= Solution
The charged two-pion and three-pion channels can be assigned to the same spin-zero <kaon> by their parent <mass> and lifetime. For two spinless <pions>, total <angular momentum> zero forces their relative <orbital angular momentum> to zero, so the product of their <Intrinsic parity>[intrinsic parities] gives
$$
\boxed{P_{2\pi}=(-1)^2(-1)^0=+1.}
$$
For three spinless <pions>, use Jacobi orbital angular <momenta> $l,L$. Coupling them to total zero requires $l=L$, and hence
$$
\boxed{P_{3\pi}=(-1)^3(-1)^{l+L}=-1.}
$$
Thus both channels cannot conserve <parity> in decays of one parent with a definite <parity>. The <Weak interaction>[weak decay] interaction permits the observed coexistence.
<Dalitz plots> identify the three-body events, determine their internal <kinematics>, and allow <Probability amplitude>[amplitude] and <Angular momentum>[angular-momentum analyses] through their populations and <resonance> structures. Together with the <spin> and parent-identity evidence, they support the <parity> assignment. They are not a standalone parity-odd observable: reversing all three <momenta> leaves every $s_{ij}$, and therefore every point on the plot, unchanged. A flat distribution by itself cannot establish <parity violation> without the channel and <spin> information.
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