Contextuality and Sequential Measurement Order: Distinct Obstructions with a Shared MTT Interface

Quantum contextuality and sequential measurement order effects are related, but they are not the same mathematical phenomenon. Kochen–Specker contextuality is a static obstruction to gluing locally compatible value assignments into one global noncontextual assignment. An order effect is a dynamical statement about the noncommuting composition of quantum instruments, including their state-update maps. We formulate both structures explicitly and prove two separation results. First, projective qubit measurements exhibit an exact order effect even though the original projective Kochen–Specker obstruction does not apply in dimension two. Second, two instruments can have the same effects and identical one-step outcome probabilities while producing different sequential statistics. Effect or valuation data therefore cannot determine order dependence. A common MTT carrier may nevertheless source both structures. We state the required context-indexed source, instrument, measure, and naturality data for such a unification and identify the missing comparison theorem. The current q79 binary one-anchor recorder supplies an exact stopped-output law for one restricted apparatus domain; it does not yet provide the family of contexts needed for a contextuality theorem or a general contextuality–order equivalence.