed. Poured 2oz into a Boston round sample bottle on day one, sealed it tight. Tasted the bottle at 1 week, 2 weeks, and 4 weeks alongside the day-one sample. Result: definite difference at 2 weeks. The open bottle was noticeably smoother and the caramel notes were more prominent. At 4 weeks the difference was less dramatic — the open bottle was maybe slightly better but it was getting hard to tell. My conclusion: it's real, but the improvement has diminishing returns after the first couple weeks.

Related tip: if you want to speed up the opening process, pour the bourbon into a glass and let it sit for 15-20 minutes before drinking. Most of the "tight" or "hot" notes that people attribute to a freshly opened bottle will dissipate in the glass. A lot of what people call "bottle rest" might just be them getting more comfortable with the pour over time.