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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

arXiv:2610.34297v1astro-ph.IMcs.AIcs.CLphysics.hist-ph

TL;DR

Specialists compared diary observations with computed positions tablet by tablet; this paper automates that astronomical comparison through parsed clauses, language-model review, and ranked candidate years. In 120 dated records with decisive clauses, the first tied group contains the published year in 96%, and the reported strict set does so in 119 of 120.

Abstract

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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.

Results

For dated benchmark records with decisive clauses, the top tied group contains the published year in 96% of cases, and the reported strict set contains it in 99%. The system also produces ranked candidate years for undated entries, while showing how much astronomy narrows each date.

Results

  • 3,193 parser clauses rise to 4,010 reviewed clauses; reviewed clauses match published years in 93.6% of testable cases versus 93.8% for parser clauses.A separate confirming call must cite text supporting each change, and fixed checks test returned clauses against the clause format.Source: Step 1. Reading the text into clauses · p. 2
  • For X301492, five decisive clauses narrow their individual candidate counts from 138, 116, 54, 50, and 49 years to the published year, 150 BCE.Three clocks agree at 150 BCE, totaling 16.3 decisive bits; removing one decisive statement at a time expands the safety set to seven years.Source: Figure 3 · p. 4, Three clocks leave one year for record… · p. 5
  • 96% of the 120 records with decisive clauses have the published year in the first tied group; 84 of 86 single-year first groups give the published year.The first two groups contain the published year in 119 records; supporting-only records reach 86% in the first group, but their groups hold many years.Source: Figure 4 · p. 5, Tests on a benchmark of 179 dated… · p. 5
  • The strict set contains the published year in 119 of 120 records with decisive clauses (99%), with a median size of 15 years.In the sole miss, X301582, the published year remains in the safety set.Source: Tests on a benchmark of 179 dated… · p. 5
  • Across three held-out rounds, first-group inclusion is 96% and strict-set inclusion 99%, matching the full benchmark; alternative settings change rates little.Removing the tiers lowers inclusion in the strict set.Source: Tests on a benchmark of 179 dated… · pp. 5–6
  • For 11 of 12 non-joining, nonduplicate ADART IV addenda with decisive clauses, both the first group and strict set contain the published year.The rules and test scores were fixed before these new diaries were read.Source: Tests on a benchmark of 179 dated… · p. 6
  • Among 238 dated records outside the benchmark, 28 of 29 with a decisive clause include the published year; all 10 single-year commitments in the dated corpus match it.The outside-benchmark strict sets have a median of 87 years, compared with 15 in the benchmark.Source: Tests on a benchmark of 179 dated… · p. 6
  • 56 of 399 ADART IV entries with astronomical clauses have a decisive clause and receive ranked years; their strict sets reduce 701 candidates to a median of 102.Most retain one decisive clause before a month heading; many strict sets repeat regularly, and a second-clock clause could narrow those series.Source: Ranked candidate years for 56 undated… · p. 6

Discussion and Conclusion

The system automates comparison of diary observations with computed positions under shared rules, and reports how astronomy narrows candidate years. Its open evidence supports reruns and specialist review.

Discussion and Conclusion

  • For each tablet, the output shows how far astronomy alone narrows the year and where other evidence is necessary.Candidates are ranked with the evidence behind each.Source: Discussion and Conclusion · p. 6
  • The system automates tablet-by-tablet comparison of recorded skies with computed positions, applying the same rules across the corpus.A new reading, join, or calendar can be tested in one rerun.Source: Discussion and Conclusion · p. 6
  • The open evidence lets specialists test undated ADART IV candidates against joins and historical reports.Review, search, and dating of the 179 benchmark records cost about $3.Source: Discussion and Conclusion · p. 6
  • The same division of labor could also be used to date Greek horoscopes, Chinese eclipse reports, or calibrate published radiocarbon dates.These are proposed applications, not reported evaluations.Source: Discussion and Conclusion · p. 6

Materials and Methods

The study uses dated ADART I–III records and undated ADART IV scans, then applies a defined calendar, ephemeris, and rules to astronomical observations. Published dating information is withheld until clauses, verdicts, and candidate sets are final.

Materials and Methods

  • The corpus includes 417 ADART I–III records with published dates; 393 have edition text and 332 have an English translation.ADART IV was read from a scan of the printed volume using optical character recognition.Source: Materials and Methods · p. 6
  • The language model checks the parser’s reading and adds missed observations; the month and day are taken from text headings.The specified review-and-search model uses low reasoning effort and a fixed output schema.Source: Step 1. Reading the text · p. 6
  • The candidate calendar covers 701 Babylonian years from 626 BCE to AD 75, using Parker and Dubberstein month starts and DE441 daily positions.It excludes 652–627 BCE, including the earliest diaries and one dated record; eclipse circumstances are computed for Babylon with the Swiss Ephemeris.Source: Step 2. Calendar, ephemeris and rules · p. 6
  • Longitudes of date are converted to the star-fixed Babylonian zodiac, with Y denoting Julian centuries from astronomical year 0.Each zodiac sign spans 30° of Babylonian longitude.Source: Step 2. Calendar, ephemeris and rules · p. 6
  • Most clause tests use the Julian interval of the Babylonian month; distance rules use one cubit = 2° and 24 fingers = 1 cubit.The Moon and planet tolerances are 3° and 2°, respectively; lunar eclipses must match a catalog event visible at Babylon within the stated ΔT uncertainty.Source: Step 2. Calendar, ephemeris and rules · p. 6
  • Published dates and other date-bearing fields are withheld until clauses, verdicts, and candidate sets are final.Year statements inside a tablet are used only to determine the difference between two year headings.Source: Blinding · p. 6
  • The interactive page follows each record and links the repository, which contains code, protocol, clauses, benchmark, results, and calendar tables.The repository’s linked materials include the tables read from Parker and Dubberstein.Source: Blinding · p. 6

