The construction
Outcomes are y ∈ {0, 1}³. Demand i requires y_i = 1, so A_i = {y : y_i = 1}. The organization 𝒪 can attain
ℛ(𝒪) = {(1,1,0), (1,0,1), (0,1,1)}.
- For each pair i ≠ j, ℛ(𝒪) ∩ A_i ∩ A_j ≠ ∅: (1,1,0) meets demands 1 and 2, (1,0,1) meets 1 and 3, (0,1,1) meets 2 and 3.
- ℛ(𝒪) ∩ A₁ ∩ A₂ ∩ A₃ = ∅: no attainable outcome has all three coordinates 1.
So 𝒦(𝒪) has every vertex and edge and no triangle. {1, 2, 3} is a minimal structurally frustrated collection (CLAIM-347).
The reorganization. Through differentiation and coordination the organization acquires a new composite policy that can also produce (1,1,1). Then ℛ(𝒪) ⊊ ℛ(𝒪′) = ℛ(𝒪) ∪ {(1,1,1)}. The acceptance sets are unchanged, no demand is removed or weakened, and 𝒦(𝒪′) gains the triangle, losing nothing. By CLAIM-347 this is relief of structural frustration.
What it shows
Some organizational conflicts are not problems of choosing among competing demands. They are problems of functional organization: the existing repertoire cannot realize a jointly demanded outcome, and a differentiated or recomposed repertoire can. This is CASE-115’s point (a split of a shared parameter removes a frustration) in combinatorial form, and it is the first of CLAIM-360’s three effects, a larger realizable set, rather than a better choice within the old one.
It also shows pairwise compatibility failing to fix collective compatibility. Every pair is compatible and the triple is not, as in ecological communities where pairwise coexistence does not determine multispecies coexistence (Hofbauer and Schreiber 2022 on invasion graphs). THEORY-598 is the caution in the other direction: some apparent higher-order dynamics reduce to pairwise interactions. Here the higher-order fact is real: the complex is not determined by its 1-skeleton.
What it does not show
That specialization tends to produce such relief. Differentiation can also add costs or dependencies and shrink what is attainable. Whether and when it enlarges ℛ is QUESTION-133.