With the ceasefire expiring tomorrow, what does economic research say about how energy shock reversals affect inflation persistence?

The US-Iran ceasefire expires April 21. If it extends and oil stays soft, we've had roughly six weeks of elevated energy prices followed by partial normalization. If it lapses and oil spikes again, the energy shock continues.

My question is about the asymmetry in inflation dynamics between the two scenarios.

The standard view is that energy price increases pass through to CPI relatively quickly, especially through gasoline and transport costs. But the reversal is typically slower — businesses that raised prices in response to higher input costs don't immediately reduce them when inputs get cheaper.

Given that CPI in March already came in at 3.3% with a 0.9% monthly gain, and given that the Fed's Beige Book showed businesses adjusting pricing and hiring decisions in response to the energy shock, how persistent should we expect inflation to be even if oil returns to pre-war levels?

Specifically: is there empirical evidence on how much of an oil-driven CPI increase reverses within three to six months of an oil price decline versus how much becomes embedded in services prices and wages?

And from a central bank perspective — if the Fed's framework allows them to "look through" temporary oil-driven inflation, does that framework change once the oil price has been elevated for six weeks and started showing up in core services pricing? Is there a duration threshold after which "temporary" stops being an accurate characterization?