It's looking like inflation is just about over (i.e. core down in the 2-3% range), but the official numbers won't show it for many months due to lag.
40% of core inflation is from housing, all of that is based on rent. (Homeowner costs are estimated based what it would cost to rent their property.) Rents for new contracts have been plummeting the last 3 months, but the "inflation" rents are what renters are paying on current contracts that are usually 12 months long. So "average" rents are still way up over last year, while new contracts are getting cheaper.
Net result is that over the next 9 months or so, Core CPI is going to show misleadingly high numbers until average rents are in line with new contracts.
Rents do have a seasonal pattern, but the Oct/Nov numbers are far lower than the seasonal pattern would suggest. Rents are dropping quickly even seasonally adjusted.
BTW here is "super core"- core CPI excluding shelter and used cars and vehicles. I made this chart with the data so far this year. Gives you an idea of inflation outside of shelter.