SI Appendix

The appendix documents the corpus, procedures, checks, scoring, and audits used in dating the tablets, and evaluates the method’s sensitivity and performance on held-out records and new ADART IV addenda. It also reports candidate-year results for undated ADART IV entries.

S1. Corpus, input and benchmark

  • The benchmark contains 179 records with fixed published years; the model receives arbitrary record labels, and year statements are checked only after dating.Records had at least three parser clauses when the benchmark was fixed, and two-year tablets are scored by their first year.Source: S1. Corpus · p. 8

S2. Reading the text (step 1)

  • 3,142 parser clauses were kept and 51 modified; 795 of 8,123 proposed observations passed checks, yielding 817 clauses and 4,010 total clauses.For ADART IV, the model kept 533 of 539 parser clauses, modified 6, and added 179 clauses.Source: S2. Reading the text (step 1) · p. 8
  • Without coding-agent reading rules, each rate falls by at most two points and the median strict set grows by about a third, though the rules add reading coverage.Accepted proposals were human-reviewed, authored as general code rules, and tested against clauses at published dates.Source: S2. Reading the text (step 1) · p. 8

S3. Calendar (step 2)

  • The calendar converts Babylonian dates to Julian dates, accounts for intercalary months, and corrects 10 OCR transcription errors in Parker and Dubberstein’s tables.After correction, month starts fall a median of 1.7 days after computed new moons.Source: S3. Calendar (step 2) · p. 9

S4. Astronomical rules (step 2)

  • Astronomical tests use daily DE441 positions and type-specific rules; lunar distance tolerances are the smallest 0.5° multiples covering 89% of published-date differences by body class.A cubit is treated as 2°; eclipse visibility is tested at Babylon, and joint positions require planets to share a sign at the same time.Source: S4. Astronomical rules (step 2) · pp. 9–10

S5. Evidence tiers and agreement at the published years (step 3)

  • The decisive tier selects physically eligible types with at least 80% agreement in at least three testable cases, while other testable types support ranking.Solstice, equinox and Sirius clauses nearly always agreed at published years; distances between outer planets agreed in 3 of 6 cases, while lunar eclipses agreed in all 3.Source: S5. Evidence tiers and agreement at… · p. 11, Table S4 · p. 11

S6. Scoring and candidate sets (step 3)

  • Scoring assigns bits to informative clauses, counts contradictions by source statement, and groups tied years; removing a decisive statement helps form a safety set.Linked clauses share bits, but each clause counts for its own clock.Source: S6. Scoring and candidate sets (step 3) · pp. 11–12

S7. Sensitivity

  • The sensitivity audit tests 32 fixed configurations on the same 179 records and reports published-year inclusion, median first-group size, and strict-set inclusion for 120 records with decisive clauses.Configurations vary one convention or rule at a time.Source: S7. Sensitivity · p. 12
  • Making longitude-only distances supporting shifted each rate by at most one point, while testing the Moon over two nights shifted each by at most three.Conventions including the cubit, zodiac zero point, ∆T, and tolerances each moved a rate by at most three points.Source: S7. Sensitivity · p. 12
  • Counting contradictions in the strict set or removing tiers let one misread clause rule out the published year; ranking contradictions first or equal within-tier weights left rates unchanged.In the first two variants, the strict set shrank to about one year, more often the wrong one.Source: S7. Sensitivity · p. 12
  • Across 31 settings, rates changed little; tiers protected the strict set, month context shaped candidate-set width and ranking, and removing one planet more than tripled its median size.A clause tested over a whole year agrees with more years; different planetary periods help clocks narrow the years left by other planets.Source: S7. Sensitivity · p. 12, Figure S1 · p. 13

S8. Held-out test

  • With settings refit on two ADART I–III volumes and tested on the third, both pooled rates matched the full-benchmark rates, passing the five-point margin.The test chose settings without the test records; the pass condition was fixed before testing.Source: S8. Held-out test · p. 13, Table S6 · p. 14
  • Table S6 includes the registered test on the ADART IV addenda, which neither join nor duplicate a record of ADART I to III; this passage states no test outcome.Source: Table S6 · p. 14

S9. ADART IV

  • The ADART IV input comprised 867 undated diary entries from printed pages 95–575, of which 860 had English translations; dating omitted date and ruler information.It also omitted the printed Date and Comments sections, catalog number, and page position; only the post-dating check used the full translation.Source: S9. ADART IV · p. 14
  • 47 of 56 ranked entries had one decisive clause; their first groups spanned a median 100 years, and 53 entries’ decisive clauses lacked month context.Those monthless clauses were tested over the whole year; the appendix provides strict candidate sets and the first three ranked groups.Source: S9. ADART IV · p. 14, Figure S2 · p. 14, Table S7 · p. 14
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