  We present a number of observables-based proofs of the Kochen-Specker (KS)
theorem based on the N-qubit Pauli group for N >= 4, thus adding to the proofs
that have been presented earlier for the two- and three-qubit groups. These
proofs have the attractive feature that they can be presented in the form of
diagrams from which they are obvious by inspection. They are also irreducible
in the sense that they cannot be reduced to smaller proofs by ignoring some
subset of qubits and/or observables in them. A simple algorithm is given for
transforming any observables-based KS proof into a large number of
projectors-based KS proofs; if the observables-based proof has O observables,
with each observable occurring in exactly two commuting sets and any two
commuting sets having at most one observable in common, the number of
associated projectors-based parity proofs is 2^O. We introduce symbols for the
observables- and projectors-based KS proofs that capture their important
features and also convey a feeling for the enormous variety of both these types
of proofs within the N-qubit Pauli group. We discuss an infinite family of
observables-based proofs, whose members apply to all numbers of qubits from two
up, and show how it can be used to generate projectors-based KS proofs
involving only nine bases (or experimental contexts) in any dimension of the
form 2^N for N >= 2. Some implications of our results are discussed.
