The Wayeb is the seam, and it is the reason the Haab and the Tzolk'in mesh the way they do. Five days is not a multiple of twenty, so the closing period shifts the alignment between the two counts by five positions each year, and it is that shift, repeated, which restricts the possible Year Bearers to four signs spaced five apart in the twenty.
The arithmetic runs like this. A Haab year of 365 days advances the Tzolk'in day sign by five places, because 365 leaves a remainder of five on division by twenty, so a year seated on Kan is followed by one seated on Muluc, then Ix, then Kawak, then Kan again. Four years exhaust the set and the fifth returns to the start, which is why the Yucatec sources speak of the four bearers as a closed group.
The day number behaves differently. Thirteen and 365 share no common factor, so the number attached to the bearer advances by one each year and takes thirteen years to return. Four bearers and thirteen numbers give fifty-two named years, which is the Calendar Round expressed in years rather than in days, and the whole structure follows from the five days of the Wayeb.
The Wayeb is also where the two Mesoamerican traditions come closest in practice. Central Mexico closed its 365-day count with five days called nemontemi, likewise regarded as unlucky and likewise standing outside the eighteen twenty-day periods. The parallel is structural and well attested on both sides; the specific observances are recorded separately for each and should not be merged.