PHANTOM TIMES? IS THE LOWERMOST CRONOLOGY OF BABYLON MORE PROBABLE THAN THE EXCISION OF CHARLEMAGNE?
President; Matter Evolution Subcommittee
of the Geonomy Scientific Committee of the Hungarian Academy of Sciences
CRIP, H-1525 Bp. 114. Pf. 49., Budapest, Hungary
This work belongs to the activity of the Matter Evolution Subcommittee about Arrows of Time.
3 new historical hypotheses drastically change chronologies. In all cases, however, dating is not really stable, because no sure Arrow of Time-type quantity found so far.
In recent years 3 astronomically motivated historical theories try to topple the orthodox historical chronology. They are, in decreasing radicality, as follows:
1) The New Chronology of A. T. Fomenko (Academician and Department Leader, differential Geometry, Russia), based originally on recalculations of historical eclipses. This theory recognises that with the recent tidal friction historical eclipse datings are conform with orthodox chronology only from c. 1300 AD. Between 700 and 1300 the agreement is bad and sporadic, and for eclipses before 700 AD in orthodox chronology the agreement would require cca. 0 friction in average bw. the eclipse and present, which is hardly physical. Suggestion: political history before 1300 AD is infected with falsifications, the events of Classical Antiquity, if not imaginary, must be brought up bw. 700 & 1300, while history before 700 AD is mainly unknown yet. For the eclipses see , for New Chronology I give here directly  plus my sites where the Reference Lists are extensive , , .
2) The Invented History or Phantom Time of H. Illig (History of Art, Bavaria), based originally on observed anomalies in architecture, especially in the style of the Aachen Palace; but also using astronomical arguments about the time of vernal equinox (the continuous slip in the Julian calendar from March 21). This theory considers Charlemagne mythological or product of later historians, and suggests to excise the interval (Aug. 614 - Aug. 911) from Orthodox Chronology. All other statements, if not directly connected with Charlemagne or with prehistory of the Saxonian (Ottonian) dynasty, are authentic in first approximation, so all events before 614 must be brought upwards by 297 years. See e.g. .
3) The Lowermost Chronology of V. Gurzadyan (experimental particle physics, Armenia). He recalculated Shulgi's Lunar Eclipse, Simanu 14, 2050 BC in Orthodox Chronology, but also got doubts on the basis of History of Art, namely about evolution in artistic styles of Babylonian pottery. He got that with the recent best tidal friction value, causing cca. 20"/century2 lunar longitudinal deceleration, the 2050 eclipse differs from the description, while one in 1954 is good. So he suggests to put the year of Fall of Babylon (the invasion of the Hittite King Murshilis I) to 1499 BC, and bring up all the earlier data of Middle Chronology with 96 years. See  & 
Obviously Theory 1 can be checked on any reliable dating of Clasasical Antiquity. I.e. C14 dating seems to work, and gives data incompatible with the theory. However it seems that the present best Lunar Theory is incompatible with Orthodox Chronology, and for a physicist (I mean: me) it is a nontrivial choice what to do if Quantum Mechanics (radioactive decay) and Newtonian Gravity (Lunar motion) lead to incompatible results .
As for Theory 2, the astronomical basis of the theory is seriously challenged by astronomers. However observations about architectural anomalies cannot be handled astronomically. As for C14 check, the 297 years discrepancy is marginal for Late Antiquity and within error for Early Antiquity. So for me it seems rather hopeless to check this theory via Natural Sciences. I note here only that the leading argument comes from History of Art. The secondary, astronomical, argument tells that Pope Gregory had to correct 10 days in 1584 and the Julian Calendar would have caused 12 or 13 day discrepancy between Iulius Caesar & Pope Gregory. This is true; if the vernal equinox was fixed to 21 March by Caesar.
As for Theory 3, the astronomical argument is strong enough, but note that if we accept that, we should also accept Theory 1, contradicting Theory 3. I, being physicist, cannot decide the strength of the argument about pottery styles, but they are clearly of the same style as that of Theory 2; and Theories 2 and 3 are compatible. Also, clearly 96 years are within 1s error in C14 for Babylonian times, so by radioactive decay we cannot check Theory 3.
My goal is in principle the comparison of the 3 theories and the Null Hypothesis (Orthodox Chronology) for Babylonian and related contexts. However this must necessarily be rather formal for Theory 1.
This Internet version is preliminary. I am planning a paper-based publication. Therefore here some parts of the argumentation will be compressed, and References sporadic.
