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REVIEW 4 major objections 5 minor 7 references

A Revision for the Draconic Gearing of the Antikythera Mechanism, the eclipse events of Saros spiral and their classification

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

Pith's one-line read A revised 229-tooth gear train reproduces the Antikythera Mechanism's Saros eclipse events from gear ratios alone, the paper argues.

desk verdict A serious but over-fitted reconstruction: the new gear ratios and six-sector eclipse classification are worth engaging with, but the central claim of pure mechanical generation rests on unpreserved gears and on limits fitted to the same inscriptions they are said to predict. read the letter →

arxiv 2412.07023 v3 pith:OO4G2R5H submitted 2024-12-09 astro-ph.IM astro-ph.EPphysics.hist-phphysics.pop-ph

classification astro-ph.IMastro-ph.EPphysics.hist-phphysics.pop-ph
keywords AntikytheraMechanismDraconicgearingeclipsepredictionSarosspiraleclipticlimitsgearerrorsFragmentDancientGreekastronomy
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that a missing train of four gears—three of them entirely hypothetical—once sat on the right side of the Antikythera Mechanism and drove a Draconic pointer giving the Moon's latitude relative to the ecliptic. With gear counts chosen so that one Saros equals about 242.000 Draconic turns, the eclipse events engraved on the Saros spiral, including events in cells whose inscriptions are lost, can be generated by turning the mechanism itself rather than by recording observed eclipses. If this is right, the Mechanism was a self-contained eclipse computer: preserved and missing eclipse events, and the classification words on the Back Plate, follow from gearing alone. The paper also uses a 3% shrinkage correction for the largest gear to explain why two engraved eclipse pairs are absent from the mechanical prediction and two extra events appear: marginal ecliptic-limit positions plus gear errors.

What carries the argument

The load-bearing object is the proposed Draconic gear train $b1 \to a1 \to r1 \to s1 \to s2 \to t1$, with tooth counts 229, 48, 63, 57, 56, and 22. This train locks the Draconic cycle to the Saros so that 223 synodic months produce almost exactly 242 turns of the Draconic pointer. A second object is the revised ecliptic-limit scale, divided into a Node area and six unequal sectors labeled with the Greek magnitude words Minor, Medium, Large, Greatest, and Major, which converts the pointer's position into an eclipse classification. A third object is the 3% linear shrinkage estimate derived from the 354 versus 365 calendar-ring hole count, which is what justifies raising the annual gear's tooth count to 229.

What would settle it

A decisive check would be to measure every surviving gear-tooth arc on Fragment A and reconstruct the original $b1$ tooth count from the measured radii; if that count comes out below 228 (several current measurements give 216–226), or if a physical bronze model of the proposed $s1$–$s2$–$t1$ gear cluster cannot fit between the internal and external casements on the right side of Fragment A, the proposed gearing relation is falsified. In addition, an independent recalculation using the exact ancient value 5458 synodic = 5923 Draconic, which gives 241.998 rather than 242.000 turns per Saros, would show whether the paper's claimed error of +0.00029 turns per Saros is genuinely negligible across the spiral's 50-event span.

Watch

Extended reading notes

Core claim

The central claim is that the Antikythera Mechanism encoded the Draconic lunar cycle through a revised gear train expressed by Equation (1): $18.029787234 \times \{(229/48) \times (63/57) \times (56/22)\} = 242.0002901$ Draconic-pointer turns per Saros, with a second option using a 228-tooth $b1$ gear. The train starts from the annual gear $b1$, runs through the preserved crown gear $a1$ and the Fragment D gear $r1$, then through three unpreserved gears $s1$, $s2$, and $t1$, ending at a Draconic pointer mounted on the right side of the casing. With revised ecliptic limits—6.5° South and 22.5° North around Node-A and 5.7° North and 15.3° South around Node-B—a recalculation reproduces the preserved eclipse events and supplies events from lost cells. The paper concludes that the eclipse events are therefore calculated by pure mechanical processing and are not documented observed events, and that the four discrepancies (two missing and two additional events) are explained by marginal pointer positions and endogenous gear errors.

