Bully Metric Realized Timestamps

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Current Bully Timestamp (GitHub)

There have been over 700,000 realized Bully timestamps during the more than 65 years of modern atomic time keeping (1958 AD ... present). Given the availability of atomic clocks, it is anticipated that Bully timestamps will continue to be realized with great regularity for the foreseeable future. Each Bully timestamp should be considered "realized" after it occurs and is measured using precise clocks with an accuracy of $10^{- 10}$ or better.

Leap Seconds (1972 - Present)

The below table (derived from the Wikipedia "Leap Second" article), lists all leap second insertions that have occurred since the introduction of leap seconds in 1972. For each leap second insertion, the below table lists the preceding Bully timestamp (that had been "realized" immediately prior to the leap second insertion), and the subsequent Bully timestamp (that was "realized" immediately after the leap second insertion).

A few details are worth noting in the table. The TAI and UTC already differed by 10 seconds at the beginning of 1972 due to rubber seconds (see discussion below), so when Bully Timestamp 8209 ECFB E7FB was realized, the TAI time was 1972-06-30 23:34:45 TAI, whereas UTC time was 1972-06-30 23:34:35 UTC. An additional 27 leap seconds were inserted into UTC during the period between 1972 and 2016, making a total of 37 leap seconds difference, so when Bully Timestamp 8209 ED02 EBC0 was realized, the TAI time was 2017-01-01 00:32:00 TAI, whereas UTC time was 2017-01-01 00:31:23 UTC. Notably, Bully timestamps are always realized during TAI times with a seconds value ending in five or zero. The Bully timestamp and TAI both measure elapsed time as determined by atomic clocks at sea level on Earth, so these systems will always have this simple relationship.

