The paper examines the ancient Khorezmian Koi-Krylgan-kala complex from the point of view of archaeoastronomy. Previously, it was assumed that the main structure of the complex is oriented along the azimuth of 69°, which is associated with the direction of sunrise in the middle of the time interval between the spring equinox and the summer solstice and / or in the direction of the sunrise point of Fomalhaut (a Southern Fish).

Based on a comparison of the archaeological plans of the Khorezm expedition with high-precision satellite images from the Google Earth program, it is shown that in some cases the measured magnetic north was not recalculated to the true north or the recalculation was made incorrectly. In particular, it is revealed that the main axis of the Koi-Krylgan-kala complex is oriented along the azimuth of 80°. This result invalidates all previous conclusions.

According to historical information, the third flood of the Amu Darya was called the "flood of the star" in ancient times, and the Pleiades asterism in pre-Islamic times was called the "Star". During the beginning of the complex's operation, the heliacal sunrise of the Pleiades coincided with the moment of the third flood of the Amu Darya, and the moment of visibility of the Pleiades occurred at an azimuth of 78°-79°. Hence, we hypothesize that the main axis of the Koi-Krylgan-kala complex is oriented along the sunrise of the Pleiades, which were of particular importance in the ancient Khorezmian culture.

Key words: archeoastronomy, astronomical orientation, Koi-Krylgankala.

HISTORY OF RESEARCH OF THE KOI-KRYLGAN-KALA COMPLEX

The Koi-Krylgan-kala complex was discovered in 1938 by the Khorezmian archaeological and ethnographic expedition of the USSR Academy of Sciences under the leadership of S. P. Tolstov. The site was built between the VI and III centuries BC and was used until the IV century with a break from the II to I centuries BC. The complex is a round two-story building with a diameter of 44.5 m and a height of about 9.5 m, surrounded by a ring of fortress walls about 7 meters thick. Between the central building and the wall, there are remnants of outbuildings and residential buildings. The cultural layer contains a large number of ceramics, jewelry, weapons, cult figurines, ceramic vessels, bas-reliefs and frescoes. Probably, the complex at first was a Zoroastrian temple with the burial of Khorezmian kings.

Astronomy and Koi-Krylgan-kala. In [Vorobyova et al., 1969], the Koi-Krylgan-kala architectural complex was first studied from the point of view of the history of astronomy. The authors studied astronomically significant azimuths, which correspond to the sunrises and sunsets of the Sun and the brightest stars. Let's present the most significant results of the study.

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"...The building's (central) axis connecting the windows in rooms I and V deviates from the east-west direction by 21° (true azimuth of the east end is 69°, the west end is 159°)... " [ibid., p. 19].

"...The windows of Koi-Krylgan-kala did not allow you to observe the sunrise and sunset at the equinoxes. However, in the history of astronomy, it is known that any openings, including stairs, could serve as places for such observations. The diagonal of the staircase No. 2 of Koi-Krylgan-kala, running in an easterly direction, makes an angle a with the central axis of the building close to 21°, i.e., the angle of deviation of this axis from the east-west line. ...If we take into account the direction of the central axis of the building, then from the staircase No. 2, sunrise and sunset could be observed on the days of the spring and autumn equinoxes " [ibid., p. 21].

"...Thus, the calculations showed that the building could be oriented 1) along the azimuth of sunrise in the middle of the interval between the spring equinox and the summer solstice with the declination of the Sun δ = +15°30', which makes an angle of 90° with Fomalhaut, or in the direction of the sunrise point of Fomalhaut [a South Fish]. It can also be assumed that the building was oriented at a time when observations of both the Sun and Fomalhaut were simultaneously used for this purpose, i.e. at the moment of the heliacal sunrise of Fomalhaut" [ibid., pp. 28-29].

According to M. G. Vorobyova and co-authors, the heliacal sunrise of Fomalhaut and the moment of sunrise at azimuth 69° occurred in the IV century BC around May 4 and coincided with the beginning of the Amu Darya flood. The agriculture of ancient Khorezm was based on irrigation farming, so it was important to be able to predict the beginning of a river flood. The methodological shortcomings of the work include the fact that the authors did not investigate the issue of the Amu Darya flood. If Fomalhaut does indeed have its first morning visibility in early May, it is unclear how this event relates to the time when the river began to flood.

M. G. Vorobyova's point of view was later developed in the work of M. S. Bulatov (1978), who linked the rising of Fomalhaut with the third flood of the Amu Darya and the Ajgar holiday. He refers to the work of Y. G. Gulyamov, according to which the Amu Darya flood occurs in four stages.

Ya. G. Gulyamov wrote that since ancient times there was a flood calendar in Khorezm, in which the signs of certain changes in the river regime were accurately established. The first flood on this calendar was called " flood of green reeds "(kok reeds tashuvi). It begins at the time when the first, young reeds grow on islands and lakes. This time corresponds to the twentieth of March. The second flood is called the "white fish tip" (ak-balyk-tashuvi) and occurs in mid-April, since at this time the movement of white fish from the Aral Sea up the Amu Darya begins. The third - "star tip" (Yulduz-tashuvi) - falls in mid-May; the fourth - "flood of forty days of heat" (kyrk-chilgav tashuvi) - begins in the second half of June and ends in early August. The duration is 40 days (Gulyamov, 1957, p. 237).

The name of the third flood directly indicates that it is associated with a certain star. According to the calculations of I. N. Veselovsky, Fomalhaut rises on May 4, and the flood occurs in mid-May. The difference between these events is about one and a half weeks, therefore, Fomalhaut may be a harbinger of the Amu Darya flood. We do not have any direct arguments that confirm that the third flood is connected with Fomalhaut. However, M. S. Bulatov's hypothesis supports the study [Vorobyova et al., 1969] with independent historical arguments.

Let us consider the remaining hypotheses of M. S. Bulatov, which combine the use of the Koi-Krylgan-kala complex within the cultural traditions of that era. First, the author connects the sunrise of Fomalhaut and the beginning of the third flood with the Ajgar holiday, which, in his opinion, corresponds to the beginning of agricultural work.

