The public transportation in Stockholm is owned by SL (Stockholms Lokaltrafik). They are in charge of the subway, buses, trams and commuter trains.
In order to travel with SL student discount legally, you need a Mecenat card with the SL logo on it. To get the SL logo on your card, you need to study for at least 100 % study rate for 15 weeks or 75 % study rate for 20 weeks. This corresponds to 22,5 hp/semester. Mecenat automatically receives information from Ladok about your study rate.
Doctoral students get their activity registered in Ladok afterwards, which is why Mecenat instead looks at the previous semester to decide whether you get the SL logo or not. If you are planning on being more than 75 % active the current semester, but don’t have enough activity from the previous semester, you need to prove this directly to Mecenat in order for them to give you the SL logo. Your first semester registered as a PhD student you automatically get the SL logo on your Mecenat card.
More information about the SL discount can be found on mecenat.com.
In case you need to prove that you are entitled to the SL student discounts before you have received your Mecenat card, you can download the Mecenat mobile app or order an sms certificate from Mecenat. Remember that you always have to carry a valid student ID (the physical Mecenat card or the card in the mobile app) with you at all times when you travel with the SL student discount to not risk fines.