Finite-Jet Observability and a Computer-Assisted Multisheet Lower Bound for the Planar Newtonian Three-Body Problem

This preprint studies finite-jet reconstruction for the translation- and O(2)-reduced planar Newtonian three-body flow. Exact rational calculations establish generic finite-jet observability for five permutation-symmetric observables. The released computation uses the actual derivative jets, restoring the factorial scaling from the normalized Taylor coefficients used internally. Under the definition in the manuscript, the generic minimum implicit algebraic differential order is seven, or five after adjoining the conserved energy and squared angular momentum. At one equal-mass physical target with side lengths (4,5,6), at least four distinct real physical S3-orbits are rigorously certified, implying at least 24 labeled physical reduced roots modulo O(2). A FLINT/Arb Krawczyk implementation certifies 48 distinct scalar-continuation/S3-orbit representatives of the complexified inverse problem. Exact particle-relabeling symmetry and certified pairwise-distinct edge coordinates imply at least 288 labeled complex roots. The associated fifth-derivative enclosures are pairwise disjoint. The counts 48, 24, and 288 are certified lower bounds, not completeness theorems. This work does not provide a closed-form solution of the general three-body problem. Preprint status: not peer reviewed. The research and manuscript were substantially AI-assisted. No independent human specialist has yet reviewed the full proof, software, or novelty claims. The named author accepts responsibility for the contents.