Causal Flow Equations and the 1/3--2/3 Conjecture: Exact Resolution for Low Bottleneck Count

We introduce the \emph{Causal Flow partition}, a decomposition ofthe linear extensions of a finite poset into adjacent, flexible, andrigid components. Two involutions --- the Adjacency Involution andthe Flexible Buffer Involution --- annihilate all symmetriccontributions, yielding the \textbf{Skewness Equation}: the net biasof any incomparable pair equals the imbalance of its rigid buffervolume. Using this framework, we prove the 1/3--2/3 Conjecture withthe exact bound $1/3$ for every finite poset whose dominant linearextension has at most three disjoint adjacent bottleneck pairs --- astructural class defined for all~$n$. This reduces the fullconjecture to a single explicit obstruction: posets admitting four ormore disjoint bottleneck pairs in their dominant extension. For thelatter case, we establish a volumetric lower bound (the HypercubeSqueeze) and a structural rigidity constraint (Rigid Necessity) thattightly circumscribe the remaining open territory. All analyticalresults are machine-verified in Lean~4.