Can perfect knowledge of DNA-pattern probabilities distinguish an evolutionary tree from a network? This candidate gives an exact example where it cannot.

The network has three observed species and two reticulations, where a lineage has a choice of parental path. Its four displayed trees share mutation parameters according to the network.

At an explicit parameter point, this network produces exactly the same sixty-four pattern probabilities as an ordinary three-leaf tree. Every probability agrees in exact arithmetic. Both models use continuous-time mutation with transitions favoured over transversions. But the rate ratio may differ between edges.

That qualification matters. If both models must share one fixed rate ratio greater than one, a convexity argument rules out this particular coincidence. Different assumptions produce different answers.

An anchoring condition prevents other networks from imitating trees. Among eighty-three reduced three-leaf shapes at level three, thirty are anchored. The other fifty-three have routes to exact counterexamples on a larger stochastic parameter region. Only a subset is established under the stricter continuous-time conditions. Written arguments extend examples to more leaves and higher levels.

The package supplies exact certificates, graph witnesses, replay code and deliberate corruption tests. These internal checks are not external peer review or formal verification.

This is a precise limit of identification, not a claim that networks are generally undetectable or that these parameters are typical of real data. Read the paper and evidence package on Evidence Press. This is synthetic speech.