Now, interestingly enough, the authors of Theories 1 & 2 get political criticism. Fomenko is called "Russian nationalist", which is probably true but irrelevant when a mathematician calculates lunar motion; and Illig is called "revisionist", which, when applied on historians in Germany, generally indicates that the person wants to reinterpret World War II. Since the existence of Charlemagne has no connection to World War II, such an argument seems to indicate either high emotions about Charlemagne or lack of other arguments. In Hungary we generally work within Orthodox Chronology, but in the same time we know that Frankish sources lie a lot about Charlemagne’s Avar campaigns. In some cases we believe to know why; you can find a very brief summary in the Appendix. But I think that emotional approaches are not necessary here. While the present work will not give final results, it may show useful methods.
ARROW OF TIME
Chronologies would rather need a well established idea about some Arrow of Time. Dating is possible if something monotonously was clicking between the particular event and present. We may or may not find such. However, surely the chronology cannot be stable without something at least changing monotonously. Imagine a remote country, whose history is available for us up to isolated names of a very few rulers mentioned by neighbours. We shall then be able to date isolated rulers by these synchronisms, but nothing more. If, in addition, we find a lot of tombstones with names, we still cannot establish a sequence, so cannot write a history. If, however, the relative ages of tombstones can be arranged via corrosion, aeolic damage or anything, we know the sequence (from an entropy-type quantity). But also we may be successful if each tombstone names seven ancestors.
Arrows of Time are given by various quantities. E.g. in closed systems entropy is growing, so we can order the randomised photographs of a closed system. Then at least a relative "chronology" is established.
Closed thermodynamic systems are extremely rare in practice. For open thermodynamic systems the work is still going to find Arrows of Time. However it seems that in stationary environments some production rates are decreasing. The natural idea is entropy production rate; but observe that the entropy production seems to be proper only for constant conduction coefficients, which is rather a strong assumption. Still, with utmost caution we can learn something; and as an example I would tell that palaeology seems to give the same sequence of fossils of synapsid evolution as the decreasing entropy production of the reconstructed living organisms. (Increasing internal temperature + increasing thermal insulation by hair + increasing oxygen intake by diaphragm + increasing efficiency of feed via differentiating dentition.)
As for fossils, another Arrow of Time comes from radioactive decay. Let us take e.g. one of the decay sequences starting with uranium or thorium. If the original processes producing Th and U are not repeated, their concentrations are monotonously decreasing and those of various decay products increasing. Surely, the U- and Th-geneses did not repeat since the SN event just before the formation of the Solar System; spontaneous fusion beyond Fe56 is impossible. Of course, local processes may wash away the signals (emigration of decay products or immigration of U and Th later from other minerals), but Geology claims that it can recognize disturbances. The Arrow of Time is at least established.
For historical timescales, however, U and Th cannot be used. By analogy, then, we may utilize C14 decay of cca. 5700 y half time. However the C14 production seems to be not a unique event but rather continuous. Fortunately, C14 is produced from N14, and non-living systems practically do not take nitrogen up; also not animals and most plants. So carcasses inherit the C14 content of the living state, and then this level is decaying exponentially in time. However the original level may in principle be anything.
The solution is calibration. This is a difficult but well established task, whose details I will ignore here. However observe that one can check the existence of the particular Arrow of Time simply on the final calibration curve. If kinks appear, i.e., by other words, there are C14 levels yielding more than one age, then there are problems with this Arrow of Time (the method being, however, still partially informative). Obviously different authors use different calibration curves. I consulted with Ref. , where the first (minor) kink appears c. 400 AD, and they are not at all rare before 1st century BC. While for earlier times the method remains informative with caution, the Arrow of Time is no more well established.
As for dating via eclipses, there is practically no Arrow of Time behind it at all. For simplicity assume that the Sun-Earth-Moon system consists of 3 mass points. Then the 3-body system contains an entropy-like quantity, but its growth is practically unobservable in mere 4000 years. Two-body systems are exactly perpetua mobilia, repeating similar configurations endlessly. Because of tidal friction the length of day is growing, which is an Arrow of Time, but about historical eclipses we cannot observe the length of day (and in the Introduction we saw that just the tidal friction makes the confusion with/in Orthodox Chronology).
In fact, we know that lunar eclipses are more or less recurrent in few years; indeed Late Sumerian datings can be triplets with 5-5 years of shifts. To be sure, eclipses remain useful for dating, but only with great caution. Direct and naive approaches may be completely misleading (as e.g. Ref.  demonstrates it); because of the lack of the Arrow of Time widely differing datings are possible.
