  The point of this work is to explore axiomatisations of concurrent
computation using the technology of proof theory and realizability. To deal
with this problem, we redefine the Concurrent Realizability of Beffara using as
realizers a $\pi$-calculus with global fusions. We define a variant of the
Conjunctive Structures of \'E Miquey as a general structure where belong
realizers and truth values from realizability. As for Secuential Realizability,
we encode the realizers into the algebraic structure by means of a combinatory
presentation, following the work of Honda & Yoshida. In this first work we
restricted to work with the $\pi$-calculus without replication and its
corresponding type system is the multiplicative linear logic (MLL).
