I want to know why statsPeriod on List a Project's Issues still returns the same set of issues no matter what value I pass.
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On List a Project's Issues, statsPeriod only controls the stats timeline in the response (24h, 14d, or "" to disable). It does not filter which issues are returned. The default issue filter is is:unresolved.

To limit issues by time on that endpoint, use query - for example, lastSeen:-14d or age:-24h. See issue searchable properties.

Prefer the replacement endpoint, List an Organization's Issues. There, statsPeriod sets the query window, while groupStatsPeriod controls the per-issue stats timeline. To scope the results to a project, use project=.