Of course, eclipse calculations plus historical arguments together may suffice. However it is not trivial to sum up the two very different types of informations
In Orthodox Chronology Rinascimento is a period, mainly in Italy and rather the XIVth and XVth centuries, when people rediscovered antique Rome and some intellectuals tried even to reborn Roman society. Toynbee  considers Rinascimento a special case of a more general phenomenon: connection with past cultures. The usual term is "Renaissance", both meaning "Rebirth". But in Italy Rinascimento meant really rebirth of past (Italian people studied real remnants of local past, Latin language was marginally understandable for Italians &c.), while in France Renaissance meant importing ideas from Italy.
Orthodox Chronology contains a lot of Rinascimenti. Historians recognise e.g. a "Karoling Renaissance" about 800 AD, an Egyptian Renaissance in the Late Empire after the Ramessids, and a "Neo-Babylonian Renaissance" in VII-VIth c. BC. The Karoling Rinascimento returns to Classical Latin from very late Vulgar Latin just becoming Archaic French, the Egyptian texts try to return to linguistic forms 2 millenia old, and the Neo-Babylonian rulers start to use millenium-old titles and formulae. Regarding the present topic, I concentrate on Babylonian examples.
1) King Nabupolassar calls himself King of Sumer and Akkad. Nabupolassar (625-605 BC), first independent ruler of Babylon after the Assyrian vassalage, on an inscription calls himself: shakkanakku of Babylon, King of Sumer and Akkad. The shakkanakku is cca. "governor". On one hand, this formula goes back to the Ur III dynasty when there was a unified Sumer and Akkad, and a local governor under the King in Babili (Kadingirra), and on the other, to the introduction of Hammurabi's Law Stele. Observe that for Nabupolassar Babylon is not the Empire, but a city.
2) Nabukudurriusur as isshiakku. Nabukudurriusur (Nebokadnesar; 605-562) does call himself "King of Babylon", however also calls himself "the august isshiakku". Now, "isshiakku" is the Akkadian mirror translation of the Sumerian "ensi", the older Sumerian ruling title, with some priest-king annotations. It was in fashion in the first half of 3rd millenium, then the fully lay "lugal", "Great Man" started to compete it.
3) Nabunaid's historical interest. Nabunaid, last king of Babylon (555-539) performs historical researches. This interest in Past is something unusual in ancient times. Now, during the reconstruction of the Ebarra Temple in Sippar he performs a regular excavation until the original founding brick of Naram-Sin (from XXIV. c) is found "in 18 fathom depth". While he overestimates its age by 70 %, that error may come from the tradition of Mesopotamian King Lists where parallel dynasties are linearly arranged. He finds also Hammurabi's brick, whom he puts 700 years before Burraburiash, instead of the correct 400.
Rinascimenti sometimes disturb history: it is hard to date inscriptions, to distinguish authentic finds from ancient similes &c. The problem is again about the lack of accepted Arrows of Time in sociology.
Now, minimal historical theories do not like Rinascimenti, and indeed, if we get the habit to like them, we may extend the past without limit. Theory 2) of Illig eliminates the "Karoling Renaissance", as later falsification. I am not an architect, so I only state the alternative, will not argue about.
In Orthodox Chronology architecture first went up in Classical Antiquity; with the big communal project of the Roman State as Pantheon, Colosseum, Hagia Sophia, &c. Then it declined because of the breakdown of the Empire in the West, and with the feudalisation of Western society. Cities become secondary, power was at countryside. Lot of tricks became forgot or ignored. Then came Charlemagne, who revived (temporarily) the central power, with his power he could start again big projects and specialists congregated around him. After his reign the group of experts decayed away, so again the used technical level went down and some 150 more years were needed to climb back.
This story is without a priori self-contradiction, so it shows that either average or top technical level of a society is not an Arrow of Time. However the Devil is in the details. Illig claims that the Aachen Chapel cannot be earlier than XIth century; this question belongs to History of Art.
THE CHRONOLOGY OF BABYLON IN FOMENKO'S NEW CHRONOLOGY
As far as I see, Babylonian chronology is not too much elaborated in Ref. ; a few pages contain all the events older in Orthodox Chronology than the Ptolemaic Kings of Alexandria. Since the book considers Egyptian pharaohs rather XIVth century AD, and note that some part of Cairo is/was called Babylon, one gets the idea that in New Chronology some part of the Babylonian documents are falsified but some other part may come from, say, XIVth century AD, or near. Indeed, independent reports exist for a place in recent Cairo called Fortress of Babylon. Clearly, detailed Babylonian chronology in New Chronology will come later.
It seems that New Chronology accepts in first approximation Western European records about contemporary history from 1300 AD upwards. The first such scientific report about ruins of Babylon and cuneiform writing comes from Piero della Valle in the beginning of XVIIth century, so anyway, even in New Chronology Babylonian Kings must be earlier at least by centuries. However this is not a serious constraint.
