Evolutionary data can fit more than one history. Sometimes even perfect knowledge of the observed distribution cannot tell those histories apart. This research candidate asks a different question: which histories are compatible, and when have we collected enough data to certify the answer? The paper studies a model with three sampled leaves and one hybridisation event. Different orientations of its triangle network can overlap. The authors calculate the information distance to a different complete answer, restricting rival distributions to those the model actually allows. That restriction matters. The nearest ordinary sign change can lie outside the model, making a simpler method unnecessarily conservative. In one exact example, using the model reduces the leading expected sample requirement by about fifteen per cent. That is a high-confidence limiting comparison, not a guaranteed saving for every data set. The sequential procedure permits repeated inspections while controlling the chance of an incorrect conclusion. But more observations do not solve every question. The diagram on this page gives an exact boundary example with four nearby answers. All include orientation three, so that useful statement can be certified. The complete set varies, and reliable finite-time certification of that complete answer is obstructed. These are mathematical guarantees under specific assumptions: independent observations, a particular substitution model and no coalescence. They are not a test of whether the model fits biological reality. The universal results depend on written proofs. Rational certificates and numerical experiments check narrower implementation facts. This is Evidence Press, Information-optimal anytime certification of triangle-network compatibility, released on the twenty-sixth of September twenty twenty-six, version one point zero candidate. It is unrefereed. The paper and complete evidence package are linked on this page. This AI-generated synthetic voice adds no scientific evidence.