  Game semantics is a denotational semantics presenting compositionally the
computational behaviour of various kinds of effectful programs. One of its
celebrated achievement is to have obtained full abstraction results for
programming languages with a variety of computational effects, in a single
framework. This is known as the semantic cube or Abramsky's cube, which for
sequential deterministic programs establishes a correspondence between certain
conditions on strategies (''innocence'', ''well-bracketing'', ''visibility'')
and the absence of matching computational effects. Outside of the sequential
deterministic realm, there are still a wealth of game semantics-based full
abstraction results; but they no longer fit in a unified canvas. In particular,
Ghica and Murawski's fully abstract model for shared state concurrency (IA)
does not have a matching notion of pure parallel program-we say that
parallelism and interference (i.e. state plus semaphores) are entangled. In
this paper we construct a causal version of Ghica and Murawski's model, also
fully abstract for IA. We provide compositional conditions parallel innocence
and sequentiality, respectively banning interference and parallelism, and
leading to four full abstraction results. To our knowledge, this is the first
extension of Abramsky's semantic cube programme beyond the sequential
deterministic world.