THE CHRONOLOGY OF BABYLON IN ILLIG'S "PHANTOM TIME" SCENARIO
Babylonian history is too old to have direct connecton with Charlemagne, so let us first briefly discuss "Phantom Time" in itself. First, I note that there is an astronomical Arrow of Time in this case, maybe there is another, architectural, and there may or may not be others, from pure History, Ethnology and such.
Precession is cyclic, but with a long cycle time, so the process is unidirectional between Classical Antiquity and present. Now we know where is the vernal equinox point now (at the boundary of Pisces and Aquarius). Hipparchus put it to the boundary of Aries and Pisces. Hence, if the boundaries of the asterisms meant the same then and now, one can calculate the necessary time with the present angular velocity of the precession. Astronomers repeatedly report the performation of this check, with the result that 297 years cannot be excised. I refer here only . Leaving the details for a complete work, I list only the problems, together with the ways of handling them.
With the present angular velocity the full precessional circle would take 25,700 years, while Ptolemy measured 36,000 years. This would not support the constancy of the angular velocity. Moreover, there is an obscure date  suggesting that in Mesopotamia the cycle time was measured as 43,200 years (12 shars). However theory does not support such big changes, and "round numbers" can be expected. Both old data are round in the sexagesimal system. Also, remember that Babylonians seem to have overestimated past ages by some 70 %.
Borders of asterisms may have changed. However Hipparchus gives the distance between the vernal equinox point and Spica, and it is believed that that observation happened in 126 BC. From the present distance and precession velocity again we can get a time between 126 BC and present.
Spica has also moved. But that we can take into account, true, only with the present proper motion of Spica.
And so on. For the present goal it is enough to conclude that an Arrow of Time is present and we may utilize it.
However there is another. Illig argues against the Aachen Palace Chapel to be from bw. 614 & 911 (in Orthodox Chronology), because the architecture shows solutions unknown yet in 911. In principle discoveries also establish an Arrow of Time, because the new ones are often based on the older ones. However rediscoveries do sometimes happen. Since I am not an architect, I am not the proper person to settle this point.
Even if this Arrow of Time is good, Charlemagne may have existed if the Aachen Chapel was built by somebody later and then attributed to Charlemagne. I do not know the probability of this. Or, consider a scenario. (I do not guarantee the details.) 1) Charlemagne builds a modest chapel in Aachen. 2) Under his weak successors Aachen declines. 3) When Otto III (or if needs be, another Emperor later) revives Imperial Power, he needs symbols. He wants to restore the Imperial Building but it turns out to be in utter ruins. To avoid scandals, he orders complete rebuilding, of course in "best style", but tells that it was only a minor restauration. Outside Aachen nobody can check this. 4) Later successors of course believe that they see the original Chapel. Illig guesses that the chapel was built c. 1050.
Theory 1 of Fomenko eliminates all Rinascimenti, so it is indeed a minimal theory. Namely, Karolings are falsifications/clones, for the older ones see the next Chapter, and the Italian Rinascimento, while real, is not a Rinascimento: the "reborn" Past did not exist.
Societies do change, and sometimes the changes are unidirectional. Sometimes they are not.
Theory 2 would eliminate one Avar dynasty (the post-Baianic one) from the Carpathian Basin, plus the whole Late Avar time. What is more, it would make a "smooth" connection between sons of Khagan Baian and direct descendants of Duke Árpád, the Conqueror. (In Orthodox Chronology Duke Árpád rules bw. 895 & 907, all Phantom Time in Theory 2, so excised.) Now Hungarian archaeology observes 3 different styles of steppe people between Huns and Magyars, which, tentatively, are attributed to Original Avars, Avars of post-Baianic times and Late Avars (who were probably not Avars at all but Onogurs and may have arrived simultaneously with the Danube Bulgarians. I do not know if the differences between the "3 Avar groups" are unidirectional or not. If they are then we have an Arrow of Time for Avar finds, and then the said time cannot be excised.
However this question is not trivial from purely historical point of view. Namely, a Hungarian prestige chronicle, the Illustrated Vienna Chronicle, made in the Hungarian Royal Court, and probably checked by the Royal Chancellery, puts the Conquest of Duke Árpád to 677, instead of the usual 896 . The chronicle is Orthodox Chronology, the Pope and Eastern Emperor are the expected persons for year 677, but Duke Árpád is translocated by 219 years in Illig's Phantom Time.
