The Fundamental Conjecture of Superposition

Let a superposition be a product of mutually compatible slices, and let a slice be a component obtained by a slicing algorithm from the initial syntax of a superposition. An order-1 fragment is a fragment of order one, and the vector of ions implied by a collection of order-1 fragments is the vector determined by those fragments. The Fundamental Conjecture of Superposition. The following equivalent statements hold:

1. Every product of slices is a superposition.
2. Every product of order-1 fragments is a superposition, with respect to the smallest possible vector of ions implied from all of the order-1 fragments.

The conjecture asserts that products formed from slices, equivalently from order-1 fragments with the minimal compatible ion vector, always admit a superposition structure. The supplied text gives no evidence that the conjecture has been resolved.