Load-bearing premise

The entire result rests on the assumption that three completely unpreserved gears with 57, 56, and 22 teeth existed, meshed exactly in the proposed order, and that the original annual gear had 229 teeth after a uniform 3% shrinkage correction; if the real tooth counts or the physical fit on the right side of the casing were different, the 242-turn relation would fail.

Editorial extensions

If this is right

  • If Equation (1) is correct, the Saros spiral's 64 eclipse events can be regenerated purely by rotating the mechanism's input, with no need for an observational record of individual eclipses.
  • The four mismatches between engraved and predicted events become a diagnostic: they bound the endogenous gear errors, roughly ±1° to ±4° in pointer position, and give a quantitative quality criterion for functional reconstructions.
  • The revised Draconic scale maps the Back Plate's magnitude words onto sectors of the ecliptic zone, so the classification letter attached to an event follows from where the Draconic pointer sits at that event.
  • The same gearing supplies the Moon's second coordinate: the Draconic pointer, combined with the Lunar Disc pointer, gives a 3D lunar position and also makes star occultations by the Moon predictable from the mechanism alone.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: the same shrinkage argument used to raise the $b1$ tooth count to 229 could be tested against other gear diameters in Fragment A; if shrinkage is not uniform, the chosen tooth counts are an average rather than a unique reconstruction.
  • Beyond the paper: the claim that the events are 'not documented observed events' is stronger than the evidence requires; the mechanism could still have been calibrated or checked against earlier Babylonian eclipse records even if its daily operation was purely mechanical.
  • Beyond the paper: the six-sector classification scheme is a testable model—applying it to another Saros series and comparing the predicted sector order with an independent ancient eclipse catalog would show whether the sector widths in Table 5 are stable or merely fitted to this one spiral.
  • Beyond the paper: a bronze reconstruction with the proposed gear counts would directly reveal whether the 22-tooth end gear turns smoothly at the claimed 242-turn ratio or whether accumulated gear errors exceed the paper's assumed ±4° pointer uncertainty.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper proposes a revised Draconic gearing for the Antikythera Mechanism, correlating Fragment D with Fragment A and introducing three unpreserved gears (s1, s2, t1). Equation (1) yields 242.0002901 turns of the Draconic pointer per 223 synodic months, matching the Saros relation. The authors use this gearing with a recalibrated DracoNod-V2 program to regenerate the eclipse events of the Saros spiral, claiming that the events were mechanically pre-calculated rather than recorded observations. They also propose an eclipse classification based on Eudoxus papyrus and the Back Plate Inscription, and report a revised set of ecliptic limits and sector boundaries for the Draconic scale.

Significance. If the central claim were established, it would settle a long-standing question in Antikythera research: whether the engraved eclipse sequence was an observational record or a mechanically generated prediction. The paper has the merit of making an explicit, quantitative gear-ratio proposal (Eqs. 1–3), engaging with the physical deformation and shrinkage of the fragments, and providing a detailed, letter-by-letter comparison of the Back Plate Inscription with a running simulation. However, the strength of these virtues is limited by the fact that the proposed gear train contains three entirely hypothetical wheels, the key gear-b1 tooth count is assumed after a uniform shrinkage correction, and the simulation's ecliptic limits are fitted to the very inscriptions the paper claims to predict.