From the reports of Biruni about the calendar reform carried out in 959 by the penultimate representative of the ancient Khwarezmshah dynasty, Ahmed ibn Muhammad, it is known,

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that by this time the time of the Ajgar festival, dedicated to the beginning of agricultural work, was completely lost. The date of this holiday could not be restored by medieval scholars, including Biruni himself [Bulatov, 1978, p. 50].

It seems to follow from the above quotation that the time of Ajgar Biruni celebration was unknown. In fact, the situation is different. Biruni states that the Ajghar festival falls in the middle of summer. In addition, he writes that many agricultural works were counted from Ajgar for dozens of days in advance. However, the problem associated with Ajgar was that due to the difference in the length of the year according to the Khorezm calendar from the tropical year, an error appears that accumulates over time. As a result, the civil calendar no longer corresponds to weather events. To eliminate this discrepancy, the calendar was reformed.

"And Khorezmshah said: the case was thrown into disarray and forgotten. The people rely on these days and determine from them the middle of the four seasons, thinking that they are stable and do not change [their place; they believe] that Ajgar is the middle of summer, and Nimhab is the middle of winter, and at certain intervals after these days [set] the times of sowing and plowing. ...Some, [for example], believe that the time to sow wheat comes 6-10 days after Ajghar. Others say more, while others say less" [Biruni, 1957, p. 262].

"And the khwarezmshah was told that there is no more valid method for this than to coincide the beginning of the Khwarezmian months with certain days of the months of the Rum and Syrians, as al-Mu'tadid did, and to supplement the months in their image. And [the Khwarezmians] did this in 1270 [959 A.D.] A.D. Alexander and agreed that the first day of Nausarji would be on the third day of the Syrian Nisan, so that Ajgar would always fall in the middle of Tammuz. In accordance with this, the time of agricultural work was set... "[ibid., p. 263].

Thus, the Ajgar festival in the Middle Ages fell in the middle of summer. The claim that the time of Ajghar celebration was lost contradicts Biruni's testimony. Therefore, an attempt to link Ajgar to the beginning or middle of May is illegal.

The second assumption of M. S. Bulatov relates to the dating of the construction of the Koi-Krylgan-kala complex by means of a solar eclipse. During the construction period, Khorezm was dominated by Zoroastrianism, whose adherents worshipped fire and light. Therefore, the author thinks that the entire complex combined the functions of the temple of Mithras, treasury and observatory. Referring to the canon of eclipses by T. Oppolzer, he suggested that the impetus for the construction of the structure was the total solar eclipse of February 29, 356 BC. e. Note that in the canon of Oppolzer, the dates of eclipses are given in the astronomical count of years, which for convenience of calculations contains the zero year. In chronology, year zero is not used, so the year zero corresponds to the first year B.C. according to the historical year count. Therefore, the eclipse occurred in 357 BC.

According to our calculation under the EmapWin program, this eclipse was a private one in Khorezm. The maximum phase of the eclipse at the site of Koi-Krylgan-kala was 0.86. In total, from 450 to 250 BC, about two dozen eclipses with a phase greater than 0.80 could be observed in Khorezm. This means that eclipses with high phases occur quite often, so the eclipse of 357 BC was not remarkable. The eclipses of May 31, 436 BC and April 2, 303 BC were visible as total eclipses in the territory of Khorezm. Moreover, the first of the eclipses had a phase at the site of Koi-Krylgan-kala of 0.99, i.e. it was complete in its vicinity.

The hypothesis that the construction of the Koi-Krylgan-kala complex was caused by the observation of a particular eclipse should have justification, but at present they are not available.

The third hypothesis of an astronomical nature, which is presented by M. S. Bulatov, is associated with the use of the round shape of the number 56 in the construction of structures. &

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With Koi-Krylgan-kala, he examined two Bactrian structures Dashly-3 (XVIII-XV centuries BC) and Kutlug-Tepe (V century BC). On each structure, the author distinguishes the number 56 (or a fractional number close to it) in a different way and connects it with the prediction of eclipses.

"This brings us to the question of the probability of priests using saros with a cycle 19+19+18 years to determine the time of solar and lunar eclipses" [Bulatov, 1978, p. 46].

Saros is a period equal to the interval of 223 synodic months or 6585 days, which is 18 years and 10.33 (11.33) days, depending on the year (leap or non-leap). If you know the date of one eclipse, then you can accurately calculate the date of another eclipse by adding saros to this date. Since saros is not an integer, the "extra" 0.333 days give an offset of the eclipse time by 0. 333x24=8 hours. As a result, the Moon or Sun may be below the horizon and the eclipse will be invisible in this geographical location. If saros is tripled, we get the integer number of days 19756 days = 54 years and 32 days. The tripled saros is called exeligmos. This cycle provides a very high probability of eclipse prediction, even for solar eclipses where phase detection is required. The lunar eclipse is predicted with the help of exceligmosis almost one hundred percent. A quasiperiod of 56 years is not suitable for predicting eclipses.

M. S. Bulatov appeals to the work of J. R. R. Tolkien. Hawkins and J. White's "Unraveling the Stonehenge Mystery" (Hawkins and White, 1984), in which an algorithm for predicting eclipses using holes by J. R. R. Tolkien is proposed. Aubrey. The number of holes is 56, and under certain rules of shifting, this algorithm allows you to predict an eclipse if at the initial moment of time the balls are laid out in the desired holes. But there is no evidence that this algorithm was actually used in ancient times. We have no direct or indirect evidence that the Stonehenge builders were able to predict eclipses.

M. S. Bulatov tries the concept of Stonehenge on Central Asia, which raises even more questions, since there are many written sources on this region. It is known that Babylonian astronomers of the 1st millennium BC developed methods for predicting lunar eclipses. According to the logic of M. S. Bulatov, it turns out that there was an ancient algorithm for predicting an eclipse, which was not mentioned in any written source. Then the knowledge about it was lost, but the sacred number 56 remained, which can be traced in architectural traditions.

Thus, the astronomical concept of the Koi-Krylgan-kala complex proposed by M. S. Bulatov is untenable.

RESEARCH ON THE ACCURACY OF LRHEOLOEIC PLANS

The above ideas about the astronomical use of the Koi-Krylgan-kala structure are based on the analysis of a single selected azimuth. According to the authors (Vorob'ev et al., 1969), this azimuth is 69°, but there are no comments on how it was obtained. Most likely, the authors took the archaeological plan of the structure and used the tools of that time-a ruler and a protractor. This is a perfectly acceptable way to determine angles, but the question of the accuracy of archaeological plans remains open.