Announced leap seconds to date
Year	30 Jun	31 Dec	Bully Timestamp	International Atomic Time (TAI)	Coordinated Universal Time (UTC)
1972	+1	+1	8209 ECFB E7FB 8209 ECFB E7FC 8209 ECFB FC4F 8209 ECFB FC50	1972-06-30 23:34:45 TAI 1972-07-01 00:25:40 TAI 1972-12-31 23:45:05 TAI 1973-01-01 00:36:00 TAI	1972-06-30 23:34:35 UTC 1972-07-01 00:25:29 UTC 1972-12-31 23:44:54 UTC 1973-01-01 00:35:48 UTC
1973	0	+1	8209 ECFC 24A2 8209 ECFC 24A3	1973-12-31 23:57:50 TAI 1974-01-01 00:48:45 TAI	1973-12-31 23:57:38 UTC 1974-01-01 00:48:32 UTC
1974	0	+1	8209 ECFC 4CF4 8209 ECFC 4CF5	1974-12-31 23:19:40 TAI 1975-01-01 00:10:35 TAI	1974-12-31 23:19:27 UTC 1975-01-01 00:10:21 UTC
1975	0	+1	8209 ECFC 7547 8209 ECFC 7548	1975-12-31 23:32:25 TAI 1976-01-01 00:23:20 TAI	1975-12-31 23:32:11 UTC 1976-01-01 00:23:05 UTC
1976	0	+1	8209 ECFC 9DB6 8209 ECFC 9DB7	1976-12-31 23:30:50 TAI 1977-01-01 00:21:45 TAI	1976-12-31 23:30:35 UTC 1977-01-01 00:21:29 UTC
1977	0	+1	8209 ECFC C609 8209 ECFC C60A	1977-12-31 23:43:35 TAI 1978-01-01 00:34:30 TAI	1977-12-31 23:43:19 UTC 1978-01-01 00:34:13 UTC
1978	0	+1	8209 ECFC EE5C 8209 ECFC EE5D	1978-12-31 23:56:20 TAI 1979-01-01 00:47:15 TAI	1978-12-31 23:56:03 UTC 1979-01-01 00:46:57 UTC
1979	0	+1	8209 ECFD 16AE 8209 ECFD 16AF	1979-12-31 23:18:10 TAI 1980-01-01 00:09:05 TAI	1979-12-31 23:17:52 UTC 1980-01-01 00:08:46 UTC
1981	+1	0	8209 ECFD 531C 8209 ECFD 531D	1981-06-30 23:19:00 TAI 1981-07-01 00:09:55 TAI	1981-06-30 23:18:41 UTC 1981-07-01 00:09:35 UTC
1982	+1	0	8209 ECFD 7B6F 8209 ECFD 7B70	1982-06-30 23:31:45 TAI 1982-07-01 00:22:40 TAI	1982-06-30 23:31:25 UTC 1982-07-01 00:22:19 UTC
1983	+1	0	8209 ECFD A3C2 8209 ECFD A3C3	1983-06-30 23:44:30 TAI 1983-07-01 00:35:25 TAI	1983-06-30 23:44:09 UTC 1983-07-01 00:35:03 UTC
1985	+1	0	8209 ECFD F484 8209 ECFD F485	1985-06-30 23:55:40 TAI 1985-07-01 00:46:35 TAI	1985-06-30 23:55:18 UTC 1985-07-01 00:46:12 UTC
1987	0	+1	8209 ECFE 597D 8209 ECFE 597E	1987-12-31 23:40:35 TAI 1988-01-01 00:31:30 TAI	1987-12-31 23:40:12 UTC 1988-01-01 00:31:06 UTC
1989	0	+1	8209 ECFE AA3F 8209 ECFE AA40	1989-12-31 23:51:45 TAI 1990-01-01 00:42:40 TAI	1989-12-31 23:51:21 UTC 1990-01-01 00:42:15 UTC
1990	0	+1	8209 ECFE D291 8209 ECFE D292	1990-12-31 23:13:35 TAI 1991-01-01 00:04:30 TAI	1990-12-31 23:13:10 UTC 1991-01-01 00:04:04 UTC
1992	+1	0	8209 ECFF 0EFF 8209 ECFF 0F00	1992-06-30 23:14:25 TAI 1992-07-01 00:05:20 TAI	1992-06-30 23:13:59 UTC 1992-07-01 00:04:53 UTC
1993	+1	0	8209 ECFF 3752 8209 ECFF 3753	1993-06-30 23:27:10 TAI 1993-07-01 00:18:05 TAI	1993-06-30 23:26:43 UTC 1993-07-01 00:17:37 UTC
1994	+1	0	8209 ECFF 5FA5 8209 ECFF 5FA6	1994-06-30 23:39:55 TAI 1994-07-01 00:30:50 TAI	1994-06-30 23:39:27 UTC 1994-07-01 00:30:21 UTC
1995	0	+1	8209 ECFF 9C4B 8209 ECFF 9C4C	1995-12-31 23:12:05 TAI 1996-01-01 00:03:00 TAI	1995-12-31 23:11:36 UTC 1996-01-01 00:02:30 UTC
1997	+1	0	8209 ECFF D8B9 8209 ECFF D8BA	1997-06-30 23:12:55 TAI 1997-07-01 00:03:50 TAI	1997-06-30 23:12:25 UTC 1997-07-01 00:03:19 UTC
1998	0	+1	8209 ED00 1560 8209 ED00 1561	1998-12-31 23:36:00 TAI 1999-01-01 00:26:55 TAI	1998-12-31 23:35:29 UTC 1999-01-01 00:26:23 UTC
2005	0	+1	8209 ED01 2FDC 8209 ED01 2FDD	2005-12-31 23:45:40 TAI 2006-01-01 00:36:35 TAI	2005-12-31 23:45:08 UTC 2006-01-01 00:36:02 UTC
2008	0	+1	8209 ED01 A8F0 8209 ED01 A8F1	2008-12-31 23:18:40 TAI 2009-01-01 00:09:35 TAI	2008-12-31 23:18:07 UTC 2009-01-01 00:09:01 UTC
2012	+1	0	8209 ED02 3604 8209 ED02 3605	2012-06-30 23:45:00 TAI 2012-07-01 00:35:55 TAI	2012-06-30 23:44:26 UTC 2012-07-01 00:35:20 UTC
2015	+1	0	8209 ED02 AEFC 8209 ED02 AEFD	2015-06-30 23:32:20 TAI 2015-07-01 00:23:15 TAI	2015-06-30 23:31:45 UTC 2015-07-01 00:22:39 UTC
2016	0	+1	8209 ED02 EBBF 8209 ED02 EBC0	2016-12-31 23:41:05 TAI 2017-01-01 00:32:00 TAI	2016-12-31 23:40:29 UTC 2017-01-01 00:31:23 UTC

Rubber Seconds (1958 - 1971)

Prior to 1972, the rate of UTC atomic clocks was offset from a pure atomic time scale by the BIH to remain synchronized with UT2, a practice known as the "rubber second" (see figure 2). The rate of UTC was decided at the start of each year. Alongside this shift in rate, an occasional 0.1 s step (0.05 s before 1963) was also implemented as needed.

As shown in figure 2, for 1958-1961, the offset rate was −150 parts per 10¹⁰ (or 0.47 seconds per year). This stretching of UTC "rubber seconds" meant that fewer of them would occur during a Bully Timestamp. For example, during the 1958-1961 time period, each Bully timestamp was realized after exactly 3055 seconds TAI, which corresponded to 3054.999955264 seconds UTC. For 1962–63 the offset rate was set to −130 parts per 10¹⁰ (or 0.41 seconds per year, or 3054.999960285 seconds UTC per Bully timestamp), and then for 1964–65 the offset rate was returned to −150 parts per 10¹⁰.