And now: what happens with Babylonian chronology if Theory 2 is true? Assume that the methods used in Babylonian chronology are in themselves correct. Now, as we shall see in the next Chapter, Babylonian chronology roughly uses a combination of contemporary records and eclipse datings. Now, excising 297 phantom years with phantom Late Merowings and all Carolings, celestial mechanics happens in real time, so we should go first backward with 297 years, and then look for eclipses in neighbouring years. This has not been done so far. In first approximation, anyway, Fall of Babylon should go back (according to Gurzadyan) near to 1796 BC. However, not being Arrow of Time in eclipses, surely we could find other eclipses too, nearer to 1499 (Gurzadyan) or 1595 (Middle Chronology.)
THE LOWERMOST CHRONOLOGY OF GURZADYAN AND SOME HISTORICAL CONSEQUENCES
Let us recapitulate the sketch of Babylonian chronology. Babylonians and their precedessors were people being fanatic to make records on baked brick tablets which can survive millenia.
For the oldest times we have . It starts before the Flood (anything that may have been), and goes into the times of the Isin I dynasty. There are two problems. First, the beginning of the list gives extremely long ruling periods; this can be handled , but for our present goal the problem will not arise. Second, the scribes recorded parallel dynasties (in different cities) in sequence. However contemporary records sometimes inform us that two kings separated on the King List by many names warred so they must have been parallel contemporaries.
It is enough now to go back until the Ur III dynasty, because dating is done by King Shulgi's lunar eclipse in his 47th year. In Orthodox Chronology it is 2050; as we told, Gurzadyan recalculated it to 1954. Anyway, from Shulgi's eclipse to Fall of Ur it is 44 years.
Now, the first King of Isin, Ishbí-Erra started as a rebel against Ibbí-sín, last King of Ur, so there are a few parallel years. Since some royal correspondence of Ur is extant, we explicitly know that in Ibbí-Sín’s 9th year Isbí-Erra was still his officer, while in the 19th, as ensi of Isin, he was open enemy of Ur. Experts tell that he started with the independence in the 13th year. Isin I is 223 years total , so its end is 254 years after Shulgi's eclipse.
Here we may stop for a moment. First, most versions  does not contain the last Isin I king, Damiq-Ilishu, so it seems that that some bricks were compiled 23 years before the end of Isin I; or that there was something anomalous about the end of the Isin I dynasty. Second,  disproves 2 natural guesses about Arrows of Time in Sumerian history.
First, one might expect that early kings are considered supernatural, but later comes History. In Sumerian-Akkadian texts there is a God determinative. Now, at the beginning of the List there are indeed a few God-determinatives; the last at Gilgamesh, in the XXVIIth century. But God-determinatives reappear later in the Ur III dynasty, just with Shulgi.
Second, one may expect a switch from Sumerian names to Shemitic, parallelly with the shrinking of Sumerian population. Indeed, the last king of Ur III has Shemitic name, and Isin I starts already with Shemitic names; but later Sumerian names reappear.
So in Orthodox Chronology, where Shulgi's eclipse is 2050, the end of Isin I must be cca. 1794. Now comes the first problem. We have a list about the Larsa dynasty, and it is easy to see that it is parallel with Isin I. But we have the king list of the Babylon I dynasty, it is partially parallel with both Isin I and Larsa, but it may have started in any time.
Fortunately Hammurabi of Babylon occupied the whole Southern Mesopotamia, and his reign is well documented. His royal year-names report the occupation of Isin in his 7th year, and victory over King Rim-Sin (of Larsa) in the 31st. Because of the end-Isin I anomalies there is a few year uncertainty, but essentially the 6th year of Hammurabi depends only on the dating of Sulgi’s Eclipse; and the Larsa list checks it. We can fix that Rim-Sin's 60th year was Hammurabi's 30th (because the 31st year was already named about Victory on Larsa), and then, being all periods in Babylon I known, we get that
Babylon I total = 299 years
Hammurabi's 30th = Babylon I's 132nd
so if Shulgi's 47th is 2050, then
Babylon I starts (Sumuabum): 1894
Babylon I ends (Samsuditana): 1595
What is strange, there is just no overlap between Hammurabi and Dámiq-ilíshú, last king of Isin I, although 6 years should be. But it is possible that there was a very last Isin king who did not belong to the old dynasty, and, as enemy of Hammurabi, later became ignored. Remember, there is a problem about the end of Isin I.
The datum 1595 depends only on the dating of Shulgi's eclipse, and this is directly the Middle Chronology. If Hammurabi's 30th is Rim-Sin's 60th, there is no alternative until Shulgi's Eclipse is 2050.
But the end of Samsuditana is the Fall of Babylon, since Murshilis I of Hatti ended Samsuditana and Babylon I. The city became empty for a time. Of course, if Shulgi's Eclipse is 1954, then the Fall of Babylon is 1499. The complications come afterwards. The story continues on 3 lineages: one direct and 2 indirect ones. In physics we are familiar with the fact that one cannot modify a law or an observational datum without many consequences. We shall see the same in cuneiform studies.