To study the accuracy of orientation of archaeological plans of fortresses and residential structures of ancient and medieval Khorezm, obtained by the archaeological and ethnographic expedition of the USSR Academy of Sciences under the leadership of the Joint Venture. Tolstov [Tolstov, 1948 (1); Tolstov, 1948(2); Tolstov, 1953; Tolstov, 1962; Fieldwork, 1959; Fieldwork, 1960; Fieldwork, 1963(1), (2); Koi-Krylgan-kala, 1967; Priaralie, 1998], we we scanned all the existing architectural design schemes in the works.

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structures based on the correct geometric shape. Electronic image processing with modern graphics software packages allows you to scale schemes, accurately combine and transfer vectors. Using image processing, we determined the geodetic azimuths that each structure is oriented to.

The archaeological plan is a diagram that shows a contour indicating the walls of the structure and the direction of the meridian (north-south line). For each plan, you can define the angle formed by the walls of the building with the meridian line. If we have several archaeological plans of the same structure at once, we can determine the amount of change in the corresponding angle from different plans.

Using high-precision satellite photos from the Google Earth program (hereinafter - GE) allows you to independently verify the accuracy of archaeological plans. To do this, the geographical coordinates of the structure must be known with an accuracy of seconds of arc, and the monument itself must have a sufficient degree of preservation.

Method for determining azimuths based on archaeological plans. To determine the angle that the building wall forms with the direction of the meridian, we used Adobe Photoshop tools and applied the following algorithm.

1. Draw a meridian line on the original image and move it to the central area of the image.

2. Create a copy of the image in a separate layer and make it semi-transparent.

3. Use the "Rotate" tool to rotate and, if necessary, move the layer so that the wall selected on the plan coincides with the meridian line.

4. The value of the rotation angle that corresponds to the desired angle will be displayed in a separate window.

Estimation of the size of errors. Let's say that we have made an archaeological plan of a certain structure and determined the "control angle" A t, which is formed by one of the walls of the structure with the meridian line. Let us assume that this angle A0 is absolutely known to us. Let us consider all possible sources of errors that lead to the deviation Δa = A t — A 0.

The first error Δ A1 is related to the error in determining the north on the topographic plan of the area by the participants of the archaeological expedition. It is generally assumed that the accuracy of determining the azimuth using a compass is ±5° and using a bussoli ±1°. Given the duration of the expedition, it can be assumed that both instruments were used in the measurement process. However, for each specific plan, there is no information about which tool was used to measure azimuths.

The secondΔΑ2 is related to the error in determining the azimuth from a GE topographic plan or photograph. First, the walls of a building are not always perfectly straight, and, therefore, it is not always possible to draw a vector through the wall unambiguously. The same observation can be applied to photos where we determine the azimuth by the most contrasting fragments that correspond to the walls of the structure or their shadows. Partially destroyed structures cast uneven shadows, which increases the azimuth detection error. We make small mistakes when drawing the direction of the meridian and combining the contour of the wall with the meridian arrow.

The following technique was used to estimate the magnitude of the azimuth error obtained during image processing from the GE program. We determined the values of the reference azimuths independently of each other and calculated the discrepancy for each pair. From the entire set of residuals, we constructed a frequency histogram, which was approximated by the Gaussian distribution (Fig.
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Figure 1. Distribution of azimuth residuals obtained when processing the same image by different researchers.

Numerical estimates of the discrepancy show that the level of 1σ corresponds to the value σ ≈ 1.5°. In addition, there is a small taxonomy of x with ≈ 0.8°, which is most likely associated with different preferences for drawing azimuths among researchers. Taking into account both errors, we obtain an estimate of the direction determination error equal to ΔΑ 2 ≈ 1.7°.

Consider the impact of both errors. The resulting error will be:

Then, using the archaeological plan, we can determine the direction with an error of ΔA min ≈ 2.0° when using the theodolite with a bussole, and ΔΑ Μax ≈ 5.3° when using a compass. If we compare two archaeological plans that are drawn up using a single measuring tool, the total error increases several times and amounts to ΔA min ≈ 2.8° and Δ Α Μax ≈ 7.5°, respectively. If the plans were made using different instruments, i.e. one using a compass and the other using a theodolite, the error will be Δ Α ≈ 5.7°.

For a confidence interval of 2σ, all the above estimates of values are doubled.

Analysis of azimuth distribution. For further analysis, we selected only those structures for which both the GE image and the archaeological plan are available at the same time (Appendix 1). Using the algorithm described above, the "control" azimuth was determined, visible to the walls of the structure. The western and/or eastern walls of the structure were usually used as the reference azimuth. As a result, we obtained two estimates of the same azimuth AGE (based on the GE image) and Amap (based on the archaeological plan) and determined their discrepancy Δ Α = AGE- Amap(Table 1).

In some cases, there are several archaeological plans for the same site (for example, Chirik - Rabat-kala, Toprak-kala). For each archaeological plan, the value of the discrepancy was determined independently. If there are two structures on the same archaeological plan at once (for example, Ayaz-kala-1 and Ayaz-kala-3), the average value of the discrepancy was determined. In Fig. 2 shows the frequency histogram of the residuals.

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Table 1

№

Construction site

AGE

Aman

ΔA

A source

1

Angka-Kala

45

35

10

Tolstoe 1948(1), p. 50

2

Ayaz-kala-1

-12

0

-12

Tolstoe 1948(1), p. 40

Ayaz-kala-3

0

18

-18

Tolstoe 1948(1), p. 40

Ayaz-kala-3

0

9

-9

Priaralie 1998, p. 117

3

Babish Mullah-1

3

-12

15

Polsv. Is. 1963, p. 59

4

Bazaar-kala

23

22

1

Tolstov 1948(1), p. 47

5

B. Guldursun (East) wall)

25

23

2

Tolstoe 1948(2), p. 95

B. Guldursun (zap. wall)

34

29

5

Tolstov 1948(2), p. 95

6

Janbas-kala

64

56

8

Tolstov 1948(1), p. 29

7

Duman-kala

15

12

3

Tolstov 1948(1), p. 57

8

Koi-Krylgan-kala

80

73

7

Tolstov 1955, p. 202

80

76

4

Vorobyova 1969, p. 1

9

Kurgashin-Kala

50

51

1

Tolstov 1948(1), p. 46

10

Pil kala (citadel)

