Week 1 and the first Thursday
ISO week 1 is the week containing January 4. An equivalent rule says it is the week containing the year’s first Thursday. Weeks always begin Monday and end Sunday.
Because a week cannot be split between two ISO week-years, some late-December dates belong to week 1 of the following year, while some early-January dates belong to the previous year’s final week.
A year-boundary example
December 30, 2024 is a Monday. The week from that day through January 5, 2025 contains January 4, so the entire week is ISO week 1 of 2025.
A useful week result therefore includes both pieces: “week 1 of 2025,” not only “week 1.”
Why some years have week 53
Most ISO week-years have 52 weeks. A year can have week 53 when its weekday pattern leaves enough days for an additional full ISO week. A reverse lookup should validate week 53 instead of assuming it exists every year.