A common intuition for monotone Markov chains is that the lowest and highest starting states should remain the furthest apart. This anonymous, unrefereed candidate shows that the intuition fails in the general reversible setting. The example has only four states, arranged as a diamond: a bottom state, a top state, and two states in between that cannot be compared. A random-scan heat-bath update uses Gibbs weights one, one half, two, and one. The resulting chain is monotone, reversible, irreducible and aperiodic. Yet after every positive number of steps, the two incomparable middle states are further apart in total variation than the bottom and top. Their distance is exactly four thirds of the extremal distance at every time. The note goes further. It derives exact formulas for an entire two-spin family and proves that four states are the smallest possible cardinality for this kind of failure when the order has a unique minimum and maximum. The boundary matters. The example uses opposing site-dependent fields, so it does not answer the separate zero-field Ising question on every graph. An exact search found no zero-field failure across all connected labelled simple graphs with at most four vertices for five temperatures and six times, but that is a finite screen, not a theorem. The public archive passed exact replay, mutation controls, deterministic PDF rebuilding, fresh-extraction checks, four public Python matrix jobs, and producer-organised internal review. Those checks do not establish independent reconstruction, formal verification, specialist review, journal peer review, novelty or priority. This synthetic-voice briefing is a communication aid, not additional mathematical evidence.