major comments (4)
  1. [§3.1, Eq. (1)] The 242-turn ratio is achieved by setting b1 = 229 (or 228 in Eq. 2) and by postulating gears s1 = 57, s2 = 56, t1 = 22. Table 1 shows measured b1 estimates between 216 and 231 teeth; the value 229 is not independently derived but is chosen 'to improve its precision' (Section 3.1). Since Eq. (2) reaches nearly the same ratio with a different set of unpreserved gears (63/34, 61/40), the tooth counts are evidently fitted rather than fixed by evidence. The central claim of the paper therefore rests on an underdetermined parameter set.
  2. [§5, Table 3] The ecliptic limits in Section 5 are explicitly revised 'in order to improve the best match to the preserved eclipse events.' Consequently, the agreement between DracoNod-V2 and the inscriptions in Table 3 is to a significant degree a calibration artifact. The four residual mismatches (Cells 130, 166, 177, 189) are attributed to 'gearing errors' without a quantitative error budget, which prevents the reader from testing whether the proposed gearing plus errors is actually consistent with the data. As it stands, the argument is circular.
  3. [§3.1, Fig. 2] The physical feasibility of the proposed gear train is asserted but not demonstrated. The paper does not provide dimensional data from Fragment A or Fragment D showing that gears with 57, 56, and 22 teeth fit in the space between the casement and mesh with gear-r1 as drawn. Since these gears are entirely hypothetical, the claim that this is the Mechanism's original Draconic gearing requires evidence that the parts existed and could mesh, not merely that the ratio works.
  4. [Abstract, §8 (Epilogue)] The paper's conclusion that 'the eclipse events are calculated by pure mechanical processing and that they are not documented observed events' (Abstract) is not supported by the evidence presented. The preserved events are used to calibrate both the gearing (b1 tooth count) and the ecliptic limits; showing that a fitted model reproduces the calibration data does not demonstrate that the ancient instrument generated the events mechanically.
minor comments (5)
  1. [Abstract] The phrase 'the Mechanism s parts' contains a typo; it should read 'the Mechanism's parts.'
  2. [§3.2, Eqs. (2)–(3)] The transition from Eq. (2) to Eq. (3) is confusing: Eq. (2) uses (61/40), but Eq. (3) replaces t1 = 40 with t1 = 20 to double the turns; this should be stated more explicitly for the reader.
  3. [§5, Fig. 7] The definitions of 'Ecliptic Zone A' and 'Ecliptic Zone B' are given in a paragraph below Fig. 7; consider presenting them in a table or as a bulleted list to improve clarity.
  4. [§7, Table 5] The sector labels 'NL, NF, NCA, SCA, SF, SL' are used without an explicit glossary; define them at first use.
  5. [§4] The reference 'Voulgaris et al., 203b' appears to be a typo for 'Voulgaris et al., 2023b'; please correct this and check for similar citation errors throughout.

Circularity Check

3 steps flagged · score 6.0 of 10

The 242-turn/Saros result is baked into chosen hypothetical gear counts, and the eclipse-event agreement is produced by ecliptic limits and sector boundaries fitted to the very inscriptions the paper claims to reproduce.

  1. fitted input called prediction [Section 3.1, Equations (1)-(2) and Figure 2]
    "We set 229 teeth for gear-b1 (or 228 for the 2nd option)... the gear-r1 (63 teeth, Freeth et al. 2006, Supplementary Notes) of Fragment D is attached and is engaged to the hypothetical gear-s1 (57 teeth). Then gear-s1 is fixed the gear-s2 (56 teeth) which is engaged with gear-t1 (22 teeth). ... 18.029787234 * {(229/48) * (63/57) * (56/22)} = 242.0002901 Equation (1)"

    The tooth counts s1=57, s2=56, t1=22 are explicitly called hypothetical, and b1=229/228 is assumed after a uniform 3% shrinkage correction over measured estimates spanning 216-231 teeth. The product is chosen so that 18.029787234 years times the gearing equals 242.000 turns of the Draconic pointer per Saros; Equation (2) reaches the same 242 value with a different set of hypothetical gears. Thus the 242-turn 'result' is the Saros target imposed as an input constraint, not a quantity derived from preserved mechanism evidence.

  2. fitted input called prediction [Section 5, Table 3]
    "For the recalculation of the eclipse events we re calibrated DracoNod(-V2) visualization program (Voulgaris et al., 2023b) by revising the ecliptic limits in order to improve the best match to the preserved eclipse events, see Figure 7."

    The ecliptic limits are fit parameters adjusted to maximize agreement with the preserved eclipse events, and Table 3 then lists the 'Revised Eclipse events generated by DracoNod-V2' as matching those same preserved events. The agreement is therefore partly by construction rather than an independent prediction. The four residual discrepancies are attributed to 'gearing errors,' which further shields the fitted model from refutation.

1 more flagged steps
  1. fitted input called prediction [Section 7, Figure 10 and Table 6]
    "The division of the eclipse zone is calibrated as close as possible to the preserved index letters classification, but as the gearing errors alter/(“deform”) the pointers’ theoretical position, they create some declinations or mismatches, see Figure 10 and Figures A4-A7 in Appendix-A."

