Three tested variants of chronology reconstruction are based on one general principle: extent of historical processes is reduced 15-20 times, and events start to look reliable: prophets lived not 900 years, but 70-80, and wars lasted not 100 years, but 5-7maximum. The variant which I have chosen, assumes the following:
Root of chronological problems in transfer from the octal numeration system to the decimal one: figures IV and V, meaning two variants of writing of number 4, began to mean 4 and 5; figures IX and X, meaning two variants of writing of number 8, began to mean 9 and 10, and figure L meaning 32 before, began to mean 50. Here is the true meaning of the basic figures, confirmed with old engravings:

I — 1
II — 2
III — 3
IV — 4
V — 4
VI — 5
VII — 6
VIII — 7
IX — 8
X — 8
XI — 9
XII — 10
XIII — 11
XIV — 12
XV — 12There is one duplicate decade for each 50 years, where figures L (32) and XXXX (32) are duplicated; it periodically make oneself visible in chronology.
The second root of chronological problems is the change of the lunar calendar, where the basic time unit is a lunar month, to the solar one, where this function is carried out by the solar year. As a result of the reform of the numeration and the calendar, 12 indictions, meaning the numbers of lunar months before that change, began to be interpreted as 15 years.

I — March — 1st indiction
II — April — 2nd indiction
III — May — 3rd indiction
IV — June — 4th indiction
V — June — 5th indiction
VI — July — 6th indiction
VII — August — 7th indiction
VIII — September — 8th indiction
IX — October — 9th indiction
X — October — 10th indiction
XI — November — 11th indiction
XII — December — 12th indiction
XIII — January — 13th indiction
XIV — February — 14th indiction
XV — February — 15th indiction

Every month it is doubled, that is why a certain 5-year cycle is formed in the history mentioned in the chapter about the Roman numeration system.
The previous time numeration system was based on the eight-year cycle during which three extra lunar months, one of which was redeemed at the end of 4 years, and two — at the end of 8 years. After the numeration system and calendar reform these extra months in the past would be interpreted as anniversary years. Coincidence is clearly proved: after 48 months of every 4-year period, there comes the 49th or 49-50th anniversary. I will remind that more exact 19-year Metonic cycle did not get accustomed (Wikipedia) that is why the 8-year cycle became the main basis in chronology.
As a result, I got rather huge table of recalculation with a great number of variants of placing of the unary and doubled anniversary months and slipping order of the simple doubled months. Reliability of this algorithm of reconstruction has not been proved today, but the approach is definitely true, as it works effectively in case large quantity of dated events and shows exactly what it is necessary to show.

TESTING METHOD
It is clear that the same events were regularly fixed both in the solar, and lunar calendar, thus, comparison of the number of events, dated in a traditional way and with the reconstructed dates (transferred from the solar years back into the lunar months), should show certain correlation. In practice it works, and there are not only splashes which correlate, but also general dynamics of growth of the number of events.

If to observe only those events which involve only active forces (France, Britain, Holland…), the 6-linear filter is not necessary, 2-linear filter would be enough. The correlation is extremely clear.

ALGORITHM PARAMETERS
In the current version of the algorithm the World was created (5508 BC) in 1457, Jesus was born in 1742, 1000 coincides with April, 1794, 1348 — January, 1812, 1453 — November, 1817, 1648 — July, 1828, and since January, 1837 the order changes for the return one, and traditional dates exceed the reconstructed ones. 1837 we take as an extreme date because just before it was the last time when Halley’s Comet passed — one of the main defining points of medieval chronologists.
Hardly this model is ideal, but it is quite enough to begin restoration of the original chronology of events.

THE SIMPLIFIED ALGORITHM
It is possible to calculate similar values of the reconstructed dates very quickly with accuracy of two years. You should divide the year from the world Creation by 19.25 and add 1457. The second variant: divide year A.D. by 19.25 and add 1742. The main thing is to remember that along with the distorted dates in the chronology there are also true ones.