0

0

0

Tolstov 1948 (1), p. 67

11

Toprak-kala

70

70

0

Tolstov 1948(2), p. 49

70

60

10

Tolstov 1962, p. 208

70

66

4

Priaralie 1998, p. 37

12

Chirik-Rabat-Kala

57

51

6

Tolstov 1948(2), p. 98

(citadel)

57

56

1

Polev. Is. 1960, p. 24

57

41

16

Tolstov 1962, p. 141

13

Khazarasp

0

-5

5

Pol. Is. 1963(1), p. 118

14

Eres-kala

0

0

0

Tolstov 1948(1), p. 58

15

Yakke-parsan

10

-1

11

Pol. Is. 1963(1), p. 4

2. Frequency histogram of residuals Δ Α = A CE-A map.

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The maximum of the frequency histogram f(0) = 6 corresponds to the situation when the azimuths determined from GE images and archaeological plans coincide within the half-width of the channel Δa = / A GE - A map / ≤ 1.25°. The residuals that fall in the ranges Δa ≤ 2σ min and Δa ≤ 2σ Max can be explained by adding up the errors discussed earlier. In three cases, the value of the residuals reaches Δ A ≈ 15°, which can no longer be explained within the accepted error model.

The shape of the histogram has a pronounced asymmetric shape with a mathematical expectation of M(f) = 3.8. 2 residuals fall into the negative range of values, while 15 residuals fall into the positive range. The expected event would be to obtain a symmetric histogram whose shape is close to the Gaussian distribution with the mathematical expectation M(f) ≈ 0. Thus, the nature of the resulting distribution of residuals indicates the presence of an unaccounted error, which is systematic in nature.

It is most likely that the source of this error is the need to recalculate the magnetic north to the true north. The value of the magnetic declination of Khorezm for the epoch of the expedition is δt = 5°38'E. It can be assumed that in some cases the magnetic declination was not taken into account. If the magnetic declination δm is added to the azimuths of A tap, which have positive values of residuals, then the frequency distribution becomes more symmetrical. In addition, two of the three strongly deviating residuals will fall within the acceptable range of 2σ Max. However, in each particular case, we can only assume that the magnetic declination was not taken into account.

Analysis of azimuths of individual structures. Let's move on to considering structures for which there are several archaeological plans and a GE image at once. These are Chirik-Rabat-kala, Toirak-kala and Koi-Krylgan-kala.

Chirik-Rabat-Kala. According to the GE image, the western and eastern walls of the Chirik-Rabat-Kala citadel show an azimuth of GE = 57°. Measuring the same azimuth according to the plans [Tolstoe, 1948(2), p. 98] gives the azimuth A map = 51° and the value of the residual ΔA1 = 6°. The obtained value is close to the magnetic declination δt = 5.63° and the estimation error Δax ≈ 5.4° Δa ≈ δt ≈ σ Max. This makes it impossible to accurately determine the origin of this error. From a later work [Fieldwork, 1960, p. 24], the azimuth value A map = 56° and the value of the residual Δa1 = 1° follow, which corresponds with good accuracy to the direction of true north. I.e., if in the previous work there could be an error caused by the fact that the magnetic declination was not taken into account, then in the next work, it was most likely corrected. It is impossible to say this for sure, since not taking into account the magnetic declination could be compensated for by the direction of the estimation error.

Finally, from the last paper [Tolstov, 1962, p. 141], tap41° and the largest value of the residual Δa1 = 16°follow. The last result differs most significantly from all previous measurements, although the drawing of the details of this plan exactly coincides with the plan [Fieldwork, 1960]. The only difference is in the direction of north. Given the generalizing nature of the work [Tolstov, 1962], there is reason to believe that all the archaeological plans given there are the results of borrowing from previous studies. I.e., the plan [ibid., 1962] is a consequence of the plan [Fieldwork, 1960]. The error of the plan (Tolstov, 1962) can be explained in two ways. First of all, its compiler may have made an accidental blunder when redrawing. The possibility of such an error always exists, but it should not have a high probability and should be repeated frequently.

Second, the magnetic declination was not taken into account. Suppose that the azimuth Amap =41°was obtained during field studies. Taking into account the correction for magnetic declination, we obtain the azimuth A map =47° [Field studies, 1960], which differs from the true value by less than 2 σ Μαx: Δ A ≈ 10° < 2σ Max ≈ 11°.

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Toprak-kala. A similar situation is observed with the Toprak-kala monument, for which there are three archaeological plans. The azimuth calculated from [Tolstoe, 1948 (2), Fig. 49 (interstitial insert without number)] corresponds exactly to the azimuth found from the GE image AGE = Amap= 70°. From the subsequent work [Tolstov, 1962, p. 208, fig. 121], the azimuth Amap = 60°is again underestimated. The discrepancy ΔA1 = 10° can only be explained by an error of ~ 2σMax, or we must assume that the plan has a magnetic north direction. Finally, the latest paper [Priaralie, 1998, p. 37] estimates the azimuth Amap = 66°. This value corresponds equally well to the previous results within the margin of error. On the other hand, the work [ibid., 1998] is rather late, so it can be based on a plan taken from the work [Tolstov, 1962], with the correct recalculation to the true north.

Koi-Krylgan-kala. Unlike the previous structures, the Koi-Krylgan-kala structure has a circular shape. The main axis of the building is considered to be a line passing through rooms I and V [Vorobyova et al., 1969, fig. 1 (pasting without page number)] (Fig.3).

Consider the azimuth that forms a straight line drawn through the centers of these rooms, with a meridian line. GE image processing gives the azimuth AGE = 80° (Fig. 4), and according to the archaeological plans (Tolstov, 1955, p. 202; Koi-Krylgan-kala, 1967, Fig.1), we have a pair of azimuths Amap = 73° and Amap = 76°, respectively. It is most likely that the direction to magnetic north is given in the foreground, although in both cases the deviations ΔΑ fit into the stated errors.

Conclusions about the azimuths of sunrise and Fomalhaut are correct only if the building's axis forms an angle A ≈ 69°with the true meridian line.

