We introduce the 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 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.
Juan Pablo Silva Alvarado (Sun,) studied this question.