DTV12 — week-of-year to day-of-year conversions ignore overlap

In clause 12.5, the very first Necessity reads:
" Necessity: Each week of year shares the Gregorian year of days scale with each Gregorian day of year."

According to 10.9 that means that each week of year corresponds to some time point sequence in Gregorian day of year. This is not possible. The week of year scale has 53 time points and any given Gregorian year has either 52 weeks (364 days) or 53 weeks (371 days). So, in a year that has 53 weeks, there must be at least 5 days that have no counterpart.

Even in a 52-week year, the first and last weeks of the year may include days from the prior or following year. The mapping to day of year can work, but not necessarily to days of the same year; one must consider the repeating aspect, and time point sequences that wrap around the end of the finite scale. For example, week of year 1 can convert to day of year 364, 365, 1, 2, 3, 4, 5, if the year begins on Wednesday. If that is a valid 'time point sequence' on the year of days scale, then the rules given for the conversions in clause 12.5 do not support it.

The Necessity is false. The problem is not overlap; the time point sequence can wrap around the end of the Gregorian day of year scale. The problem is that there is no single time point sequence on the Gregorian year of days that corresponds to the same time intervals as any given week of year (see 10.9). Both Necessities following Figure 12.4 are false. Some of the Examples are true, but only because they fall outside the related time sets. They have nothing to do with sharing the time scale.
Similarly, the conversion to time sets on the year of days scale is misleading, because the wrap around the end of the Gregorian year of days causes the time points to refer to time periods in different Gregorian years. So, it would be necessary to add additional rules to explain the complex correspondences of the time sets to time intervals.
The intent of this section cannot be preserved. The generic relationships between the year of weeks and the Gregorian year of days are defined by the year of weeks itself. There are no others. When the Gregorian year is given, the specific correspondences can be determined from the common Gregorian days scale, on which all of them are based.