However, according to GE data, this azimuth is equal to GE = 80°, and the difference with the estimate [Vorobyova et al., 1969] reaches Δa = 11°. In our opinion, such a large value of the discrepancy has a simple explanation. The authors considered that the archaeological plan indicated the magnetic meridian, and to bring it to the true meridian, they introduced a correction for the magnetic declination, which is = 5.63°. However, instead of adding the magnetic declination correction to the magnetic azimuth, the authors made a subtraction. Therefore, the resulting azimuth discrepancy is equal to twice the magnetic declination ΔΑ ≈ 2 δ T. On the other hand, the value of ΔΑ ≈ 2σMax allows us to explain this discrepancy in terms of measurement errors.

Statistical analysis shows that the archaeological plans of the Khorezm expedition show different meridians. Most often, the true meridian is given, which indicates the direction to the pole of the world. However, in some cases, the direction of the magnetic meridian is reported, which is shifted to the east by ≈5.5°relative to the true meridian. Using the example of the Koi-Krylgan-kala construction, it is demonstrated that sometimes the recalculation from the magnetic to the true meridian was carried out incorrectly. The reason for the error was that the magnetic declination was taken into account with the wrong sign. Possibly present in Fig. The presence of three residuals with |ΔΑ / = 15° can be explained by incorrect conversion of the plan from magnetic north to the true one.

CHECKING THE AZIMUTH A = 80°

The true azimuth that the main axis of the central structure of Koi-Krylgan-kala sees is 80°, not 69°, as previously thought. You can determine the sunrise dates that correspond to the azimuth of 80°, and which bright stars rise at this azimuth for the era of the proposed construction.

The sun passes this azimuth twice a year around April 12 and September 10. The first date coincides with the date of the second flood (belorybitsa), which, according to M. S. Bulatov, at-

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3. Plan of the drsvnshorszmi monument of the IV century BC Koi-Krylgan-kala. The corner formed by the meridian line and the central axis of the building is drawn. According to the calculation of the authors (Vorobyova et al., 1969) , the value of the marked angle is close to 69°

I went to the middle of April. The second date is located near the Ajgarminik festival, which is the predecessor of Ajgar (Biruni, 1957, p. 258). According to Biruni, in ancient times Ajghar was celebrated in autumn.

"Chiri month. The fifth day of this month is called Ajghar, which means "firewood" and "burning". In the past, this was the beginning of the period when you had to warm up by the fire because of the weather change in autumn, and in our time this day coincides with the middle of summer."

If the first month of the Khorezmian year of Nauruz fell on the summer solstice, then the fourth month of the year corresponds to the autumn equinox. Subtracting from the date

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4. GE image of the Koi-Krylgan-kala monument. The corner formed by the meridian line and the central axis of the building is drawn. This angle is close to 80°

equinoxes are 15 days old, we get to the area of the date of September 10, when Ajgarminik was celebrated. But in this case, it would be more logical to orient the structure according to the azimuth of sunrise, which corresponds to the date of Ajgar celebration.

It is most likely that the azimuth of Koi-Krylgan-kala does not reflect the solar azimuth, but the stellar azimuth. It is no coincidence that the third flood of the Amu Darya was called the flood of the star. In the concept of the author's team of M. G. Vorobyova and M. S. Bulatov, such a star was Fomalhaut, but the orientation of the structure adopted by them is erroneous. Fomalhaut actually rises a week and a half before the third tip of the river, but now it is not connected with any azimuth.

Other bright stars at azimuth A = 80° include Aldebaran (a Tai) and Procyon (a CMi). Aldebaran rises around June 9 at an azimuth of A ≈ 81°, and Procyon rises around July 23 at an azimuth of A ≈ 82°. However, these days are not connected with the Khorezm holidays known to us and do not correspond to the moment of the third flood of the Amu Darya.

Let us turn to Biruni's work "The Book of Admonition to the rudiments of the science of the Stars" (Biruni, 1973). In the section devoted to astronomy, there is a chapter "Are these fixed stars known by other names?". In it, the author talks about the old pre-Islamic names of stars.

"Third parking lot [Moon parking lot or lunar parking lot. - Auth.] - Pleiades. These are six stars gathered like a bunch of grapes. This is the Taurus hump. In the people, especially among poets, it is believed that there are seven of them, but they are wrong. The Pleiades, as separate from them, is called a Star.

The fourth parking lot is Aldebaran. It is a bright and beautiful star in the eastern eye of Taurus, and the head of Taurus is placed in the form of a bowl, facing north. Aldebaran is called following the Star, that is, behind the Pleiades" [ibid., p. 74].

Biruni twice calls the Pleiades "Star", and not in the common sense, but in the proper sense of the word. In the description of the fourth lunar parking lot, he clarifies this.

page 31
Similar information can be found in A. A. Akhmedov's comments on Ulugbek's Zij [Zij, 1994].

"The Pleiades are the daughters of Pleiona, and Ulugbek-Surayya has the 3rd Moon station. .. Muslim Surayya is a diminutive of the Arabic sarua - " wealth ", "abundance". The Arabs associated with it an abundance of rain, food, fodder and cattle offspring. It was also called Najm, i.e. "star".

Aldebaran - (from Ad-dabiran) - 4 parking lot of the Moon alpha Taurus, the Arabic name comes from "following in the wake" [for the Pleiades. - Auth.], since the Arabs believed that it is located behind the Pleiades and, together with several nearby stars, forms the Arabic letter "dal"; it is located at one end of this letter, above the right eyebrow of Taurus. It [i.e., the star Aldebaran] was called "Belonging to Najm", "First Najma" and "Eye of Taurus" " [ibid., p. 413].

It should be noted that A. A. Akhmedov is a modern author. He does not disclose the source on which his comments are based. Perhaps he is using information from the mentioned book by Biruni. But it is possible that A. A. Akhmedov knows another source. G. E. Kurtik reports the following about the Pleiades::

«MUL.MUL. Reading option: mul MUL; title entry option: MUL 2. MUL 2 (TE.TE), MUL X.MUL X (AB 2.AB 2,), MUL 4. MUL 4, UL. UL=zappu; Sumerian "Stars", Akkadian "Bristles "" [Kurtik, 2007, p. 338].