    The six unequal Sectors used to classify eclipse magnitudes are calibrated to the preserved index-letter classifications, so Table 6's 'theoretical' classification of events is not an independent test of the mechanical scheme: the sector boundaries were chosen to reproduce the very inscriptions being explained. This fitted classification is then combined with the Eudoxus-papyrus nomenclature to support the reconstructed Back Plate headings.

full rationale

The paper contains at least two constructive steps presented as results. First, Equation (1)'s 242.0002901 turns per Saros is produced by 'hypothetical' gear counts and an assumed b1 count, with Equation (2) showing an equally admissible alternative reaching the same 242 value; the Saros ratio is thus an input constraint, not a derived prediction. Second, the ecliptic limits are explicitly revised to improve the match to the preserved eclipse events, yet Table 3 is reported as agreement with those same events, and the sector divisions are calibrated to the preserved index letters. These fits make the eclipse-event agreement partly by construction, and the four residual mismatches are absorbed by 'gearing errors,' so the central claim of pure mechanical pre-calculation is underdetermined. The astronomical Saros relation itself and the Eudoxus/BPI lexicographic analysis are independent content and are not circular; the circularity lies in presenting fitted gear counts, fitted limits, and fitted sectors as predicted outcomes. Accordingly, the central claim reduces to a fit in part, warranting a score of 6 rather than a higher score that would require the entire derivation to be definitionally equivalent to its inputs.

Assumptions & free parameters 6 free parameters · 5 assumptions · 2 invented entities

The central claim rests on multiple fitted or postulated elements: the tooth counts of three unpreserved gears, an assumed gear-b1 tooth count after a uniform shrinkage correction, ecliptic limits and sector widths calibrated to the preserved inscriptions, and an initial calibration date from the authors' prior work. The gear-error parameters are adjustable and are used to explain any mismatch, which reduces the falsifiability of the reconstruction.

free parameters (6)
  • gear-b1 tooth count = 229 (option 1) or 228 (option 2)
    Set by the authors considering a ~3% shrinkage correction; the measurements cited range 216-238, so the chosen value is selected to make the Saros ratio near-integer rather than directly measured.
  • hypothetical gear teeth s1, s2, t1 = 57, 56, 22 (option 1); 34, 61, 20 (option 2)
    No fragments for these gears exist; counts are chosen so the composite ratio yields 242.000 turns per Saros.
  • Ecliptic zone limits = Zone A: 6.5S / 22.5N; Zone B: 5.7N / 15.3S
    Described as 'revised ... to improve the best match to the preserved eclipse events' (Section 5).
  • Sector boundaries of the six eclipse classes = Unequal sectors calibrated to preserved index letters
    Section 7: 'The division of the eclipse zone is calibrated as close as possible to the preserved index letters classification.'
  • Initial calibration date and pointer offsets = 22/23 December 178 BC, Draconic pointer at Node-A, New Moon at Apogee
    Adopted from the authors' prior work (Voulgaris et al. 2023a-c); the eclipse recalculations depend on this starting phase.
  • gear error magnitudes = eccentricity 0.1-0.3 mm, pointer deviations ±1-3 or ±4 deg
    Invoked post hoc to absorb the four mismatches between the model and the preserved cells (Section 5, Table 3 notes).
assumptions (5)
  • domain assumption 223 synodic months = 242 draconic months = 239 anomalistic months (Saros relation)
    Standard ancient/astronomical relation used in Equations (1)-(3) and the DracoNod-V2 recalculation.
  • domain assumption The preserved eclipse cells on the Saros spiral reflect the original instrument's output
    The authors take the cells marked in Freeth 2014/2019 and Iversen/Jones 2019 as ground truth against which the model is matched.
  • ad hoc to paper The Mechanism's input was via gear b3 rather than a1
    The ergonomic and kinesiology arguments in the Introduction are the authors' own reasoning; this choice motivates the Fragment D correlation.
  • domain assumption Shrinkage of the bronze fragments is about 3% and can be corrected by multiplying linear dimensions by 1.03
    Section 2 infers 354/365 holes as shrinkage for Fragment C and applies the same correction to gear-b1 tooth counts.
  • domain assumption The Eudoxus papyrus terms map directly to the BPI magnitude words
    The paper interprets 'Megiste', 'Meizones', 'Elattous' as corresponding to the preserved BPI words 'Mikrai', 'Mesai', 'Megalaia', a philological assumption not independently established.
invented entities (2)
  • Hypothetical gears s1 (57), s2 (56), t1 (22)
    purpose: Transmit rotation from Fragment D's gear r1 (63 teeth) to the Draconic pointer with the ratio needed for 242 turns per Saros.
    No fragments of these gears are preserved; they are placed on the right side of the Mechanism inside the wooden casement (Section 3.1, Figure 2).
  • Draconic scale and pointer on the right side of the Mechanism
    purpose: Display the Moon's ecliptic latitude and allow the user to see when an eclipse is imminent.
    The scale is not preserved; its geometry is proposed by the authors.

