Automated, auditable dating of the Babylonian Astronomical Diaries with language models and astronomical tools

Lucas Carrit Delgado Pinheiro; Yuan-Sen Ting; Jon Clindaniel; Lu Li; Yingbin Liang; Ness Shroff

astro-ph.IMOct 25, 2026

Automated, auditable dating of the Babylonian Astronomical Diaries with language models and astronomical tools

Authors: Lucas Carrit Delgado Pinheiro, Yuan-Sen Ting, Jon Clindaniel, Lu Li, Yingbin Liang, Ness Shroff

Organizations: Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210, USA · Department of Astronomy, The Ohio State University, Columbus, OH 43210, USA · Center for Cosmology and AstroParticle Physics (CCAPP), The Ohio State University, Columbus, OH 43210, USA · Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany ·

Abstract

The Babylonian Astronomical Diaries record the sky over nearly six centuries. Many tablets are broken and have lost their date formula. Experts dated many of them one tablet at a time in the standard edition, Astronomical Diaries and Related Texts from Babylonia (ADART). They used the recorded sky and other evidence, such as year formulas and royal names. Our system automates the astronomical part for all tablets with the same rules. A rule-based parser turns the recorded observations into clauses, short statements with fixed fields. A language model checks them against the text and adds observations that the parser missed. Astronomical tools test the clauses in all 701 years from 626 BCE to AD 75. The system ranks the years by how well they agree with the clauses. The system withholds published dates until its results are final, and the output lists the passages and computed positions behind each candidate year. On 120 dated tablets, the years tied at the top of the ranking include the published year in 96% of cases. For 86 of them, this top group is a single year, the published year in 84. In 119 of the 120, the reported candidate set contains it. For 56 undated entries of ADART IV, the system gives ranked candidate years. For each tablet, the results show how far astronomy alone narrows the year. An interactive page at https://tingyuansen.github.io/Babylonian_Dating/ follows each tablet and links the code, protocol and results.

Figures & tables

Figure 1: The automated workflow, with a worked example. The banner at the top names the written protocol of the rules and the held-out test ( SI Appendix , sections S2 and S8). In step 1, the parser turns a passage of the text into a clause, with its fields and marks. The language model checks it and adds the clauses that the parser missed. In step 2, astronomical tools, which agents can call through MCP, give each clause (grid row) a verdict in each candidate year. The grid shows eight clauses in eight of the 701 years. Bits

u_{j}

follow from the verdicts of a row (Eq. 1 ). Only decisive clauses (orange bits), whatever their bits, decide which years stay in the strict set. Supporting clauses (blue bits) only order the years. Column T is the one year with which all decisive rows agree. Step 3 shows 91 years of the example, and each clock row marks the years with which the clauses of that clock agree. Fixed rules count the decisive clocks

K

that agree with each year and add up its decisive bits

I_{D}

(Eq. 2 ). Year T leads on both and forms the strict set

S

(Eq. 3 , orange). The supporting bits

I_{S}

(blue) order the years. The system then commits to one year, ranks the years or declines (Eq. 6 ).

Panel of Figure 2 — Figure 2: A diary tablet and the information in its clauses. (a) ADART I no. $-322$ B (British Museum, BM 45962), a diary for 323/322 BCE that records the death of Alexander the Great. Photograph by Shaunnol, Wikimedia Commons, public domain. (b) The opening of X301322 from ADART III, one tablet line per row, colored orange for a decisive and blue for a supporting clause. Square brackets mark text that Sachs and Hunger restored. Each log-scaled bar shows the number $n$ of years that agree with the row’s strongest clause, labeled with $\log_{2}(701/n)$ bits (Eq. 1 gives the scoring). Gray rows hold unscored text, and their bars reach all 701 years (dashed line) at 0 bits.

Figure 3: Five decisive clauses of X301492 narrow the candidates to one year. (a) Gray ticks mark the years that each clause agrees with on its own. Blue ticks mark the running intersection, and the counts of both are at the right. The orange row is the strict set computed from

K

and

I_{D}

, the single year 150 BCE. (b) Decisive bits

I_{D}

of each candidate year. 150 BCE agrees with three clocks, and the five years with the next highest

I_{D}

agree with two each.

Figure 4: Inclusion of the published year for the 120 benchmark records with decisive clauses, the 59 supporting-only records and all 179. (a) Percentage of records whose published year is among the first

n

candidate years, on a logarithmic axis that ends at all 701 years. A record counts at

n

only when each year ranked above or tied with its published year also lies within the first

n

. (b) Percentage of records whose published year is in the first one or two groups, each a set of tied years.