"...(5) Date intervals between the dates of heliactic sunrises: 20 days from the rising of the Stars to the rising of the Celestial Bull" (i.e. Aldebaran, author) [ibid., p. 340].
So, in ancient Mesopotamia, the Pleiades were called "Stars", Biruni reports the old Khorezmian name of the Pleiades - "Star", A. A. Akhmedov confirms it. Thus, it is highly probable that in pre-Islamic Khorezm the Pleiades were called "the Star". Therefore, the third flood of the Amu Darya, which was called the flood of the star, may be associated with the rising of the Pleiades.

In this case, we have a specific astronomical problem. It is necessary to calculate the date of the first morning visibility of the Pleiades and determine the azimuth, which corresponds to the moment of their visibility at sunrise. If the date of sunrise corresponds to the date of the third flood of the river, and the azimuth of sunrise corresponds to 80°, the astronomical orientation of the complex will be associated with the Pleiades.

However, there are several uncertainties involved. First, what is meant by the appearance of the Pleiades? The brightest of the Pleiades (n Tai) has an apparent brightness of t = 2.9 m. The observer could record the moment of appearance of the brightest star or the appearance of a ladle characteristic of the Pleiades. To observe the ladle, it is necessary to see dimmer stars with a brightness of t = 3.8 m. Secondly, there is a dependence of the date of observation on the atmospheric absorption coefficient (extinction coefficient). Because the Pleiades are made up of dim stars, they become visible higher above the horizon compared to bright planets and stars. Therefore, for the Pleiades, the dependence of the observation date on the extinction coefficient will be less.

As a result, we have four variants describing the beginning of visibility of the Pleiades. The first option corresponds to the most transparent atmosphere and visibility of the bucket; the second option corresponds to the average state of the atmosphere and visibility of the entire bucket; the third option corresponds to the clean atmosphere and visibility of the brightest star of the Pleiades; the fourth option corresponds to the average transparency of the atmosphere and visibility of the brightest star of the Pleiades. The results of calculations implemented using the model [Belokrylov et al., 2011] are presented in Table 2.

According to various calculation options, we got a date range from May 22 to June 7. As expected, the extinction coefficient has little effect on the sunrise date. Basically, the date of sunrise is determined by whether we observe the entire dipper of the Pleiades or only the brightest of the stars.

We will use the last excerpt from [Kurtik, 2007, p. 340], where it is stated that the Pleiades rise 20 days before Aldebaran. Central Asia and Mesopotamia are culturally connected, and if the Khorezmians borrowed the Sumerian name of the Pleiades, then it is reasonable to assume that the methods of observation were also borrowed. According to calculations,

page 32
Table 2

№

Extinction coefficient

Maximum visible sound value

Arc of visibility [degrees]

Date of Heliacal sunrise

Sunrise azimuth [degrees]

1

0.20

t = 3.8 m

21.5

June 5

78

2

0.25

m = 3.8m

22.5

June 7

78.5

3

0.20

t = 2.9 m

16

May 22

78

4

0.25

t = 2.9 t

17.5

May 25

78.5

Aldebaran rises on June 9 with an average transparency of the atmosphere. Subtracting 20 days from this date, we get the date of sunrise of the Pleiades-May 20. According to our calculation, with the same extinction coefficient, the Pleiades rise 5 days later.

Given the number of uncertainties associated with atmospheric models, the error of the calculation model, and the accuracy of Babylonian data and calendar translations, this correspondence is good. Thus, if you rely on the Mesopotamian tradition of observing the Pleiades, you should choose the 3rd and 4th version of the date of sunrise of the Pleiades. Thus, ancient observers recorded the sunrise of the brightest star from the Pleiades, which occurred on May 22-25 (depending on the purity of the atmosphere), a week after the beginning of the third flood of the Amu Darya.

The sunrise of the Pleiades occurs at azimuth A = 78 ° ÷79°, which corresponds with good accuracy to the orientation of the main axis of the central structure of Koi-Krylgan-kala. Hence, we can put forward the following hypothesis. The main azimuth of the Koi-Krylgan-kala complex is oriented to the azimuth of the Pleiades sunrise. Sunrise of the Pleiades occurs on the 20th of May, during the third flood of the Amu Darya. Due to the coincidence of these two events, the third flood of the Amu Darya was called the "flood of the star" (yulduztashuvi).

It should be noted that Y. G. Gulyamov connects the Yulduz-Tashuvi flood with the appearance of the Pleiades, which fully corresponds to our reconstruction:

"The third [flood. - Auth.] - "Yulduz-tashuvi" (flood of the Pleiades constellation) - falls on the middle of May. The Khwarezmians timed this flood to coincide with the appearance of the Pleiades constellation" (Gulyamov, 1957, p.237).

Analyzing the architectural composition of Koi-Krylgan-kala, M. Mammadov writes:"...the very idea of seeing religious concepts embedded in the architectural forms of buildings seems very fruitful... " [Mammadov 2003, p. 92].

In fact, it is no longer necessary to specifically prove that any religious edifice 1 is a picture of the world (a model of the universe) of its creators in its most concentrated form 2. It is important to take into account that

1 And in relation to antiquity and not only cult.

2 In this connection, the discussion concerning the use of the term var in the Avesta (Vd. 2, 25) when describing the structure built by Ai at the behest of Ahura Mazda for people, cattle, small cattle, dogs, birds, and for "burning red lights" is significant. SP. Tolstoe, based on the translations known to him, connected with it a number of quadrangular structures in the plan of Khorezm (the so - called "settlements with residential walls"-Kalaly-gyr and Kyuzsli-gyr [Tolstoe, 1948, pp. 80-81]). Later, I. M. Stcblin-Kamcnsky [Stcblin - Kamcnsky, 1995, p.307-310] came to the conclusion that the Avestan var is a circular structure consisting of three concentric circles with nine passages in the outer, six in the middle and three in the inner circle. At the same time, as an example, he cited first of all the structures discovered in Northern Afghanistan by V. I. Sarianidi. B. A. Litvinsky also adhered to the idea of a var as a round structure [Litvinsky, 2004, p. 9-10]. V. V. Vsrtogradova (oral communication) believes that the Avestan var is neither a square nor a circle, but a concept, i.e., ideas about an "ideal settlement" that could be embodied in a square,square or square structure. and in a circular planning scheme. The synthesis of a square and a circle is a cosmological scheme of the world, in which a square symbolizes the four cardinal directions, and a circle serves as a symbol of the sky [Mammadov, 2003, p. 91]. "Creating their own settlements, people... Obviously, they were performing a ritual - they were re-creating the universe " [Shabnov, 2010, p. 48].

page 33
"...various models of mythological reflection of reality are most consistently displayed, apparently, in various numerical codes... " [Vrtanesyan, 2010, p.412].

