Real question that nobody has yet answered: With what data CPI is even calculated? The data sources are all hidden.
If they're not giving you a one-page report on the methodology for how they arrived at each individual point-in-time price figure that they recorded, well, I'm sorry, it's true, their methods are in that sense "hidden".
Publishing the particular products looked at, or even the particular stores visited, would invite market manipulation of the CPI figure by re-pricing the included goods.