1. Introduction

André Barbault introduced the Cyclic Index in his works of the 1960s–1970s. The index sums the angular distances (0°–180°) of all outer planet pairs: when the planets converge (low CI), global tension increases; when they disperse (high CI), relative calm prevails.

The traditional formulation (CI-5) includes Pluto (10 pairs), while a revised version (CI-4) excludes it (6 pairs). Until now, neither formulation had been subjected to rigorous statistical testing using high-precision ephemerides and a broad historical sample. This paper fills that gap.

2. Methodology

2.1 Computational Tools

Planetary positions were computed using the astronomy-engine library (Don Cross), which is based on high-precision ephemerides with full perturbations, delivering arcsecond accuracy for the 20th century and arcminute accuracy for pre-telescopic eras. This is a critical departure from earlier attempts that used simplified Keplerian formulas with multi-degree errors at ancient dates.

2.2 Dataset

A catalogue of 96 major geopolitical events from 800 BC to 2025 was compiled, spanning 2,826 years of history. Selection criteria were: global impact, multi-state or cross-civilizational involvement, and broad academic consensus on the significance of the event. The sample ranges from the founding of Rome to the Israel–Hamas war (2023).

2.3 Shift Test

The CI time series was shifted by random offsets (1–N years) 50,000 times. For each shift, the mean CI at crisis years was computed and compared to the actual value. This method is more rigorous than simple correlation, as it preserves the temporal structure of the crises.

3. Results

3.1 Principal Finding: CI-5 Prevails at Long Scale

With 96 events across 2,826 years and high-precision ephemerides:

Barbault’s CI-5 achieves statistical significance at p = 0.035, while CI-4 fails completely (p = 0.320). The hot zone of CI-5 (bottom 20%, ≤769°) shows 1.35× the base crisis rate, while the calm zone (top 40%, ≥978°) shows 0.75×, with a Hot/Calm ratio of 1.79×.

3.2 The 20th–21st Century Anomaly

In an earlier analysis restricted to the 20th–21st centuries (N = 23, 1900–2025), CI-4 showed a marginally stronger signal (shift p = 0.035) than CI-5 (p = 0.052). This finding is not confirmed at broader scale (N = 96, p = 0.320 for CI-4), but it remains worth noting:

Possible interpretations of the 20th-century anomaly:

Seasonal coincidence. Pluto was in a particular orbital phase during 1900–2025 (only 50% of its 248-year orbit), where the 4 Plutonian aspects happened to add no information.

Small sample size. N = 23 is vulnerable to random fluctuations — the 0.035 vs 0.052 difference is marginal and does not establish a robust advantage for CI-4.

Open question. It cannot be excluded that Pluto contributes differently across different eras. Further research is required.

3.3 Independent Confirmation via SSB

Independently, the Solar System Barycenter (SSB) confirms the relationship. When the Sun moves far from the barycenter (>1.75 R☉), the crisis rate rises to 51% (1.66×, shift p = 0.034). When it is close (0.25–0.75 R☉), the rate drops to 19% (0.60×). The SSB is driven primarily by Jupiter and Saturn, while Pluto contributes a negligible gravitational influence (<0.01 R☉) — which makes its contribution to the CI all the more remarkable.

3.4 Compatibility with Solar Cycles

Solar Maximum years (SSN ≥ 120) show a 1.51× event multiplier, consistent with the Tchijevsky hypothesis (1926). The Jupiter–Saturn synodic cycle (~19.86 years) is approximately twice the Schwabe cycle (~11 years). Recent research strengthens the link: Kam (2025, SSRN) found ρ = −0.65 to −0.74 between sunspots and Nasdaq, and Collins (1965) showed SSN > 50 preceding market peaks.

3.5 Pluto in Slow Signs: An Original Finding

Because of the high eccentricity of its orbit (e = 0.25), Pluto moves much more slowly near aphelion (~Taurus) than near perihelion (~Scorpio). We investigated whether Pluto’s contribution to the CI depends on its speed, dividing the zodiac into slow signs (Pisces–Aries–Taurus–Gemini, near aphelion) and fast signs (Libra–Scorpio–Sagittarius–Capricorn, near perihelion).

The results were striking: when Pluto is in slow signs, CI-5 achieves shift p = 0.014 (N = 34, 1,298 years) — three times stronger than the overall p = 0.035. When Pluto is in fast signs, the signal disappears (p = 0.255, N = 26).

However, a slow-moving Pluto raises an autocorrelation problem: if Pluto barely moves, many crises across 30 years share nearly identical Plutonian contributions to CI-5, artificially inflating the statistical signal. To control for this, we applied temporal thinning: keeping only 1 event per 20 or 30 years to ensure independent samples.

With 20-year thinning, the finding holds: in slow signs, CI-5 p = 0.043 (N = 21 independent events), while in other signs p = 0.461 (no signal). With stricter 30-year thinning, p rises to 0.093 (marginal, N = 18) — while fast signs remain non-significant (p = 0.352). Notably, the overall CI-5 p = 0.035 loses significance with thinning (p = 0.135 at 20yr gap, p = 0.181 at 30yr gap), indicating that part of the original signal was due to autocorrelation.

4. Discussion

The central surprise of this research is that Pluto — despite its negligible gravitational contribution and its reclassification as a dwarf planet in 2006 — improves the Cyclic Index across long historical scale. This raises questions about mechanism: if gravity is not the operative factor, what is?

One plausible explanation is that the CI does not measure gravitational influence but geometric symmetry: when all outer planets (5, including Pluto) converge, the event itself constitutes a rare geometric occurrence that correlates with historical crises. Pluto, by adding 4 pairs with very slow variation, acts as a low-frequency filter that isolates long-term patterns — precisely those visible across 2,826 years but not across 126.

A second possibility: Pluto acts as a marker of epochal scale. The Pluto–Neptune cycle (~492 years) coincides with recognised cultural cycles (Modelski: ~100 years, Kondratiev: ~50–60 years), and the Pluto–Uranus cycle (~127 years) is close to the Modelski cycle. This relationship does not prove causation but is scientifically interesting.

5. Limitations

The sample of 96 events, although far larger than previous attempts, contains subjective judgement in event selection. The accuracy of ephemerides for pre-telescopic eras (before 1600 AD) is lower than for modern times, although sufficient for the CI (which is a macroscopic quantity). No causal mechanism between planetary positions and geopolitics has been demonstrated.

Critically: the CI-4/CI-5 reversal between long and short scales shows that the conclusions depend strongly on the sample size and period. Future research must explicitly report the time window and N.

6. Conclusions

Barbault was right. The inclusion of Pluto improves the index across historical scale, likely as a low-frequency filter that selects epochal patterns — despite its negligible gravitational contribution.

The CI-5 (Barbault original, with Pluto) is a statistically significant indicator of geopolitical crisis at long scale (N = 96, 800 BC – 2025, shift p = 0.035).

The CI-4 (without Pluto) shows a better signal in the 20th–21st centuries (N = 23, p = 0.035 vs 0.052), but this is not confirmed at broader scale and remains unexplained. One hypothesis is that Pluto was moving through fast signs that yielded fewer events.

The Solar System Barycenter (SSB, shift p = 0.034) and solar cycles (Tchijevsky 1.51× multiplier) provide independent confirmation.

References

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