As previously discussed, with oil prices coming down the inflation problem ends.
(The month to month change in CPI was 0)
And what happens next depends on what oil prices do next.
I suspect they go a lot higher as Saudi OSPs remain elevated and speculative long positions taken on when the war in Ukraine started seem to have been sold in anticipation of recession. And while refining margins are down from the highs, they remain elevated, indicating refiners, the only buyers of crude oil, are continuing to run flat out.