Well it's a bit of a stretch dude ngl lol but the idea is that if distortions caused by fiat could be removed simply by canceling out the denominator then those distortions wouldn't exist. When you remove the denominator you're throwing away information, like a lossy form of compression, you're losing context. And this shows OK the fact that two different commodities have different price changes, part due to their own market forces but partly because the distortions caused by fiat affect different parts of an economy to different degrees, as a result of this, you can't measure inflation across an economy simply by measuring the price change of any one commodity, hence CPI.