Well Posed Origin Anywhere Consistent Systems in Celestial Mechanics

The paper’s Theorem 3.1 proves RS1 is invariant under arbitrary C2 translations and (by appeal to standard ODE results) is WPOACS; the candidate solution mirrors this by explicitly rewriting RS1 as a closed system in relative variables, verifying local Lipschitzness off the collision set, and invoking Picard–Lindelöf for local well-posedness (uniqueness modulo translations). The paper’s proof sketch is terse and cites general ODE theory for existence/uniqueness without detailing the Lipschitz domain, but is essentially correct; the model provides the missing details and the gauge-fixing uniqueness interpretation. See the statement and proof sketch of Theorem 3.1 and its initial-data constraints r1k(t0) ≠ 0 and r1k(t0) − r1j(t0) ≠ 0 in the paper , the WPOACS desiderata in Section 3 , and their reliance on basic ODE theory (pages 1–7 of [2]) for existence/uniqueness ; cf. the NCME local well-posedness statement in Theorem 1.1 .