states are sets of mutations, such that ⊔ is set union and each operation simply adds to the set of mutations; a bit more on ⊔ is coming up; also, this formalism as presented is overdone and not particularly elegant; with more space/time, this can be simplified--feel free to email me) “I don’t live my life by anybody else’s clock. If I feel like doing something, I don’t care what time it is. I just do it.” --Dennis Rodman, Bad As I Wanna Be. New York: Delacorte Press, 1996. Print. Invariant I and set of operations T are coordination-free if, given initial state Di , every pair of states Dj and Dk resulting from any two valid series of operations in T applied to Di can be merged into a valid database state* Coordination-freedom is required for simultaneously maintaining application-level consistency, availability, and convergence Single-step(s) case (from diagram): Invariant I and set of operations T are coordination- free if ∀ t1 ,t2 ∈ T: I(D)⋀I(t1 (D))⋀I(t2 (D)) 㱺 I(t1 (D)⊔t2 (D))