We reconstruct the 2PI vertex Γ(k,p;q) from Monte Carlo measurements of the connected two-particle correlator for the two-dimensional single-component φ4 lattice field theory and follow it across the Ising transition. Resolving the vertex in the irreducible representations of the point group C4v
Nearby in the stack
, we find that the instability is driven by the
A1
(ferromagnetic) channel at zero transfer, whose leading eigenvalue of the symmetrized Bethe--Salpeter kernel approaches unity. Substantial
B1
(nematic) and
B2
(diagonal nematic) contributions cooperate with
A1
across all system sizes, highlighting that the soft sector is multidimensional. In real space, the vertex is short-ranged away from criticality while it develops a power-law tail at the critical point. In the ordered phase, the
q=0
eigenvalue collapses because the ferromagnetic weight has condensed into the (one-particle-reducible) order parameter (or collective coordinate for a finite system), although finite-momentum fluctuations persist. By stripping the crossed-channel ladders, we obtain the fully irreducible vertex, which is a local contact -- to a very good approximation. Inserted into the parquet and Schwinger--Dyson equations, this contact reproduces the Monte Carlo self-energy with an accuracy better than one-tenth of a percent. This provides a first-principles benchmark of the dynamical local-vertex approximation (D
Γ
A). Additionally, we demonstrate that in the critical region, the physical solution of the parquet equations behaves as a repulsive fixed point, driven initially by a single order-parameter mode.