The UTC rate of −150 parts per 10¹⁰ turned out to be notably inadequate during the 1964-1965 time period, and multiple 0.1 s steps were needed (see figure 2). Beginning in 1966, the offset rate was set to −300 parts per 10¹⁰ (or 0.94 seconds per year, or 3054.99990835 seconds UTC per Bully timestamp), and this continued until the inauguration of Leap Seconds in 1972.

At the beginning of 1958, the TAI and UTC clocks were in sync, with 1958-01-01 00:00:00.000 TAI occurring at the same time as 1958-01-01 00:00:00.000 UTC. By the end of 1972, the UTC clock had been adjusted (using rubber seconds and time steps) by ten leap seconds, so that 1972-01-01 00:00:10.003 TAI occurred at the same time as 1972-01-01 00:00:00.003 UTC. The following table illustrates the slow accumulation of leap seconds prior to 1972, resulting in this ten second difference.

Rubber Seconds and Accumulative (TAI - UTC) Time Delta
Approximate Bully Timestamp Approximate International Atomic Time (TAI) Coordinated Universal Time (UTC)	(ΔTAI - ΔUTC)	Accumulative Difference
8209 ECF9 9F04 (+2820.0 sec) . . . 8209 ECF9 EFAA (+1290.9 sec) 1958-01-01 00:00:00.000 TAI . . . 1960-01-01 00:00:00.943 TAI 1958-01-01 00:00:00.002 UTC . . . 1960-01-01 00:00:00.000 UTC	0.943 sec	0.943 sec
8209 ECF9 EFAA (+1290.9 sec) . . . 8209 ECFA 1819 (+1386.4 sec) 1960-01-01 00:00:00.944 TAI . . . 1961-01-01 00:00:01.418 TAI 1960-01-01 00:00:00.000 UTC . . . 1961-01-01 00:00:00.000 UTC	0.474 sec	1.418 sec
8209 ECFA 1819 (+1386.4 sec) 1961-01-01 00:00:01.418 TAI . . . 1961-01-01 00:00:01.423 TAI 1961-01-01 00:00:00.000 UTC	0.005 sec	1.423 sec
8209 ECFA 1819 (+1386.4 sec) . . . 8209 ECFA 2F85 (+406.6 sec) 1961-01-01 00:00:01.423 TAI . . . 1961-08-01 00:00:01.698 TAI 1961-01-01 00:00:00.000 UTC . . . 1961-08-01 00:00:00.000 UTC	0.275 sec	1.698 sec
8209 ECFA 2F85 (+406.6 sec) 1961-08-01 00:00:01.698 TAI . . . 1961-08-01 00:00:01.648 TAI 1961-08-01 00:00:00.000 UTC	-0.050 sec	1.648 sec
8209 ECFA 2F85 (+406.6 sec) . . . 8209 ECFA 406C (+621.8 sec) 1961-08-01 00:00:01.648 TAI . . . 1962-01-01 00:00:01.846 TAI 1961-08-01 00:00:00.000 UTC . . . 1962-01-01 00:00:00.000 UTC	0.198 sec	1.846 sec
8209 ECFA 406C (+621.8 sec) . . . 8209 ECFA 8A54 (+1622.5 sec) 1962-01-01 00:00:01.846 TAI . . . 1963-11-01 00:00:02.597 TAI 1962-01-01 00:00:00.000 UTC . . . 1963-11-01 00:00:00.000 UTC	0.751 sec	2.597 sec
8209 ECFA 8A54 (+1622.6 sec) 1963-11-01 00:00:02.597 TAI . . . 1963-11-01 00:00:02.697 TAI 1963-11-01 00:00:00.000 UTC	0.100 sec	2.697 sec
8209 ECFA 8A54 (+1622.6 sec) . . . 8209 ECFA 9111 (+2147.7 sec) 1963-11-01 00:00:02.697 TAI . . . 1964-01-01 00:00:02.766 TAI 1963-11-01 00:00:00.000 UTC . . . 1964-01-01 00:00:00.000 UTC	0.069 sec	2.766 sec
8209 ECFA 9111 (+2147.7 sec) . . . 8209 ECFA 9B1F (+977.8 sec) 1964-01-01 00:00:02.766 TAI . . . 1964-04-01 00:00:02.884 TAI 1964-01-01 00:00:00.000 UTC . . . 1964-04-01 00:00:00.000 UTC	0.118 sec	2.884 sec
