Arugula (cool-season leafy green) is classed hardy in the cited extension guidance. The timing rules below are relative to your local freeze dates — enter a location to turn them into calendar dates.
The rules this site applies
Method
Frost-relative window
Rule & reconciliation
Fall planting
44–30 days before the median first fall freeze
Cornell Garden-Based Learning caps successive arugula sowings at "about a month before your average first frost date", so the fall sowing window is the 14 days ending at that cutoff (first fall frost minus 44 to minus 30 days); Wisconsin Horticulture agrees arugula tolerates frost but gives no numeric offset.
No direct-sow outdoors window: Cornell times spring arugula only by soil condition — "Plant as soon as soil can be worked in spring." — which is not an offset from a freeze date, so no spring window is computed here. The window above is the last succession sowing before the first fall freeze.
Variety assumption: No spring window is published: every extension page fetched gives only soil-workability language ("as soon as soil can be worked") or the unquantified "several weeks before the last frost", neither of which yields an honest numeric offset, so only the frost-anchored fall cutoff is encoded.