How many signatures are required to start the formal decision making stage of a direct democracy mechanism?

FEDERAL CONSTITUTION OF THE SWISSCONFEDERATION

(Adopted1999; last amended 2013)

http://www.admin.ch/ch/e/rs/c101.html

Title 4: The People and the Cantons

Chapter 2: Initiative and Referendum

Art. 138 Popular initiative requestingthe complete revision of the Federal Constitution

(1) Any 100,000 persons eligible to vote may within 18 months of theofficial publication of their initiative propose a complete revision of theFederal Constitution.

(2) This proposal must be submitted to a vote ofthe People.

Art. 139 Popular initiative requestinga partial revision of the Federal Constitution in specific terms

(1) Any 100,000 persons eligible to vote may within 18 months of theofficial publication of their initiative request a partial revision of theFederal Constitution.

(4) If the Federal Assembly is in agreement withan initiative in the form of a general proposal, it shall draft the partialrevision on the basis of the initiative and submit it to the vote of the Peopleand the Cantons. If the Federal Assembly rejects the initiative, it shallsubmit it to a vote of the People; the People shall decide whether theinitiative should be adopted. If they vote in favour, the Federal Assemblyshall draft the corresponding bill.

(5) An initiative in the form of a specificdraft shall be submitted to the vote of the People and the Cantons…

Art. 141 Optional referendum

If within 100 days of the official publicationof the enactment any50,000 persons eligible to vote or any eight Cantons request it, thefollowing shall be submitted to a vote of the People…