Some times later Babylon is again a capitol, and the country is ruled by a Kasshú dynasty. The Kasshús were horse-charioteers, but not Indo-Europeans. According to King Lists, the dynasty ruled 576 years, but that 576 years must have started before the Fall of Babylon. Namely, the first Kasshú king in Babylon was Agum II, while the 2nd King of the dynasty was Agum I. Since 8 names are unreadable, some freedom exists to locate Agum II in time. However the 16th Kadashmanharbe was contemporary to Amenhotep III of Egypt, while the 19th Burnaburiash II to Akhenaton. Since in addition we know all ruling periods from Burnaburiash II, obviously the end of the dynasty is 1155 (and this datum depends primarily on Egyptology), so the beginning is 1731. Since this is after the well-documented Hammurabi, there is no problem in Middle Chronology. However in Gurzadyan's Lowermost Chronology Hammurabi rules bw. 1696 and 1654 , and then it is strange that none of his extant inscriptions mention Kasshús, including the year-names and his Law Stele.
The first roundabout connection is via Assyria. It is generally accepted that King Shamshi-Adad I was "older contemporary" of Hammurabi. One piece of information is that somebody in the 10th year of Hammurabi made an oath to "God Marduk, Samshi-Adad & Hammurabi", other is the Mari archives preserving some critical correspondences. So Samshi-Adad still lived about the 10th year of Hammurabi’; and from the year names it seems that Hammurabi took Mari in his 32nd year. Instead of further argumentation, I cite here , telling that Hammurabi ascended the throne after Shamshi-Adad, but still in his life. You can find more details in Zimri-Lim’s story. According to this, in the Middle Chronology Shamshi-Adad’s son Ishmé-Dagan I dies in 1741. Then comes 10 undated kings of whom we, however, know that Asshur-dugul ruled 6 years.
Then comes Bélu-Báni. From him to the end of Asshur-shadduni we know that 227 years lasted. Then comes 2 kings without readable years, an uninterrupted sequence of 297 years, again 2 kings of unknown lengths, and then an uninterrupted 369 years until the accepted solar eclipse in 763. So Bélu-báni's first year is (1662+x), where x is the total of 13 kings.
Now in Middle Chronology, since Ishmé-dagan dies in 1741, x=79 years, which, for 13 kings, is a convenient 6.1 year/king. However bringing Hammurabi nearer to present by 96 years (the Lowermost Chronology) Shamshi-Adad (the older contemporary) also must come nearer, and then we have x=-17 years for the 13 kings! By other words there does not remain time even for the excellently documented Assyrian kings. For the dating see  and , and further references therein.
Observe that until Samsuditana the chronology is fixed in the past by Shulgi's Eclipse, but from Bélu-báni the Assyrian sequence is fixed in the future, by the solar eclipse in 763. There is no big matter to move a lunar eclipse in the very deep past, but it is much more serious to move a late solar eclipse.
The second roundabout connection goes via the Hittite Kings. While they are not so well documented, even they do not like Lowermost Chronology. Namely, victorious Murshilis I is killed a few years (say 5) after the Fall of Babylon, while Shuppiluliumas I is contemporary of Tut-ankh-Amon (and sends his son to the widow, but the Prince dies). Now Egyptian chronology is independent of Shulgi's Eclipse, so we may accept that Shuppiluliumas starts in 1357. Between Murshilis and Shuppiluliumas the lists generally fill in cca. 13 kings. (See e.g. .)
Now in Middle Chronology for this 13 kings we have 233 years. However in the Lowermost Chronology only 137 years remain. An average of 10.5 years/king is convenient in itself; but observe that in this interval there is first the change to the New Empire, and then 3 great kings, Tudhaliyas, Arnuwandas and Hattushilis II.
So, while the Lowermost Chronology is convenient for the restoration of Babylon (only 3 years in utter ruins) and for the evolution of pottery styles, it is bad for the Kasshú chronology, inconvenient for the Hittite one, and rather impossible for the Assyrian Kings.
NE SUTOR ULTRA CREPIDAM
That is: cobbler, do not go behind sandals. This is the usual argument against Illig: that he is not really a historian but a historian of art; and that his arguments against Charlemagne are only about styles of architecture & so. However the original motivation about excising a century from Babylonian history was a difficulty about too long history of pottery!
Of course, it is not important what was the original idea if the eclipse could not happen at any other date than 1954. However look, what happened. Decades ago somebody calculated 2050. But in that time the lunar equations did not contain tidal friction, while they did contain empirical corrections.