In this regard, the most interesting explanation is the typological proximity of the architectural plans (and numerical codes used in them) of the Koi-Krylgan-kala complex and the round temple of Dashli-3 (Dashli oasis in northern Afghanistan), dating at least to the middle of the second millennium BC (Qutlug-depe 3 in the Farukobad oasis in northern Afghanistan and At-Chapar in Bactria (both of the Achaemenid period) are not so significant in this case, since they are actually contemporaries of Koi-Krylgan-kala).

The temple on Dashly-3 consists of two rows of walls, forming a clear circle in the plan and enclosing a kind of circular corridor. Along the perimeter to the outer wall at a certain distance from each other, nine turrets adjoin. According to M. Mammadov, "... the number of turrets symbolically corresponded to nine months of fertility... " [Mammadov, 2003, p.60].

M. S. Bulatov believes that the consolidation of the union of tribes of the agricultural Bactrian state was accompanied by the unification of different tribal gods (each owned one of the towers) into a single pantheon [Bulatov, 1988, p. 31]; he also points out that according to the original plan of the towers there should have been 7 [ibid., p. 32], communicating with a bypass corridor divided into several compartments, passageways. There are three passageways in the outer wall of the structure. In the center of the entire complex are the remains of a building with a set of rectangular rooms that may have had a special religious purpose. K. Jatmar (1981) believed that this is an arena for performing shamanic rites. V. I. Sarianidi, who discovered this monument and pointed out its connection with the early architecture of Mesopotamia, referring to the "oval temple" In Khafaj, the "round house" on the Tepe of Le Havre (Sarianidi, 1977, p. 40), adheres to the hypothesis that the round building belongs to the temple of fire worshippers. according to: Mammadov, 2003, p. 60] suggests that Dashly-3 is not a temple, but a fortress (which is doubtful due to the presence of three entrance openings and insufficient wall thickness). At the time of the joint venture. Tolstoe also believed that Koi-Krylgan-kala is a fortress surrounded by a "wall forming a regular circle" with 9 towers (Tolstoy, 1948(1), p. 100). The center of the circle is occupied by a regular 18-sided citadel (with 5 loopholes on each face) with a round (built-up) platform inside.

"After a long scientific search..., drawing on iconographic material with similar compositions of plans of structures of the burial cult of the Sako-Massagst ethnic group and comparing them with solar signs that have become widespread in this region, drawing on the history of religious beliefs of Khorezm and neighboring countries, data on the penetration of Zoroastrianism into the steppe expanses, analyzing various burial rites in comparison with With the traces of fire found on Koi-Krylgan-kale, researchers concluded that this is a monument of a funerary cult " (Bulatov, 1988, p. 48).

Naturally, the question arises why in this case 9 towers are not associated with nine months of fertility. According to G. S. Vrtanesyan:

3 The planning principle of the Dashly-3 Bronze Age temple (the central circular complex is surrounded by dense buildings, among which two circular brick fences stand out, the external contour of the settlement is almost square) is preserved in the cult structure of the early teardrop period of Kutlug-depe: three rings inscribed into each other, surrounded by a pentagonal moat; the ring walls form two bypass corridors communicating M. Makhmsdov believes that the architectural and planning solution of Kutlug-depe is one of the later examples of principles that were "finally" formed in the architecture of the Bactrian-Margian region as early as 11 thousand BC. They " subsequently, as a result of close historical and cultural contacts, influence in a certain sense the architecture of neighboring countries, in particular Parthia and Khorezm "[Makhmsdov, 1991, p. 14]. At the same time, however, it remains unclear how the "numerical code" of Dashla-3 can be considered to be more pronounced in Kutlug-depa, and not in the Khorezm Koi-Krylgan-kala.

page 34
"Any natural phenomenon can be described quantitatively, first approximately, and then accurately, in the form of numbers. The most fundamental and vital survival factor is more or less effective adaptation to the repetition of natural processes. Therefore, it is advisable to correlate the most frequently used (i.e., the most important) numeric codes with the problem of counting and time accounting-the calendar" [Vrtanesyan, 2010, p. 412].

It is unlikely, however, that we can be sure of the identity of the calendar systems used in Bactria II millennium BC and Khorezm I millennium BC. It is possible, of course, to see an element of chance in the coincidence of architectural plans and numerical codes of the religious buildings Dashly-3 and Koi-Krylgan-kala, but there are reasons to say on the common religious and cultural traditions of their builders. Perhaps not the last place in these traditions is played by astronomical observations.

list of literature

Biruni Abu Rihan. Monuments of past generations / Translated and edited by M. A. Sals / / Selected Works, vol. 1. Tashkent: Fan, 1957.

Bsruni Abu Rayhan. Kniga vrazumleniya nachatkam nauki o zvezdakh [The Book of admonition to the rudiments of the science of stars] // Selected works, Vol. VI. Tashkent: Fan Publ., 1973.

Bulatov M. S. Geometric harmonization in the architecture of Central Asia in the IX-XV centuries. Moscow: Nauka, 1978.

Vorob'eva M. G., Rozhanskaya M. M., Vsselovsky I. N. Drsvnshorsmiysky monument of the IV century BC Koi-Krylgan-kala from the point of view of the history of astronomy.

Vrtanesyan G. S. Kalsndarnoe-chislovaya simvolika v arkheologicheskikh kul'turakh Baktriya i Margiana pozdnoy bronzy [Kalsndarno-chislovaya simvolika v arkheologicheskikh kul'turakh Baktriya i Margiana pozdnoy bronzy]. Collection of articles dedicated to the 80th anniversary of V. I. Sarianidi. Proceedings of the Margian Archaeological Expedition / Ed. by P. M. Kozhin, M. F. Kosarev, and N. A. Dubova, St. Petersburg: Alstsya Publ., 2010.