Outcome	Record and passage	Result
Parser clause modified	X300993, “Around the 6th, Mars’ last appearance in Gemini”	The parser read the appearance without its day. Review proposed day 6 from the same sentence, and the field check accepted it.
Restored mark added	X202270, “solar [eclipse”	The parser did not mark the clause as restored. Review cited the bracket before “eclipse”, and the field check accepted the mark.
Proposed change rejected	X202552, “moon was] 1 1/2 cubits behind $\eta$ Tauri”	Review proposed month V from a heading in an earlier sentence. The confirming call rejected it, because the month came from another sentence.
Missed observation recovered	X301323, “the moon having passed a little to the east, it stood 3 cubits in front of Venus to the west”	The parser missed this relation, whose subject is “it”. The search found it, and code bound “it” to the Moon named earlier in the sentence.
Astronomical but unsupported	X102732, “Mercury, which had set, was not visible”	The search found an astronomical report, but the invisibility of a planet lies outside the rules. It was recorded in a separate category.
Search proposal rejected	X102812, “[… Ni] ght of the 21st”	The search proposed the Moon in front of $\alpha$ Virginis and cited this heading with a wrong letter. Code did not find the citation in the translation and rejected the proposal before any astronomical test.

Table S1: Examples from the review and search steps.

Clause type	Test	Window or tolerance	Example
Planet in a named sign	The planet is in the stated Babylonian sign during the month	The month	“Mars was in Sagittarius” (X301492)
First or last appearance in a sign	The planet is in the stated sign. The date of visibility is not tested	The month	“Mercury’s last appearance in the east in Libra” (X301492)
Planet station	The planet’s apparent motion along the ecliptic reverses	The month $\pm$ 20 days	“Jupiter became stationary in Aquarius” (X301492)
Station against a Normal Star	A station of the stated kind lies at the measured distance from the star	The month, or $\pm$ 2 days of a stated day, and $2^{\circ}$	“when Saturn became stationary to the west, it became stationary 1 cubit behind $\beta$ Geminorum” (X300873)
Planet enters a sign	The planet crosses into the stated sign, in either direction of motion	The month $\pm$ 20 days	“Mars reached Capricorn” (X301492)
Moon against a star or planet	The relation holds in ecliptic longitude	$3^{\circ}$	“the moon was 2 1/2 [cubits] below $\alpha$ Librae” (X301322)

Table S2: Astronomical rules. Each rule returns agree, contradict or untestable for one clause in one candidate year. Here the month is the Julian interval of the Babylonian month that applies to the clause. Examples are passages of the ADsD translation.

Observation type	Clauses	Testable	Years	Bits	Decisive (%)
Moon or planet against a Normal Star	2062	1330	548	0.4	1
Planet in a named sign	683	659	123	2.5	35
Moon against a planet	357	219	84	3.1	19
First appearance in a sign	229	229	436	0.7	15
Last appearance in a sign	222	222	534	0.4	0
Planet enters a sign	101	101	460	0.6	16

Table S3: Information and decisive share by observation type, for 4,010 clauses from 321 records of ADART I to III. Clauses counts all clauses of the type, and Testable those testable in at least one of the 701 years. Years and Decisive count the testable clauses, and each row has at least five of them. Years is the median number of candidate years with which such a clause agrees. Bits are

\log_{2}(701/m)

for the median

m

, while the scoring uses Eq. 1 of the main text. Decisive is the percentage of the testable clauses that meet the conditions of the decisive tier.

Observation type	Clauses	Testable	Agree	Contradict	Untestable	Agreement (%)
Moon or planet against a Normal Star	2062	1330	1224	106	732	92.0
Planet in a named sign	683	658	643	15	25	97.7
Moon against a planet	357	219	203	16	138	92.7
First appearance in a sign	229	228	219	9	1	96.1
Last appearance in a sign	222	220	207	13	2	94.1
Planet enters a sign	101	101	98	3	0	97.0

Table S4: Agreement at the published year of the 4,010 reviewed clauses from 321 dated records of ADART I to III. A testable clause receives agree or contradict at the published year. Agreement is

100\times

agree / testable. For the parser clauses alone, from 316 records, 2,169 of 2,313 testable clauses agree (93.8%).