Now it contains the tidal friction in a roundabout way (being impossible to calculate from first principles), but it seems that there is still something missing. With a constant tidal friction the Delta-T curve should be a parabola, and from cca. 1300 AD until present it is more or less a parabola; but it does not follow the "empirical" curve (meaning that the curve obtained with Orthodox Chronology, Delta-T calculated from eclipses). The deviation is cca. 2 hours in Plutarch's time, and cca. 8 hours in Shulgi's one.
Now, Plutarch describes a solar eclipse, but too soon, cca. 2 hours earlier than the calculations would like it . Of course, it is possible that Plutarch remembered incorrectly or he simply imagined an eclipse; but the two deviations roughly agree. Also, with an 8 hours shift just the 2050 eclipse will start above horizon (the Moon going up "too early").
The whole problem should be well known since 1982, when Stephenson published an article in Scientific American . He calculated back a total solar eclipse observed on April 15, in Orthodox Chronology 136 BC. First he calculated the eclipse without tidal friction. The totality strip at the latitude of Babylon would have crossed Morocco, some 47° West of the location where indeed the total eclipse was observed.
That cannot be true. So he calculated now with the recently observable tidal friction; shorelines cannot have changed too much since 136 BC. Now the totality went too East by some 23°.
Now this leaves a multiplicity of possibilities. With the 2/3 of the present tidal friction the April 15 eclipse would have been total in Babylon, but nobody ever observed this friction value.
Also: if there were no tidal friction at all until the VIth century AD, and then it switched to the present value, then everything is OK about totality in Babylon in 136 BC; but still we do not know why Earth is switching to and fro, and it is rather impossible not to have tidal friction.
Stephenson tells  that a mere 1.2 m of decrease of sea level in 2500 years could cause sufficient speed up of the rotation. This is true, if that water has vanished. If, however, has gone into atmosphere, the rotation has slowed down. At this moment it is better to remain with the statement that our postdictions about eclipses before Middle Ages are uncertain.
Also, it is possible that there is a problem with chronology. Then anything may happen, but observe that if we are looking for a year when the totality line with the present friction crossed Babylon, then an unexpected year may have obtained, and this may turn into Fomenkoism. If, moreover, we assume that the time between us and 136 BC is not 2138 years but less (for more moderate slowdown) then it is excised time a la Illig, albeit not necessarily 297 years.
There is still no easy way to avoid serious troubles. For any (still unknown) reason before the Early Middle Ages we cannot simulate observed eclipses. But we must have known this since 1981, publication of Ref. .
While reasons are unknown, it is better to remain with historical dating before 1300. If not, we may run into historical difficulties, as demonstrated here.
The search for the source of the discrepancy would deserve careful collaboration of people in celestial mechanics & history.
APPENDIX: CHARLEMAGNE AS SEEN FROM THE CARPATHIAN BASIN
Hungary is the inheritor of the Avars. They lived here, in the Carpathian Basin, for more than 200 years, went out of history (details obscure), and we excavate their material traces. Hungarian mainstream historians are orthodox for Chronology; but they are Hungarian.
Charlemagne had his historians, mainly younger contemporaries; but of course Theory 2 regards them as falsifications. However one history starts well before 614 ("the Phantom Times"), and with continuators goes up to 768. That is the Codex Fredegarius. So let us see first Fredegarius. He is the Historian of the Dark Ages. He knows it, and, in the Prologue, writes modestly: "Mundus iam senescit, ideoque prudentiae acumen in nobis tepescit, nec quisquam potest huius temporis, nec presumit oratoribus praecedentibus esse consimilis. Ego tamen, ut rusticitas et extremitas sensus mei valuit, studiosissime de hisdem libris, quantum plus potui, aptare praesumpsi."  No comment; I think, he is right. A Hungarian expert of Fench linguistic history tells that Fredegarius is the nadir of Latinitas, and sometimes his grammar is so special that one cannot know what he told. Indeed, he wrote Latin, but a Latin without norms, local and intuitive.
Fredegarius starts in 583. Avars are already in the Carpathian Basin, but they are mostly ignored. He writes something about them in connection with the Frankish (?) merchant Samo, who maybe allied with some Slavs against Avars; all our Slavic neighbours are looking for his traces for more than a century but the search is still unsuccessful. Maybe because of the obscure text. Then he records the war of Avars and Persians against Byzance in 626. We know that just after this the dynasty of Khagan Baian died out, c. in 630; nothing such in Fredegarius. But in 630 he records that some Bulgarians entered the Basin, then had a conflict with the Avars, some 9,000 Bulgarians fled to King Dagobert of the Franks, they settled down in Bavaria, but the Bavarians killed them.
