Rabbinic tradition takes the red heifer as the standing example of a statute whose reason cannot be reached by reasoning, a decree kept because it was given rather than because it can be justified. It is usually the first case cited when that category is being explained, and the paradox above is why: a purifying agent that defiles the people who make it cannot be accounted for by any straightforward notion of cleaning.
The other striking thing about the rite is how rarely it happened. A single burning produced ashes enough to last a very long time, since only a small quantity was needed for each vessel of water, so it did not recur on a calendar as the daily and festival offerings did. The Mishnah devotes a tractate to it and preserves a count of how many red heifers had ever been prepared, from Moses onward, together with a dispute over the total in which one figure stands at seven and another at nine. That a body of law this detailed could not settle how many times its own subject had been carried out says a good deal about the character of the evidence, and it is the reason the atlas records the historical count as unknown rather than as disputed. Nobody holds a defended position on the true number; there is simply no independent record.
After the destruction the rite stopped, and unlike the offerings it could not be met by a substitution, because what it produced was a physical substance rather than an act. The consequence inside halakhah is that corpse impurity has had no remedy since, and that premise underlies a great deal of later legal discussion. The atlas records the rite as its sources give it and leaves what follows from that premise outside the entry.