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Cite this review

Pith. "Pith review of A Revision for the Draconic Gearing of the Antikythera Mechanism, the eclipse events of Saros spiral and their classification." pith.science (2026). https://pith.science/paper/OO4G2R5H

@misc{pith2026241207023,
  author       = {Pith},
  title        = {Pith review of: A Revision for the Draconic Gearing of the Antikythera Mechanism, the eclipse events of Saros spiral and their classification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OO4G2R5H}},
  note         = {Machine review of arXiv:2412.07023}
}
read the original abstract

Our research is focused on the missing, but important and necessary Draconic gearing of the Antikythera Mechanism. The three Lunar cycles Sidereal, Synodic and Anomalistic are represented on the Mechanism by correlating the Fragments A and C (part of the Front plate), whereas the fourth Lunar cycle Draconic results after correlating the unplaced Fragment D with Fragment A. Considering the deformation of the Mechanism s parts during 2000 years underwater and their shrinkage after their retraction from the sea bottom, we present a revised gearing scheme of the Draconic scale. The existence of the Draconic gearing is crucial, because both the preserved and the missing eclipse events can be precalculated by the phase correlation of three pointers: of the Lunar Disc, of the Golden sphere/Sun-ray and the Draconic. This means that the eclipse events are calculated by pure mechanical processing and that they are not documented observed events. The phase coordination of the three lunar cycles can be used as a quality criterion for a functional model of the Mechanism. Eudoxus papyrus was the key for the lost words completion of the Back Plate inscriptions eclipse events classification of the Antikythera Mechanism.

Figures

Figures reproduced from arXiv: 2412.07023 by the authors.

Figure 2
Figure 2. Top-left panel, the configuration of the revised Draconic gearing. The annual gear-b1 rotates the crown gear-a1, and afterwards via gears r1, s1, s2, the motion is transmitted to gear-t1. The Draconic pointer is attached to shaft-t. The gearing is located at the right side of the Mechanism inside the External Wooden Casement (Voulgaris et al., 2019b). Top-right panel, the three parts of Fragment D (gear-r1 fixed on … view at source ↗
Figure 3
Figure 3. The geometrical relation between the Ecliptic plane – Ecliptic longitude (which is defined by the Zodiac Dial ring of the Mechanism) and the Draconic scale/pointer’s position - Ecliptic latitude, at the right side of the Mechanism. The Lunar Disc pointer aims to the Golden sphere-Sun (Bitsakis and Jones 2016b). When the Draconic pointer aims to the Ascending (ΑΝΑΒΙΒΑΖΩΝ, Panel A) or to Descending (ΚΑΤΑΒΙΒΑΖΩΝ) Node … view at source ↗
Figure 8
Figure 8. A) Close-up on the Back Plate Inscription visual photograph of Fragment A2 (photo by first author). B) Multi-combined AMRP X-ray tomography of Fragment F1 at the area with the preserved Inscriptions. The tomography slices are oriented to the surface with inscriptions. The orientation and the slices were processed by the authors using Real 3D VolViCon software. The numbers correspond to the numbering of lines accordi… view at source ↗

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Reference graph

Works this paper leans on

7 extracted references · 7 canonical work pages

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