No Primary Sources Linking Continued-Fraction Convergents to Lunar Month Ratios or Eclipse Cycles — E8 Intelligence Research

FINDING: Search returned only pedagogical/algorithmic content on continued fractions (Stein §5.3.1, convergent recursion, WxMaxima computation) plus a sidereal-vs-synodic month explainer — no primary source or dataset linking continued-fraction convergents to the synodic/anomalistic/draconic month ratios or eclipse-cycle genealogy. | MATH: Standard convergent recursion: pₙ = aₙpₙ₋₁ + pₙ₋₂, qₙ = aₙqₙ₋₁ + qₙ₋₂, with p₋₁=1, p₋₂=0, q₋₁=0, q₋₂=1; convergent value pₙ/qₙ → x. Best-approximation property: |x − pₙ/qₙ| < 1/(qₙqₙ₊₁). No month-ratio constants (29.530589, 27.554550, 27.212221 d) appear in any retrieved item. | CONNECTION: None supported by evidence. The relevant harmonic link (Saros ≈ 223 synodic ≈ 242 draconic ≈ 239 anomalistic months; Metonic 19 yr ≈ 235 synodic; φ = [1;1,1,1,…] with convergents Fₙ₊₁/Fₙ → 1.618) is *not* present in these findings — it is the missing target, not a result. | DEPTH: 2 — the mathematical machinery (convergent recursion, best-rational-approximation) i Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com