Pax Calendar

The Pax calendar was invented by James A. Colligan, SJ in 1930 as a perennializing reform of the annualized Gregorian calendar.
Design.
The common year is divided into 13 months of 28 days each, whose names are the same as in the Gregorian calendar, except that a month called "Columbus" occurs between November and December. The first day of every week, month and year would be Sunday.
Unlike other perennial calendar reform proposals, such as the International Fixed Calendar and the World Calendar, it preserves the 7-day week by periodically intercalating an extra seven days to a common year of 52 weeks (364 days). 
In leap years, a one-week month called "Pax" would be inserted after "Columbus".
To get the same mean year as the Gregorian Calendar this leap week is added to 71 of the 400 years in the cycle.
The years with leap week are years whose last two digits are a number that is divisible by six (including 00) or 99: however, if a year number ending in 00 is divisible by 400, then Pax is cancelled.
Duncan Steel mentions the Pax Calendar proposal:
New Year's Day.
Unlike the International Fixed Calendar, the Pax calendar has a new year day that differs from the Gregorian New Year's Day. This is a necessary consequence of it intercalating a week rather than a day.
The following tables compare the Gregorian dates (left column) of New Year's Day in the Pax Calendar for various years. Dates in December occur in the preceding Gregorian year. Dates in bold are Sundays. The Pax years run sequentially down each column (from second-left to right), and a new column is begun when the year would need to go further up the column. Places marked "leap" means that there was no Pax year in the sequence which corresponded to that Gregorian date.
 Jan 04 1931 
 Jan 03 1932 1937 1943
 Jan 02 leap 1938 1944 1949 1955 
 Jan 01 1928 1933 1939 leap 1950 1956 1961 1967
 Dec 31 leap 1934 1940 1945 1951 leap 1962 1968 1973 1979
 Dec 30 1929 1935 leap 1946 1952 1957 1963 leap 1974 1980 1985
 Dec 29 1930 1936 1941 1947 leap 1958 1964 1969 1975 leap 1986
 Dec 28 leap 1942 1948 1953 1959 leap 1970 1976 1981 1987
 Dec 27 leap 1954 1960 1965 1971 leap 1982 1988
 Dec 26 leap 1966 1972 1977 1983 leap
 Dec 25 leap 1978 1984 1989
 Dec 24 leap 1990
 Jan 02 2000
 Jan 01 leap
 Dec 31 2001 2007
 Dec 30 1991 2002 2008 2013 2019
 Dec 29 1992 1997 2003 leap 2014 2020 2025 2031
 Dec 28 leap 1998 2004 2009 2015 leap 2026 2032 2037 2043
 Dec 27 1993 1999 leap 2010 2016 2021 2027 leap 2038 2044 2049 
 Dec 26 1994 2005 2011 leap 2022 2028 2033 2039 leap 2050 
 Dec 25 1995 2006 2012 2017 2023 leap 2034 2040 2045 2051 
 Dec 24 1996 leap 2018 2024 2029 2035 leap 2046 2052 
 Dec 23 leap leap 2030 2036 2041 2047 leap 
 Dec 22 leap 2042 2048 2053 
 Dec 21 leap 2054
The next table shows what happens around a typical turn of the century and also the full range (18 Dec to 6 Jan) of 19 days that the Pax Calendar New Year Day varies against the Gregorian calendar.
 Jan 06 2301 2307
 Jan 05 2302 2308
 Jan 04 2303 leap
 Jan 03 2304 2309
 Jan 02 2101 2107 leap 2310
 Jan 01 2102 2108 2305 2311
 Dec 31 2103 leap 2300 2306 2312
 Dec 30 2104 2109 leap
 Dec 29 leap 2110
 Dec 28 2105 2111 2291
 Dec 27 2100 2106 2112 2292 2297
 Dec 26 leap leap 2298
 Dec 25 2293 2299
 Dec 24 2091 leap 2294
 Dec 23 2092 2097 2295
 Dec 22 leap 2098 2296
 Dec 21 2093 2099 leap
 Dec 20 2094 
 Dec 19 2095
 Dec 18 2096 
Alternative proposals by Colligan.
Colligan published multiple alternative methods of organising the months, including three 12-month plans in addition to the 13-month plan, and in a follow-up work focused on two possible 12-month calendars, in which Pax would be between September and October. He also provided two alternatives to the leap week plan, either extending one or two Mondays per year to 48 hours or making Pax a month of 28 or 21 days to be added 18 times in 400 years.