Lagrange Point Stability and a Structural Hypothesis from Gaussian Integer Arithmetic

The Lagrange points L4 and L5 of the restricted three-body problem are local maxima of theeffective potential, yet they are dynamically stable. Over 15,000 Jupiter Trojan asteroids haveoccupied these hilltop equilibria for 4.5 billion years. Standard celestial mechanics explains thisstability through the Coriolis force in the rotating frame, but at least four features of the Trojansystem remain unexplained or inadequately addressed: (1) Why does a force that performs zerowork control the topology of orbits? (2) Why is the L4 population approximately 1.6 times theL5 population, when both points are dynamically identical in the standard treatment? (3) Whydoes the stability threshold involve the quantity 1/27, with 27 = 3^3 appearing as a cubicinvariant rather than a quadratic or linear one? (4) Why does the equilateral geometry at 60degrees produce stability when no other angular configuration does?This paper presents the standard derivations of these results, surveys the current state of eachopen question in the literature, and proposes a structural hypothesis drawn from Gaussian integerarithmetic. The hypothesis connects the characteristic quartic equation of Lagrange stability tothe fourth power of the Gaussian integer z = 2+i, identifies the Coriolis force as a perpendicularstabilizer analogous to the imaginary component of complex multiplication, and offers adirectional asymmetry prediction for the L4/L5 population ratio. All claims are categorized byevidence level: proven standard results (Category A), structural identifications (Category B), andtestable predictions (Category C). The paper is self-contained and requires no prior knowledge ofthe author's broader research program.