Also any discussion on inflation would be incomplete without a mention of the Personal Consumption Expenditures Price Index (PCE) which is under the purview of the US Department of Commerce, Bureau of Economic Analysis.

The PCE is arguably a better indicator for macro-economic inflation (for various reasons, which I won't get into - it's a rabbit hole in it of itself), as it's also the metric that the Federal Reserve uses as its inflation barometer.

Not to say that the CPI is unimportant, social security benefits are adjected using the CPI which has rippling effects throughout the economy - but for talks about macroeconomic inflation the PCE is generally a better metric. (But even then, the two are highly correlated anyway)