Geometry of Vector Addition Systems

We will prove the missing line conjecture for VAS. The proof proceeds in three steps, all based on the basic units of VAS: Periodic sets. 1) Prove an easy special case. 2) Explain all closure properties of classes interesting for VAS. 3) The closure properties non-trivially combine to produce a partition, which shows that w.l.o.g. 1) is actually the general case. Afterwards, we quickly mention additional applications of the partition.