Gulyamov Ya. G. History of irrigation in Khorezm from ancient times to the present day. Tashkent: Publishing House of the Academy of Sciences of the Uzbek SSR, 1957.

"Zij". Novye Guraganovye astromicheskie tablety [New Guraganov astronomical tables]. and the decree of A. A. Akhmsdov. Tashkent: Fan Publ., 1994.

Koi-Krylgan-kala - pamyatnik kul'tury Drevnego Khorezma IV v. B.C. - IV v. N.E. [Koi-Krylgan-kala-monument of culture of Ancient Khorezm IV v. B.C.-IV v. N.E.]. Trudy Khorezmskoy arkheologo-etnograficheskoy expeditsii, vol. 5, Moscow: Nauka, 1967.

Kurtik G. E. Starry sky of ancient Mesopotamia. St. Petersburg: Alstsya Publ., 2007.

Field research of the Khorezm expedition in 1954-1956 / / Materials of the Khorezm Expedition edited by S. P. Tolstov. Issue 1. Moscow, 1959.

Litvinskiy B. A. Viktor Ivanovich Sarianidi - legenda arkheologii Tsentral'noi Azii [Viktor Ivanovich Sarianidi-legend of the Archeology of Central Asia]. Collection of articles dedicated to the 75th anniversary of Viktor Ivanovich Sarianidi. Moscow: Stary Sad Publ., 2004.

Mamsdov M. Ancient architecture of Bactria and Margiana. Ashgabat: Cultural Center of the Embassy of the Islamic Republic of Iran in Turkmenistan, 2003.

Makhmsdov M. Monuments of the Bronze and Early Iron Age of Bactria and Margiana. Abstract of the dissertation. Alma-Ata. 1991.

Field research of the Khorezm expedition in 1954-1956 / / Materials of the Khorezm expedition edited by S. P. Tolstov. Issue 1. Moscow: Publishing House of the USSR Academy of Sciences, 1959.

Field research of the Khorezm expedition in 1957 / / Materials of the Khorezm expedition edited by S. P. Tolstov. Issue 4. Moscow: Publishing House of the USSR Academy of Sciences, 1960.

Field research of the Khorezm expedition in 1958-1961 / / Materials of the Khorezm expedition edited by S. P. Tolstov. Issue 6. Moscow: Publishing House of the USSR Academy of Sciences, 1963(1).

Field research of the Khorezm expedition in 1958-1961 / / Materials of the Khorezm expedition edited by S. P. Tolstov. Issue 7. Moscow: Publishing House of the USSR Academy of Sciences, 1963(2).

Priaralie v drevnosti i srednevekovye: Sbornik k 60-letiyu Khorezmskoy arkheologo-etnograficheskoy expeditsii [The Aral Sea Region in Ancient and Medieval Times: A collection dedicated to the 60th anniversary of the Khorezm Archaeological and Ethnographic expedition].
Sarianidi V. I. Ancient farmers of Afghanistan. Materials of the Soviet-Afghan expedition of 1969-1974. Moscow: Nauka Publ., 1977.

Tolstoe S. P. Ancient Khorezm. Opyt istoriko-arkheologicheskogo issledovaniya [Experience of historical and archaeological research]. Moscow: MSU Publishing House, 1948 (1).

Tolstoe Rural Settlement In the footsteps of the Ancient Khorezmian civilization. Moscow: Publishing House of the USSR Academy of Sciences, 1948(2).

Thick With. Results of the work of the Khorezm Archaeological and Ethnographic expedition of the USSR Academy of Sciences in 1955. 1955. № 3.

Tolstoe Rural Settlement Po drevnim deltam Oksa i Yaxarta [On the ancient deltas of the Oxus and Yaxarta]. Moscow: Izd. vostochnoy literatury, 1962.

Hawkins J., White J. Razgadka tysti Stonehenge [The Solution to the Stonehenge mystery]. Moscow: Mir Publ., 1984.

Shabnov R.N. On some similarities of religious and mythological representations of the population of the Ural "land of cities" with Vedic and Avestan ones // Ethnogenesis and early history of the peoples of Eurasia. Mate-

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Rials of the International scientific and practical conference (April 5-6, 2010) / Editorial Board: Volkov S. N., Doroshin B. N., Kashparova E. Penza-Prague. 2010.

Bclokrylov R.O., Bclokrylov S.V., Nickiforov M.G. Model of the stellar visibility during twilight // BlgAJ. Vol. 16.2011.

Jatmar K. Fortified Ceremonial Centers of lndo-lranians // Proceedings of the International Symposium on Ethnic Problems on the history of Central Asia in antiquity (II millennium BC). Moscow, 1981.

Stcblin-Kamcnsky I.M. Avcstan kamcit caiprusanam // East and West. Vol. 45. N 1—4. Roma. 1995.

ABBREVIATIONS

VDI Vestnik Drevnoi Istorii [Bulletin of Ancient History].
OR Istoriko-astronomicheskie issledovaniya [Historical and astronomical Research], Moscow: Nauka.
BlgAJ Bulgarian Astronomical Journal. Sofia.

Appendix 1. List of Khorezmian structures with known coordinates, for which there is at least one archaeological plan.

№

Construction site

Google Earth coordinates

1

Construction site

41ο45'31"61°09'04"

2

Angka-Kala

42°00'51"61°01'45"

3

Ayaz-kala-1

42°00'38"61°01'32"

4

Ayaz-kala-2

42°00'19"61°01'50"

5

Ayaz-kala-3

44°25'10"63°06'49"

6

Babish Mullah-1

41°49'31"61°11'23"

7

Bazaar-kala

41°41'36"60°58'54"

8

B. Guldursun

41°51'30"61°18'13"

9

Janbas-kala

41°44'17"60°52'30"

10

Duman-kala

41°45'19"61°07'01"

11

Koi-krylgan-kala

42°02'03"61°19'19"

12

Kurgashin-Kala

41°55'50"60°49'12"

13

Toprak-Kala (city)

41°42'18"60°44'15"

14

Pil-kala

44°05'06"62°54'44"

15

Chirik-Rabat-Kala

41°18'52"61°05'32"

16

Khazarasp

41°40'03"61°05'28"

17

Eres-kala

41°55'16"61°01'06"

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