8209 ECFA 9B1F (+977.9 sec) 1964-04-01 00:00:02.884 TAI . . . 1964-04-01 00:00:02.984 TAI 1964-04-01 00:00:00.000 UTC	0.100 sec	2.984 sec
8209 ECFA 9B1F (+977.9 sec) . . . 8209 ECFA AC06 (+1193.1 sec) 1964-04-01 00:00:02.984 TAI . . . 1964-09-01 00:00:03.182 TAI 1964-04-01 00:00:00.000 UTC . . . 1964-09-01 00:00:00.000 UTC	0.198 sec	3.182 sec
8209 ECFA AC06 (+1193.2 sec) 1964-09-01 00:00:03.182 TAI . . . 1964-09-01 00:00:03.282 TAI 1964-09-01 00:00:00.000 UTC	0.100 sec	3.282 sec
8209 ECFA AC06 (+1193.2 sec) . . . 8209 ECFA B980 (+2243.4 sec) 1964-09-01 00:00:03.282 TAI . . . 1965-01-01 00:00:03.440 TAI 1964-09-01 00:00:00.000 UTC . . . 1965-01-01 00:00:00.000 UTC	0.158 sec	3.440 sec
8209 ECFA B980 (+2243.5 sec) 1965-01-01 00:00:03.440 TAI . . . 1965-01-01 00:00:03.540 TAI 1965-01-01 00:00:00.000 UTC	0.100 sec	3.540 sec
8209 ECFA B980 (+2243.5 sec) . . . 8209 ECFA C005 (+1048.6 sec) 1965-01-01 00:00:03.540 TAI . . . 1965-03-01 00:00:03.617 TAI 1965-01-01 00:00:00.000 UTC . . . 1965-03-01 00:00:00.000 UTC	0.076 sec	3.617 sec
8209 ECFA C005 (+1048.7 sec) 1965-03-01 00:00:03.617 TAI . . . 1965-03-01 00:00:03.717 TAI 1965-03-01 00:00:00.000 UTC	0.100 sec	3.717 sec
8209 ECFA C005 (+1048.7 sec) . . . 8209 ECFA CD7F (+2098.8 sec) 1965-03-01 00:00:03.717 TAI . . . 1965-07-01 00:00:03.875 TAI 1965-03-01 00:00:00.000 UTC . . . 1965-07-01 00:00:00.000 UTC	0.158 sec	3.875 sec
8209 ECFA CD7F (+2098.9 sec) 1965-07-01 00:00:03.875 TAI . . . 1965-07-01 00:00:03.975 TAI 1965-07-01 00:00:00.000 UTC	0.100 sec	3.975 sec
8209 ECFA CD7F (+2098.9 sec) . . . 8209 ECFA D459 (+429.0 sec) 1965-07-01 00:00:03.975 TAI . . . 1965-09-01 00:00:04.055 TAI 1965-07-01 00:00:00.000 UTC . . . 1965-09-01 00:00:00.000 UTC	0.080 sec	4.055 sec
8209 ECFA D459 (+429.1 sec) 1965-09-01 00:00:04.055 TAI . . . 1965-09-01 00:00:04.155 TAI 1965-09-01 00:00:00.000 UTC	0.100 sec	4.155 sec
8209 ECFA D459 (+429.1 sec) . . . 8209 ECFA E1D3 (+1479.3 sec) 1965-09-01 00:00:04.155 TAI . . . 1966-01-01 00:00:04.313 TAI 1965-09-01 00:00:00.000 UTC . . . 1966-01-01 00:00:00.000 UTC	0.158 sec	4.313 sec
8209 ECFA E1D3 (+1479.3 sec) . . . 8209 ECFB 35E5 (+2171.2 sec) 1966-01-01 00:00:04.313 TAI . . . 1968-02-01 00:00:06.286 TAI 1966-01-01 00:00:00.000 UTC . . . 1968-02-01 00:00:00.000 UTC	1.973 sec	6.286 sec
8209 ECFB 35E5 (+2171.1 sec) 1968-02-01 00:00:06.286 TAI . . . 1968-02-01 00:00:06.186 TAI 1968-02-01 00:00:00.000 UTC	-0.100 sec	6.186 sec
8209 ECFB 35E5 (+2171.1 sec) . . . 8209 ECFB D3E0 (+809.9 sec) 1968-02-01 00:00:06.186 TAI . . . 1972-01-01 00:00:09.891 TAI 1968-02-01 00:00:00.000 UTC . . . 1971-12-31 23:59:59.999 UTC	3.707 sec	9.892 sec
8209 ECFB D3E0 (+809.9 sec) 1972-01-01 00:00:09.891 TAI . . . 1972-01-01 00:00:09.999 TAI 1971-12-31 23:59:59.999 UTC	0.109 sec	10.000 sec