Mainstream Hungarian historians guess a temporal transposition. They tell that Bulgarians arrived at the Lower Danube in 681, so the story belongs to that period, half a century later. If this is true, we do not have the original Fredegarius.
In 641 Fredegarius' own (?) text ends, but anonymous continuators go up until 768. No more mention about Avars, although we do know from excavations that Avaria is reorganised c. 680. New population arrives from the general direction of the Caucasus (Bulgarians?), but the Codex Fredegarius does not detect it. Avaria's Western border is stationarily the River Enns, as we know from excavations (and also from folk tales: Óperencia, i.e. Ober Enns is the Fairyland of Extreme West in Hungary).
The Annales Regni Francorum (from 741 to 829) do write about Avars; but now let us see te Hungarian historian I. Bóna . He is mainstream historian.
As for beginning he states that historians of the Frank Empire, when the Empire had solidified, wrote histories justifying the Empire and making it nice. Now let us go to 788. In that year Tassilo, Dux of Bavaria and Desiderius, King of Langobards, revolted against Charlemagne. They lost. But Bóna detects something. The texts tell that the Avars sent troops to help the rebels, the Franks gave battle East of the Enns and won. Now, the Enns had been the border, and in 791 still was the border; so the story is impossible. His guess is that the Franks attacked and lost. Not a big lie.
Anyway, in September 791 Charlemagne attacks. In the Frankish texts he wins. However...
In the middle of September the great host starts in two column, on the two sides of the Danube. They find Avar forces near Vienna, at Zeiselmauer. Of course the Franks won and the Avars fled. Except that Sindbert, Bishop of Regensburg dies on 29 Sept. Hungarian traditions do know about the Zeiselmauer battle (under the name Cezumaur), of course as if the foreigners lost. However surely the Frank host continued the advance to East. According to the Frank sources Charlemagne marced to the confluence of Danube and Raab; this is the present city of Gyôr. The Hungarian historian tells that it was impossible to detect exactly, which water is which, and the Frank host stopped rather at Gönyü. That is an interesting place: the confluence of Little and Old Danubes. Namely there lots of branches of the Danube exist (and also those of Raab). And then he could see the other column on the northern shore; but could not cross. And no enemy anywhere. (The usual nomadic warfare: the Western and Eastern European readers should think about Napoleon vs. Kutuzov.)
Charlemagne waits a few days, and then starts withdrawing. He is taking "innumerable PoW's and treasure"; but without details. But on 23 Oct. dies Angilramm, Archbishop of Metz, the priest of the Aachen Palace Chapel, and on 8 Nov. Wiomadus, Bishop of Trier. On the last day of the campaign, probably near to the border. Certainly the Avars continuously attacked the withdrawing enemy. Charlemagne crosses the border, thanks God for the "great victory" and dissolves the army. This cannot have been a victory; and still, this is the official Imperial history.
The Saxons revolt in the next year, 792, and in 793 they kill out the troops of Theoderich, Dux of Frisia, going just against the Avars. It definitely was not a Frank victory.
In 796, indeed, the Franks subjugated Avaria. Not Charlemagne, to be sure, but Eirik, Dux of Friuli. We do not know the details, because the Annales Regni Francorum does not give a coherent text. But the text, plus excavations, suggest, that the Khagan and the Iugurrus started an internecine war, and the Tudun, the Lord of Westmarch, did notwant to take sides. Maybe he invited Eirik. The West was partially Christian; at least excavations find cross motifs in graves. After a few years the historians can write that 791 was a victory; who can check anymore.
This is Orthodox Chronology and History. In the Orthodox paradigm I note that in 788 Bavarians and Avars were allies against Charlemagne and Heribert Illig, writing a Charlemagne-free history, is Bavarian. I wonder how the story sounds in the Illig paradigm.
 A. T. Fomenko: Celestial Mechanics 25, 33 (1981)
 G. V. Nosovskiy & A. T. Fomenko: Imperiya. Faktorial, Moscow, 1995
 B. Lukács: http://www.rmki.kfki.hu/~lukacs/FOMENKO1.htm
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 H. Illig: Das erfundene Mittelalter - Die grösste Zeitfälschung der Geschichte. Econ, Mönchen, 1998
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 S. Smith: Alalah and Chronology. London, 1940
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 The text of Codex Fredegarius can be found in Monumenta Germanicarum Scriptorum r. Merovingarum, Vol. 2, p. 127 sqq, but I read it on Internet: http://hbar.phys.msu.su/gorm/chrons/fredegar.htm.
 I. Bóna: Nagy Károly nyomdokain. In: Évezredek hétköznapjai, ed. V. Szombathy, Panoráma, Budapest, 1973, p. 141
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