Quantity	Symbol	What it is	How it is used
Verdict	$v_{j}(y)$	Agree, contradict or untestable, for clause $j$ in candidate year $y$	Basis of all later quantities
Bits	$u_{j}$	$\log_{2}(C_{j}/A_{j})$ , from the numbers of testable and agreeing years of clause $j$ (Eq. 1 )	Summed in $I_{D}$ or $I_{S}$ , shared equally among clauses with identical verdicts
Tier		Decisive if of a decisive type, unrestored, not marked as unobserved, and securely dated or tested over its whole year (section S5), and supporting otherwise	Only decisive clauses decide which years stay in the strict set
Clock	$c$ , $K(y)$	Mars, Jupiter, Saturn, lunar eclipses, or the solar year. $K(y)$ counts the clocks that agree with year $y$ (Eq. 2 )	Counts independent agreement, apart from bits
Summed bits	$I_{D}(y)$ , $I_{S}(y)$	Summed bits of the agreeing decisive or supporting clauses (Eq. 2 )	$I_{D}$ forms the strict set, and $I_{S}$ only orders
Contradictions	$N_{C}(y)$	Number of source statements that contradict the year	Only order the years

Table S5: The quantities of steps 2 and 3, in the order in which the system uses them for each tablet. Equation numbers refer to the main text.

Figure S1: Sensitivity of the benchmark for the 120 records with decisive clauses, with the baseline values as dashed orange lines. (a) Published year in the first group, with all tied groups kept. (b) Median number of years in that group, on a logarithmic axis. (c) Published year in the strict set, on an axis that starts above zero. Each row changes one convention, removes one rule or clock, or changes one scoring policy. Group headers mark the six kinds of change, and section S7 defines each row. The row “Fixed Delta T shift” shifts ephemeris time, separately from the three eclipse trials of the baseline.

Test volume	Records	First group	First three groups	Strict set	Median strict set
ADART I	33	31 (94%)	33 (100%)	33 (100%)	9 years
ADART II	26	25 (96%)	26 (100%)	26 (100%)	49.5 years
ADART III	61	59 (97%)	60 (98%)	60 (98%)	17 years
All three rounds	120	115 (96%)	119 (99%)	119 (99%)	15.5 years
Rules from all volumes	120	115 (96%)	119 (99%)	119 (99%)	15 years
ADART IV addenda	12	11 (92%)	11 (92%)	11 (92%)	64.5 years

Table S6: Held-out test by volume. Each of the first three rows dates the benchmark records of one volume with rules set on the other two. Rates are for the records with decisive clauses, as in the main text. All three rounds pools the three test volumes. Rules from all volumes repeats the rates of the main text, where the rules saw all three volumes. The last row gives the registered test on the ADART IV addenda that neither join nor duplicate a record of ADART I to III.

Figure S2: Strict candidate sets of the 56 ADART IV entries that keep a decisive clause. Each row is one entry, from the narrowest set at the top to the widest at the bottom, in the order of Table S7 . Dark marks are strict candidates over the 701 years. Marks that repeat at a fixed spacing come from one clock, such as Jupiter, which returns to a sign about every 12 years.

Entry	Page	Museum number	Clocks	$\|S\|$	$\|L_{1}\|$	Groups
805	539	BM 99671	Jupiter, Saturn	21	21	$L_{1}$ : 21 years, $L_{2}$ : 75 years, $L_{3}$ : 115 years
303	274	BM 35863	Saturn †	52	52	$L_{1}$ : 52 years, $L_{2}$ : 649 years
853	567	MNB 1877	Mars, Saturn	54	20	$L_{1}$ : 20 years, $L_{2}$ : 34 years, $L_{3}$ : $-433$ , $-228$ , $9$
264	252	BM 35685	Mars, Saturn	56	56	$L_{1}$ : 56 years, $L_{2}$ : 28 years, $L_{3}$ : 411 years
209	214	BM 35294	Mars, Saturn	57	57	$L_{1}$ : 57 years, $L_{2}$ : 27 years, $L_{3}$ : 411 years
837	558	Rm 780	Mars, Saturn	58	58	$L_{1}$ : 58 years, $L_{2}$ : 35 years, $L_{3}$ : 378 years

Table S7: Ranked candidate years of the 56 ADART IV entries with a decisive clause, in the order of Fig. S2 . Clocks names the clocks of the decisive clauses, and a dagger marks the three entries with a decisive clause that has a month.

|S|

and

|L_{1}|

count the years in the strict set and in the first group. Groups gives the size of each of the first three groups, or its years when it holds at most ten. Years are in astronomical numbering, so that

-149

is 150 BCE. The repository gives all years of each group.

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