The division into eighty-one chapters is universal in modern printing, is used by every citation, and is not a feature of the earliest witnesses.
Eighty-one is nine squared, and nine carries weight in Chinese numerology, so the figure is not neutral. The Mawangdui silk manuscripts do not divide the text this way. The Guodian slips have no chapter division at all, and their groupings do not correspond to the received chapters. The division as it stands is associated with the received commentarial recensions rather than with any manuscript of the text alone.
Two positions on this are current. On one, the Laozi is an anthology of independent sayings drawn from a body of oral material, and the chapters, the parts and the number are Han period editorial work imposed on it; on that reading, arguing about where one chapter ends and the next begins is arguing about an editor. On the other, many of the units are genuine compositional wholes and the received arrangement preserves older groupings rather than inventing them; the rhyme schemes and the internal parallelism of individual chapters are the evidence usually adduced.
The disagreement has practical consequences. It bears on whether a chapter should be read as a unit with an argument, or as several sayings that a later hand put next to each other, and translators differ accordingly, some presenting the text as connected exposition and some as an assembly of fragments.
The atlas uses the chapter numbers, because a reader needs an address, and records that the address is editorial.