= Solution
The three <On shell>[on-shell] spatial <momenta> have nine components. Four <Conservation law>[conservation] constraints leave five, and an unobserved overall <Rotation>[spatial rotation] removes three for the <Scalar field>[scalar] decay, leaving two internal kinematic variables. The pair invariants obey
$$
\boxed{s_{12}+s_{13}+s_{23}=M_0^2+m_1^2+m_2^2+m_3^2.}
$$
Thus two determine the third. They also determine each rest-frame daughter <energy>,
$$
E_i=\frac{M_0^2+m_i^2-s_{jk}}{2M_0},
$$
and hence all <momentum> magnitudes and pairwise angles. The <momentum> triangle is fixed up to <Rotation>[overall orientation]. The <Dalitz plot> describes this internal <kinematics>, rather than claiming to record three independently oriented <Four-vectors>. Polarized parents or additional measured <spin> information can require orientation variables beyond the two invariant axes.
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